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INFRARED NEURAL STIMULATION AND FUNCTIONAL
RECRUITMENT OF THE PERIPHERAL NERVE
By
ERIK JOHN PETERSON
Submitted in partial fulfillment of the requirements
For the degree of Doctor of Philosophy
Dissertation Adviser: Dr. Dustin J. Tyler
Department of Biomedical Engineering
CASE WESTERN RESERVE UNIVERSITY
May 2013
[Type text]
CASE WESTERN RESERVE UNIVERSITY
SCHOOL OF GRADUATE STUDIES
We hereby approve the thesis/dissertation of
Erik John Peterson
Candidate for the Doctor of Philosophy degree*.
(Signed) Dustin J. Tyler, Ph.D. (chair of the committee)
Dominique M. Durand, Ph.D.
Hillel J. Chiel, Ph.D.
Andrew M. Rollins, Ph.D.
(date) January 24th, 2013
*We also certify that written approval has been obtained for any proprietary material contained
therein
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DEDICATION
This work is dedicated to Charissa, Karen, John, Janis, Bruce, Carmen, my
family, and friends, with whom I have been blessed to share my life with. Without
their support, none of this would have been possible. Thank you.
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TABLE OF CONTENTS Dedication ............................................................................................................................ i
Table of Contents ................................................................................................................ ii
List of Tables .................................................................................................................... vii
List of Figures .................................................................................................................. viii
Acknowledgements ............................................................................................................ ix
List of Abbreviations ........................................................................................................ xii
Abstract ............................................................................................................................ xiii
Chapter 1: Introduction ...................................................................................................... 1
Anatomical Overview ..................................................................................................... 1
The Neuron .................................................................................................................. 1
Neural Circuits ............................................................................................................. 4
Peripheral Nerves ........................................................................................................ 5
Neural Interfaces Used to Treat Injury and Disease ....................................................... 6
Central Nervous System Interfaces ............................................................................. 7
Peripheral Nerve Interfaces ......................................................................................... 7
Surface Stimulation .................................................................................................. 9
Implanted Interfaces............................................................................................... 10
Extraneural Interfaces ................................................................................................ 10
Interfascicular Interfaces ........................................................................................... 12
Intrafascicular Interfaces ........................................................................................... 13
Regenerative Neural Interfaces ................................................................................. 14
Neural Interfacing Modalities ....................................................................................... 15
Electrical and Magnetic Neural Interfaces ................................................................ 15
Chemical Neural Interfaces ....................................................................................... 16
Optogenetic Neural Interfaces ................................................................................... 17
Infrared Neural Stimulation ....................................................................................... 18
Research Motivation ..................................................................................................... 22
Chapter 2: Dissertation Objectives and Organization ...................................................... 24
Introduction ................................................................................................................... 24
Aim 1 ............................................................................................................................. 25
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Aim 2 ............................................................................................................................. 26
Aim 3 ............................................................................................................................. 27
Appendices .................................................................................................................... 28
Chapter 3: Motor Neuron Activation in Peripheral Nerves Using Infrared Neural
Stimulation ........................................................................................................................ 30
Abstract ......................................................................................................................... 30
Introduction ................................................................................................................... 31
Methods ......................................................................................................................... 33
Surgical preparation and EMG recording .................................................................. 33
Electrode fabrication .................................................................................................. 35
Infrared delivery ........................................................................................................ 35
Optical stimulation .................................................................................................... 36
Electro-Infrared Stimulation ...................................................................................... 38
Data Analysis ............................................................................................................. 39
Results ........................................................................................................................... 41
Nerve Sensitivity to INS ............................................................................................ 41
Motor Recruitment with Infrared Stimulus ............................................................... 43
Electro-Infrared Stimulation ...................................................................................... 49
Discussion ..................................................................................................................... 52
Nerve Sensitivity to INS ............................................................................................ 52
Infrared-Evoked Muscle Recruitment ....................................................................... 53
Combined Electrical and Infrared Stimulus .............................................................. 56
Infrared-Driven Neural Activation ............................................................................ 57
Conclusion ..................................................................................................................... 59
Acknowledgements ....................................................................................................... 60
Chapter 4: Modeling Mechanisms of Infrared Neural Stimulation ................................. 61
Abstract ......................................................................................................................... 61
Introduction ................................................................................................................... 61
Methods ......................................................................................................................... 64
Spatially-Lumped Membrane Models ....................................................................... 64
Spatially-Distributed Axon Models ........................................................................... 65
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Temperature-Driven Capacitive Changes ................................................................. 66
Intracellular Calcium Release .................................................................................... 68
Results ........................................................................................................................... 70
Membrane Capacitance Change - Membrane Models .............................................. 70
Membrane Capacitance Change - Myelinated and Unmyelinated Axon Models ..... 74
Intracellular Calcium Release .................................................................................... 79
Discussion ..................................................................................................................... 81
Membrane Capacitance Changes ............................................................................... 81
Beam Profile Affects Excitability .............................................................................. 82
Recruitment Order ..................................................................................................... 85
Intracellular Calcium Release .................................................................................... 85
INS Interface Design Implications ............................................................................ 86
Additional INS Mechanisms ..................................................................................... 86
Conclusions ................................................................................................................... 87
Acknowledgements ....................................................................................................... 88
Chapter 5: Conclusions .................................................................................................... 89
Aim 1 ............................................................................................................................. 89
Hypothesis 1.1 ........................................................................................................... 89
Hypothesis 1.2 ........................................................................................................... 90
Hypothesis 1.3 ........................................................................................................... 91
Hypothesis 1.4 ........................................................................................................... 91
Hypothesis 1.5 ........................................................................................................... 92
Aim 1 Summary......................................................................................................... 92
Aim 2 ............................................................................................................................. 93
Hypothesis 2.1 ........................................................................................................... 94
Aim 2 Summary......................................................................................................... 94
Aim 3 ............................................................................................................................. 95
Hypothesis 3.1 ........................................................................................................... 95
Hypothesis 3.2 ........................................................................................................... 96
Hypothesis 3.3 ........................................................................................................... 97
Aim 3 Summary......................................................................................................... 98
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Dissertation Conclusion ................................................................................................ 99
Appendix I: Predicting myelinated axon activation using spatial characteristics of the
extracellular field ............................................................................................................ 100
Abstract ....................................................................................................................... 100
1. Introduction ............................................................................................................. 101
2. Methods ................................................................................................................... 102
2.2 Activation prediction methods........................................................................... 104
2.2.1 Modified Driving Functions (MDF) ............................................................... 104
2.2.2 Activation thresholds ...................................................................................... 106
2.3 Verification ........................................................................................................ 107
2.3.1 Extracellular potential generation ................................................................... 107
2.3.2 Verification cases ........................................................................................... 108
2.3.3 Performance measures .................................................................................... 110
3. Results ..................................................................................................................... 112
3.1 Threshold value generation ............................................................................... 112
3.2 Prediction performance with single point source .............................................. 115
3.2 Prediction performance with multiple point sources ......................................... 120
3.3 Computational runtime ...................................................................................... 123
4. Discussion ............................................................................................................... 124
4.1 Activation thresholds are a function of extracellular potential .......................... 124
4.2 Single point source performance ....................................................................... 125
4.3 Performance differences between methods ....................................................... 126
4.4 Replicating key findings from literature ............................................................ 127
4.5 Computational run time comparison ................................................................. 128
4.6 Applicability to other models ............................................................................ 128
5. Conclusion ............................................................................................................... 130
Acknowledgements ..................................................................................................... 130
Appendix I.A – Threshold Generation and Activation Prediction .............................. 131
Appendix II: NEURON Code ........................................................................................ 134
Descriptions of Membrane Dynamics ......................................................................... 134
Memcap.mod ........................................................................................................... 134
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HH_t.mod ................................................................................................................ 135
FH_t.mod ................................................................................................................. 137
Axnode_t.mod ......................................................................................................... 141
Ca_track.mod ........................................................................................................... 145
Cagk.mod ................................................................................................................. 146
CaSquare.mod.......................................................................................................... 146
CaTherm.mod .......................................................................................................... 147
Spatially-Lumped Membrane Models ......................................................................... 148
HHMembrane.hoc ................................................................................................... 148
FHMembrane.hoc .................................................................................................... 151
HHMembrane_Looped.hoc ..................................................................................... 154
Spatially-Distributed Axon Models ............................................................................ 162
HHAxon_DiamAndTempSweep.hoc ...................................................................... 162
MRGAxon_Interactive_LoadBeamShape.hoc ........................................................ 171
Appendix III: MATLAB Code ...................................................................................... 182
Recruitment Curve Plotting ......................................................................................... 182
AnalyzeAndPlotOpticalRecruitmentCurves.m ........................................................ 182
ExtractAndAnalyzeLVMData.m ............................................................................. 194
ExtractEMGStartAndStopTime2.m ........................................................................ 198
Chapter 6: References .................................................................................................... 207
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LIST OF TABLES Table 3-1 Significant recruitment differences comparing combined stimulation over
electrical-only stimulation ................................................................................................ 52
Table 4-1 Q10 and membrane capacitance, Cm, simulated in each model ....................... 65
Table 7-1 Computation time consumed by numeric simulation and each proposed
prediction method ........................................................................................................... 124
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LIST OF FIGURES Figure 3-1 Methods for infrared and electrical stimulation of rabbit sciatic nerve .......... 36
Figure 3-2 Locations of detected optically sensitive regions............................................ 42
Figure 3-3 Sensitive regions detected in rat sciatic nerve................................................. 43
Figure 3-4 Motor recruitment over time and versus pulse duration ................................. 45
Figure 3-5 Comparing response versus infrared pulse power .......................................... 47
Figure 3-6 Maximum electrical and infrared recruitment compared ................................ 48
Figure 3-7 Latency between threshold stimulus and EMG recruitment ........................... 49
Figure 3-8 Electrical and combined stimulus recruitment curves .................................... 51
Figure 4-1: Modeled membrane and axon circuit diagrams ............................................. 68
Figure 4-2: Maximum membrane depolarization versus initial temperature and membrane
potential for HH membrane model ................................................................................... 72
Figure 4-3: Peak time differences and peak values of m, h, and n gating variables in
response to transient temperature and capacitance changes ............................................. 73
Figure 4-4: Maximum membrane depolarization versus initial temperature with increased
Na+ conductance or decreased transient temperature change .......................................... 74
Figure 4-5: Maximum membrane depolarization in HH axon model with various IR
intensity profiles................................................................................................................ 76
Figure 4-6 Membrane depolarization across fiber diameters with flat and double-peaked
spatial profiles ................................................................................................................... 77
Figure 4-7 Amplitude scale factor required to trigger action potentials using a Gaussian
beam profile ...................................................................................................................... 79
Figure 4-8 Peak intracellular calcium concentrations caused by threshold calcium
currents .............................................................................................................................. 80
Figure 7-1 Electrode-axon geometries used for investigating prediction method
performance. ................................................................................................................... 110
Figure 7-2 Activation as a function of pulse duration and peak extracellular voltage ... 113
Figure 7-3 ........................................................................................................................ 115
Figure 7-4 Activation prediction method results with a single point source electrode and
100 us pulse duration. ..................................................................................................... 118
Figure 7-5 Activation prediction results across pulse duration and electrode-to-axon
spacing ............................................................................................................................ 120
Figure 7-6 Stimulation threshold error across prediction methods ................................. 121
Figure 7-7 Threshold error for an arrangement of six anodic and five cathodic electrodes
arranged in an alternating pattern longitudinally to a 10 um diameter axon. ................. 122
Figure 7-8 Stimulation threshold across prediction methods for an eleven-electrode
arrangement..................................................................................................................... 123
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ACKNOWLEDGEMENTS
I would like to thank the people without whom this work would not have been
possible. While this is not an exhaustive list, hopefully it gives some sense of the
kind of support it takes to work through a Ph.D. These important relationships came
about from a mix of planned and serendipitous interactions, teaching me that being
open and aware to deviations from my own plans is a critical and lifelong skill. I am
truly thankful for the words of encouragement, support, new perspectives,
challenges, and feedback provided by everyone.
I would like to thank my family for their role in helping me become who I
am. They are the ones that have put up with my antics, stunts, bad ideas, obsessions,
mistakes, and wrong turns for the longest time, but still showed love and support
along the way. Thank you: John, Karen, Bruce, Janis, Nicole, Andrew, and Sam. My
in-laws have been a positive and encouraging force in my life for many years as well.
Thank you: Carmen, Dan, Marie, AJ, Michelle, Kathryn, and Zoë. I wouldn’t be
writing any of this without the person that makes each day a blessing, believing in
me when I don’t, and making the whole journey a fun adventure. Thank you,
Charissa. I am the luckiest because of you.
Dr. Dustin Tyler has provided important guidance and perspective in
developing this research. Dustin was able to look at the big picture and see what was
possible when the details painted a bleak picture. I appreciate Dustin sharing his
experience and insight over these years. I am thankful to have been able to be a part
of the Functional Neural Interfaces lab.
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Dr. Hillel Chiel has gone above and beyond the duties of a guidance
committee member. Through research-based and personal conversations, Dr. Chiel
was instrumental in developing my vision beyond engineering and seeing the
excitement and possibilities in science. This invaluable mentorship was not what I
expected when I meeting a professor of biology while riding the bus.
Dr. Dominique Durand and Dr. Andrew Rollins have provided important
input as members of my guidance committee. Dr. Durand has challenged me, in
committee meetings and in the classroom, to find my limits and push beyond them.
Dr. Rollins gave important insight, looking at this research from a different
perspective and challenging assumptions along the way.
I would like to thank Dr. Erin Lavik for lending an ear and giving career
advice. Dr. Lavik shows genuine care for graduate students. I know her perspective
and encouragement have helped many students in their journeys.
Dr. Paul Marasco helped me to look at scientific investigation with the
perspective that it is one of the few frontiers available for exploration today. Dr.
Marasco also provided technical help, teaching me about electrophysiology and the
importance of maintaining an organized and focused approach to research.
The professors of the Biomedical Engineering department have played a part
in teaching and developing me as a researcher. Dr. Robert Kirsch, through
developing the training grant curriculum and personal encouragement, has helped me
to understand the larger picture that biomedical engineering fits within. Dr. P. Hunter
Peckham provided an example of what can be accomplished when you dedicate
yourself to a cause. Dr. J. Thomas Mortimer demonstrates the importance of
xi
pursuing new knowledge with new each day. Both Dr. Peckham and Dr. Mortimer
show genuine care for students, and are a part of what makes this department great.
Friends that have shown support and understanding over these years have
helped to make the hard times bearable. Thank you, Kevin M., Will C., Brian & Lisa
M., Nathan M., John T., Bill C., Manfred F., Jaime M., Harrison K., Swarna S., Chris
P., and Sreenath N. FNI lab members have also shown their support through giving
me feedback on presentations, each providing a part of setting up the lab, and sharing
knowledge and expertise. Thank you, Matt, Jimmy, Katie, Dan, Aaron, Natalie, and
Nemath. Smruta was there for all of the late-night surgeries and endless experiments,
lending an ear, a story, or a podcast to help pass the hours and keep us awake.
Funding Acknowledgements:
Funding for this project was provided by Microsystems Technology Office of
the Defense Advanced Research Projects Agency (DARPA) Centers in Integrated
Photonics Engineering Research (CIPHER) and the Lockheed Martin Aculight
Corporation. The project described was supported in part by Grant Number T32-
EB004314 from the NIBIB and the National Institutes of Health. The content is
solely the responsibility of the authors and does not necessarily represent the official
views of the National Institutes of Health
xii
LIST OF ABBREVIATIONS Dur. – Duration
EMG – Electromyogram
ENG – Electroneurogram
FINE – Flat Interface Nerve Electrode
FH – Frankenhaeuser and Huxley
HEK – Human Embryonic Kidney
HH – Hodgkin and Huxley
INS – Infrared Neural Stimulation
IR – Infrared
LG – Lateral Gastrocnemius
LIFE – Longitudinal Intrafascicular Electrode
Max. – Maximum
MG – Medial Gastrocnemius
MRG – McIntyre, Richardson, and Grill
Sol – Soleus
TA – Tibialis Anterior
TIME – Transverse Intrafascicular Multi-Electrode
xiii
Infrared Neural Stimulation and Functional Recruitment of the
Peripheral Nerve
By
ERIK JOHN PETERSON
ABSTRACT
Peripheral nerve interfaces have been used to restore motor function to paralyzed
limbs. To restore the most natural function to paralyzed muscles requires a very selective
interface. Arguably, ideal selectivity would entail independent control over each neuron.
Neural interfaces based on electrical stimulation of neurons have made the most progress
in restoring movement in paralyzed limbs, but increasing selectivity without increasing
invasiveness remains a primary goal in developing stable and chronic nerve interfaces.
Interfaces that use infrared light to stimulate may provide selective activation without
penetrating the nerve. The work presented in this dissertation explores this concept,
measuring sensitivity and motor response in peripheral nerves, and using computational
models to investigate mechanisms of activation.
The in vivo experimental work presented quantifies motor response to extraneural
infrared stimulation in the rabbit sciatic nerve. It was hypothesized that infrared light
would selectively stimulate motor response in at least three different regions of the nerve,
and do so to a functionally significant level. Combined infrared and electrical stimulation
was hypothesized to significantly change full-muscle recruitment over electrical
recruitment alone. In this study, only 81% of nerves responded to infrared stimulus, with
1.7±0.5 sensitive regions detected per nerve. Single-muscle selectivity was measured in
79±12% of sensitive regions. Infrared stimulus activated significantly less than 10% of
xiv
the muscle capability, though. Combined electrical and optical stimulation only yielded
significant differences from electrical recruitment in 7% of cases. These results highlight
challenges to address before translating infrared stimulation larger nerves.
Mechanisms of infrared stimulation were studied using computational models.
Intracellular currents generated by changes in membrane capacitance or intracellular
calcium release were hypothesized capable of triggering action potentials under
conditions determined physiologically possible. Results show that activation with
membrane capacitance changes depend on the spatial gradient of evoked currents, and
that relatively small changes in intracellular calcium concentrations can trigger action
potentials. The results of this study provide insight into how infrared light may activate
axons, and how infrared stimulation may be improved over current methods.
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CHAPTER 1: INTRODUCTION
Disease or injury can impair an individual’s nervous system, limiting ability and
quality of life. Interfaces designed to modulate behavior of the injured nervous system
can help address these neurological deficits. Behavior is modulated to increase or
decrease neural activity through controlled energy release. Examples of energy types
used include chemical, mechanical, electrical, magnetic, and optical energy. The more
targeted a particular interface is, the less likely it is to affect tissue that does not need
modulation. Focusing an interface’s effects can increase functional utility and reduce side
effects. The work presented in this dissertation is an investigation of targeted motor
neuron activation in the peripheral nerve using focused infrared light. A brief review of
neural anatomy, neural interface examples, and discussion on neural interfacing with
different energy modalities is provided as context for the presented research.
Anatomical Overview
The Neuron
Neural cells, or neurons, are comprised of five major components: dendrites,
soma, axon hillock, axon, and synaptic bouton (Lu et al., 2008; McIntyre and Grill, 2000;
Rall, 1977). Depending on the function and location of the neuron, these components
may be sized and arranged differently to better serve their purpose. Dendrites are where
information arrives from upstream neurons, and are arborous to facilitate interfacing with
many neurons (Rall, 1977). The soma, or cell body, houses the cell nucleus, synthesizes
proteins, and integrates incoming signals to control behavior (Hall and Guyton, 2011).
The axon hillock and axon are used to transmit information to downstream neurons and
2
other cells, ending in the bouton which releases chemicals or neurotransmitters that excite
or inhibit cell activity, depending on the interface type.
Neurons communicate through release of neurotransmitters, often triggered by
depolarization of the cellular membrane. At rest, the transmembrane potential of a neuron
is negative with respect to the extracellular space. Transmembrane potential is
determined by ion concentrations in the intra- and extra-cellular spaces and the relative
permeability of the membrane to each ionic species (Frankenhaeuser and Huxley, 1964;
Hodgkin and Huxley, 1952a, 1952b; McIntyre and Grill, 1999). Transmembrane potential
is modulated by changing permeability of the membrane to different ions through
conformational changes of ion channels (Frankenhaeuser and Huxley, 1964;
Frankenhaeuser and Moore, 1963; Hodgkin and Huxley, 1952b; McIntyre et al., 2002).
Ion channel states can be affected by the presence of other ions (Robitaille et al., 1993),
local transmembrane voltage (Frankenhaeuser and Huxley, 1964; Hodgkin and Huxley,
1952b; McIntyre et al., 2002), temperature (Facer et al., 2007), and ionic gradients
(Zhang et al., 2010). Ions move in or out of the cell as channels open and close, changing
the intracellular electrical potential. Ion movement can cause the transmembrane
potential to increase or decrease, depolarizing or hyperpolarizing the membrane,
respectively.
The amount that a cell is depolarized or hyperpolarized from neurotransmitter
release from an upstream neuron is dependent cell body geometry. The cell body acts as
an integrator, summing depolarizing and hyperpolarizing inputs until the activation
threshold is reached and a cascade of depolarization is triggered (Lu et al., 2008; Rall,
1977). A larger cell body has a larger intracellular volume, meaning more ions must be
3
transferred to change intracellular potential. This effect results in higher stimulus
thresholds for larger cells than smaller cells, when activated by synaptic transmission or
intracellular current injection (Henneman et al., 1965a; Kandel et al., 2000). The normal
functions of the cell work to return the cell body to the resting potential, so the effect of a
single input decreases with time (Hall and Guyton, 2011; Rall, 1977). This integrating
behavior allows each neuron to perform as a simple processing unit within the system.
As the cell body depolarizes, it eventually reaches a threshold where a cascade of
depolarization occurs. This cascade begins when the cell membrane begins to depolarize,
triggering the opening of voltage gated sodium channels that are located in a region of the
cell body near the axon called the axon hillock (Lu et al., 2008; McIntyre and Grill,
1999). As more sodium channels open, the permeability of the membrane to sodium
increases and the cell depolarizes further, causing additional sodium channels to open.
The sodium channels of the axon begin to depolarize once the axon hillock depolarizes.
The depolarization process is governed by factors that limit depolarization, or the cell
would remain depolarized. Voltage-gated sodium channel permeability is controlled by
two gating factors. The first is the activation gate, which is closed when the cell is at rest
and increases permeability to sodium ions in response to depolarization. The second, the
inactivation gate, is normally open when the cell is at rest and decreases permeability to
sodium ions in response to depolarization. The inactivation gate is slower than the
activation gate, leaving time for inward sodium currents to depolarize the cell for a brief
time (Grill and Mortimer, 1995; Hodgkin and Huxley, 1952b). The inactivation gate
remains closed for a short time once closed, causing a refractory period during which
sodium currents are halted (Hodgkin and Huxley, 1952b; Mahnam et al., 2008). Voltage-
4
gated potassium channels also limit the duration of depolarization, by increasing
potassium permeability in response to increased transmembrane potential
(Frankenhaeuser and Huxley, 1964; Hodgkin and Huxley, 1952a). The outward
potassium current drives the transmembrane potential back towards the polarized state as
the inward sodium current is inactivated. The dynamics of these channels were measured
and described mathematically by Hodgkin and Huxley (Hodgkin and Huxley, 1952a,
1952b), resulting in an electrical description of the cell membrane and enabling
investigation of cell behavior with computational models (Rattay, 1987).
As a region of the axon is depolarized, the surrounding membrane area also
begins to depolarize, triggering more ion channels to open. A wave of depolarization
propagates along the axon to the synaptic bouton. This wave is referred to as the action
potential. Depolarization at the synapse or junction causes release of neurotransmitters
that are used to communicate with downstream cells. While a given neuron will release a
certain type of neurotransmitter, its effect will depend on the type of receptor on the
downstream cell (Hall and Guyton, 2011; Kandel et al., 2000). In the special case of a
motor neuron, the chemical released by the neuron is acetylcholine, which triggers an
action potential in the downstream muscle fiber, causing contraction of that muscle fiber.
Because the action potential is the basis for much of neural communication, neural
modulation largely relies on affecting neural communication by either triggering or
inhibiting propagation of action potentials.
Neural Circuits
As neurons connect to other neurons and cells of the body, they form circuits.
Within these circuits, neurons can act as sensors, processors, or effectors. Sensory input
is provided by specialized cell structures that transduce external stimuli into action
5
potential patterns that are conveyed to processing and effector neurons (Goodwin et al.,
1995; Kandel et al., 2000; Munger and Ide, 1988). Direct connections between sensors
and effectors are responsible for many reflex actions, requiring the fastest response
possible to avoid danger or injury. The stretch reflex is an example of a simple neural
reflex circuit, where rapid stretch of a muscle triggers an action potential in a sensory
neuron which stimulates the motor neurons that innervate that muscle (Henneman et al.,
1965b; Kandel et al., 2000). Processing circuits may consist of a single or many neurons,
and operate as the control system of the nervous system. Processors integrate their
inhibitory and excitatory inputs, and generate action potentials to communicate with other
processor cells or effectors. Effector cells mediate external action, stimulating smooth or
skeletal muscle contraction, hormone release, and metabolic changes (Hall and Guyton,
2011; Kandel et al., 2000). These basic elements combine to form the nervous system of
all creatures, whether simple or complex, sensing the environment, processing an
appropriate response, and activating that response. Interruption of these circuits by
disease or injury leads to functional deficits.
Peripheral Nerves
Peripheral nerves are special structures in the body that act as a conduit for
sensory and motor signals, connecting the central nervous system to most of the body.
Peripheral nerves exit the spinal column through the intravertebral foramen and route
through the body to connect to the muscles and sensory receptors of the body. The
peripheral nerve protects and nourishes the axons of sensory and motor neurons. The
axon population within a peripheral nerve can be composed of sensory axons, motor
axons, or a mix of sensory and motor axons. Axons within the peripheral nerve are
contained in a protective tissue layer called the perineurium (Navarro et al., 2005;
6
Stewart, 2003). These axon groupings are called fascicles, and a peripheral nerve contain
several fascicles within it. Each fascicle may contain the axons of thousands of individual
neurons. Mean fascicle diameter is around 500 um, and fascicle count generally increases
with nerve size and number of axons (Gustafson et al., 2005; Stewart, 2003). Fascicles
are held together in the peripheral nerve by connective tissue called epineurium. This
connective tissue also holds the blood vessels that supply blood to the nerve along its
length. Historically, there has been debate about how functionally organized axons are
within fascicles (Stewart, 2003). When functionally-similar axons are grouped together, it
is easier to selectively stimulate using interfaces that rely on proximity to stimulation
sources. Low functional organization would mean that proximity-based stimulation
would activate axons that contribute to several different functions. There is evidence that
suggests functional organization within the peripheral nerve (Badia et al., 2010; Brushart,
1991).
Neural Interfaces Used to Treat Injury and Disease
Interfaces with the nervous system have been successfully implemented as a
means to treat disease and restore function after injury in clinical applications (Butson
and McIntyre, 2006; Dommel et al., 2009; Fisher et al., 2009; Oakley et al., 2007;
Pfingst, 2011; Polasek et al., 2009a). The need for effective neural interfaces is high. For
example, according to the National Spinal Cord Injury Statistical Center, in 2010 the
number of people living with spinal cord injury is estimated to be around 262,000 and the
average loss in wages, benefits, and productivity was estimated at $65,384 per person per
year (Chen, 2010). With roughly $17 billion lost each year to reduced ability following
spinal cord injury, not to mention the increased cost of additional care, the potential
7
benefit of restoring even partial function to reduce these costs is sizable. Neural interface
options are as diverse as the regions of the nervous system to which they are applied,
including interfaces used to treat Parkinson’s disease and other movement disorders,
hearing loss, and a growing list of other applications. The effects of an interface depend
on the region of the nervous system with which it interfaces, and whether the interface
records or modulates activity.
Central Nervous System Interfaces
Interfaces with the central nervous system span a wide variety of applications.
Recordings from the cortex have been used as command signals to control computer
cursors and robotic arms (Felton et al., 2007; Foldes and Taylor, 2011; Marathe and
Taylor, 2011; McFarland and Wolpaw, 2008). Interface options include implanted and
non-implanted recording arrays. Stimulation of the basal ganglia within the brain has
been used to treat movement disorders, including Parkinson’s disease and dystonia
(Benabid, 2003; Hwynn et al., 2012). Stimulating interfaces have been used to deliver
sensory feedback (Dhillon and Horch, 2005; Rossini et al., 2010). Cochlear stimulation is
routinely used to restore hearing by stimulating cells within the cochlea that correspond
to the frequency content of detected sounds (Pfingst, 2011). Retinal implants are under
active development to help restore visual information to individuals with blindness
(Dommel et al., 2009). Spinal cord stimulation has been used to treat chronic pain by
interrupting pain signals as they are transmitted from the body to the brain (Oakley et al.,
2007).
Peripheral Nerve Interfaces
The peripheral nerve is an attractive interface point when a bridge between the
central nervous system and either sensors or effectors is needed. Direct electrical
8
stimulation of muscles can be accomplished, but each stimulated muscle requires at least
one electrode, more if the muscle is large and has a distributed motor point (Crago et al.,
1980; Fisher et al., 2009). Sensory endpoints are also distributed throughout the volume
of the body, and in the case of amputation may no longer be present. The spinal cord and
brain provide an alternative with access to more densely concentrated cell bodies that are
spatially organized. Spatial organization helps with activating functionally-similar
neurons at a time, but high cellular density increases the likelihood of activating non-
targeted cells. Immune responses can reduce the chronic effectiveness of central nervous
system interfaces (Fraser and Schwartz, 2012; Potter et al., 2012). The peripheral nerve
offers a balance between distributed endpoints and dense central arrangement. Peripheral
nerve interfaces provide access to multiple muscles from the same implant site, and the
ability to improve selectivity by choosing appropriate branch points to isolate the muscles
accessed (Fisher et al., 2009; Rodriguez et al., 2000; Schiefer et al., 2010; Sweeney et al.,
1990; Tarler and Mortimer, 2004).
Peripheral nerve interfaces are typically used to restore sensory input or motor
activation. Peripheral nerve recordings are under development for use as natural
command sources for controlling prosthetic limbs (Lawrence et al., 2004; Micera et al.,
2008; Wodlinger and Durand, 2009). High frequency stimulation of peripheral nerves can
block action potentials and either block pain signals or prevent muscle contractions
(Ackermann et al., 2009; Kilgore and Bhadra, 2004; Peng et al., 2004; Vučković and
Rijkhoff, 2004). Stimulation applied to peripheral nerves remaining after limb amputation
is being developed as a means to provide sensory information from prosthetic limbs to
improve control and integration of prosthetic limbs (Rossini et al., 2010). Peripheral
9
nerve stimulation can also be used to activate muscles and restore function to paralyzed
limbs (Branner et al., 2001; Dowden et al., 2009; Fisher et al., 2009; Micera et al., 2008;
Polasek et al., 2009a; Rodriguez et al., 2000; Rutten et al., 1991; Sweeney et al., 1990).
Restoring motor function after neurologic injury is an important goal in treating deficits
left by spinal cord injury and stroke.
While the peripheral nerve offers a balance between distributed and high density
interfacing, controlling exactly which axons are activated remains an important interface
design challenge (Choi et al., 2001; Fisher et al., 2009; Lertmanorat et al., 2006;
Leventhal and Durand, 2003; Schiefer et al., 2010). The close grouping of functionally
different axons with a given fascicle increases the possibility of unwanted activation or
effects caused by the interface. The ability to activate targeted cells while leaving other
cells unaffected is referred to as the selectivity of the interface (Choi et al., 2001;
Dowden et al., 2009; McIntyre and Grill, 2000; Polasek et al., 2009b; Schiefer et al.,
2008). Often times, increasing selectivity comes at the expense of increasing invasiveness
to the nerve (Navarro et al., 2005; Sergi et al., 2006). Invasiveness can range from non-
nerve stimulation through the skin to requiring axon regeneration after transection.
Surface Stimulation
Nerve interfaces that stimulate using electrodes applied to the skin are the least
invasive, as they require no surgical procedure. Surface stimulation has been used to treat
conditions like foot-drop following stroke (Van Swigchem et al., 2011), and have been
used clinically and commercially . Stimulation of nerves from surface electrodes can
activate cutaneous sensory receptors, though, and cause undesirable sensation during use.
Surface stimulation also requires that the target nerve to be close to the surface, limiting
10
nerves that can be targeted. Additionally, non-target nerves near the targeted nerve are
also likely to be activated.
Implanted Interfaces
Implanted neural interfaces can avoid cutaneous nerve activation by minimizing
the amount of tissue between stimulation source and target, provide access to nerves deep
within the body, and allow selective stimulation of nerves that are close to each other, but
require surgical procedures to do so. Implanted peripheral nerve interfaces are often
designed to direct stimulation towards the target nerve, minimizing activation of adjacent
tissue (Branner et al., 2000; Fisher et al., 2009; Lawrence et al., 2004; Polasek et al.,
2009b; Schiefer et al., 2010). Interfaces may have a single channel of stimulation, or
many. The number of sources will depend on the number of independent functions an
interface must perform. As the number of targeted muscles or functions increase, often
times the number of stimulus channels needed also increases (Schiefer et al., 2008;
Wodlinger and Durand, 2009). Because stimulus channels can be activated together to
generate different activation patterns (Tarler and Mortimer, 2004), there is not a defined
relationship between the number of functions and the number of channels needed.
Extraneural Interfaces
Extraneural peripheral nerve interfaces with multiple stimulating channels
typically employ an insulating cuff that encircles the nerve, stabilizes the stimulating
contacts, and directs the stimulation toward the neural tissue. Stimulation can be applied
through a single channel at a time, or through multiple channels simultaneously to change
the axon population affected (Choi et al., 2001; Gorman and Mortimer, 1983; Rodriguez
et al., 2000; Tarler and Mortimer, 2004; Vuckovic et al., 2008). Stimulation parameters
can be adjusted to affect selectivity of the stimulation achieved. Short pulse durations
11
have been shown to activate axons located closer to electrical contacts, and
hyperpolarizing pre-pulses have been used to inhibit some axons while the depolarizing
pulses that follow are used to activate other axons (Grill and Mortimer, 1996, 1995).
Single-channel stimulators are often used to stimulate the entire nerve to which
they are applied (Castoro et al., 2011; Kilgore and Bhadra, 2004; Scheiner et al., 1994;
Tosato et al., 2007). Full-nerve interfacing is limited to cases where either the axon
population of the nerve is functionally homogenous, or where activation of non-targeted
cells causes acceptable side effects. Vagal and recurrent laryngeal nerve stimulators use
helical electrodes designed to maximize activation of the entire nerve (Broniatowski et
al., 2001; Scheiner et al., 1994). Placement of these interfaces along the nerve and on
appropriate nerve branches helps in targeting the desired axons and minimizing side
effects. High frequency nerve block typically requires stimulation amplitudes that affect
the entire nerve at the stimulation site (Ackermann et al., 2009). For applications using
high frequency block to prevent pain in residual nerves after limb amputation, activation
of residual motor axons has no negative effect. Single-contact interfaces are limited,
though, in applications requiring multiple functions.
Multi-contact interfaces are typically chosen when multiple functions must be
accomplished by the same interface. The four-contact spiral cuff electrode has been
evaluated in chronic clinical studies, and shown to provide stable stimulation parameters
and utility in restoring standing function and arm movement to subjects with paralysis
(Fisher et al., 2009; Polasek et al., 2009a). The spiral nerve cuff is designed to
accommodate a range of nerve sizes by coiling around the nerve circumference (Gorman
and Mortimer, 1983; Polasek et al., 2009b). The major drawback to this design is that
12
axons that are located in the center of the nerve are difficult to activate without first
activating axons close to the perimeter (Veltink et al., 1988; Veraart et al., 1993). The flat
interface nerve electrode (FINE) is a multi-contact interface designed to complement the
oblong shape that many nerves exhibit, and reshape the nerve somewhat to further spread
out the fascicles contained within the nerve (Schiefer et al., 2010, 2008; Tyler and
Durand, 2003, 2002). This results in safely reducing the distance between axons and the
nearest stimulation channel, as long as pressures chronically applied to the nerve do not
exceed 60 mmHg (Tyler and Durand, 2003). FINE electrodes have been applied in
intraoperative clinical experiments (Schiefer et al., 2010), and preclinical experiments
(Choi and Lee, 2006; Hess et al., 2007; Leventhal and Durand, 2003). Implementations of
the FINE indicate good fascicle-level selectivity, but there is less evidence supporting its
use in selectively activating only portions of a fascicle at a time.
Interfascicular Interfaces
An approach used to reduce spill-over of stimulation from one fascicle to another,
improving fascicle-level selectivity, is to mechanically and electrically separate fascicles.
Designs that mechanically separate the fascicles of the nerve include the multigroove
electrode, the book electrode, and the slowly penetrating interface nerve electrode
(Brindley et al., 1986; Koole et al., 1997; Tyler and Durand, 1997). The multigroove and
book electrodes require dissection of the epineurium to provide access to the fascicles,
and the slowly penetrating interface nerve electrode relies on application of low level but
steady pressure to insert electrodes and insulating barriers between the fascicles of the
nerve (Tyler and Durand, 1997). Design of these interfaces requires some a priori
knowledge of the fascicle structure at the interface point, and may not be viable in
regions with high anatomical variability.
13
Intrafascicular Interfaces
Sub-fascicular selectivity from an extraneural electrical interface is impeded by
the resistive barrier that the perineurium surrounding axons poses. Because the
endoneurial space within the perineurium is much less resistive than the perineurium,
stimulation strong enough to penetrate the perineurium spreads easily throughout the
perineurial space (Veltink et al., 1988). Spreading stimulation reduces the ability to
selectively activate subpopulations of axons within a fascicle; referred to as sub-
fascicular selectivity. Electrical interfaces that penetrate the perineurium to more directly
interface with axons have been developed with the aim of achieving sub-fascicular
selectivity. The longitudinal intrafascicular electrode (LIFE) and the transverse
intrafascicular multichannel electrode (TIME) each involve threading fine wires or flat
polyimide electrode arrays into individual fascicles (Badia et al., 2011; Lawrence et al.,
2004; Malagodi et al., 1989; Micera et al., 2008). Utah Slanted Electrode Array (USEA)
introduces small electrodes into the endoneurial space by penetrating the perineurium
with an array of pointed silicone probes. The USEA consists of a 10 by 10 two-
dimensional array of electrodes, fabricated to varying lengths to interface with axons 0.5-
1.5 mm from the nerve surface (Branner et al., 2000; Dowden et al., 2009). These
interfaces have been shown capable of increasing selectivity for acute preclinical
applications to achieve sub-fascicular selectivity (Badia et al., 2011; Dowden et al., 2009;
Yoshida and Horch, 1993), but chronic implantation of these interfaces can lead to
changes in axon morphology, resulting in losses of large-diameter axons and endoneurial
area (Agnew et al., 1989; Yoshida and Horch, 1993). The foreign body response that
occurs in response to all electrode implantations results in an encapsulation of the
electrode in a resistive barrier of collagen, which may reduce the selectivity achieved by
14
the increased invasiveness of these approaches when applied chronically (Branner et al.,
2000). The utility of these interfaces will remain limited until chronic performance can be
addressed.
Regenerative Neural Interfaces
In an effort to further increase intimacy between electrode and axon, regenerative
interfaces have been developed to encourage small groups of axons to grow around
electrodes. Taking advantage of the peripheral nerve’s ability to repair itself, regenerative
neural interfaces are placed between the two cut ends of a transected peripheral nerve.
Severed axons are then encouraged to re-grow through an array of small holes lined with
electrodes (Edell, 1986; Fitzgerald et al., 2012; Kovacs et al., 1992). The physical size of
the holes limits how many axons can regenerate through each, providing isolated
interfacing to 100-300 axons (Dario et al., 1998; Fitzgerald et al., 2012). The drawback to
this approach is the lack of control over which axons will regrow through each channel.
This means that even though a small number of axons are activated, the activity may or
may not be selective. There is also evidence that not all axons re-grow (Fitzgerald et al.,
2012), which could limit muscle activation in motor stimulation interfaces.
In the ideal interface, selective control would be established over each axon.
Intermediate approaches attempt to provide selective activation of the most functionally
similar populations of axons. For many of the electrical interfaces employed, efforts
selectively activate small populations of axons comes at the expense of increased
invasiveness to the nerve (Navarro et al., 2005; Sergi et al., 2006). Since maximizing
selectivity and minimizing invasiveness of an interface are both important design goals, it
15
is worthwhile to explore other methods of interfacing with the peripheral nerve that may
provide selective activation without increased invasiveness.
Neural Interfacing Modalities
Electrical current is only one modality that can be used to modify neural activity.
Magnetic, optical, and chemical energies can also be used to influence neural behavior,
each with its own effects and differences from electrical activation.
Electrical and Magnetic Neural Interfaces
Electric fields generated in conductive media follow Poisson’s equation relating
potential, ϕ, to charge density within the medium, ρ (Eq. 1-1):
The electric field generated by a current source will depend on the quantity and
geometry of charged particles and geometry of the volume conductors within the space
around the charged particles. A very simplified case is a point source located in an
infinite homogeneous medium. The electric potential, V, generated is related to the
current from the point source, I, the conductivity of the medium, σ, and the distance at
any point from the point source, r, by (Eq. 1-2):
In tissue, conductivity can be high, reducing the distance over which significant electric
fields can be generated and increasing the need to minimize distance between target
axons and electrode.
An alternative to electrical stimulation that can still be used to activate neurons is
magnetic stimulation. The electric field generated by a magnetic field changing in time
16
can stimulate neurons. Magnetic fields can stimulate deeply into tissue because they do
not attenuate in tissue as electric fields do (Esselle and Stuchly, 1992). The drawbacks to
this type of stimulation include difficulty in spatially localizing delivery, and generating
time-varying magnetic fields require large currents passed quickly through large wire
coils. This results in large and high-powered stimulating hardware that is typically not
considered for chronic and long-term stimulation.
Chemical Neural Interfaces
Chemical energy can be used to influence neural activity once delivered to the
neural environment. The effect and timescale of chemical interfaces varies depending on
the time it takes for the chemical to be broken down or depleted, and the method of
activation on the cell. Chemicals that act on the neuron via second-messenger cascades or
influence genetic expression within the neuron can have very long lasting effects (Alberts
et al., 2002; Zai et al., 2009). Neurotransmitters delivered to the synapse between two
cells can cause depolarization or hyperpolarization of cell bodies. Chemicals such as
ouabain and tetrodotoxin can be used to prevent action potential propagation by blocking
the function of ion channels along the axons of neurons. Chemical interfaces can be
selective to cell type (Kandel et al., 2000), affecting only those with appropriate
receptors, but focused spatial delivery is a challenge (Matar et al., 2009). Additionally,
the time course over which the effect takes place will depend on the ability of the body to
clear the chemical. An approach demonstrated to improve spatial resolution of delivery of
neurotransmitters is to chemically bind the neurotransmitters in an inactive state, then
selectively unbind them with externally supplied energy that is localized to the target
cells (Matar et al., 2009). This approach requires that the supply of bound
neurotransmitter be maintained in the neural environment in order to provide an effect.
17
As a chronic motor stimulation interface, bound neurotransmitter and unbinding energy
would have to be applied either to the spinal cord or at the neuromuscular junction.
Neurotransmitter release in the spinal cord may affect neurons other than the targeted
motor neurons, and release at the neuromuscular junction would require very broad
delivery of the uncaging energy and many of the same disadvantages of intramuscular
electrodes.
Optogenetic Neural Interfaces
Interfacing with neurons using optical wavelengths is an emerging method to
potentially achieve very selective activation. Optical energy can be generated at precise
wavelengths, intensity, and timing. Ignoring scattering effects, light penetration into a
medium follows the Beer-Lambert law:
Intensity, I(x), is strongest at the surface, and then decreases exponentially depending on
the wavelength-dependent absorption coefficient of the material, µa. The penetration
depth is defined as the point where the intensity is decreased to e-1
of the intensity at the
surface. Optical energy delivery can be controlled using lenses, mirrors, shutters,
splitters, holograms, and diffraction gratings to provide very precise spatial control over
delivery (Abaya et al., 2012; Dummer et al., 2011; Llewellyn et al., 2010; Matar et al.,
2009). Cells that are not inherently light-sensitive can be made so by changing genetic
expression of the target cells, triggering production of light-sensitive ion channels. This
process, called optogenetics, offers a unique vector for tuning selectivity because cells
can be targeted based on their genetic expression (Aravanis et al., 2007; Deisseroth,
2011; Diester et al., 2011; Hegemann and Moglich, 2011; Zhang et al., 2008). Using this
18
method, cells that are adjacent to each other, but genetically different, can be selectively
activated or inhibited. Ion channels that are sensitive to different wavelengths and
selective to different ions have been developed and can provide inhibitory and excitatory
control over neurons (Diester et al., 2011; Zhang et al., 2008). Expression of these ion
channels occurs along the entire membrane, meaning that light sources can be applied at
various points along the neuron, including the axon within the peripheral nerve
(Llewellyn et al., 2010). It is conceivable, then, that optogenetics could be used to target
expression of light sensitive channels selectively in motor or sensory neurons, and
applied visible light would only activate these modified cells, or different wavelengths
could be used to activate either group independently (Zhang et al., 2008). A challenge in
using optogenetics for motor activation is controlling selectivity among genetically
similar, but functionally different motor neurons within the same peripheral nerve. If cells
cannot be targeted based on functionality, then selective activation will depend on the
interaction between tissue and the light applied. Wavelengths that pass through the tissue
easily will activate larger areas than wavelengths that are absorbed by the tissue.
Infrared Neural Stimulation
An alternative to building light sensitivity into targeted cells is to use wavelengths
to which the neural tissue is inherently sensitive to. Wells et al. demonstrated that
infrared light could be used to elicit motor response in rat sciatic nerve (Wells et al.,
2005a). Wells et al. measured the stimulation and ablation energy thresholds as a function
of wavelength and found that wavelengths most absorbed by water to provide the greatest
safety margin between these two thresholds (Wells et al., 2005b). Wells et al. investigated
the mechanism by which light triggered neural activity, and concluded that electric field
generation, photochemical, and mechanical effects are unlikely driving mechanisms
19
(Wells et al., 2007a). Based on observations that changes in the baseline nerve
temperature did not change the stimulation thresholds for infrared neural activation,
Wells et al. concluded that the thermal gradient generated by rapid heating of a localized
region of the nerve was necessary to driving activation with INS (Wells et al., 2007a).
Because the penetration depths of the wavelengths used for infrared neural
stimulation are 300-600 um in water, and water content of tissue is high, infrared delivery
is expected to be very spatially localized within the tissue, and thermally confined
(Richter et al., 2011a; Wells et al., 2007a, 2007b). These properties may help infrared
neural stimulation (INS) serve as a selective neural interface. Wells et al. demonstrated
that motor response to INS could be changed as beam position on the nerve surface was
changed in the rat sciatic nerve (Wells et al., 2007b), and established damage thresholds
and stimulation repetition rate limits (Wells et al., 2007a, 2007c). These results, paired
with penetration depth data, indicated that INS may provide selective peripheral
activation on the sub-fascicular level without penetrating the epineurium or perineurium
of the nerve, if the high energy requirements and low safety margins could be addressed.
Soon after INS was demonstrated in the mammalian peripheral nerve, Izzo et al.
applied infrared light to the gerbil cochlea and reported success in reliably activating
spiral ganglion cells using an optical fiber inserted into the round window of the cochlea
(Izzo et al., 2007; Moreno et al., 2011; Richter, Claus-Peter and Matic, 2012). Stimulation
was shown to occur along the path of the applied beam using activity-dependent staining
of spiral ganglion cells (Moreno et al., 2011), and neural activity was recorded in
response to stimulus applied at 200 Hz continuously for 10 hours (Rajguru et al., 2010).
Selectivity of INS in the cochlea is currently being evaluated and compared to acoustic
20
activation (Richter et al., 2011b). Cochlear stimulation was observed at radiant exposures
two orders of magnitude lower than that required for peripheral nerve INS (Richter,
Claus-Peter and Matic, 2012). The drastic difference in energy thresholds still remains
unknown.
To date, infrared light has been used to stimulate many types of tissue. INS has
been applied to cortical neurons (Cayce et al., 2011), sensory neurons in dorsal root
ganglia (Katz et al., 2010), and cardiac myocytes (Dittami et al., 2011; Jenkins et al.,
2010). Recordings in stimulated cortex indicate a reduction in spiking frequency in
response to INS (Cayce et al., 2010), but it is unclear whether this was due to activation
of inhibitory neurons, or inhibition of firing. Katz et al. observed activation when
stimulating cell bodies in the dorsal root ganglia, with threshold radiant exposures similar
to peripheral nerve INS (Katz et al., 2010). This would indicate that the low stimulation
thresholds in cochlear stimulation are not simply due to targeting the cell body instead of
the axon. Katz et al. also reported a reversal potential for the observed effect that was
40 mV more negative than that expected for a thermally-sensitive transient receptor
potential (TRP) channels (Katz et al., 2010). Infrared light has also been used to activate
cardiac myocytes and pace embryonic hearts (Dittami et al., 2011; Jenkins et al., 2010),
indicating that the driving mechanism may not be neuron-specific. Dittami et al. found
that application of infrared light to cardiac myocytes triggered an intracellular release of
calcium that could be prevented by blocking calcium release from mitochondria (Dittami
et al., 2011). Shapiro et al. applied infrared light to non-excitable Xenopus oocytes,
human embryonic kidney cells, and an artificial lipid bilayer, and observed a
temperature-driven change in membrane capacitance (Shapiro et al., 2012). Capacitance
21
changed in response to weakening of hydration bonds of the ions nearest to the
membrane interface, and was shown to cause depolarization of the cell by 6-10 mV
(Genet et al., 2000; Shapiro et al., 2012). These investigations give clues into the
mechanism behind INS, but additional work is necessary to demonstrate that these are
driving mechanisms and not just secondary effects of rapid heating or infrared light
absorption by the cellular structures.
In an effort to reduce the energy requirements of INS, Duke et al. combined INS
with electrical stimulation. Duke et al. were able to use electrical stimulation to lower the
optical activation threshold, or vice versa, activating neurons when both stimulation
modalities were applied below their individual respective thresholds (Duke et al., 2009).
Duke et al. further refined parameters for combining electrical and infrared fields to
reduce variability in response, and found that the response was localized to particular
regions of the nerve (Duke et al., 2012a). Recent work involving Xenopus peripheral
nerves and computational models has demonstrated that infrared light can also increase
electrical stimulation thresholds, and even block action potential conduction (Mou et al.,
2012). This indicates that INS may be useful in causing excitation or inhibition in
peripheral nerve interfaces. These results expand the options for using INS to modulate
behavior, as combination with electrical stimulation may enable more selective activation
by activating only the overlap between the two applied fields.
The results from these studies provide compelling evidence that INS may be
useful in achieving sub-fascicular selectivity, without penetrating the protective tissue
layers of the nerve. In order to investigate whether INS truly provides a selective and
functionally relevant interface for peripheral nerve interfaces, stimulation parameters
22
relevant to interface design must be investigated. Wells et al. began this process by
investigating tissue effects and damage thresholds associated with INS. Wells et al.
determined that applying infrared to tissue at stimulation thresholds for peripheral nerves
caused a linear increase in temperature during energy deposition to a peak increase of 8-
15 ºC, with an exponentially decaying temperature after the beam is turned off (Wells et
al., 2007a, 2007c). Similar temporal dynamics were observed by Shapiro et al. for
transient changes in temperature and membrane capacitance (Shapiro et al., 2012). The
time constant of the exponential decay was measured between 90-100 ms, and limited the
rate at which stimulation could be applied without significantly raising the baseline tissue
temperature (Shapiro et al., 2012; Wells et al., 2007a). Stimulation at rates above 4 Hz
did not allow sufficient time between pulses for energy to dissipate, causing a sustained
increase in tissue temperature (Wells et al., 2007a). By performing a dose titration and
investigating the resulting histology, Wells et al. also determined that radiant exposures
only twice as high as the stimulation threshold resulted in neural damage in acute
experiments (Wells et al., 2007c). These limitations must be considered when designing
peripheral nerve interfaces using INS.
Research Motivation
While previous INS investigations have established that INS can trigger motor
response, important knowledge gaps must be addressed before INS can progress towards
functional implementation. A neuroprosthesis intended to restore motor function will
require stimulation rates at or above 12 Hz. With threshold stimulation at a single site
limited to 4 Hz (Wells et al., 2007a), higher stimulation rates may be achieved by
interleaving stimulation across multiple, thermally-independent sites. Previous data
23
previously reported only reports response along a single 400-600 um band of the nerve
(Wells et al., 2007b). With previous investigations primarily focused on stimulation
response at threshold, motor recruitment capabilities of INS are unknown. With a narrow
range between stimulation and damage thresholds, the output response may or may not
provide enough gradation to be useful. Previous studies have investigated motor
activation in nerves of rat and sea slug (Duke et al., 2012a; Wells et al., 2005a). The high
spatial localization of INS that makes it attractive as a selective interface may also be a
limiting factor when the size of the target nerve is increased. Previous studies also
generally involve application of infrared light to the nerve surface through bare fiber tips.
This approach may not provide the most efficient delivery of INS. Computational models
can be helpful in optimizing stimulus parameters (Schiefer et al., 2008), and may provide
means of improving stimulation using infrared light.
This thesis describes the studies performed to quantify parameters important to
designing extraneural peripheral nerve INS interfaces. Experimental in vivo work was
performed on a nerve model larger than that used in previous literature to quantify
parameters relevant to INS interface design. This provides a first step towards
understanding challenges of translating INS towards clinical applications. We also
designed and performed computational modeling studies to evaluate the feasibility of
proposed mechanisms of INS. The results of this study highlight the challenges to
implementing a peripheral nerve INS interface. The modeling results provide parameters
under which proposed mechanisms may cause activation, and provide initial direction for
alternative beam profiles that may more effectively activate axons.
24
Chapter 2: Dissertation Objectives and Organization
Introduction
The primary objective of this dissertation is to quantify peripheral nerve
sensitivity and response to infrared stimulus applied extraneurally. The eventual goal of
implementing multichannel infrared-based peripheral nerve interfaces is driven by the
need to develop peripheral nerve interfaces that are highly selective but minimally
invasive. Prior studies indicate that motor response rat peripheral nerves can be elicited
using focused infrared light. Spread within tissue of the infrared wavelengths used is
limited by absorption of water, and infrared pulse deposition is thermally confined. Based
on these facts, infrared light has potential to provide highly localized activation of neural
tissue. Infrared stimulus comes with challenges to implementation, though, as high power
limits the maximum repetition rate at which infrared light can be applied, the entire nerve
does not exhibit sensitivity to infrared stimulus, and the evoked response is small.
Previous work indicates that electrical stimulus can be used to lower infrared activation
thresholds, which may provide a means of improving response to infrared stimulus.
Further optimization of infrared-based interfaces hinges on understanding the mechanism
by which infrared light triggers action potentials. Mechanistic work performed to date
indicates transient temperature changes, membrane capacitance changes, and intracellular
calcium release as possible, but not conclusive, mechanisms.
The presented work evaluates the use of infrared stimulus in the rabbit sciatic
nerve to quantify nerve sensitivity and motor response evoked by infrared stimulus.
Electrical and infrared stimuli are combined to determine the synergistic effect on full
muscle recruitment. Finally, computational models of the proposed infrared stimulus
25
mechanisms are developed to determine the feasibility of each mechanism as a means of
activation.
Aim 1
The first aim is to investigate parameters relevant to design of a multi-channel,
infrared-based peripheral nerve interface. This includes quantifying sensitivity of a multi-
fascicular mammalian peripheral nerve model to extraneural infrared stimulus, and
characterizing the response evoked by a single channel of stimulus. The specific
hypotheses developed for this aim are:
Hypothesis 1.1:
Rabbit sciatic nerve sensitivity to extraneural infrared stimulus is high
enough to yield at least 3 regions exhibiting entrained motor response to applied
infrared pulses.
Hypothesis 1.2:
Rectified and integrated motor response to increasing infrared pulse energy,
applied by increasing duration of fixed-power pulses, follows a sigmoid relationship
to increasing pulse duration/energy.
Hypothesis 1.3:
Motor recruitment within optically sensitive regions of the nerve will exhibit
a lower activation threshold than any other muscle recruited in the same region in
at least 50% of optically sensitive regions.
Hypothesis 1.4:
26
Short duration, high power infrared pulses are more efficient than longer
duration, lower power pulses in minimizing activation threshold and maximizing
evoked motor response.
Hypothesis 1.5:
Maximal motor response evoked by infrared stimulus applied at below the
calculated damage threshold will result in activation of at least 10% of a single
muscle
Nerve sensitivity and motor response are measured using exposed rabbit sciatic
nerves. This nerve model is larger than those previously used for studying peripheral
infrared stimulation, and is an important first step in translating infrared stimulus towards
clinical applications. Experimental methods, results, and hypothesis testing is performed
in Chapter 3 of this dissertation.
Aim 2
The relatively small muscle twitches evoked by infrared stimulus place limits on
its utility. The second aim of this study is to investigate whether extraneural infrared
stimulation affects a significant portion of the nerve, but to a sub-threshold level. This is
tested by applying entrained infrared and electrical pulses to mimic reports of synergistic
combinations of the two modalities. Because electrical stimulation is expected to lower
the activation threshold of axons, those stimulated to a subthreshold level should activate
when graded electrical stimulus is applied. Modulating electrical stimulation amplitude
from below threshold to supra-maximal activation levels will ensure that all motor axons
are activated. Differences between electrical and combined infrared and electrical stimuli
would indicate a population of axons that is influenced by the infrared stimulus.
27
Hypothesis 2.1
Combining extraneural, entrained electrical and optical stimuli will
significantly alter recruitment over electrical stimulation alone, by shifting
recruitment curves to lower stimulus levels, or reducing recruitment curve slope as
some axons are selectively activated.
Previous work combining electrical and infrared stimuli either deals with shifting
activation thresholds, or with application of each at frequencies showing significant inter-
pulse interactions. This study examines the effect of independent pulses to determine
whether a significant population of axons is stimulated to subthreshold levels.
Experimental methods and hypothesis testing of this aim are contained in chapter 3.
Aim 3
Infrared neural stimulation has not been mechanistically described, but previous
work has demonstrated thermally driven changes in membrane capacitance and
intracellular release of calcium by mitochondria in non-neuronal cells. Both of these
phenomena would be expected to cause depolarization of the cell, but it is unclear
whether this depolarization is significant enough to drive action potential generation. The
third aim of this study uses computational models to evaluate whether action potentials
can be generated in spatially-lumped membrane models or spatially-distributed axon
models, using these possible mechanisms.
Hypothesis 3.1
Thermally driven capacitance changes can trigger action potentials in
spatially-lumped membrane models.
Hypothesis 3.2
28
Thermally driven capacitance changes can trigger action potentials in
spatially-distributed axon models, depending on thermal gradients along the
membrane length.
Hypothesis 3.3
Intracellular release of calcium ions, modeled as an intracellular calcium
current, can trigger action potentials in spatially-lumped membrane models without
exceeding physiologic intracellular calcium concentration levels.
By determining whether these modeled phenomena offer feasible explanations for
infrared neural stimulation observed in mammalian axons, this study will help direct
future experimental work investigating infrared neural stimulation. The experimental
methods of this study, results, and hypothesis testing are contained in Chapter 4.
NEURON code used to perform simulations is contained in Appendix II.
Appendices
Appendix I contains a reproduction of an article published in the Journal of
Neural Engineering (2011, Vol 8, Issue 4). This work investigated the use of spatial
characteristics of an electric field to predict whether it would trigger an action potential
when applied to a myelinated axon model. This approximation method achieved a
reduction in computation time by a factor of ~20,000, and is currently being employed in
research implementing genetic algorithms to optimize stimulating electric fields for
peripheral nerve interfaces.
Appendix II contains code written for the NEURON simulation environment to
model effects of infrared neural stimulation on excitable cell membranes. Both “.hoc”
29
simulation files and “.mod” membrane dynamic files are included. This code pertains to
simulations performed and discussed in Chapter 4.
Appendix III contains the MATLAB code used to analyze and summarize
recordings from in vivo experiments, related to the findings reported in Chapter 3. Code
used in recruitment curve generation, including EMG response detection and
measurement, is included.
30
CHAPTER 3: MOTOR NEURON ACTIVATION IN PERIPHERAL
NERVES USING INFRARED NEURAL STIMULATION
Abstract
Function can be restored to paralyzed limbs using selective peripheral nerve
interfaces. Previous approaches to achieve sub-fascicular selectivity have done so by
penetrating the protective perineurial barrier, increasing invasiveness to the nerve.
Infrared neural stimulation (INS) may provide a means of localized neural activation
from an extraneural interface, because of high infrared absorption by water and
thermally-constrained pulse delivery. A series of experiments were performed delivering
1875 nm infrared light from a continuous-wave source to the rabbit sciatic nerve.
Infrared-sensitive regions (ISR) of the nerve were measured to quantify available
extraneural interface sites. INS motor recruitment of medial gastrocnemius, lateral
gastrocnemius, soleus, and tibialis anterior were measured to quantify selectivity.
Maximum infrared recruitment was compared to maximal electrical recruitment to
quantify activation capabilities of a single channel of INS. Infrared and electrical stimuli
were applied simultaneously to measure differences in full-muscle recruitment over
electrical-only stimulus. 81% of nerves tested were sensitive to INS, with 1.7± 0.5 ISR
detected per nerve. INS was selective to a single muscle within 81% of identified ISR.
Activation energy threshold did not change significantly with stimulus power, but
recruitment amplitude decreased significantly when pulse power was decreased.
Maximum INS levels typically recruited 2-9% of any muscle. Combined stimulus
recruitment differed significantly from electrical recruitment in 7% of cases. A nerve
stimulated by INS exhibits selectivity to a single muscle, and may have the potential for
augmenting rehabilitation. However, significant challenges remain in delivering INS to
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the nerve to increase sensitivity and response magnitude, before it will have a significant
clinical impact.
Introduction
Peripheral nerve interfaces have been used to help restore function to paralyzed
limbs by stimulating axons of motor neurons (Polasek et al., 2009a; Popovic et al., 2007;
Weber et al., 2005). The ability to affect targeted axons while leaving non-targeted axons
unaffected is the measure of an interface’s selectivity (Choi et al., 2001; Dowden et al.,
2009; Polasek et al., 2009a; Schiefer et al., 2008). Improving interface selectivity is a key
design parameter, as increased selectivity improves control and functionality (Badia et
al., 2011; Butson et al., 2011; Fisher et al., 2009; Maks et al., 2009; Nielsen et al., 2011;
Richter et al., 2011b; Schiefer et al., 2010). The perineurium surrounding groups of axons
in peripheral nerves is resistive and impedes selective activation of subpopulations of
axons using electrical current. One approach to increase selectivity is to penetrate this
protective barrier (Badia et al., 2011; Dhillon and Horch, 2005; Dowden et al., 2009;
Fitzgerald et al., 2012; Rutten et al., 1991; Sergi et al., 2006). Interfaces that penetrate the
protective perineurial barrier of the nerve have been shown effective in activating very
small populations of axons in acute studies (Badia et al., 2011; Dowden et al., 2009).
However, disruption of the perineurial barrier leads to regeneration of a connective tissue
barrier in the chronic environment that may reduce selectivity gains of these approaches
(Branner et al., 2000).
Focused infrared light can evoke motor response in the peripheral nerve, without
introduction of exogenous chemicals or genetic material (Duke et al., 2009; Richter et al.,
2011a; Wells et al., 2007c, 2005b). Infrared wavelengths are highly absorbed by water in
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tissue (Wells et al., 2007b), and energy is deposited before significant thermal diffusion
occurs (Wells et al., 2007a). The result is spatially localized delivery of infrared energy.
Infrared neural stimulation (INS) has been shown capable of activating localized regions
of peripheral nerves, the resulting activation pattern of which can be modulated by
repositioning infrared delivery to the nerve surface (Wells et al., 2007b). Infrared-based
neural interfaces may therefore provide means of activating small populations of axons
via extraneural delivery.
There are limitations to INS to consider in interface design. Wells et al.
demonstrated that INS applied at peripheral nerve stimulation thresholds resulted in
sustained tissue heating when applied at rates above 4 Hz (Wells et al., 2007a). Motor
activation at rates above 4 Hz for tonic contraction may be achievable by interleaving
stimulation across multiple, thermally independent sites, though. Radiant exposure
damage thresholds for acute INS have also been measured to be 2-4 times the activation
threshold (Wells et al., 2007c). This leaves a narrow range for safely modulating INS
response. Applying entrained electrical energy has been shown to lower infrared
stimulation thresholds, and suggested as a means of addressing high INS energy
thresholds (Duke et al., 2009). By lowering activation thresholds, electrical energy may
also help increase maximum INS recruitment by facilitating activation of sub-threshold
axons.
The goal of our study was to quantify parameters necessary to enable
multichannel INS interface design. Previous peripheral INS work has been applied to rat
sciatic nerve (Duke et al., 2009; Wells et al., 2007b). Because water absorption limits the
penetration depth of INS, investigating response in larger nerves will be important to
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translating INS toward clinical implementation. The rabbit sciatic nerve, which is roughly
twice the diameter of the rat sciatic nerve, (Hsu et al., 2011; Tyler and Durand, 2003) was
chosen for this study. The first aim of this study was to quantify nerve sensitivity, and
characterize evoked motor response to INS. We hypothesized that at least 3 infrared-
sensitive regions (ISR) could be identified on each nerve, as this is the minimum number
of ISR required to implement interleaved 4 Hz stimulation to achieve a 12 Hz motor
response. We hypothesized that motor recruitment would follow a monotonic relationship
to pulse energy below the acute damage threshold, that at least 50% of ISR provide
selective activation of a single muscle, and that a single channel of INS stimulation
would recruit at least 10% of a muscle. Finally, entrained electro-infrared stimulation was
compared to electrical stimulation, to determine whether INS affected a functionally
significant population of axons. We hypothesized that increased activation of a
significant subpopulation of axons by INS or co-activation with the two modalities would
provide significant differences in full-muscle recruitment over electrical stimulation
alone.
Methods
Surgical preparation and EMG recording
The following procedures were approved by the Case Western Reserve University
Institutional Animal Care and Use Committee (IACUC). New Zealand white rabbits
(Oryctolagus cuniculus) (Male, 2.8-4.5 kg) were initially anesthetized using Ketamine
and Xylazine. Anesthesia was maintained using continuously supplied Isoflurane at 2-4%
supplied through an endotracheal tube. Reflex checks and vital signs were used to
determine anesthesia level. Heart rate, temperature, pulse oximetry, and exhaled carbon
34
dioxide were measured to maintain stasis. Blunt dissection techniques were used to
separate the semitendinosis and biceps femoris and expose the sciatic nerve proximal to
the popliteal fossa. Similar procedures were also applied to three male Sprague-Dawley
rats (Rattus norvegicus). Initial anesthesia for rats was performed using 2-4% Isoflurane
administered with oxygen in a chamber. Due to anatomical differences between rat and
rabbit, the rat sciatic nerve was accessed using blunt dissection along the muscle plane
just rostral to the biceps femoris.
Motor response to INS was measured by recording electromyogram (EMG)
signals using bipolar intramuscular electrode pairs placed in the Lateral and Medial
Gastrocnemius muscles (LG and MG, respectively), Soleus (Sol), and Tibialis Anterior
(TA) (Figure 1 A). To improve coverage of the physically larger MG and LG muscles,
two EMG recording channels were implanted in each of these muscles. Intramuscular
electrodes were made by removing 3-5mm of insulation from 100 um 316LVM stainless
steel wire (Fort Wayne Metals, Fort Wayne, IN), and implanted using a hypodermic
needle tip. EMG signals were amplified with a gain of 330 and filtered 10-500 Hz with a
60 Hz notch filter (1902 Amplifier, Cambridge Electronic Design, Cambridge, England,
UK). Amplifier output was sampled at 5000 Hz to accurately capture EMG shape and
timing, digitized and recorded using data acquisition hardware (USB-6259 BNC,
National Instruments. Austin, TX). Electrical and infrared stimulus triggers and data
recording were controlled using custom LabVIEW software (LabVIEW 2010, National
Instruments. Austin, TX). Stimulator triggers were recorded along with EMG signals.
EMG recordings started approximately 40 ms before and continued approximately 50 ms
after the infrared stimulus trigger.
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Electrode fabrication
To emulate stimulation geometries previously identified effective in hybrid
applications (Duke et al., 2012a, 2009), a nerve cuff with three electrodes was developed
(Figure 3-1B). Polydimethylsiloxane (PDMS) was mixed and cured in 3D-printed molds
to form flat-interface nerve electrodes (FINE) (Tyler and Durand, 2003). The nerve
channel cross section was 0.8 mm by 4.5 mm. A 1.3 mm by 4.5 mm opening spanning
the width of the nerve channel was cut in the top PDMS layer to allow direct IR delivery
to the nerve. Square, 0.64 mm2 platinum electrodes were located on either side of this
window on the top half of the nerve channel, longitudinal to the nerve and 1.3 mm apart
to reflect hybrid stimulation found effective in rat sciatic nerve (Duke et al., 2012a). A
third electrode was placed directly below the window on the bottom half of the nerve
channel, to test conditions similar to the hook electrode used in early hybrid
implementation (Duke et al., 2009).
Infrared delivery
A Capella 1870 continuous-wave diode laser (Lockheed-Martin Aculight. Bothell,
WA) was used to generate 1875 nm wavelength infrared energy. Infrared light was
coupled to a 400 µm diameter optical fiber (Ocean Optics. Dunedin, FL), rated for
wavelengths 400-2100 nm. Infrared energy was output to the nerve through a bare fiber
tip that was polished, inspected for defects at 200x magnification, and profiled with the
knife edge technique (Khosrofian and Garetz, 1983) and a power meter (PS19Q,
Coherent Inc. Santa Clara, CA) prior to each experiment. The bare fiber tip was secured
and positioned near the nerve using a 3-axis, 10 um resolution micromanipulator (M325,
World Precision Instruments. Sarasota, FL). Energy deposition was controlled by
adjusting pulse power and duration. Infrared pulses were applied at 1-2 Hz to allow
36
dissipation of thermal energy between pulses, and minimize inter-pulse interactions
(Wells et al., 2007a).
Optical stimulation
Radiant exposure to INS was limited to 2.6 J/cm2 to avoid the acute damage
thresholds measured by (Duke et al., 2012a, 2009; Wells et al., 2007a). Pulse power and
Figure 3-1 Methods for infrared and electrical stimulation of rabbit sciatic nerve
A) Infrared light was generated with a continuous wave laser, and coupled onto a
400 um diameter optical fiber. The bare, polished fiber tip was positioned above the
nerve with a micromanipulator. EMG response was recorded using intramuscular
electrodes inserted in Medial Gastrocnemius, Lateral Gastrocnemius, Soleus, and
Tibialis Anterior. B) Polydimethylsiloxane (PDMS) nerve cuff used to combine optical
and electrical stimulation. Optical stimulation was applied directly to the nerve
through the IR delivery window. C) Electrical and optical stimuli are aligned so
cathodic electrical stimulation ends with the IR pulse.
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duration was initially set to target energy density of 1.3 J/cm2 when the fiber is positioned
~750 um from the nerve. The tip of the optical fiber was positioned between 250 and
1000 um from the nerve surface using the micromanipulator. The nerve was scanned to
identify regions where applied INS triggered a detectable EMG response. The nerve
surface was scanned side to side in 100-200 um transverse rows along the accessible
length of the nerve. When the edge of the scanning region was reached, the nerve was
scanned in the longitudinal columns, top to bottom and side to side until completely
scanned. If no ISR were observed, radiant exposure was increased and the surface was
rescanned.
When an optically sensitive region was detected, fiber positioning was tuned in all
three dimensions to center the infrared beam over the sensitive region based on evoked
EMG amplitude. The red pilot light of the laser was used to visualize the location of the
ISR on the nerve surface. The ISR position was recorded on a diagram of the nerve
relative to the common peroneal and sural branches (Figure 3-1A). When time permitted,
response was measured as a function of position on the nerve. The ISR was scanned in
the longitudinal and transverse directions in 50-100 um steps with 0.7-2.6 J/cm2
pulses.
The largest above-threshold region across all pulse durations tested was taken as the
spatial measurement of the ISR.
Early data collection revealed periodic decreases in recruitment response that
would return a few minutes later. The points where response dropped did not correspond
to particular pulse energies/durations, but instead may have been due to application of
saline to rehydrate the nerve. Recruitment response was measured over time with fixed
stimulus and periodic application of 0.25-0.5 ml lactated Ringer’s solution to the nerve
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surface. At least 30 seconds were allowed to pass between applications of 8 infrared
pulses, delivered at 2 Hz. The response rate to stimulus was defined as the ratio of
detected EMG responses to applied infrared pulses, and the threshold for response rate set
to 30% to exclude random twitches and noise events. When the recruitment response rate
dropped below the threshold during data collection, data points were excluded until the
response rate recovered. Because the response rate was defined as the ratio of detected
EMG signals to applied pulses, changes in recruitment amplitude would still be captured
for detectable EMG responses.
Motor recruitment curves at ISR were recorded in response to infrared pulse
durations from 0.2-3.4 ms in 0.1 ms steps. Maximum pulse duration was limited based on
infrared power to remain below the calculated damage threshold. Order in which pulse
duration was applied was randomized, and at least 8 pulses were applied at each pulse
duration level, at a rate of 2 Hz. The activation threshold of a recruitment curve was
defined as the lowest pulse duration or energy at which the 30% response rate threshold
was exceeded.
Electro-Infrared Stimulation
Electrical stimulation was delivered through electrodes stabilized in a PDMS
FINE nerve cuff. Electrodes were positioned as close as possible to identified ISR. After
device implantation, optical fiber position and radiant exposure was adjusted to re-
establish infrared-evoked response if possible. Electrical stimulation was supplied using a
custom current-controlled stimulator (FSPG, Crishtronics LLC. Cleveland, OH).
Stimulus pulses were biphasic with a rectangular stimulus phase and passive, current-
limited charge-balancing phase (Figure 3-1C). Muscle recruitment was measured as a
function of electrical pulse amplitude in response to pure electrical or combined electrical
39
and infrared stimulus. A total of 9 electrode configurations were tested. Each
configuration employed one of the three electrodes to deliver cathodic stimulation, with
anodic return through either one of the other two contacts or a distant percutaneous
electrode. Infrared stimulus was set to ~150% of the previously observed infrared
threshold. This ensured some safety margin below damage thresholds, while maximizing
the number of axons affected by INS. Electrical and optical stimulation was entrained so
the stimulation phases of each ended at the same time (Figure 3-1D), to reflect the
stimulus parameters reported by Duke et al. (Duke et al., 2009). Application of electrical
and optical stimuli was controlled using custom LabVIEW software (LabVIEW 2010,
National Instruments. Austin, TX). Electrical amplitude was randomized with at least 6
repeat measures spread throughout the trial. At each measurement, an electrical-only and
a combined stimulus pulse were each applied at the same electrical amplitude in
randomized order. All stimuli were applied at 1-2 Hz to reduce inter-pulse interaction and
fatigue.
Data Analysis
EMG response was the primary outcome measure used in analyzing response to
applied stimuli. Stimulus triggers were used as reference time points for identifying
evoked responses. Early EMG responses were analyzed manually to determine that EMG
response typically began within 5 ms and was complete within 10-13 ms of the trigger.
An automated process was developed to measure evoked EMG response. The DC offset
of all EMG signals was removed, and the RMS value of the signal during the 40 ms prior
to the trigger was computed to estimate baseline noise. Threshold was set at 6 times this
RMS, and the algorithm detected threshold crossings in the 15 ms after each stimulus
trigger. Contiguous signal deflections that maintained the same polarity for longer than
40
0.5 ms but less than 4 ms were classified as part of the EMG signal and used to determine
EMG start and stop times. Muscle recruitment was measured as the rectified EMG signal
integrated from start to stop time.
Delay between stimulus and EMG initiation was compared for infrared and
electrical stimuli applied to the same nerve region. Infrared light was delivered through
the opening in the nerve cuff, and electrical stimulation applied through each of the
contacts 0.6 mm proximal and distal to the opening. Recruitment curves were generated
with each energy modality, varying pulse amplitude for electrical stimulation and pulse
duration for infrared stimulation. Delay between stimulus and the start of evoked EMG
was measured manually by plotting EMG signals relative to the stimulus triggers. The
electrical stimulation start time was set as the end of the 50-100 us cathodic stimulus
phase. The end of a minimum-duration infrared pulse eliciting an EMG response was
used as the start time for measuring infrared-evoked EMG delay. The initial signal
deflection of the EMG signal was used as the stop time for delay measurements of both
modalities.
All statistical testing was performed with a significance level of α = 0.05.
Wilcoxon signed rank tests were used when comparing measured results against a
hypothesized mean. Wilcoxon rank sum tests were used to compare pairs of distributions.
Significance and confidence intervals for selectivity were computed using a proportions
test, with each sensitive region classified as selective or not. Differences in recruitment
curves between electrical and hybrid stimulation were tested using a two-sample
Kolmogorov-Smirnov test sensitive to differences in shape and location of the cumulative
distribution of two samples (Chen et al., 2009). Recruitment pairs identified as
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statistically significant were examined visually to determine whether consistent changes
in activation were present in response to combined stimulus. Changes in recruitment
threshold or slope were considered functionally relevant, but statistically significant
changes in recruitment at a few stimulation amplitudes was not considered functionally
significant. Plotting, data analysis, and statistical computations were performed using
MATLAB 2012a (Mathworks. Natick, MA), and Minitab 16 (Minitab Inc. State College,
PA).
Results
Nerve Sensitivity to INS
30-50 mm sections of 2.5-4.5 mm wide sciatic nerves (N=32, 25 rabbits) were
scanned to identify infrared-sensitive regions (ISR). An ISR was classified as unstable if
motor response was observed, but could not be maintained long enough to record any
recruitment data. Adding a stabilizing stage below the nerve helped decrease movement
of the nerve and increase response stability. 26/32 (81%) scanned nerves were responsive
to infrared pulses. 1.7 ± 0.5 (mean ± 95% confidence interval) ISR per nerve were
observed across all 32 nerves. 2.0 ± 0.5 (mean ± 95% confidence interval) ISR per nerve
were observed among the 26 infrared-sensitive nerves. A typical result is illustrated in
(Figure 3-2A), and a composite result across all nerves is illustrated in (Figure 3-2B). The
maximum number of ISR detected on a single nerve was 6. Scans of the sural sensory
branch did not yield any motor response, as expected. Lower reported ISR frequency
proximal to the common peroneal branch or distal to sural branch (Figure 3-2B) was due
to nerve-to-nerve variation in branch point locations and physical limitations of scanning
above and below these points, rather than intrinsic lower sensitivity. Evoked EMG
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responses in 11 ISR were measured as a function of position and pulse energy. Average
transverse and longitudinal measurements were 360 ± 90 um and 470 ±140 um (mean ±
95% confidence interval), respectively.
Using a similar scanning technique to that used for sensitivity measurement in the
rabbit sciatic, three rat sciatic nerves were also scanned to identify ISR. Only MG, LG
and TA were monitored for EMG response, and no distinction was made between stable
and unstable regions (Figure 3-3). Scanned nerves were 0.9-1.8 mm wide, and the
exposed and scanned region was 18-25 mm in length. 6.0 ± 1.53 ISR (mean ± standard
error of the mean, N=3) were detected across the three trials performed.
Figure 3-2 Locations of detected optically sensitive regions
Infrared-sensitive regions (ISR) detected on the rabbit sciatic nerve. Identified regions
were classified as stable if response was observed for many minutes without adjusting
stimulation. Unstable regions exhibited sensitivity, but responses disappeared after only
a few minutes or less. Infrared sensitivity was observed in 26/32 scanned nerves. A)
Typical result from one trial exhibiting infrared sensitivity. B) Composite of all
identified sensitive regions observed, n = 32 nerves/25 rabbits.
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Motor Recruitment with Infrared Stimulus
Recruitment from fixed stimulus was measured over time to investigate effects of
hydration on motor response. 12 trials were performed across 6 animals. LRS was added
prior to each trial, and at least 3 minutes were allowed to elapse before iteration 1 began.
For 8/12 trials, LRS was applied twice mid-trial (Figure 3-4 A, B), whereas in 4/12 trials
no LRS was added once the trial began. 4/8 of the mid-trial hydration cases showed a
significant decrease in response immediately following LRS application (Figure 3-4A).
The other 4/8 cases showed no significant change in recruitment after saline application
(Figure 3-4B). Of the 4 trials where the nerve was not hydrated mid-trial, only 1/4 trials
showed any significant change in recruitment with a brief reduction of response that
returned within a few minutes.
Optical recruitment as a function of pulse duration/energy was recorded in 42
sensitive regions (21 nerves, 18 rabbits). Stimulation was applied with pulse durations
between 0.2 and 3.4 ms, in 0.1 ms increments. Recruitment curves were analyzed across
Figure 3-3 Sensitive regions detected in rat sciatic nerve
Infrared-sensitive regions (ISR) detected on the rat sciatic nerve in three experiments.
Nerves were 0.9-1.8 mm wide. Scanned length was 18-25 mm. Motor output was
measured in MG, LG, and TA.
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recorded EMG channels to measure selectivity. Each ISR was classified as sensitive if a
single muscle could be recruited before another reached threshold (Figure 3-4C), and
classified as non-selective if multiple muscles reached the 30% threshold response rate at
the same pulse duration (Figure 3-4D). Single-muscle selectivity was observed in 34/42
sensitive regions (95% confidence interval: 67-91%, single-parameter proportions test)
When the definition of selectivity was relaxed to allow co-activation of the functionally-
similar MG and LG, 39/42 cases exhibited selectivity (95% confidence interval: 81-
99%). Most sensitive regions allowed stimulation of multiple muscles below the
calculated damage threshold. 12/42 (29%, 95% confidence interval: 16-45%) sensitive
regions only a single muscle was activated below the damage threshold.
Mean recruitment was observed to follow a generally monotonic relationship with
increase pulse duration. Spearman’s rank-order correlation was chosen to evaluate this
relationship, as Pearson’s correlation tests indicated the relationship was not linear.
Across 209 recruitment curves (21 nerves, 17 rabbits) ρ = 0.68 ± 0.04 (mean ± 95%
confidence interval), and was significantly greater than zero for 83% of the recruitment
curves.
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To examine whether short, high power infrared delivery was more effective than
longer, lower power delivery, recruitment curves were generated using 100%, 80%, and
55% laser power levels. Data was collected at 12 sensitive regions across 7 nerves/rabbits
at 100% and 80% levels, but time only permitted collection at 55% in 4 trials. Threshold
Figure 3-4 Motor recruitment over time and versus pulse duration
A, B) Infrared recruitment was dependent on nerve hydration. Recruitment
measured with fixed stimulus over time. A) Example recruitment reduction after
application of 0.25-0.5 ml of lactated Ringer’s solution (LRS). B) Example with
steady recruitment after LRS application. C, D) Recruitment curves generated as
a function of pulse duration showing C) selective recruitment and D) non-
selective recruitment.
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pulse duration increased significantly with decreased laser power (Figure 3-5A), but
energy required to activate did not change significantly with laser power (Figure 3-5B).
Maximum recruitment decreases significantly with decreased laser power when
compared to activation at 100% power for all cases tested (Figure 3-5C). Soleus (Sol) and
tibialis anterior (TA) lacked sufficient sample numbers at 55% power to compute
confidence intervals or significance. ANOVA showed laser power (p=0.04), but not
muscle (p=0.93), to be a significant factor in maximum recruitment compared to 100%
power stimulation.
Maximum optical and electrical recruitment was compared across 57 recruitment
curves (12 nerves, 10 rabbits). INS recruitment was lower magnitude than electrical
recruitment (Figure 3-6A). Mean maximum INS recruitment across muscles was 2-9% of
the muscle capability. Cases wherein muscles were not activated to any detectable level
were excluded. Wilcoxon signed rank test results indicated that mean infrared activation
for all muscles fell significantly below 10% of maximum activation (Figure 3-6B).
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Figure 3-5 Comparing response versus infrared pulse power
A) Pulse duration required for activation decreases with increasing pulse power. B)
Pulse energy required for activation does not change significantly with pulse power. C)
Maximum recruitment at 80% and 55% power compared to maximum recruitment
with 100% power.
*p < 0.05, **p < 0.01 A,B) Wilcoxon rank sum test. C) Wilcoxon signed rank test.
48
Figure 3-6 Maximum electrical and infrared recruitment compared
A) Example electrical and infrared recruitment curves for a single muscle B) Percentage
of maximum electrical recruitment achieved with infrared stimulation across 12 nerves
in 10 rabbits. Computed mean with 95% confidence intervals, and p-values for
Wilcoxon signed rank test results against mean = 10%.
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Delay from infrared or electrical stimulation to EMG response start time was
recorded with electrical stimulus applied 0.6 mm proximal or distal to a region stimulated
by infrared (3 nerves, 3 rabbits) (Figure 3-7). The minimum pulse duration activation
threshold was determined for each muscle activated by infrared. Activation with infrared
light resulted in significantly longer latencies to EMG activation than electrical
stimulation. Mean infrared response latencies ranged 0.96-2.5 ms longer than mean
electrical response latency. Activation thresholds for infrared stimulation ranged 0.8-
2.0 ms.
Electro-Infrared Stimulation
Combined extraneural electrical and infrared stimulation was tested in 12 nerves
in 7 rabbits using the windowed nerve cuff (Figure 3-1B). In 7/12 nerves EMG response
to infrared stimulus was observed before beginning the trial. Analysis of paired electrical
Figure 3-7 Latency between threshold stimulus and EMG recruitment
EMG delay measurements between threshold stimulus delivery and start of EMG
response for electrical and infrared stimuli for a single experiment. Electrical
stimulation was applied 6 mm proximal and 6 mm distal to infrared stimulus. EMG
start time was significantly longer for muscles activated by infrared pulses, than
activated by electrical stimulus.
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and combined stimulus recruitment curves with a 2-sample Kolmogorov-Smirnov test
identified 873/930 (93%) recruitment pairs as not statistically different. Of the 67 (7.2%)
significant pairs, 31 (46%) were generated on the same nerve during a single experiment
and exhibited strong inhibition of soleus (Figure 3-8A), mixed inhibition of MG and LG,
and decreased activation threshold for TA. All EMG responses were very small when this
trial was performed, indicating that the entire muscle was not activated by electrical or
combined stimulation. This may be due to fatigue, or other confounding factor affecting
the nerve state. 13/36 of the remaining statistically significant pairs showed electro-
infrared activation at pulse amplitudes below the electrical-only activation threshold
(Figure 3-8B), but recruitment differences between the two modalities disappeared above
the electrical threshold. Of the remaining 23 statistically significant pairs, combined
stimulus shifted recruitment to slightly higher thresholds or decreased slope in 11 pairs;
showed an increase in recruitment slope in 3 pairs; exhibited high variability in either or
both recruitment curves in 9 pairs; and showed no identified trend in 2 pairs. Results are
summarized in Table 3-1. Of the 9 different electrode configurations, 21/36 (58%) of the
significant recruitment pairs were generated when the contact directly below the infrared
delivery window was involved as cathode or anode. Of the other electrode arrangements,
only the distal anode with proximal cathode appeared more often than chance, with 7/36
(19%) cases involving this arrangement.
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Figure 3-8 Electrical and combined stimulus recruitment curves
Examples of full muscle recruitment using electrical and combined electrical and
infrared stimulation. A) Inhibition of soleus, example observed in 31/67 statistically
significant recruitment curves. B) Example case, significant due to optical activation
below the electrical activation threshold. Inset: Example of optical activation below the
electrical activation threshold. Electrical amplitude = 0.05 mA.
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Table 3-1 Significant recruitment differences comparing combined stimulation over
electrical-only stimulation
No. Significant Cases (%)
Increased Recruitment Slope 8 (0.8%)
Decreased Recruitment Slope 19 (2.0%)
Threshold Increased 19 (2.0%)
Threshold Decreased 5 (0.5%)
High Response Variability 31 (3.3%)
Decreased Recruitment Amplitude 31 (3.3%)
Discussion
Nerve Sensitivity to INS
Nerve sensitivity to extraneural INS will drive design of extraneural interfaces.
Nerve sensitivity to INS was low, with typically only 1-2 sensitive regions measured per
nerve (Figure 2A), and was observed in only 81% of nerves. This result contrasts with the
more uniform sensitivity reported by Wells et al. (2007b) in rat sciatic nerve, but are in
accordance with reports from Duke et al. (2012a) that sensitivity is localized to small
regions and only occurred in 76% of rat sciatic nerves (Duke et al., 2012a; Wells et al.,
2007b). Stimulation of the rat sciatic nerve resulted in an average of 6 ISR detected per
nerve (Figure 3-3). Approximating the areas scanned as roughly rectangular, the rabbit
sciatic nerve yielded 0.009-0.027 ISR/mm2 and the rat sciatic nerve yielded 0.13-0.37
ISR/mm2. Observed differences in sensitivity may be due to differences in nerve size
between rat and rabbit, as the rabbit sciatic nerve is roughly twice the diameter of the rat
sciatic nerve (Hsu et al., 2011; Tyler and Durand, 2003). Since penetration depths of the
wavelengths used are expected to be 300-600 um, a smaller portion of the rabbit nerve is
exposed to infrared than in the rat. This may be a significant limitation to be addressed in
scaling INS to larger nerve targets. Results of this study also indicate that shorter and
higher-power pulses are more effective for stimulation (Figure 4). The pulsed laser
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source used by Wells et al. (2007b) delivers shorter and higher power pulses than could
be achieved with the continuous-wave source used in this study, which may have resulted
in more regional over uniform sensitivity. Finally, Wells et al. (2007b) monitored a
different set of muscles than those observed in this study or the that by Duke et al.
(2012a) (Duke et al., 2012a). If non-recorded muscles were activated, it was not enough
to cause visible movement leg movement. Because the focus of this study was evaluating
functional output, undetected activation of small muscles should not alter conclusions
about functional utility targeting large muscles used for foot positioning and control.
Measurements of the spatial extent of response to infrared light indicate that ISR
are small, typically less than 400-500 um in the longitudinal or transverse directions,
similar to that reported in the rat sciatic nerve (Duke et al., 2012a). The primary caveat to
these measurements is that infrared energy was applied using a 400 um diameter fiber,
which sets a lower limit on reliable feature size measurement. These results do provide an
upper bound on optically sensitive region size, though, and indicate sensitive regions are
relatively small.
Infrared-Evoked Muscle Recruitment
Previous INS work indicated that rehydration of the nerve was necessary for
maintaining nerve viability (Wells et al., 2007a, 2007b), but the effect on INS response
was not reported. Trials involving fixed stimulus applied over regular intervals showed
that application of lactated Ringer’s solution (LRS) may temporarily reduce or abolish
response to INS (Figure 3-4A, B). This result could be due to absorption of infrared light
by excess water on the nerve, reducing energy delivery to nerve tissue. Once this effect
was identified, application of LRS was tracked and controlled more closely, but these
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results indicate that to reduce variability in future studies nerve hydration should be
closely controlled.
With recent work indicating that applied INS can prevent action potential
generation or increase stimulation thresholds (Mou et al., 2012), it was necessary to
confirm that the working range for INS motor activation is not narrower than that already
constrained by acute damage thresholds. We hypothesized that INS recruitment would
follow a monotonic relationship with pulse duration, allowing for use of the entire range
of pulse between the activation and calculated damage threshold for INS. The
Spearman’s rank-order correlation was computed for mean recruitment as a function of
pulse duration in 209 recruitment curves, resulting in an average ρ = 0.68. When each
correlation was tested whether it was greater than zero, indicating a relationship that was
generally monotonic and increasing, 83% of correlations were significant. Based on this
result, it was concluded that response between stimulation and damage thresholds does
not decrease, and pulse durations above threshold and below the damage threshold could
be used in INS.
While infrared energy delivery at the wavelengths used for INS is expected to be
thermally constrained over the pulse durations used (Wells et al., 2007a), axon response
may be sensitive to the duration over which INS is delivered. Recruitment curves
generated at varied power levels showed that lowered power significantly increased
activation threshold pulse durations, but this significance disappeared when activation
thresholds were scaled to compare total energy delivery (Figure 3-5A, B). Comparing the
maximum recruitment achieved with lower power stimulation showed a significant
decrease when compared to full-power recruitment (Figure 3-5C). In some cases, the
55
muscles activated using full power stimuli were not activated at lower power levels. That
activation energy thresholds were maintained when activation was achieved, but
maximum recruitment was not, suggests that a certain population of axons was not
activated despite delivery of the same energy. Currents generated by infrared energy may
have diffused within these axons during the additional time it required to supply lower
power stimulus. This would suggest that while the energy delivery is still thermally
constrained, dynamics within axons may be an important factor in designing INS
delivery. Other INS studies report increased response and reliability when using a pulsed
Holmium: YAG laser, which stimulates with short, high-power pulses, over the
continuous-wave diode laser that delivers energy over a longer duration, despite
generating wavelengths with similar absorption characteristics (Duke et al., 2012a; Wells
et al., 2007a). These results indicate that short, high-power INS is more effective in
activating motor neurons.
In 34/42 (81%) of ISR, a single muscle could be activated before another reached
threshold. This result was significantly above 50%, indicating that the localized delivery
of INS generally results in the ability to selectively activate a single muscle, when an ISR
can be identified. This result, paired with the results indicating that a very small
proportion of the muscle can be activated with INS (Figure 3-6), indicates that selective
sub-fascicular activation is achievable using extraneural INS.
Mean maximum infrared-evoked response was low, though, activating 2-9% of
the muscle. Measuring the maximum percentage of a muscle activated by a single
channel of extraneural INS helps to provide guidelines in estimating the number of
channels necessary for full coverage of a single muscle. Consider a hypothetical
56
neuroprosthesis that uses infrared stimulation to provide graded recruitment up to 20% of
muscle activation, using electrical stimulation for the remaining 80% to reach full
activation. With mean maximum activation by a single channel between 2 and 5% of the
full muscle capability, 2-10 channels of infrared delivery would be necessary for 4 Hz,
20% stimulation at a single site. Interleaved stimulation to deliver at least 12 Hz, 20%
stimulation would increase the number to 6-30 channels for activation of a single muscle
at 20%. If not all stimulation sites stimulate the target muscle, this number would be
increased further. These requirements far exceed the 1-2 available ISR typically found on
the nerves investigated.
Combined Electrical and Infrared Stimulus
The population of axons stimulated to an above-threshold level with INS was
observed to offer limited motor recruitment capabilities (Figure 3-6), but it was unknown
whether a significant population was activated to a subthreshold level. Early work
exploring combination of electrical and infrared stimulus indicated that entrained
application of electrical stimulus could be used to lower the activation threshold for
infrared stimulation (Duke et al., 2009). Electrical stimulation was added to infrared
stimulation and swept from subthreshold to supramaximal activation of the nerve to
highlight any subthreshold activation due to INS. Electrode arrangement relative to
optical stimulus and identification of ISR was indicated as important for combined
stimulation by (Duke et al., 2012a). The electrode cuff used in this study was designed to
accommodate these needs, providing longitudinal contacts and the ability to tune infrared
delivery directly to the nerve to ISR through the window. Combining electrical and
infrared stimulus revealed significant differences in only 7% of paired comparisons. Of
the cases that were significantly different, the largest difference observed was recruitment
57
inhibition observed in a single trial. This behavior resembled the action potential
generation block observed by Mou et al. (Mou et al., 2012), rather than an increase in
excitability from INS (Figure 3-8A). If infrared-only delivery in this study was causing
inhibition in regions of the nerve in some cases, then there may be inhibitory ISR that
were not detected by our methods. Results presented by Mou et al. and Duke et al. (Duke
et al., 2012b; Mou et al., 2012) indicate that applying infrared light continuously or at
frequencies above 4 Hz, which would be expected to cause sustained tissue temperature
increases, can have excitatory and inhibitory effects. Controlling local nerve temperature
may be a useful method of modulating electrical excitability using a single channel of
infrared stimulus. While some of the results of our investigation indicate the inhibitory
effects of INS can be achieved with entrained stimulation, the overwhelming majority of
recruitment curves did not reveal an INS-mediated effect for entrained, extraneural
combined stimulus.
Infrared-Driven Neural Activation
Comparing infrared-evoked and electrically-evoked EMG responses provided support
that infrared light activates motor neurons directly, and that electrical and infrared
stimulation activate axons differently. Support that infrared activates motor neurons
directly comes from the latency difference between the two methods (Figure 3-7).
Electrical stimulation is expected to directly activate motor neurons instead of a reflex
pathway, supported by results showing electrical latencies less than 2 ms in this study.
That infrared latencies are only 0.96-2.5 ms longer than electrical latencies does not
support motor activation of INS through a monosynaptic reflex pathway. Reports of the
Hoffmann’s response (H-reflex) latency are 5 ms in the rat sciatic nerve and is reported to
58
be longer in the sciatic nerve of the anesthetized rabbit (Chen and Wolpaw, 1995; Zheng,
1988; Zhou et al., 1997).
With response delay differences ranging 0.96-2.5 ms, generated action potentials
either occurred well after the infrared pulse ended, or resulted in activation of smaller
diameter axons and muscle fibers. Wells et al. presented data showing 2.6 ms delay
between threshold energy delivery and ENG measured on the rat sciatic nerve 6 mm from
the stimulation site (Wells et al., 2007a). This translates to a conduction velocity of
2.4 m/s, and either a sub-0.5 um diameter myelinated or ~1.1 um unmyelinated fiber,
based on conduction velocity over the stated distance (Ritchie, 1982). It is possible that
reported ENG results were recorded from an unmyelinated axon, but because this delay is
similar to the response delay difference observed in EMG this study, a simpler
explanation for both observations is that the mechanism of activation takes longer
electrical activation of the nerve. This does not preclude the possibility of a combination
of both mechanism delay and smaller fiber activation, though.
The mechanism of INS is still unknown (Richter et al., 2011a). Previously
reported evidence indicates a photothermal effect over photochemical, photomechanical,
and photoelectric mechanisms (Wells et al., 2007a). Transient temperature-driven
changes in cell membrane capacitance have been shown capable of causing
depolarization of 8-10 mV in non-excitable cells (Shapiro et al., 2012), and intracellular
calcium release from mitochondria in response to infrared stimulus has been recorded in
cardiac myocytes (Dittami et al., 2011). The presence of temperature-sensitive channels
in peripheral nerves leaves open the possibility of a channel-driven mechanism for INS
(Facer et al., 2007; Thyagarajan et al., 2009). Possible mechanisms like membrane
59
capacitance changes and temperature-sensitive channels may be expected to be more
easily triggered than the sensitivity results of this study suggest. If changes due to
capacitance or temperature-sensitive channels must occur at nodes of Ranvier, then
sensitivity may be lower. Mitochondrial density is also expected to be highest around
nodes of Ranvier (Chiu, 2011). The scanning process used in this study should have
resulted in stimulation of many nodes of Ranvier, as a node of Ranvier is likely to be
found within a 64 um-diameter hemisphere, or volume of 8.5x103 um
2 (Rutten et al.,
1991). In this study of infrared light was delivered in a 400-500 um wide spot. Assuming
penetration of only 100 um into the endoneurial space with amplitude sufficient to
stimulate, 12.5x106 um
2 of the endoneurial space would be illuminated, making it
possible for over a thousand nodes to be stimulated by infrared light. The spot size limits
how many nodes on a single axon can be affected, though, and only the smallest diameter
axons will have multiple nodes of Ranvier within the beam spot. A response may only be
observed when enough small-diameter axons occur within a region sufficiently
stimulated by infrared light, resulting in a small observed response because only a few
small fibers are activated. Most INS studies deliver INS to the nerve surface with a
Gaussian beam profile from a bare polished fiber (Wells et al., 2007a). The possibility
that this is not the optimal spatial distribution of infrared light for activation also remains,
and activation may occur only at nerve regions where the infrared profile experienced by
the axons is warped enough by tissue layers to provide an activating profile. The answers
to these questions will help in determining whether stronger response or lower energy
thresholds can be achieved in INS applied to the peripheral nerve.
Conclusion
60
Extraneural INS was investigated as a means to provide selective motor activation
without penetrating the epineurium or perineurium. Rabbit sciatic nerve was used in this
study to investigate INS in a larger nerve model than had been previously investigated.
Results indicate that nerve sensitivity to extraneural INS is localized to small regions of
the nerve, but these regions occur too infrequently with current INS techniques to be
valuable in functional applications. The evoked motor response was found to be selective
to a single muscle in the majority of regions identified, but the maximum achieved
recruitment fell below functional motor activation levels. Combining entrained electrical
and infrared stimuli offered limited utility over electrical stimulation alone. Therefore,
INS is limited to a very small population of axons producing selective, but non-functional
motor output.
Acknowledgements
The authors would like to thank Prof. Hillel Chiel for discussions regarding
infrared stimulation, Smruta Koppaka for input and help with performing experimental
procedures, the Jansen lab at Vanderbilt University for discussions and demonstrations
regarding infrared delivery, and Profs. Dominique Durand and Andrew Rollins for
feedback in developing this manuscript.
Funding for this project was provided by Microsystems Technology Office of the
Defense Advanced Research Projects Agency (DARPA) Centers in Integrated Photonics
Engineering Research (CIPHER) and the Lockheed Martin Aculight Corporation. The
project described was supported in part by Grant Number T32-EB004314 from the
NIBIB and the National Institutes of Health.
61
CHAPTER 4: MODELING MECHANISMS OF INFRARED
NEURAL STIMULATION
Abstract
Neural interfaces rely on selective activation of neurons to treat disease and
injury. Infrared neural stimulation (INS) may provide high selectivity neural interfaces,
but high energy requirements remain a challenge. Previous works have optimized and
improved electrical stimulation with the use of computational modeling. Computational
models of INS may be useful in optimizing and improving INS efficiency. The goal of
this work was to implement two proposed mechanisms of INS in membrane and axon
models to evaluate whether the tested mechanisms could be used to explain infrared
activation. The two mechanisms examined included: 1) transient temperature-driven
changes in effective membrane capacitance and 2) intracellular calcium release.
Investigation of each mechanism also included thermal effects on ion channel rate
variables. Results show that under appropriate conditions both mechanisms could trigger
action potentials. Action potentials were generated in spatially-distributed axon models,
depending on the distribution of infrared-evoked intracellular currents along an axon.
Beam profiles with flat or positive curvature were effective in triggering action potentials
with temperature-driven capacitance changes. Small-diameter axons exhibited lower
activation thresholds in spatially-distributed models, suggesting that INS may provide
recruitment that more closely matches physiologic recruitment.
Introduction
Neuromodulation has been used in restoring function to individuals whose nervous
systems have been compromised by disease or injury (Ahuja et al., 2011; Butson and
McIntyre, 2006; Dhillon and Horch, 2005; Pfingst, 2011; Rodriguez et al., 2000; Rossini
62
et al., 2010). Many clinical neuromodulation devices rely on applied electrical stimulus to
affect neural behavior. Examples include devices to restore hearing, reduce chronic pain,
restore motor function, interrupt seizure activity, and reduce symptoms of movement
disorders (Benabid, 2003; Fisher et al., 2009; Oakley et al., 2007; Pfingst et al., 2011).
Computational models of the interaction between the nervous system and electrical
stimulus have helped to optimize and improve electrical interface designs, by providing a
means to quickly evaluate design performance before fabrication and testing in vivo
(Butson et al., 2011; Mahnam et al., 2008; Maks et al., 2009; McNeal, 1976; Schiefer et
al., 2008; Veltink et al., 1988; Wongsarnpigoon et al., 2010).
Infrared neural stimulation (INS) has been investigated as a means of improving
neural interface selectivity, because light can be delivered to the body in unique ways.
Infrared light has been shown capable of both activating motor axons and increasing
activation thresholds in peripheral nerves (Mou et al., 2012; Wells et al., 2007b).
Currently, infrared stimulation of the peripheral nerve requires high energy levels that
limit stimulation at threshold to 4 Hz and below and result in a narrow safety margin
between stimulation and damage levels (Wells et al., 2007a, 2007c). While experimental
work has shown entrained electrical stimulus as one means to lower optical stimulation
thresholds (Duke et al., 2012a, 2009), the parameter space for designing spatial and
temporal delivery of more effective infrared stimulation is vast. Computational models of
infrared stimulation would enable investigation of this parameter space to focus
experimental efforts toward interface design.
A mechanistic understanding of INS would provide a basis for computational
models of infrared stimulation. Wells et al. concluded that photochemical, photoelectrical,
63
and photomechanical are unlikely causes of INS activation, and noted the need to establish
a spatial/temporal thermal gradient in the activated tissue (Wells et al., 2007a). More
recently, transient temperature changes caused by INS have been shown to change the
effective capacitance of the membrane, by weakening hydration bonds on the ions near the
membrane (Genet et al., 2000; Shapiro et al., 2012). The resulting capacitive current has
been modeled as a depolarizing intracellular current source, and shown to trigger action
potentials in a spatially-lumped membrane model at 6.3 ˚C initial temperature (Shapiro et
al., 2012). Triggered release of intracellular calcium by infrared light has also been
suggested as a possible INS mechanism. Infrared light has been shown to trigger
intracellular calcium release from mitochondria in cardiac myocytes (Dittami et al., 2011).
An intracellular release of positively charged calcium ions may trigger further calcium-
induced calcium release within the cell (Berridge et al., 2000), increasing depolarization.
Currently, calcium dynamics in response to infrared light have not been reported for
axons, but intracellular calcium release can be included in computational models to
evaluate calcium release levels necessary for activation by this mechanism.
Models of INS have been limited to spatially-lumped membrane models at
temperatures not relevant to experimental INS investigations, or investigating changes in
excitability from localized temperature changes from constant infrared pulses (Mou et al.,
2012; Shapiro et al., 2012). The goal of this study is to model membrane capacitance
changes and intracellular calcium release at a wide range of initial temperatures and in
both spatially-lumped membrane models and spatially-distributed axon models. Using
electrical models of neuronal membranes, both mechanisms were tested to measure the
effects on depolarizing the cell and triggering action potentials. Capacitive intracellular
64
currents were hypothesized to trigger action potentials in axon models when focused by
controlling infrared energy is distribution along the axon. Intracellular calcium release was
hypothesized to cause membrane activation without requiring intracellular calcium
concentrations to exceed 10 times the baseline intracellular concentration (Berridge et al.,
2000). By exploring common infrared delivery parameters, these models provide direction
on future investigation of INS interfaces.
Methods
Spatially-Lumped Membrane Models
Electrical models of neuronal membranes described by Hodgkin and Huxley (HH)
(Hodgkin and Huxley, 1952a), and Frankenhaeuser and Huxley (FH) (Frankenhaeuser
and Huxley, 1964) were used as the bases for spatially-lumped excitable membrane
models (Figure 5-1A). Ion channel gating rates were scaled with initial temperatures and
transient temperature changes using the Q10 factors reported for each (Table 5-1) (Moore
et al., 1978). The Q10 temperature coefficient increases exponentially with temperature,
and is the factor by which conduction rates change for each 10 °C change in temperature.
Values greater than 1.0 cause rates to increase with temperature, 1.0 causes no change
with temperature, and values less than 1.0 decrease rates with increased temperature.
Initial membrane temperatures ranging 6-38 ºC were tested. Responses of the sodium
activation (m), sodium inactivation (h), and potassium activation (n) gating variables
were measured to understand the effects of temperature on activation. All simulations
were performed using NEURON 7.2 (Hines and Carnevale, 1997).
65
Table 4-1 Q10 and membrane capacitance, Cm, simulated in each model
Model Parameter Value
HH
Q10m 3
Q10h 3
Q10n 3
Cm 1 uF/cm2
FH
Q10m (αm/βm) 1.7/1.8
Q10h (αh/βh) 2.8/3.2
Q10n (αn/βn) 2.8/2.9
Cm 1 uF/cm2
MRG
Q10Naf,m 2.2
Q10Naf,h 2.9
Q10Nap 2.2
Q10n 3
Cm 2 uF/cm2
Spatially-Distributed Axon Models
Three spatially-distributed axon models provided the basis for investigating
effects of axonal geometry and infrared energy distribution along the axon. The first
model was an unmyelinated axon constructed with HH membrane dynamics and 20 um-
long segments. The second model was a myelinated axon based on the McNeal frog axon
model with FH membrane dynamics at the nodes of Ranvier with internodal membrane
and myelin modeled as an open circuit (McNeal, 1976). The third model was based on
the double-cable McIntyre, Richardson, and Grill (MRG) mammalian axon model (Table
5-1) (McIntyre et al., 2002). The MRG model separates the internodal region into 10
segments with myelin segments modeled as perfect insulators. Transient changes in
axoplasmic resistance for all three models were modeled with a Q10 factor of 1/1.3
(Frijns et al., 1994). All simulations were performed using NEURON 7.2 (Hines and
Carnevale, 1997).
Wells et al. demonstrated that the spatial temperature profile generated by an
infrared beam was proportional to the beam profile (Wells et al., 2007a). Three infrared
66
beam profiles were used to investigate activation. The first beam profile tested was a
Gaussian beam profile with a 1/e2 spot size of 400 um designed to resemble delivery
from a bare fiber optic tip (Wells et al., 2007a), and centered on the axon. The second
profile consisted of two superimposed Gaussian peaks with center-to-center spacing 400-
2000 um. The third beam profile resembled collimated delivery, with a flat top and
Gaussian roll-off on each side. Width of the flat region was varied between 400-2000 um.
All infrared distribution beam profiles were centered to the centermost node of Ranvier
or axon segment.
Temperature-Driven Capacitive Changes
Temperature-driven capacitive changes were modeled in spatially-lumped and
spatially-distributed models. The primary output measure maximum the depolarization of
the membrane. Rapid heating of tissue water by absorption of infrared light increases the
local temperature of the membrane, Tm, and weakens hydration bonds between ions and
water molecules (Genet et al., 2000; Wells et al., 2007a). This causes changes in the ionic
double layer capacitance on either side of the membrane, and causes an effective change
in the membrane capacitance, Cm (Shapiro et al., 2012). The capacitive current of the
membrane, icap, depends on the time derivatives of both membrane potential, Vm, and Cm
(Eq.1, 2).
Eq. 1
Eq. 2
The reversal potential for the capacitive current, Vr, depends on surface charges and ionic
concentrations on the intracellular and extracellular membrane surfaces (Genet et al.,
2000; Shapiro et al., 2012). Vr was set to 140 mV to reflect conditions reported by
67
Shapiro et al. (2012). The first term of Eq. 2 is included in membrane models that assume
constant Cm. The second term is the temperature-dependent component of the capacitive
current, icap(T, t), and was modeled as an intracellular current source added in parallel to
existing membrane dynamics (Figure4-1 A, B).
Experimental measurements showed that changes in Cm were proportional to Tm,
with Tm increases of 15 ºC causing Cm to increase by 8% (Shapiro et al., 2012). Infrared-
pulses have been shown to cause linear temperature increases during energy deposition
with rectangular pulses, followed by exponential decay after the pulse (Shapiro et al.,
2012; Wells et al., 2007a). Based on these reports, transient changes in Tm and Cm were
modeled as linear increasing ramps followed by exponential decay, described by Eq. 3, 4.
Eq. 3
Eq.4
Infrared pulse duration, PD, was varied from 0.1-1.0 ms, but peak temperature and
capacitance increases were kept constant, simulating constant-energy but varied-power
pulses. Shapiro et al. (2012) simulated 8% increase in Cm and 15 ºC increase in Tm over a
1.0 ms pulse, roughly approximating response to a 5.6 mJ pulse (Shapiro et al., 2012).
This is within the range of other reports of INS in peripheral nerve involve pulse
durations ranging approximately 0.25-2.0 ms to deliver 2.3-7.1 mJ pulses (Duke et al.,
2009; Wells et al., 2007a). The decay time constant, τ, was set to 90 ms (Shapiro et al.,
2012; Wells et al., 2007a). Scale factors, k1 and k2, were either scaled together or
68
independently. In spatially-lumped models the intensity factor, I(x), was set to unity. For
spatially-distributed models I(x) was scaled between 0 and 1 to model beam profiles that
change along the length of the axon.
Intracellular Calcium Release
Figure 4-1: Modeled membrane and axon circuit diagrams
A) Typical excitable membrane model with membrane capacitance, Cm, nonlinear
conductance, Gm, and equivalent reversal potential, Veq. B) Variable capacitor and
capacitive current used to simulate transient membrane temperature and capacitance
changes. Gm and Veq depend on model formulation: Hodgkin & Huxley (HH),
Frankenhaeuser & Huxley (FH), McIntyre, Richardson, and Grill (MRG). C) Axon
model used for HH unmyelinated and FH myelinated axons. D) MRG mammalian
myelinated axon.
69
Intracellular calcium release was modeled as an intracellular current source in a
spatially-lumped membrane model with HH dynamics. The primary outcome measure was
the peak intracellular calcium concentration that occurred in response to minimum-
amplitude calcium currents that evoked action potentials. Activation resulting in peak
intracellular calcium concentration less than 10 times the baseline concentration were
considered physiologically achievable (Berridge et al., 2000).Measurements by Dittami et
al. showed that intracellular calcium released from mitochondria increases steadily over
280 ms in cardiac myocytes (Dittami et al., 2011). If intracellular calcium is to cause
activation within neural cells, sufficient release and activation needs to occur within 2-
5 ms of infrared application (Wells et al., 2007a). Calcium dynamics are expected to vary
considerably among cell types, and among structures of the same cell (Berridge et al.,
2000; Shen and Shuai, 2011). Because infrared-evoked calcium has not been reported for
axons, calcium release profiles are speculative. For this study, assumptions about calcium
release profiles were made to determine plausibility of activating neural models with
calcium release and understand conditions under which activation is likely to occur.
Investigation was limited to measuring depolarization caused by an increase in divalent
cations in the intracellular space. Additional signaling and second order effects that
calcium can trigger were not included.
Two temporal profiles of intracellular calcium current were tested: a single-phase,
square pulse and a two-phase, linear ramp to peak and exponential decay (Eq. 5, 6).
Eq. 5
70
Eq. 6
The square pulse was chosen to represent a generic current release (Eq. 5). The linear
ramp and exponential decay was chosen to reflect the time course of temperature and
capacitance changes observed in cells exposed to IR pulses (Eq. 6) (Shapiro et al., 2012;
Wells et al., 2007a). Pulse duration, PD, ranged 0.1-10 ms. Transient Tm and Cm changes
were included in calcium release models, as they 5:would be expected in all rapidly
heating membranes (Shapiro et al., 2012). Calcium release was delayed relative to
transient Tm and Cm changes by a delay factor, tCa, which was varied from 0-2.0 ms.
Calcium current amplitude, k3, was tuned in a binary search algorithm to determine
threshold amplitudes for each combination of PD and tCa. To determine whether
activation of calcium gated potassium currents significantly interfered with depolarization;
models were run both with and without calcium gated potassium channels included.
Results
Membrane Capacitance Change - Membrane Models
The resting potential for the HH membrane model was -65 mV. Maximum
depolarization of the HH membrane model exhibited strong dependence on initial
membrane temperature (Figure 4-2A). Results obtained at an initial temperature of 6.3 ºC
closely matched those reported by (Shapiro et al., 2012), but as initial temperature
increased, maximum depolarization decreased. The results showed two phases in the
relationship to temperature. The first phase is quickly decreasing, where active spiking is
still observed, even when Vm does not increase above 0 mV (Figure 4-2C). In the second
phase, the slope flattens out and cell depolarization resembles passive charging and
71
discharging of the capacitive membrane (Figure 4-2D). Decreasing PD to 0.1 ms,
simulating a tenfold increase in infrared stimulus power, only shifted the inflection point
between active and passive depolarization from 16 ºC to 20 ºC (Figure 4-2A).
The amount of time that the depolarizing m gate was open compared to closing of
the inhibiting h gate or opening of the hyperpolarizing n gate decreases rapidly as
temperature increases from 6-14 ºC with a 1.0 ms pulse (Figure 4-3A), or 6-18 ºC with a
0.1 ms pulse (Figure 4-3B). Above these temperatures, the m gates were open longer
before the h and n gates began to offset activation, but reached a very low peak value
(Figure 4-3C, D).
72
Figure 4-2: Maximum membrane depolarization versus initial temperature and
membrane potential for HH membrane model
A) Maximum membrane depolarization of a Hodgkin & Huxley membrane model
versus initial membrane temperature. The membrane is only a positive potential for
initial temperatures below 12 -14 oC. B) Membrane is fully depolarized by an action
potential, replicating model results reported by Shapiro et al. (2012). C, D)
Depolarization diminishes with increasing initial temperature.
73
Sodium channel density was increased by increments of 10% from 100%-150%
of the Hodgkin and Huxley reported values. Increases above 150% resulted in an unstable
membrane that fired spontaneously. Similarly, decreases in potassium channel density
quickly led to unstable transmembrane voltages. Increasing sodium channel density
increased the maximum depolarization observed at all temperatures, but active currents
were not observed above 22 ºC (Figure 4-4). Decoupling the transient Tm and Cm changes
(k1 k2 = 1 ) helped to increase the temperature range over which active currents were
Figure 4-3: Peak time differences and peak values of m, h, and n gating variables in
response to transient temperature and capacitance changes
A,B) Plots of peak time differences between h and m, and n and m illustrate the amount
of time the depolarizing m gate is active before h or n interfere with depolarization
typically decreases with temperature. Pulse duration: 1.0 ms (A) and 0.1 ms (B) C,D)
Maximum (m, n) and minimum (h) values achieved for each gating variable at peak. As
temperature increases, the maximum value of the depolarizing m gate drops sharply.
74
generated by reducing the Δ Tm. Complete elimination of the transient temperature
increase (k1 = 0) only extended active current generation to 24 ºC. Exchanging the HH
membrane dynamics for FH membrane dynamics shifted the resting potential to -70 mV.
Transient temperature and capacitive changes applied to this model resulted in less than
1 mV depolarization across temperatures 6-38 ºC (results not shown).
Membrane Capacitance Change - Myelinated and Unmyelinated Axon Models
Implementing transient temperature changes in spatially-distributed axon models
revealed a strong dependence on axon geometry and beam profile (Figure 4-5). The FH
Figure 4-4: Maximum membrane depolarization versus initial temperature with
increased Na+ conductance or decreased transient temperature change
Increasing sodium channel density 50% over baseline increases maximum
depolarization achieved at all temperatures, but active currents are only observed up to
25 ºC. Decreasing the peak temperature associated with an 8% increase in membrane
capacitance extends the temperature range for active currents, but only up to 24 ºC
when the transient temperature increase is reduced to zero.
75
model exhibited no significant depolarization across all simulated conditions, and for
simplicity is excluded. Similar to the membrane models, increasing stimulation power
increased the maximum depolarization achieved (Results not shown). Maximum evoked
depolarization was measured as a function of initial axon temperature and diameter.
Stimulation with the single Gaussian beam profile did not result in depolarization above
10 mV for the HH model (Figure 4-5A). The distribution composed of two Gaussian
profiles, with center-to-center separation of 2000 um, resulted in activation across a
limited temperature range for the HH axon (Figure 4-5B), similar to that observed in the
spatially-lumped model (Figure 4-2A). The beam profile with the flat region provided the
most robust response, however, extending range of initial temperatures over which the
HH axons are activated to approximately 25 ºC (Figure 4-5C).
The MRG model exhibited very little variation in depolarization across all initial
temperatures tested, but instead showed greater dependence on fiber diameter. With the
single Gaussian profile, the MRG model did not depolarize by more than 8 mV across all
diameters and temperatures. The other two beam profiles were tested with initial
temperature set to 36 ºC. Increasing spacing between the two Gaussian peaks increased
the spatial extent of the intracellular currents generated, but also decreased the
intracellular current generated at the center node of Ranvier. All spacing values resulted
in activation of 5 um fibers, and increasing spacing to 1000 um yielded activation of
6 um fibers (Figure 4-6A), but increasing spacing to 2000 um failed to activate diameters
greater than 5 um. Increasing the width of the flat top beam increased the maximum fiber
diameter that could be activated (Figure 4-6B).
76
Figure 4-5: Maximum membrane depolarization in HH axon model with various IR
intensity profiles
Maximum depolarization in the Hodgkin and Huxley (HH) unmyelinated axon in
response to transient temperature and membrane capacitance increases. A) Single
Gaussian profile, <10 mV depolarization. B) Two-Gaussian profile, 2000 um between
peaks. All diameters are activated equally. C) Flat-top profile, 2000 um top. Small
diameters activated across a wider temperature range.
77
Figure 4-6 Membrane depolarization across fiber diameters with flat and double-peaked
spatial profiles
Maximum depolarization of the center node of an MRG axon measured for fiber
diameters ranging 5-20 um. Simulated at 36 ºC with a 1.0 ms laser pulse. A) Two
overlapping Gaussian distributions trigger action potentials in only the smallest fiber
diameters. Peak activity occurs at L = 1000 um. At 2000 um beams do not interact
enough to cause activation. B) Distribution with flat intensity and Gaussian roll-off
causes activation of larger diameter fibers as the flat region is widened.
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To investigate activation thresholds across fiber diameters using a Gaussian beam
profile k1 and k2 were adjusted by a scale factor to determine activation thresholds of
transient Tm and Cm changes. Scale factor testing began at 0.1 and was increased until
activation was observed or the model destabilized. Of the three axon models, the scale
factors necessary to activate the unmyelinated HH axon were the lowest (Figure 4-7A);
with the next lowest occurring with the myelinated MRG model (Figure 4-7C). The
highest scale factors were necessary for the FH axon, where model destabilization
occurred before activation was observed in most cases (Figure 4-7B). The MRG axon
model results show that the temperature-drive capacitive changes needed to trigger an
action potential are 5-10 times that measured experimentally by Shapiro et al.
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Intracellular Calcium Release
Transient Tm and Cm changes in response to a 1.0 ms pulse were modeled with
intracellular calcium release were added to a HH membrane model. Results show that
short-duration calcium releases are more effective in activating the membrane for both
the square and ramp with decay release profiles (Figure 4-8 A, B). Relative timing of Tm
and Cm changes and the intracellular calcium release has an effect on the how much
calcium must be released to trigger activation. As the delay between initiation of each
Figure 4-7 Amplitude scale factor required to trigger action potentials using a Gaussian
beam profile
Scale factor applied to a Gaussian beam profile necessary to trigger action potential
generation as a function of fiber diameter. A) unmyelinated Hodgkin and Huxley (HH)
axon, B) myelinated Frankenhaeuser and Huxley (FH) axon, and C) myelinated
McIntyre, Richardson, and Grill (MRG) based axon models. Note scale differences
among A-C. Baseline temperatures for each model: MRG, 37 ºC; FH, 20 ºC; HH, 6.3 ºC.
80
effect increases, the amount of calcium needed to activate also increases (Figure 4-8 C,
D). This increase continues up to 1.0 ms, and then levels out. Results presented include a
calcium gated potassium channel, but removal of this channel did not qualitatively
change presented results. Inclusion of the calcium gated potassium channel generally
increased calcium requirements, but did not qualitatively change the results compared to
the model without calcium gated potassium channels.
Figure 4-8 Peak intracellular calcium concentrations caused by threshold calcium
currents
Maximum intracellular calcium concentrations generated by threshold intracellular
calcium currents required to fully depolarize the cell membrane. Current injection was
either A,C) a square current pulse or B,D) a linear ramp followed by exponential decay.
A) and B) show that longer duration pulses generally require higher intracellular
concentrations than short pulses. C) and D) show that as the delay between transient
temperature and capacitance changes and intracellular calcium currents is increased,
the calcium required to activate also increases. Results are for 1.0 ms calcium pulse
duration.
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Discussion
Membrane Capacitance Changes
Spatially-lumped membrane models provided insight into activation triggered by
transient changes in Tm and Cm. Previous modeling of infrared-driven capacitance
changes indicated action potential generation of a spatially-lumped HH model (Shapiro et
al., 2012). While the initial membrane temperature modeled by Shapiro et al. (2012) was
not stated, it is assumed that the model used was the original description of the membrane
dynamics by Hodgkin and Huxley measured at 6.3 ˚C. Results of modeling
depolarization at a range of initial membrane temperatures demonstrated a strong
dependence on initial membrane temperature (Figure 4-2). The low-temperature results
closely matched the modeling results reported by Shapiro et al. (2012), and higher-
temperature depolarization ranging 6-10 mV in the model above 25 ˚C reflected the
experimental results observed by Shapiro et al. (2012) at 25 ºC (Shapiro et al., 2012).
These results provided verification for the implementation of the intracellular capacitive
current model used.
The relationship between ion channel activity and membrane temperature was a
result of the Q10 factors used to scale activity with temperature. Increased initial
temperature resulted in an increase of the rate constants governing sodium activation and
inactivation, and potassium activation. The amount of time that the sodium activation
gates were open prior to closing of the inactivation gates or initiation of potassium
currents reduced as temperature increased (Figure 4-3), until active currents were no
longer triggered (Figure 4-2 B-D). Depolarization less than 1 mV observed in the FH
model across all temperatures may be linked to differences in Q10 factors, because the
sodium inactivation and potassium activation rates increased with temperature almost
82
twice as much as the sodium activation rate. The relative speed-up of the inactivation
gate over the activation gate would be expected to enhance the effect of the depolarizing
pre-pulses at increased temperatures.
To better understand the effect of initial temperature on maximum depolarization,
sodium channel density and transient temperature caused by infrared stimulus were
varied in the HH membrane model. These models were not designed to replicate realistic
conditions, but to instead highlight effects of each parameter. Increasing sodium channel
density up to 50% above the model defaults increased the depolarizing effects of the
capacitive current, but not enough to extend active spiking above 25 ºC (Figure 4-4).
This indicates that activation is not limited solely by potassium currents, but also the
inactivation gate. To investigate the effect of the transient temperature increase on
excitability, the transient temperature and capacitance changes were decoupled so
temperature changes were reduced while capacitive current magnitudes did not change
from the original model. Results of decreasing the temperature from 15 to 8 and 0 ºC (0≤
k1≤ 1, k2=1) increased the temperature range for activation, but not beyond 24 ºC (Figure
4-4). This suggests that the transient temperature increase has an inhibitory effect on
activation, but that initial membrane temperature still limits activation at high
temperatures.
Beam Profile Affects Excitability
Shapiro et al. (2012) applied infrared pulses to a Xenopus laevis oocyte
transfected with voltage-gated ion channels, and reported activation could not be
achieved without first bringing the cell subthreshold with electrical stimulation first
(Shapiro et al., 2012). This suggests that either a cellular structure necessary to INS was
83
not present or the cellular and/or beam geometry was not representative of previously
observed INS. This study modeled geometries meant to more closely reflect the
stimulation of peripheral nerves. The intracellular currents generated in response to
transient temperature changes were varied in magnitude along the axon length to
investigate the effect of the beam profile in triggering activation. The simple Gaussian
beam profile caused less than 10 mV maximum depolarization in both the unmyelinated
(Figure 4-5A) and myelinated axon models (results not shown). The center axon segment
of the unmyelinated HH axon model and the spatially-lumped HH membrane model each
underwent the same changes Tm and Cm, but exhibited different depolarization levels
across temperatures (Figure 4-2A vs 4-5A). The only electrical difference between these
was the presence of adjacent membrane segments and an axial conduction path, meaning
that intracellular currents generated at the peak of the Gaussian profile could diffuse to
adjacent segments with lower capacitive currents. The bimodal and flat beam shapes
were tested to determine whether spatial gradients designed to prevent outward diffusion
of generated intracellular currents could trigger activation. Both beam profiles were
effective in triggering activation in unmyelinated and myelinated axon (Figure 4-5, 4-6).
The flat-top beam profile was more effective in triggering action potentials than the
bimodal profile. This may be due in part to the fact that this profile results in larger
intracellular currents generated over a larger portion of the membrane. The flat-top
profile did not result in progressively smaller currents generated at the center of the axon
when length was increased, as was observed with the bimodal profile as spacing was
increased. The result of improved activation with altered beam profiles is supported by a
report that infrared stimulation thresholds were reduced using a flat-top beam over a
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Gaussian beam profile (Tozburun et al., 2010), and provides an explanation for this
observed behavior.
The currents generated by rapid temperature changes caused by infrared pulses
provide a new method of generating intracellular currents to stimulate activity,
fundamentally different from extracellular electrical stimulation. Warman et al.
demonstrated that intracellular currents generated by electrical stimulation are
proportional to the gradient of the extracellular voltage field along the axon (Warman et
al., 1992). Infrared-evoked intracellular currents are instead proportional to the change in
local temperature in time. These two methods can serve to complement each other.
Infrared-evoked currents must be of the same polarity, while electrically-evoked currents
can be generated with mixed polarities along the axon. Alternatively, where generating a
wide region of constant intracellular currents along the axon is difficult with electrical
stimulation; infrared stimulus can be easily designed to do so.
The observed differences in activation with different beam profiles may explain
some of the difference in activity reported in rat sciatic nerve and buccal nerve of Aplysia
californica (Duke et al., 2012a). Duke et al. report higher success rates stimulating the
buccal nerve over the rat sciatic nerve, but also positioned the fiber optic tip adjacent to
the buccal nerve sheath and 500 um away from the rat sciatic nerve. Closer to the fiber
tip, the beam profile is expected to more closely resemble the flat profile. Whereas with
increased distance from the tip, the beam profile is expected to more closely resemble the
Gaussian profile. The confounding factors here, though, are that the axon type changes
between these two models from unmyelinated in Aplysia californica to myelinated in the
rat, as do the axon diameters, and the tissue layers between stimulus source and axon.
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Recruitment Order
Smaller diameter axons were predicted to activate at lower thresholds than large
diameter axons in spatially-distributed models (Figure 4-5B, C, 4-6A, B, 4-7). Electrical
activation from extracellular sources typically activates larger diameter fibers before
smaller (Gorman and Mortimer, 1983; Grill and Mortimer, 1995; McNeal, 1976), but
intracellular current sources typically lead to activation of small diameter axons at lower
thresholds (Henneman et al., 1965a, 1965b; Rall, 1977). If INS does activate small fibers
first, it may explain the relatively small motor activation levels reported in the rat sciatic
nerve (Duke et al., 2012a, 2012b; Wells et al., 2005b), and in Chapter 3. This would
suggest that INS may be more effective in stimulation of smaller sensory neurons, which
can be difficult to achieve with electrical stimulation (Castoro et al., 2011).
Intracellular Calcium Release
The infrared-driven calcium release dynamics used in this study make
assumptions that need to be experimentally validated for axons. The results of modeling
intracellular calcium release as an activating mechanism, while speculative, provide
insight into parameters of calcium release potentially important to driving activation.
Results indicate that shorter-duration pulses require less calcium release than longer
pulses (Figure 4-8A, B). The results of adjusting the relative timing between calcium
release and transient temperature and capacitance changes also indicate that there is some
cooperation between these two effects, as thresholds are lowest when the two changes
occur concurrently. Because timing appears to be important, if calcium release is found to
occur in response to infrared stimulus in axons, it will be important to verify that the
release dynamics are responsible for axon depolarization and not merely a parallel effect
of INS.
86
INS Interface Design Implications
Results from both of the mechanisms investigated in this study indicate that
higher-power, shorter-duration infrared pulses are likely to drive activation (Figures 4-2,
4-3, 4-7, 4-8). Additionally, results of varying beam profile in the distributed axon model
indicate that stimulus that encompasses more of the membrane is more effective (Figure
4-6B). Both of these results indicate that response to INS is increased by increased
energy application. With high energy requirements already limiting INS interface design
(Wells et al., 2007a, 2007c), increasing energy applied will not be a viable solution to
improving INS. Beam shaping may help to reduce energy thresholds (Tozburun et al.,
2010). Additional optimization across other stimulation parameters may reveal other
methods of increasing response while decreasing required energy.
If additional mechanistic work reveals that calcium release is a more significant
factor in driving INS activation, then motor activation in peripheral nerves may be
inherently limited by mitochondrial distribution. Mitochondrial distributions in peripheral
nerves have been shown to differ from central axons, with mitochondria typically
clustered around nodes of Ranvier in peripheral nerves, versus the internodal region in
central axons (Chiu, 2011). This may indicate that INS is better applied to neural
structures with high mitochondrial densities. Significant mitochondrial interaction with
infrared light may have important implications for chronic INS interfaces, for neural
tissue as well as other cells illuminated by infrared light. Infrared light has been used to
trigger release of cytochrome c, change gene expression, and trigger early steps towards
apoptosis (Berridge et al., 1998; Frank et al., 2004).
Additional INS Mechanisms
87
It is possible that INS activation observed in vivo is primarily driven by
mechanisms other than those investigated in this study. Sensory neurons are known to
express temperature-sensitive transient receptor potential (TRP) ion channels. TRPV1
and TRPV2 have been shown to cause depolarization in response to temperatures above
42 ºC (Fernandes et al., 2012). Presence of these channels in sufficient density would
further strengthen the argument that INS may be better suited for sensory stimulation
applications. TRPV1 has been observed in motor neurons at the neuromuscular junction
(Thyagarajan et al., 2009), and other temperature-sensitive TRP channels have been
observed in the cell bodies and axons of small and medium sized motor neurons (Anand
et al., 2008; Facer et al., 2007). These observations mean that it motor neuron activation
by means of these channels should not be excluded when evaluating possible mechanisms
Conclusions
Results of this study support both transient changes in membrane temperature and
capacitance and intracellular calcium release as possible mechanisms contributing to
neural activation with INS. Membrane activation using infrared-driven, capacitive
intracellular currents was temperature dependent, and did not explain INS previously
reported at temperatures 25-37 ˚C. This work indicates that infrared stimulation is more
effective with flat or biomodal beam profiles that extend along the axon than Gaussian
profiles. Results of modeling both mechanisms indicate that infrared stimulation is best
achieved with pulses that are shorter duration and higher power. Results indicate for the
first time that infrared neural stimulation may result in axon recruitment in physiologic
recruitment order. This study provides a basis for designing and optimizing infrared
delivery for axon stimulation.
88
Acknowledgements
The authors would like to thank Prof. Hillel Chiel for discussions regarding
infrared stimulation and Profs. Dominique Durand and Andrew Rollins for feedback in
developing this manuscript.
Funding for this project was provided by Microsystems Technology Office of the
Defense Advanced Research Projects Agency (DARPA) Centers in Integrated Photonics
Engineering Research (CIPHER) and the Lockheed Martin Aculight Corporation. The
project described was supported in part by Grant Number T32-EB004314 from the
NIBIB and the National Institutes of Health.
89
CHAPTER 5: CONCLUSIONS
Three studies were conducted to understand design requirements for a multi-
channel, extraneural infrared neural stimulation (INS) interface for motor neuron
activation in the peripheral nerve. Previous studies indicate that focused infrared energy
applied extraneurally may provide a highly selective neural interface that does not also
require increasing invasiveness to achieve. The presented results indicate that nerve
sensitivity to extraneural INS is low, and, while stimulation can be selective, maximally
evoked motor response to INS is below functional limits. Adding entrained electrical
stimulus to above-threshold INS also did not reveal functional gains over electrical
stimulation alone. Finally, computational modeling of proposed mechanisms of INS
indicated that the single-mode Gaussian beam profile typically used in INS studies may
not be the optimal beam profile.
Aim 1
The first aim was established to investigate parameters relevant to design of a
multi-channel, infrared-based peripheral nerve interface. The primary goals were to
quantify sensitivity of a multi-fascicular mammalian peripheral nerve to extraneural INS,
and characterize the response evoked by a single channel of stimulus. The specific
hypotheses used in evaluating this aim include:
Hypothesis 1.1
Sensitivity of the rabbit sciatic nerve to extraneural infrared stimulus will
yield at least 3 independent regions exhibiting entrained motor response to applied
infrared pulses.
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Surgically exposed rabbit sciatic nerves (32 nerves, 25 rabbits) were scanned with
focused infrared light delivered from a 400 um optical fiber maintained 250-750 um from
the nerve and scanned in the longitudinal and transverse directions. Motor response from
the medial and lateral gastrocnemii, soleus, and tibialis anterior was monitored for
entrained response to applied pulses. With only 81% of nerves exhibited any sensitivity
to INS, and of the sensitive cases only 2.0±0.5 sensitive regions were identified per
nerve, this hypothesis was rejected. Measurement of 11 infrared sensitive regions
revealed sensitivity to span 470 um in the longitudinal and 360 um in the transverse
directions on the nerve.
Hypothesis 1.2
Rectified and integrated motor response to increasing infrared pulse energy
is typically flat or increases above the activation threshold.
Previous INS studies have established stimulation and acute damage thresholds
for extraneural stimulation, but the response between these limits had not been described.
With emerging evidence that INS may be used to inhibit activation as well as activate, it
was necessary to establish the working range for INS. Motor response was measured in
response to pulse energy increased by increasing pulse duration, and the correlation
between response above threshold and pulse duration was measured. Pearson’s
correlation was computed to determine linearity of the correlation, and Spearman’s
correlation was computed to determine whether the response was monotonic. Across 209
recruitment curves, Spearman’s coefficient was calculated to be ρ = 0.68 ± 0.04 (mean ±
95% confidence interval), and was significantly greater than zero for 83% of recruitment
curves. Based on these results, the hypothesis was accepted and it was concluded that the
working range for INS spans the range between stimulation and acute damage thresholds.
91
Hypothesis 1.3
Motor recruitment within nerve infrared-sensitive regions will exhibit
selectivity to a single muscle, with a lower activation threshold than any other
muscle, in at least 50% of optically sensitive regions.
Motor recruitment as a function of infrared pulse duration was collected for
medial and lateral gastrocnemii, soleus, and tibialis anterior. The activation threshold for
any muscle was defined as the minimum pulse duration evoking EMG response in at least
30% of the applied pulses. Our results indicate that within an infrared-sensitive region a
single muscle can typically be activated before any another reaches threshold. This result
was significant with a 95% confidence interval of 67-91%, and the hypothesis was
accepted. When the definition of selectivity was relaxed to allow co-activation of medial
and lateral gastrocnemii, the confidence interval shifted up to 81-99%. These results
indicate that while in many cases multiple muscles can be activated from a given
optically sensitive region, a single muscle can be typically be activated selectively.
Hypothesis 1.4
Short duration, high power infrared pulses are more efficient than longer
duration, lower power pulses; either reducing activation thresholds or increasing
motor response.
Motor recruitment curves were measured with infrared at full, 80% of full, and
55% of full power. Activation thresholds and maximum recruitment for each muscle was
compared within the same infrared-sensitive region. Results indicate that lowering power
significantly increased the activation threshold measured as pulse duration. Reducing the
power reduced the rate of energy deposition to the nerve. The amount of energy required
to reach the activation threshold did not significantly change with decreased power.
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Comparing maximum achieved recruitment at 80% and 55% power levels to full power
stimulation indicated a significant decrease in maximum recruitment with decreased
power. Because lower power stimulation resulted in a smaller magnitude response, the
hypothesis that higher power infrared stimulus is more efficient was accepted. This result
indicates that sources developed for infrared generation should target short, high power
delivery for maximal response.
Hypothesis 1.5
Maximum motor response evoked by infrared stimulus applied at below the
calculated acute damage threshold will result in activation of at least 10% of a single
muscle.
Motor recruitment was measured in response to either increasing infrared pulse
duration or increased electrical pulse amplitude. Electrical recruitment was swept from
sub-threshold to supra-maximal activation of the distal muscles. Maximum optically
evoked recruitment was compared to maximal electrical recruitment achieved for each
optically stimulated muscle. The lower limit for functional activation was set at 10% of
maximal recruitment of a muscle, based on reports that this threshold results in a just
palpable muscle twitch (Polasek et al., 2009a, 2009b). Across the medial and lateral
gastrocnemii, soleus, and tibialis anterior, optical stimulation recruited significantly less
than 10% of the muscle, and for this reason the hypothesis was rejected. This result is
important in estimating the number of extraneural infrared channels needed for activating
muscles innervated by the stimulated nerve to a desired level.
Aim 1 Summary
Motor recruitment triggered by extraneural application of infrared light indicates
that the response can be selective and is likely to be sub-fascicular. Recruitment appears
93
to follow a flat or increasing relationship between the activation and damage limits, but is
most efficient with high-power pulses. Implementation is limited by the occurrence of
infrared-sensitive regions of the nerve, and the relatively small portion of the muscle that
is maximally activated within a sensitive region. The infrequent occurrence of infrared-
sensitive regions, paired with the small size of each region, make identification of 3
thermally-independent sensitive regions unlikely. The results of this study indicate that an
interface designed to activate 100% of a muscle at 12 Hz would require 30-50 channels
of infrared light applied to sensitive regions. This number only increases if selective
activation is necessary, or if the overlap of duplicate axon populations to interleave
stimulus and coverage of the axons innervating the muscle is not balanced. With only
typically 1-2 sensitive regions observed per nerve, even doubling this number to account
for nerve area not accessible in this study, there does not appear to be enough sensitivity
of the nerve to extraneural INS to accomplish this.
The results of this study indicate that development of a peripheral nerve interface
based on infrared-only motor recruitment is unlikely to be successful unless delivery can
be improved to increase response or decrease energy thresholds.
Aim 2
The first aim determined that the relatively small muscle twitches evoked by
infrared stimulus and low sensitivity of the nerve limit its utility. The second aim of this
study investigated whether the effects of INS may be increased by combining it with
electrical stimulation to recruit muscles. Entrained infrared and electrical stimulus was
applied, which was indicated in previous reports as most effective for reducing
stimulation thresholds. By using electrical stimulation to lower the activation threshold of
axons, it is expected that axons stimulated by infrared to a subthreshold level should
94
activate when electrical stimulus is applied. If significant portions of the nerve are
affected by INS, then significant changes in full muscle recruitment over electrical
stimulation should be evident.
Hypothesis 2.1
Combining extraneural, entrained electrical and optical stimuli will
significantly alter recruitment over electrical stimulation alone, by shifting
recruitment curves to lower stimulus levels, or reducing recruitment curve slope as
some axons are selectively activated.
Motor recruitment curves were generated with constant infrared stimulus and
graded electrical stimulus. Recruitment curves were generated using only electrical or
entrained electrical and infrared pulses. Stimulus was applied using a nerve cuff that
stabilized electrical contacts in an arrangement previously reported to improve results,
while allowing direct application of infrared light to the nerve surface. Statistical analysis
revealed significance in only 7% of all recruitment curves generated. Of this 7%, the
largest portion was generated in a single trial where significant inhibition of a muscle was
observed. Rather than infrared-facilitated activation, this is more likely an observation of
action potential generation block reported by (Mou et al., 2012). The remaining cases did
not exhibit particular trends or functionally relevant changes in recruitment over
electrical stimulation. Based on these results, Hypothesis 2.1 was rejected, as the
observed evidence did not support a functionally significant change over electrical
stimulation in the general case.
Aim 2 Summary
The results of this study indicate that entrained infrared and electrical stimulation
does not provide significant changes in activation of the entire muscle. Results of adding
95
electrical energy to lower the optical stimulation threshold indicate that there is not a
significant axon population stimulated to a sub-threshold level optically, meaning that the
spatial extent a single channel of INS is possibly too limited to achieve significant
entrained activation. Recent reports indicate that higher frequency or continuous infrared
energy may be more effective in modulating recruitment than entrained pulses (Duke et
al., 2012b; Mou et al., 2012). A better understanding of the mechanisms that drive INS
would help to understand how it may cause excitation as well as inhibition, and may
enable design of more effective INS delivery that increases the effect of entrained
stimulation.
Aim 3
The cascade of events between infrared light delivery and action potential
generation in motor neurons has not been fully described. Previous work has established
infrared driven membrane capacitance changes and intracellular release of calcium by
mitochondria in non-neuronal cells. While both of these mechanisms would cause
depolarization of the cell membrane, it was unclear whether either would be likely to
cause activation in axons. Computational models were developed to investigate these
phenomena and determine whether they could trigger action potentials in spatially-
lumped or spatially-distributed neural membrane models.
Hypothesis 3.1
Thermally driven capacitance changes can trigger action potentials in
spatially-lumped membrane models.
The Hodgkin and Huxley based membrane model exhibited action potential
generation in response to transient temperature and capacitance changes, but only at
temperatures too low to explain INS activation at room and body temperature. The low
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temperature activation did match the modeling results described by (Shapiro et al., 2012),
and the ~10 mV depolarization observed at 25 ºC matched the experimental results they
observed in cell membranes. While the hypothesis was accepted because action potential
generation was observed, the temperature range was too limited to explain observed
activation at room and body temperature. The results of this investigation, paired with the
experimental results showing limited depolarization in a large cell in vitro by (Shapiro et
al., 2012), indicated that spatial distribution of applied energy and axon geometry may be
important factors in capacitance-driven activation.
Hypothesis 3.2
Thermally driven capacitance changes can trigger action potentials in
spatially-distributed axon models, depending on thermal gradients along the
membrane length.
Spatially-distributed unmyelinated and myelinated axon models were simulated
with different beam profiles meant to represent three possible delivery methods. A
Gaussian beam profile was used to match infrared delivery through a bare fiber optic tip,
a bimodal beam profile was used to simulate application through two separate bare fibers,
and a flat-top profile was used to simulate collimated delivery. Results indicate that
action potential generation was dependent on beam profile, initial axon temperature, and
axon geometry. Action potentials were generated when the spatial gradient of the beam
profile was flat or positive, and were wide enough to affect multiple nodes of Ranvier in
the myelinated axon model. Hypothesis 3.2 was accepted based on these results. These
results indicate that a Gaussian distribution is suboptimal for axonal excitation, and may
provide insight into why axonal stimulation in peripheral nerves can be difficult.
Experimental validation with alternative beam profiles is necessary.
97
Hypothesis 3.3
Intracellular release of calcium ions can trigger action potentials in spatially-
lumped membrane models without exceeding physiologic intracellular calcium
concentration levels.
Two speculative intracellular calcium release patterns were tested to determine
the peak intracellular calcium concentration achieved by a calcium current at threshold to
trigger an action potential. The two calcium release patterns used included a simple
square pulse, and a linear ramp followed by an exponential decay. The profiles used were
chosen because calcium dynamics in the neuron in response to infrared light have not
been measured. Calcium release from mitochondria in cardiac myocytes was measured
by Dittami et al. and shown to increase over hundreds of milliseconds. This release
profile was too slow to explain neural activation by calcium release, as activation must
happen within a few milliseconds to reflect experimental observations. The square pulse
was used to model a general calcium release, and the ramp with decay was designed to
reflect the transient thermal changes observed in tissue in response to INS. Resulting
intracellular calcium concentrations were compared to a tenfold increase in baseline
concentration, based on reports that intracellular calcium concentrations can change by an
order of magnitude in certain cells. Results showed that stimulation thresholds could be
reached with currents that did not increase the intracellular calcium more than tenfold, so
the hypothesis was accepted. The conditions under which this occurred indicate that
release that occurs over a short time is more effective, and that depolarization caused by
transient temperature and capacitance changes helps to facilitate activation by calcium
release.
98
Aim 3 Summary
The primary goal of developing mechanistic models for infrared activation of
neural membranes is to provide a means of exploring and optimizing infrared delivery
parameters. INS still requires additional mechanistic investigations to demonstrate that
either of the phenomena modeled in this study truly cause INS. The results of this study
do indicate that activation by either phenomenon is plausible at physiologic levels.
Investigation of transient temperature and capacitance changes in spatially-distributed
models provide direction for testing whether INS delivery can be improved with
adjustment to beam profile. If the mechanism driving INS is more complex than that
modeled in this study, but still generally results in an intracellular current that is
proportional to the incident energy, the findings regarding beam profile and axon
geometry would be expected to remain valid. The results of varying axon diameter
indicate that small diameter fibers may be better suited for activation with INS, and
motor activation may just be the wrong target for INS. The results of this study help to
identify the need for characterizing calcium release triggered by infrared light applied to
neural tissue. Results suggest that the mechanism is feasible, and so warrants further
investigation. Experimental investigation of calcium release should also include more
complex signaling pathways caused by calcium release, beyond the simple charge release
modeled in this study.
99
Dissertation Conclusion
The contributions of this work include assessment of the capabilities of
extraneural INS as a means for activating motor neurons in peripheral nerve interfaces,
and evaluation of proposed mechanisms of INS through computational modeling. While
selective and capable of activating very small portions of the muscle, the effect of INS
was too limited to achieve functionally relevant activation INS. This study indicates that
extraneural application of INS for entrained motor activation only offers limited
effectiveness in motor stimulation. Further, increases in nerve size as INS is translated
towards clinical application may further decrease activation triggered by INS. Modeling
results indicate that the difficulty observed in using INS to trigger motor response may be
due to the use of a bare fiber to deliver infrared energy, and indicate that there is likely
room to improve INS delivery by changing beam profile. Experimental validation of the
modeling results is necessary to determine whether beam profile changes are sufficient to
increase the effects of INS to functional levels. Another conclusion that can be drawn
from the results of both studies is that motor activation may not be the optimal
application for INS. With only small percentages of any muscle activated with INS, and
modeling results indicating activation of small fibers before large, INS may be better
suited for stimulation of small sensory fibers.
100
APPENDIX I: PREDICTING MYELINATED AXON ACTIVATION
USING SPATIAL CHARACTERISTICS OF THE EXTRACELLULAR
FIELD
The following is a reproduction of:
Peterson, E.J., Izad, O. & Tyler, D.J., 2011. Predicting myelinated axon activation using
spatial characteristics of the extracellular field. Journal of Neural Engineering, Volume
8, Issue 4
Reproduced with permission.
Abstract
Computation time required for modeling the nonlinear response of an axon to an
applied electric field is a significant limitation to optimizing a large number of neural
interface design parameters through use of advanced computer algorithms. This paper
introduces two methods of predicting axon activation that incorporate a threshold that
includes the magnitude of the extracellular potential to achieve increased accuracy over
previous computationally efficient methods. Each method employs the use of a modified
driving function that includes the second spatial difference of the applied extracellular
voltage to predict the electrical excitation of a nerve. The first method uses the second
spatial difference taken at a single node of Ranvier, while the second uses a weighted
sum of the second spatial differences taken at all nodes of Ranvier. This study quantifies
prediction accuracy for cases with single and multiple point source stimulating
electrodes. While both new methods address the major criticism of linearized prediction
models, the weighted sum method provides the most robust response across single and
multiple point sources. These methods improve prediction of axon activation based on
properties of the applied field in a computationally efficient manner.
101
1. Introduction
Animal models are common developmental tools for testing design factors in
peripheral nerve interfaces, but anatomical differences between animal models and
humans limit the direct translation to clinical application (Brill et al., 2009; Grinberg et
al., 2008). Computer models of neural interfaces are a vital tool to help fill the gap
between preclinical and clinical testing when used to evaluate electrical interface designs.
Number and placement of electrodes, the stimulus amplitude, and the pulse
duration at each electrode all influence the activation pattern within a nerve by affecting
the resultant electric field. Calculation of the resultant field can be performed in several
ways, and is outside the scope of this work. Determining axon activation within an
electric field begins with sampling the electric potential in space along the length of an
axon, creating a vector of voltages. This vector is applied to a model of the axon as a
function of time, and the response of the nonlinear ion channels is solved numerically(Lu
et al., 2008; McIntyre et al., 2002; McNeal, 1976; Schiefer et al., 2008). This is a process
that works well when predicting behavior of individual axons, but becomes a limitation
when expanded to simulations of the whole nerve where hundreds to thousands of axons
are solved numerically (Schiefer et al., 2008; Veltink et al., 1988). The work presented by
Schiefer et al. involved simulating the activation patterns in a histology-based model of
the human femoral nerve and required almost 24 million axon simulations taking
approximately 90 days of computation time to complete (Schiefer et al., 2008). Schiefer
et al. only investigated cases with one of 22 electrodes was active at a time. Expanding
the investigation from a single active contact to include two or three simultaneously
active contacts would increase the number of electrode configurations to investigate from
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22 to 231 or 1540, respectively. The increase in the number of combinations virtually
eliminates the possibility of investigating field shaping with multiple active contacts or
using evolutionary optimization methods for interface design.
The computational complexity of modeling axon response can be reduced by
replacing the nonlinear ion channel dynamics with linearized approximations, but early
attempts did not scale well to nerve-level modeling. McNeal’s method of replacing
nonlinear node dynamics with linearized versions required a priori knowledge of the
electric field before the model could be simplified (McNeal, 1976). Rattay’s work
focused on analyzing electric field shape to predict activation. Rattay’s method could
only provide relative axon recruitment order, though, requiring simulation using the
nonlinear equations to determine activation (Rattay, 1989). Warman et al. (Warman et
al., 1992) developed an activation function dependent only on the second spatial
difference of the voltage field (2Ve), an activation threshold, and the duration of the
applied pulse. Determining the activation threshold required a one-time simulation of the
nonlinear axon, but once completed, prediction of axon response was a purely algebraic
function. This method has been used to enable evolutionary optimization algorithms for
electrode design (Choi and Lee, 2006). The accuracy of this method, however, has an
undesirable dependence on electrode-to-axon separation (Moffitt et al., 2004).The
dependency of the error in the Warman method as a function of separation is well
behaved. Consequently, we hypothesize that a more accurate prediction is possible by
accounting for the dependence of the activation threshold on magnitude of the
extracellular voltage to predict activation.
2. Methods
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This work presents two methods of predicting axon activation, one based on the
second spatial difference of the extracellular potential at a single node, whereas the
second implements a weighted sum of the second spatial difference at all nodes. The
performance of each was examined under conditions relevant to whole nerve simulation,
and compared to results of nonlinear active axon simulations. Simulation results
generated using the method presented by (Warman et al., 1992) were included for
comparison. Performance was examined for cases of single and multiple point source
stimulation. Single point source simulations were designed to explore sensitivity of a
given method to the position, alignment, and fiber diameter variables that are often
randomized in nerve-level simulation (Lertmanorat et al., 2006; Schiefer et al., 2008;
Veltink et al., 1988). Multiple point sources aligned longitudinally with the axon are
simulated to demonstrate the prediction accuracy for complex fields spanning multiple
nodes of Ranvier. Performance was also examined under conditions similar to those used
in previous literature to model neural response observed in live experiments(Grill and
Mortimer, 1996; Lertmanorat and Durand, 2004).
2.1 Axon models
All axon simulation waveforms were square, monophasic pulses. Applied pulse
durations ranged from 20 s to 10,000 s. Active axon simulations incorporated the
McIntyre, Richardson, and Grill (MRG) double-cable axon model. This model was
chosen because the model of the internodal space and active ion channels was developed
using numerous experimental data from mammalian myelinated axons(McIntyre et al.,
2002). Subsequent studies using this model to simulate behavior have been
experimentally confirmed, thereby showing the utility of the MRG model in predicting
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actual axon response(Kilgore and Bhadra, 2004; Kuhn et al., 2008; Schiefer et al., 2010;
Takahashi et al., 2007; Wongsarnpigoon et al., 2010). Passive axon models were created
by replacing the non-linear ion channels of active axon models with a fixed conductance,
Gm = 0.007 [mS/cm2](Moffitt et al., 2004; Warman et al., 1992). All simulated axons
were myelinated and consisted of 21 nodes of Ranvier and 20 internodal spaces. Axon
dimensions and parameters were determined based on fiber diameter, as previously
described (McIntyre et al., 2002; Schiefer et al., 2008). Fiber diameters used in this
analysis ranged from 4 to 20 m to span the physiologic range for myelinated,
mammalian axons of the peripheral nervous system. The NEURON simulation
environment (Version 7.0)(Hines and Carnevale, 1997)was used to simulate the response
of active and passive axon models to an applied extracellular potential field. In active
axon simulations, activation was defined as an action potential that propagated along at
least five nodes of Ranvier (Schiefer et al., 2008).
2.2 Activation prediction methods
Both new activation prediction methods incorporated a modified driving function
(MDF) and an activation threshold in order to predict activation. Axons were predicted
active if the output of the MDF, applied to the extracellular potential, exceeded the
activation threshold. Activation thresholds varied with fiber diameter, pulse duration, and
extracellular potential. In all verification tests the MDF was computed at each node of
Ranvier and compared to the activation threshold to determine activation, because it was
not known a priori where activation was likely to occur. Extracellular potentials and axon
length were chosen to minimize potential edge effects of a finite length axon.
2.2.1 Modified Driving Functions (MDF)
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The modified driving function for the first method, MDF1, used only the
extracellular potential at a node of Ranvier, n, and the two adjacent nodes (eq. 1) (Izad,
2009). MDF1is the second spatial difference, instead of the second spatial derivative,
which includes the term x2, as used by Rattay (Rattay, 1986).This method was termed
the single node method.
(1)
Warman et al. showed that current induced in the membrane at a node of Ranvier
was proportional to the second spatial difference of the extracellular potential(Warman et
al., 1992).Warman et al. used a weighted sum of the currents at each node to account for
redistribution of current when the extracellular potential induced current at more than one
node. The second proposed method used similar concepts to account for extracellular
potentials that influence more than single node of Ranvier, and was termed the weighted
sum method. The modified driving function for this method, MDF2, was a weighted sum
of second spatial differences along the axon.
(2)
Weights, W|n-j|, were generated using the process outlined by (Warman et al.,
1992). Briefly, using a passive axon model, the amount of depolarization caused by
current injected at a node, j, was measured at the center node, n. A step function of
current was applied to one node at a time, and the resulting depolarization was measured
at the pulse durations of interest, making W|n-j| a function of pulse duration. The value for
each W|n-j| was the ratio of depolarization caused by current injected at node j to the
depolarization caused by current injected when j=n. This decoupled W|n-j| from the
magnitude of current injected. Thus, the weight of the center node was 1.0 and decreased
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for each more distant node. Weight generation for the weighted sum method had two
primary differences from the original Warman method: First, all weights were calculated
using the MRG model, which was not yet developed at the time (Warman et al., 1992)
was published, instead of the Sweeney axon model. Second, weights were calculated
separately for each fiber diameter. Weights generated for this work are included in
supplementary table (Table S1). Simulation results obtained by replicating the full
Warman method, as described in (Warman et al., 1992), were included separately for
comparison and to highlight the improvement of each new method in addressing the
limitations demonstrated by Moffitt et al. (Moffitt et al., 2004).
2.2.2 Activation thresholds
The activation threshold for each method was generated using two steps. The first
step involved performing active axon simulations using a set of extracellular voltage
vectors and recording whether activation occurred. The second step was performed by
plotting the activation results as a function of the spatial and temporal characteristics of
the applied voltage vector. The activation threshold was defined as the boundary between
the regions of activated and inactivated points.
The first step began with creating a set of extracellular voltage vectors to apply to
the axon model. Each constructed vector had a unique combination of peak extracellular
potential (Ve), and second nodal difference (2Ve) computed at the center node of
Ranvier. The vector set was generated varying Ve from 0 to -500 mV, and 2Ve from 0 to
190 mV, each in 10mV steps, to yield 1020 unique vectors. With the three central nodal
voltages set by the requirements to satisfy Ve and 2Ve, the remaining nodal voltages were
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set to transition to a flat potential at the outermost nodes. This minimized edge effects
that could influence the observed activation. The remaining internodal voltages were
interpolated using a spline interpolation. Each vector was applied to fiber diameters
ranging from 4 m to 20 m as a square, monophasic pulse for durations between 20 s
to 10,000 s. At the end of each simulation, the axon was classified as active if an action
potential propagated along at least five nodes of Ranvier. For the second step, results
were plotted as a function of axon diameter, pulse duration, Ve, and the output of
applying each method’s respective MDF to the extracellular potential vector. The
activation threshold was defined as the border between the regions of activation and
inactivation. The activation threshold was implemented as a look up table in order to
predict activation when analyzing extracellular potential in subsequent simulations. The
resulting activation thresholds are offered for both methods in the supplemental materials
(Tables S2 and S3).
2.3 Verification
2.3.1 Extracellular potential generation
Extracellular potential fields were generated for single and multiple point source
electrodes. The conducting medium was assumed to be infinite, homogeneous, and
anisotropic, with transverse conductivity t=0.083 S/m and longitudinal conductivity
l=0.33 S/m, as described by (Moffitt et al., 2004). The system is assumed radially
symmetric. The extracellular voltage along the axon due to a single point source can be
calculated from the distance between the axon and electrode, r, and the distance along the
axon, z (eq.3).
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(3)
Multiple point sources were simulated by computing the contribution of each
source individually and summing them to create the total voltage field. Therefore, the
spatial model was assumed to be linear in nature and did not contain capacitive
components. This is a reasonable and common assumption when modeling nerve cuff
electrodes (Moffitt et al., 2004; Rattay, 1989; Schiefer et al., 2008; Warman et al., 1992).
2.3.2 Verification cases
Verification for single point source stimulation involved varying either electrode-
to-axon spacing (EAS) or alignment of the electrode to a node of Ranvier. In simulations
where EAS was varied, the electrode was aligned with the center of a node of Ranvier
(Figure 6-1.a). EAS was increased from 100 m to 3000 m with constant pulse width
and fiber diameter, to determine performance under conditions similar to those outlined
by (Moffitt et al., 2004).The sensitivity of alignment of the electrode to nodes of Ranvier
was tested with an EAS of 200 m while the electrode alignment was changed up to
±50% internodal lengths from a node (Figure 6-1.b). Relative recruitment threshold
across diameters was tested with EAS set to 200 m, with the electrode aligned with a
node of Ranvier (Figure 1.a). To investigate pulse duration-dependent spatial selectivity,
as observed by (Grill and Mortimer, 1996), EAS was varied from 100 m to 2000 m for
pulse durations 20, 50, 100, and 500 s, with the electrode aligned to a node (Figure 6-
1.a).
Multiple point source stimulation tested prediction accuracy in cases where
stimulation pulses were not localized around a single node of Ranvier. The first case
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involved two point sources, each with 200 m EAS (Figure 6-1.c). The first point source
was aligned with a node of Ranvier, while the second point source was shifted in
increments of 25% of the internodal length for up to eight nodes away from the first
electrode. The amplitude of the second source was varied as a fraction of the first.
Several fractions were tested, but the presented data is for the worst case where the
amplitude of the second source is the same as the first. To extend the investigation to
more complex electrode geometries, an alternating pattern of six anodic and five cathodic
point sources was used to generate the extracellular potential (Figure 6-1.d). This design
was based on a model and experimental study that showed that it was possible to change
the recruitment order as a function of axon diameter through manipulation of the driving
function (Lertmanorat and Durand, 2004). The adjacent electrode spacing was increased
from 400 m to 1500 m in 100 m increments; while EAS was held at 200 m. Anodic
amplitudes were set to 70% of the cathodic amplitudes on all electrodes except the
outermost, where amplitude was set to 40% of the cathodic amplitude. To investigate
whether the presented prediction methods could capture the diameter recruitment
reordering observed by (Lertmanorat and Durand, 2004), adjacent electrode spacing was
set to 650 m, while EAS was changed from 50 m to 300 m.
Performance of these methods was compared against the Warman method
(Warman et al., 1992)applied to the MRG model, as outlined in(Moffitt et al., 2004). The
Warman method could be tuned to minimize error at a given EAS. In all results, the
Warman method was tuned for EAS equal to either 200 m or 1000 m. In cases where
only one set of data is presented from the Warman method, it is data optimized to the
tested EAS of 200 m. This, therefore, represents the best possible result of the method.
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2.3.3 Performance measures
Three output measures were used in verification: stimulation threshold error,
relative stimulation threshold, and computational run time. Stimulation threshold
compares the current, Iext, required for activation of the active MRG model to those
obtained using the prediction methods. Iext of (eq.3) was tuned using a binary search
Figure 7-1 Electrode-axon geometries used for investigating prediction method
performance.
a) Electrode is aligned with a node of Ranvier, while electrode-to-axon spacing (EAS) is
changed. b) EAS is held constant while alignment of the electrode is changed. c) Two-
electrode configuration where one is always aligned with a node of Ranvier, while inter-
electrode spacing is increased. EAS of each electrode is held constant. d) Eleven-
electrode pattern of alternating anodic and cathodic stimulation, where either adjacent
electrode spacing or EAS is changed.
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algorithm until the stimulation threshold was determined within 0.01% of the stimulation
threshold magnitude. In cases of multiple point sources, all sources were scaled by the
same factor. The recorded output for each simulation or prediction was the amplitude of
Iext required for activation. Stimulation threshold error was calculated in the same manner
as (Moffitt et al., 2004)using (eq.4).
(4)
This error is positive when a prediction method over-predicts the stimulation threshold of
the MRG active axon model and is negative when the stimulation threshold is under-
predicted. In the ideal case, threshold error would be zero or at least constant across all
simulations, since constant error can be corrected for with a scale value applied to the
prediction method results.
Relative stimulation thresholds were computed by normalizing the stimulation
thresholds either across axon diameter or pulse duration. This was used to determine
recruitment order across fiber diameter and was compared to the relative activation
values for the active axon model in the same simulation conditions.
Computational run time was measured for the active axon simulation and both the
single node and weighted sum prediction methods. Simulations were performed with an
Intel®
CoreTM
2 Duo P8400 (Intel, Santa Clara, CA) processor and 4GB RAM.
Computational load in addition to the simulation or prediction method run was controlled
to be similar across all three cases. No thread optimization was used to run active axon
simulations on more than one processing core at a time. Single node and weighted sum
methods were performed using MATLAB (2009b, The MathWorks, Natick, MA) with no
thread or multi-core optimization beyond the default settings. Four simulations of 4010
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axons for pulse durations 20, 50, 100, and 200 s were performed, for a total of 16,040
simulations.
3. Results
3.1 Threshold value generation
The single node prediction method was chosen for its simplicity as well as the use
of 2Ve in current literature as a computationally fast approximation (Maks et al., 2009;
Wongsarnpigoon and Grill, 2008). Plotting active axon results, where each point
represents the result of a separate active axon simulation, against Ve and 2Veof the
applied extracellular field revealed two distinct regions of activation and inactivation
with a smooth border between the two (Figure 6-2). This transition is highlighted with
the dashed lines. The border between active and inactive regions was defined as the
activation threshold for the single node prediction method. The threshold value was
found to be a function of Ve, pulse duration, and fiber diameter (not shown). The
dependence on fiber diameter is relatively small compared to the other factors, and for
clarity the data is not presented.
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Figure 7-2 Activation as a function of pulse duration and peak extracellular voltage
Activation results plotted as a function of the extracellular voltage (Ve)and the second
nodal difference (2Ve) of the applied waveform taken at the center node of Ranvier.
Each point represents the result of a simulation. Clear activation and inactivation
regions are present. The activation threshold is the transition between these regions. The
activation threshold decreased as extracellular voltage and pulse duration increased.
114
The activation threshold for the weighted sum method was generated using the
same input voltage vectors and active axon simulation results as the single node method.
The difference from the single node method was that the ordinate value was the result of
the MDF2 applied to each voltage vector. The activation threshold for this method was
found to be a function of Ve, pulse duration, and diameter (Figure 6-3). Diameter
dependence was shown to have a greater influence at short pulse widths, and in general,
threshold was lower for larger diameter axons.
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3.2 Prediction performance with single point source
Figure 7-3
Activation thresholds generated by applying the weighted sum equation (eq.2) to the
extracellular voltage vectors used in Figure 2 and plotting the transition between
activation and inactivation regions for diameters of 6, 10, 16, and 20 um at pulse
durations a) 20 us and b) 200 us.
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The two proposed prediction methods and the method from (Warman et al., 1992)
were tested under single point source conditions and compared to active axon simulation
results. Simulations similar to those performed by (Moffitt et al., 2004) demonstrate the
improvement achieved by including Ve in the activation threshold (Figure 6-4.a). It was
found that the Warman method could be optimized to minimize error at a certain EAS,
but optimization did not change the fact that threshold error varied by almost 40% across
all EAS. Both the single node and weighted sum methods showed error across all EAS
that was more consistent and lower than the Warman method. The single node method
varied by 7.1% across all EAS. The weighted sum method showed the least variation,
with threshold error varying by 5.7%.
Stimulation threshold error was influenced by electrode alignment to the node.
(Figure 6-4.b) The Warman method results varied between 3.1% and -8.1% and
oscillated between over-estimation and under-estimation. The other two methods were
much flatter across most of the range, but both showed an increase in over-prediction of
the stimulation threshold when the electrode was directly between two nodes of Ranvier.
The single node method exhibited the largest swing in error, peaking at 20.8%. The
weighted sum method was flattest across the widest range and threshold error peaks at
7.6%. These values shifted as axon diameter and pulse duration were changed. When
axon diameter was increased to 20 m, the single node method error peaked at 20.4% and
the weighted sum method error peaked at 6.1%; both retained the same general shape as
Figure 6-4.b. The Warman method error oscillated between -69.4% and -82.2% with
diameter set to 20 m. With diameter set at 4 m, the single node error peak was 15.0%
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and the weighted sum peak was 4.4%, while the Warman error shifted to oscillate
between 146.5% and 165.7%.
Relative recruitment order as a function of axon diameter with a single point
source electrode showed that the two proposed methods match the predictions of the
active axon simulations better than did the Warman method(Figure 6-4.c). Stimulation
thresholds were largest for the smallest fiber diameter across all prediction methods and
the active axon simulations, as expected. The single node and weighted sum methods
both matched the relative recruitment order and magnitude of the active axon model,
where the Warman method showed a much greater variation in threshold change from the
smallest to the largest fibers.
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Figure 7-4 Activation prediction method results with a single point source electrode and
100 us pulse duration.
a) Electrode is aligned with a node of Ranvier, but electrode-to-axon spacing (EAS) is
increased. b) EAS is 200 um, but alignment of the electrode to the center node of
Ranvier is varied. c) Relative recruitment order across axon diameter with the electrode
aligned to a node of Ranvier and EAS set to 200um. Thresholds are normalized to the
maximum threshold value found across diameters within a given prediction method.
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The final single point source electrode investigation focused on stimulation
thresholds as a function of pulse duration and EAS. Pulse durations used were 20, 50,
100, and 500 s and EAS ranged from 100 to 2000m. This was similar to the work
presented by Grill and Mortimer(Grill and Mortimer, 1996)where they used the active
model developed by (Sweeney et al., 1987). All thresholds were normalized to the peak
threshold value found across all pulse durations and EAS values for a given method. All
three methods demonstrate the increased spatial selectivity for short pulse durations
observed by Grill and Mortimer (Grill and Mortimer, 1996) (Figure 6-5).
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3.2 Prediction performance with multiple point sources
Multiple point sources were arranged along the axon axis to investigate
performance under more complex fields. Threshold error for two point sources arranged
along the axon axis demonstrated performance differences between the single node and
weighted sum methods (Figure 6-6). Threshold error from the Warman method varied by
as much as 32.2% across EAS. The single node method displayed larger absolute swing
Figure 7-5 Activation prediction results across pulse duration and electrode-to-axon
spacing
Relative stimulation thresholds plotted across pulse duration values and EAS values for
a) active axon simulations, b) the Warman method, c) the single node method, and d) the
weighted sum method. All methods demonstrate the increased spatial selectivity for
short pulse durations originally presented by (Grill and Mortimer, 1996) Results
presented are for a 10 um diameter axon.
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of 42%, with the largest error occurring when the two electrodes are aligned with
adjacent nodes of Ranvier. The behavior of the weighted sum method is the smoothest of
the three methods, with a maximum threshold error of 14.1%.
The investigation using multiple point sources was extended to the pattern of
alternating anodic and cathodic point sources outlined in the methods. All three methods
exhibited large variation in predicting the activation threshold (Figure 6-7.a). The single
node method changed the most, with error between 42.4% over-prediction to 24.9%
under-prediction of the threshold. The weighted sum method changed less with a peak
Figure 7-6 Stimulation threshold error across prediction methods
Stimulation threshold error when the spacing between two electrodes arranged
longitudinally to the axon is increased. Pulse duration is 100 us, fiber diameter is 10 um,
and EAS is 200 um.
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over-prediction of 45.8% and under-prediction of 0.7%.The Warman method changed
with a peak 35.3% over-prediction to 11.4% under-prediction when the EAS optimization
and actual EAS match at 200 m, a slightly larger range than the weighted sum method.
The results with the Warman method tuned to EAS of 1000 m are not shown for clarity,
but showed an over-prediction between 13% and 71.6%.The other two methods do not
require optimization for different EAS values.
The eleven-electrode pattern was used to investigate whether these methods could
demonstrate the same relationship between threshold and axon diameter observed by
(Lertmanorat and Durand, 2004). The relative thresholds across all diameters tested were
plotted for the three approximations and the active axon simulation, with adjacent
electrode spacing set to 650 m and EAS set to 50 m and 300 m (Figure 6-8). With
Figure 7-7 Threshold error for an arrangement of six anodic and five cathodic
electrodes arranged in an alternating pattern longitudinally to a 10 um diameter axon.
a) Threshold error as a function of space between two adjacent electrodes. Example
extracellular waveforms from this analysis are shown for adjacent electrode spacing of
b) 500 um and c) 1000 um.
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EAS equal to50 m, the single node and weighted sum methods tracked the active axon
simulation results well, with an increase in the activation threshold peaking around 14-
16um diameter fibers (Figure 6-8.a). The Warman method, however, did not track the
active axon results. When EAS was 300um, the weighted sum method tracked the active
axon simulations best (Figure 6-8.b). The single node method did not track the active
simulation results well, with peaks at 12um and 18um and relatively low thresholds for
small diameter fibers. The Warman method did not track the behavior of the active axon.
3.3 Computational runtime
Computational runtimes were measured to quantify the computational efficiency
provided by the single node and weighted sum methods. Simulation run time results
Figure 7-8 Stimulation threshold across prediction methods for an eleven-electrode
arrangement
Normalized stimulation threshold as a function of axon diameter for an alternating six-
anode, five-cathode electrode pattern aligned longitudinally to the simulated axon.
Adjacent electrode spacing was set to 650 um with pulse duration equal to 20 us. Results
are plotted for active axon simulations and the three activation prediction methods.
Results are shown for electrode-to-axon spacing values of a) 50 um and b) 300 um.
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showed a marked increase in computational speed over the active axon simulations for
both the single node and weighted sum methods (Table 1).
Table 7-1 Computation time consumed by numeric simulation and each proposed
prediction method
Computation Runtime - 16,040 Axons
Method Time (s)
Active Axon 2701.96
Single Node Method 0.126
Weighted Sum Method 0.137
4. Discussion
4.1 Activation thresholds are a function of extracellular potential
Results from the active axon simulations revealed an important dependence on Ve
for the activation threshold. The single node method exhibited increasing threshold with
decreasing Ve values, whereas the weighted sum method showed a decreasing threshold
with decreasing Ve values (Figure 6-2 versus 6-3). The single node method only
accounts for 2Ve at a single node of Ranvier. For cathodic stimulation, 2
Vewill be
positive and large at the node most likely to activate.2Ve at the two nodes adjacent to
this node, however, will also be large but negative. Because the weighted sum method
includes these nodes with negative 2Ve, the result of the MDF2 will be lower. This effect
is increased in cases of low Ve and high 2Ve, leading to a general shift of the ordinate
values down for the weighted sum as 2Ve increases.
The most important aspect of these new methods is recognizing the impact that
the magnitude of the extracellular potential has on the activation threshold. This
relationship has not been reported previously. Including the activation threshold
dependence on Ve improved the prediction accuracy over the Warman method (Figure 6-
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4.a), addressing errors in the linearized models and activation prediction presented by
Moffitt (Moffitt et al., 2004). Axon diameter dependence was the other unique factor
included in the activation threshold of the single node and weighted sum methods, which
contributed to the improved accuracy in relative activation across fiber diameter, but
otherwise the observed impact to accuracy was small in comparison. These findings are
applicable in modeling studies that rely on 2Ve to predict activation volumes (Butson
and McIntyre, 2008; Choi and Lee, 2006; Maks et al., 2009). The implication of
increased threshold at low extracellular potential is that actual activation will be less than
that predicted using a constant threshold value. This could significantly affect
interpretation of modeling studies working to predict the mechanisms and active brain
regions resulting from treatments and therapies, such as deep brain stimulation for
movement disorders.
4.2 Single point source performance
The analysis of the presented prediction methods was
designed to investigate aspects important to nerve-level modeling. Placement within a
nerve, alignment of the nodes of Ranvier, and axon diameter are the important
randomized variables included in a nerve-level simulation (Grinberg et al., 2008; Schiefer
et al., 2008; Veltink et al., 1988).Both the weighted sum and single node methods were
robust to changes in EAS. Accuracy of these methods should not be affected by
randomized placement within the simulated nerve, whereas the Warman method would
require tuning for each EAS to minimize error (Figure 6-4.a). To verify that the MRG
model was appropriate for investigating electrode-node alignment, MRG axon simulation
results were compared to experimental data presented by (Roberts and Smith, 1973).The
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MRG axon simulations reflected this data well as alignment was changed (Results not
shown).Changing electrode-node alignment showed the weighted sum method most
closely matched the behavior of the MRG axon model (Figure 6-4.b).The flat response
observed for most electrode-node alignments using these methods is important because
nodal alignment is usually randomized with a uniform probability distribution. The
weighted sum method stimulation threshold error was below 2% across 90% of the
uniform distribution range and below 5% across 95.8% of the uniform distribution range.
The single node method was much more sensitive to misalignment than the weighted sum
method, with stimulation error maintained below 2% over only about 60% of the
distribution and below 5% for less than 80% of the uniform distribution. Predictions
based on both new methods should be robust as axon diameter is randomized; as both
new methods also showed relative activation thresholds that closely matched the active
MRG axon results (Figure 6-4.c). Recruitment order is important, but so is the relative
magnitude between diameters. The Warman method results illustrate how poor relative
magnitude tracking may hide other effects. The Warman method results showed the
correct recruitment order, but the relative change from diameter to diameter was too
great. It appears that there may have been an increase in threshold for fiber diameters 14-
16um in Figure 6-8.a, but the change is dwarfed by the change in threshold as a function
of diameter.
4.3 Performance differences between methods
With the exception of the electrode alignment to the node of Ranvier, the two
proposed methods are effectively equivalent for single point source stimulation. When
the pulse was localized to the space around a single node of Ranvier, as was generally the
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case with the single point source, both the single node and weighted sum methods could
account for the important aspects of the stimulation waveform. The weighted sum
method starts to out-perform the single node method when the spatial extent of the non-
zero field extends beyond the area around a single node and significant current
redistributes to the investigated node. Single and multiple point source data supports this
as accuracy decreased compared to the weighted sum method (Figures 6-4.a, b; 6-6; 6-
8.b).
4.4 Replicating key findings from literature
Two of the simulations performed were chosen specifically to test activation
prediction performance under conditions used in literature presenting key findings. This
is not to suggest that these methods can or should be used in future studies about specific
axon activation behavior, but is offered instead to show that these methods do capture
important behavior useful to nerve electrode design and gaining insight into behavior in
electrically stimulated systems. The first set of simulations regarding replicating key
findings looked at the relationship between pulse duration and spatial selectivity observed
and experimentally confirmed by Grill and Mortimer (Grill and Mortimer, 1996).The
results of all three prediction methods demonstrated behavior similar to the active axon
simulations and reflected the results published by Grill and Mortimer.
The second case was chosen to explore stimulation designed to influence
recruitment order. Lertmanorat et al. found that recruitment order could be influenced by
manipulating 2Ve sampled at the nodes to increase stimulation threshold for larger axons
above that for smaller axons (Lertmanorat and Durand, 2004), and later confirmed this
experimentally (Lertmanorat et al., 2006). The two key findings by Lertmanorat et al.
128
were that first, that recruitment order can be influenced by the electrode arrangement, and
second, that this effect is reduced as EAS increased. We found that both the single node
and weighted sum methods could be used to draw the first conclusion, with both showing
increased stimulation threshold for axons 14-16 m in diameter (Figure 6-8.a). Only the
weighted sum method illustrated that with increased EAS, the re-ordered recruitment
order effects were largely lost, as was the case with the active axon simulations (Figure
6-8.b). The Warman method results failed to support either of the two conclusions.
4.5 Computational run time comparison
The results of the measured computational run times show that both the single
node and weighted sum methods provided several orders of magnitude of increased
computational efficiency, as expected. For this simulation set, the single node method
was 8% faster than the weighted sum method. This helps to quantify the relative
computation cost of the more complex weighted sum method over the single node
method. The additional cost of 8% of computational speed is small when considering the
benefit of increased prediction accuracy for the weighted sum method over the single
node method. With either of the new methods, one million axons can be simulated in less
than 10 seconds with minimal error or loss of insight, compared to nearly 2 days for the
active model.
4.6 Applicability to other models
In this paper, we have shown that this method can predict activation of the
double-cable MRG axon model. The method is also extensible to other non-linear neural
models. This method has been applied to single-cable models with infinite myelin
resistance using channel dynamics described by(Frankenhaeuser and Huxley, 1964)or by
129
Sweeney et al. (Sweeney et al., 1987). In both cases, a distinct boundary between
inactivation and activation was observed that had a similar dependence on Ve as that seen
with the MRG model (results not shown). This indicates that the behavior observed here
is not merely an artifact of the double-cable formulation nor the MRG model channel
dynamics. Threshold boundaries observed with these additional models were different
from the MRG-based threshold. Consequently, activation thresholds and weights need to
be generated for the nonlinear axon model used. Fiber diameter also affected the
threshold level, so threshold and weight values should be generated for the range of fiber
diameters of interest.
The approximation does not require that the axon path be constrained to a straight
line. Activation prediction has been performed accurately for axons following non-
straight paths through an external electric field (results not shown). Because the proposed
methods are based only on the extracellular potential at nodes of Ranvier, and do not
depend on how the extracellular potential was generated, a tortuous axon path would only
result in different potential values at the nodes. This assumes that bends in the axon are
not such that they cause model variations of intracellular conductivity or channel
dynamics. The final caveat is that these methods have only been applied to axons that are
long enough to avoid termination effects from cell bodies or synapses. Therefore, this
method is not appropriate for prediction in cases of termination, dendrites, cell bodies,
split axons, or other configurations where intracellular conductivities or models that
differ between adjacent compartments.
Recent work has included a more detailed accounting of the effects of the axon on
the resulting electric field (Butson et al., 2011). In many cases the influence of axons on
130
the stimulating electric field is neglected in nerve level simulations (Choi and Lee, 2006;
Lertmanorat et al., 2006; Schiefer et al., 2008).The presented methods only consider the
extracellular potential at the nodes of Ranvier and are not dependent on how the field is
generated. If more detail to the extracellular potential field generation is to be considered,
e.g. the influence of surrounding active axons, the present methods of analysis should still
predict activation within this more complicated field.
5. Conclusion
We have presented two activation prediction methods that perform better than
previous prediction methods and are computationally efficient. Performance of both new
methods shows a decreased dependence on electrode-axon geometry over previous
methods, bringing activation prediction closer to an analysis of the spatial and temporal
properties of the applied electric field. The weighted sum method exhibits the best
prediction accuracy among the three investigated methods, and should be selected for
applications when electric field extends beyond the area around a single node of Ranvier.
This method is computationally faster than numerically solving the nonlinear axon
dynamics by orders of magnitude, but maintains important behavior of the axon. This
allows nearly instantaneous determination of activation patterns in whole nerve
simulations, and opens the door to applications of stimulation design using evolutionary
optimization methods or quickly evaluating and understanding design tradeoffs.
Acknowledgements
The authors would like to thank Prof. Hillel Chiel, Dr. Matthew Schiefer, and Natalie
Brill for their assistance and feedback in reviewing this manuscript.
131
The project described was supported by Grant Number T32-EB004314 from the NIBIB
and the National Institutes of Health. The content is solely the responsibility of the
authors and does not necessarily represent the official views of the National Institutes of
Health
Appendix I.A – Threshold Generation and Activation Prediction
Generating the activation threshold data is the most computationally intensive part
of the proposed methods. It requires active axon simulations for a set of extracellular
voltage vectors repeated across the range of fiber diameters and pulse durations of
interest. Once the activation threshold is generated, it can be used repeatedly in analyzing
extracellular potentials to predict activation without simulating active axon models. The
purpose of this section is to provide additional details on how to generate activation
thresholds and perform activation prediction. Activation thresholds are generated as
follows:
1) Create array of test vectors, each satisfying a pair of unique parameters Ve and
2Ve at the center node. Set the remaining nodal voltages to transition to flat
potential at the ends of the axon, and interpolate the internodal voltages.
2) Simulate each voltage vector, fiber diameter, and pulse duration combination
with the following characteristics:
a) Allow a short time for the model to stabilize before stimulus is applied
b) Apply the extracellular voltage vector to the active axon model in time
as a square pulse of cathodic excitation for the given pulse duration
c) Allow time after the end of the pulse for action potentials to propagate
132
3) Determine which nodes fully depolarized in order to detect whether action
potentials were triggered and propagated
4) For each simulation result, plot whether the fiber was activated or not. These
results are plotted as a function of fiber diameter, pulse duration, Ve at the
center node, and the result of applying the MDF to the extracellular potential
vector used for that particular simulation.
5) Record the threshold as the boundary between regions of activation and
inactivation.
Once the threshold is recorded, activation predictions can be made with simple
computations and the use of a look up table. To predict whether activation would occur
given an extracellular potential, apply the MDF to the extracellular potential vector.
Using the look up table, and interpolation if necessary, determine the threshold for
activation, taking into account fiber diameter, pulse duration, and Ve. If the result of the
MDF is greater than the activation threshold, then the axon is predicted active. Activation
thresholds and weight values should be recalculated for any major changes in the
underlying axon model, as we have observed that threshold values change as different
channel dynamics are implemented.
Because of the overhead required for generating the activation thresholds, these
methods are most applicable for determining the response of many axons under many
different applied electric fields. It does not make sense as a replacement for running tens
of thousands of axons if the threshold and weighted sum values have not been generated,
since the threshold generation would require active axon simulations on that order. While
in this work the set of extracellular voltage vectors were created using a regular spacing
133
of Ve and 2Ve, a binary search algorithm could instead be employed to find the
threshold transition and reduce the number of simulations required for generating the
activation threshold. To reduce overhead when using the MRG axon model, the authors
have included the weights and threshold values generated for this work in the
supplemental materials.
134
APPENDIX II: NEURON CODE
Descriptions of Membrane Dynamics
Memcap.mod : Current associated with temperature-drive membrane capacitance
change
NEURON {
SUFFIX memcap
NONSPECIFIC_CURRENT i
RANGE i, cd, dur, del
RANGE therm_relax, vr
}
PARAMETER {
del = 50 (ms) < 0, 1e9> : IR pulse delay cannot be
less than zero
dur = 0.25 (ms) < 1e-9, 1e9 > : prevent zero or negative
pulses
cd = 0 (microfarad/cm2) : capacitance delta due to laser
pulse
therm_relax = 90 (ms) < 1e-9, 1e9 > : exponential thermal
relaxation time
vr = 100 (millivolts) : reversal potential for capacitive
current
}
ASSIGNED {
i (milliamps/cm2)
v (millivolts)
}
INITIAL {
i = 0
}
: wanted to implement something like: i = v*(basecap+deltacap)'
: but NEURON does not like derivatives on the right hand side
: for this implementation, compute dC/dt and implement that as a
current source
BREAKPOINT {
if (t < del) {
i = 0
}
if (t >= del && t <= del+dur) { : energy deposition phase
i = (0.001) * ((v-vr) * cd / dur) : 0.001 converts the
result into mA from A
}
135
if ( t > del+dur ) { : thermal relaxation phase
i = (0.001) * ((v-vr) * cd * exp(-(t-
(del+dur))/therm_relax) * -1/therm_relax)
}
}
HH_t.mod
This is a modified version of the HH.mod file distributed with the NEURON simulation
environment, modified to enable setting local temperature values in distributed axon
models.
TITLE hh_t.mod squid sodium, potassium, and leak channels
COMMENT
This is the original Hodgkin-Huxley treatment for the set of
sodium, potassium, and leakage channels found in the squid giant
axon membrane.
("A quantitative description of membrane current and its
application conduction and excitation in nerve" J.Physiol.
(Lond.) 117:500-544 (1952).)
Membrane voltage is in absolute mV and has been reversed in
polarity from the original HH convention and shifted to reflect a
resting potential of -65 mV.
Remember to set celsius=6.3 (or whatever) in your HOC file.
See squid.hoc for an example of a simulation using this model.
SW Jaslove 6 March, 1992
ENDCOMMENT
: this mod file has been modified to accept a “localtemp”
variable in place of the global variable “Celsius” to allow for
temperature gradients in spatially-distributed axon models
UNITS {
(mA) = (milliamp)
(mV) = (millivolt)
(S) = (siemens)
}
? interface
NEURON {
SUFFIX hh_t
USEION na READ ena WRITE ina
USEION k READ ek WRITE ik
NONSPECIFIC_CURRENT il
RANGE gnabar, gkbar, gl, el, gna, gk
RANGE localtemp
RANGE minf, hinf, ninf, mtau, htau, ntau
THREADSAFE : assigned GLOBALs will be per thread
}
136
PARAMETER {
gnabar = .12 (S/cm2) <0,1e9>
gkbar = .036 (S/cm2) <0,1e9>
gl = .0003 (S/cm2) <0,1e9>
el = -54.3 (mV)
}
STATE {
m h n
}
ASSIGNED {
v (mV)
:celsius (degC)
localtemp (degC)
ena (mV)
ek (mV)
gna (S/cm2)
gk (S/cm2)
ina (mA/cm2)
ik (mA/cm2)
il (mA/cm2)
minf hinf ninf
mtau (ms)
htau (ms)
ntau (ms)
}
? currents
BREAKPOINT {
SOLVE states METHOD cnexp
gna = gnabar*m*m*m*h
ina = gna*(v - ena)
gk = gkbar*n*n*n*n
ik = gk*(v - ek)
il = gl*(v - el)
}
INITIAL {
rates(v)
m = minf
h = hinf
n = ninf
}
? states
DERIVATIVE states {
rates(v)
137
m' = (minf-m)/mtau
h' = (hinf-h)/htau
n' = (ninf-n)/ntau
}
? rates
PROCEDURE rates(v(mV)) { :Computes rate and other constants at
current v.
:Call once from HOC to initialize inf at
resting v.
LOCAL alpha, beta, sum, q10
:TABLE minf, mtau, hinf, htau, ninf, ntau DEPEND celsius
FROM -100 TO 100 WITH 200
TABLE minf, mtau, hinf, htau, ninf, ntau DEPEND localtemp
FROM -100 TO 100 WITH 200
UNITSOFF
:q10 = 3^((celsius - 6.3)/10)
q10 = 3^((localtemp - 6.3)/10)
:"m" sodium activation system
alpha = .1 * vtrap(-(v+40),10)
beta = 4 * exp(-(v+65)/18)
sum = alpha + beta
mtau = 1/(q10*sum)
minf = alpha/sum
:"h" sodium inactivation system
alpha = .07 * exp(-(v+65)/20)
beta = 1 / (exp(-(v+35)/10) + 1)
sum = alpha + beta
htau = 1/(q10*sum)
hinf = alpha/sum
:"n" potassium activation system
alpha = .01*vtrap(-(v+55),10)
beta = .125*exp(-(v+65)/80)
sum = alpha + beta
ntau = 1/(q10*sum)
ninf = alpha/sum
}
FUNCTION vtrap(x,y) { :Traps for 0 in denominator of rate eqns.
if (fabs(x/y) < 1e-6) {
vtrap = y*(1 - x/y/2)
}else{
vtrap = x/(exp(x/y) - 1)
}
}
UNITSON
FH_t.mod
138
This is a modified version of the FH.mod file distributed with the NEURON
simulation environment, modified to enable setting local temperature values in
distributed axon models.
TITLE FH_t channel
: Frankenhaeuser - Huxley channels for Xenopus
NEURON {
SUFFIX fh_t
USEION na READ nai, nao WRITE ina
USEION k READ ki, ko WRITE ik
NONSPECIFIC_CURRENT il, ip
RANGE pnabar, pkbar, ppbar, gl, el, il, ip
RANGE localtemp
GLOBAL inf,tau
}
UNITS {
(molar) = (1/liter)
(mM) = (millimolar)
(mV) = (millivolt)
(mA) = (milliamp)
FARADAY = (faraday) (coulomb)
R = (k-mole) (joule/degC)
}
PARAMETER {
v (mV)
celsius (degC) : 20
pnabar=8e-3 (cm/s)
ppbar=.54e-3 (cm/s)
pkbar=1.2e-3 (cm/s)
nai (mM) : 13.74
nao (mM) : 114.5
ki (mM) : 120
ko (mM) : 2.5
gl=30.3e-3 (mho/cm2)
el = -69.74 (mV)
}
STATE {
m h n p
}
ASSIGNED {
ina (mA/cm2)
ik (mA/cm2)
ip (mA/cm2)
il (mA/cm2)
inf[4]
tau[4] (ms)
localtemp (degC)
139
}
INITIAL {
mhnp(v*1(/mV))
m = inf[0]
h = inf[1]
n = inf[2]
p = inf[3]
}
BREAKPOINT {
LOCAL ghkna
SOLVE states METHOD cnexp
ghkna = ghk(v, nai, nao)
ina = pnabar*m*m*h*ghkna
ip = ppbar*p*p*ghkna
ik = pkbar*n*n*ghk(v, ki, ko)
il = gl*(v - el)
}
FUNCTION ghk(v(mV), ci(mM), co(mM)) (.001 coul/cm3) {
:assume a single charge
LOCAL z, eci, eco
:z = (1e-3)*FARADAY*v/(R*(celsius+273.15))
z = (1e-3)*FARADAY*v/(R*(localtemp+273.15))
eco = co*efun(z)
eci = ci*efun(-z)
ghk = (.001)*FARADAY*(eci - eco)
}
FUNCTION efun(z) {
if (fabs(z) < 1e-4) {
efun = 1 - z/2
}else{
efun = z/(exp(z) - 1)
}
}
DERIVATIVE states { : exact when v held constant
mhnp(v*1(/mV))
m' = (inf[0] - m)/tau[0]
h' = (inf[1] - h)/tau[1]
n' = (inf[2] - n)/tau[2]
p' = (inf[3] - p)/tau[3]
}
UNITSOFF
FUNCTION alp(v(mV),i) { LOCAL a,b,c,q10 :rest = -70 order
m,h,n,p
v = v+70
:q10 = 3^((celsius - 20)/10)
q10 = 3^((localtemp - 20)/10)
140
if (i==0) {
a=.36 b=22. c=3.
alp = q10*a*expM1(b - v, c)
}else if (i==1){
a=.1 b=-10. c=6.
alp = q10*a*expM1(v - b, c)
}else if (i==2){
a=.02 b= 35. c=10.
alp = q10*a*expM1(b - v, c)
}else{
a=.006 b= 40. c=10.
alp = q10*a*expM1(b - v , c)
}
}
FUNCTION bet(v,i) { LOCAL a,b,c,q10 :rest = -70 order m,h,n,p
v = v+70
:q10 = 3^((celsius - 20)/10)
q10 = 3^((localtemp - 20)/10)
if (i==0) {
a=.4 b= 13. c=20.
bet = q10*a*expM1(v - b, c)
}else if (i==1){
a=4.5 b= 45. c=10.
bet = q10*a/(exp((b - v)/c) + 1)
}else if (i==2){
a=.05 b= 10. c=10.
bet = q10*a*expM1(v - b, c)
}else{
a=.09 b= -25. c=20.
bet = q10*a*expM1(v - b, c)
}
}
FUNCTION expM1(x,y) {
if (fabs(x/y) < 1e-6) {
expM1 = y*(1 - x/y/2)
}else{
expM1 = x/(exp(x/y) - 1)
}
}
PROCEDURE mhnp(v) {LOCAL a, b :rest = -70
:TABLE inf, tau DEPEND celsius FROM -100 TO 100 WITH 200
TABLE inf, tau DEPEND localtemp FROM -100 TO 100 WITH 200
FROM i=0 TO 3 {
a = alp(v,i) b=bet(v,i)
tau[i] = 1/(a + b)
inf[i] = a/(a + b)
}
}
UNITSON
141
Axnode_t.mod
This is a modified version of AXNODE.mod. AXNODE.mod is available in the
model database maintained by the creators of the NEURON simulation environment.
TITLE Motor Axon Node channels
: 3/12
: Erik Peterson
:
: Adapted from original code by
: Cameron C. McIntyre
:
: Fast Na+, Persistent Na+, Slow K+, and Leakage currents
: responsible for nodal action potential
: Iterative equations H-H notation rest = -80 mV
:
: This model is described in detail in:
:
: McIntyre CC, Richardson AG, and Grill WM. Modeling the
excitability of
: mammalian nerve fibers: influence of afterpotentials on the
recovery
: cycle. Journal of Neurophysiology 87:995-1006, 2002.
:
: *Adapted to use localtemp as a range variable instead of using
the global celsius variable*
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
SUFFIX axnode_t
NONSPECIFIC_CURRENT ina
NONSPECIFIC_CURRENT inap
NONSPECIFIC_CURRENT ik
NONSPECIFIC_CURRENT il
RANGE gnapbar, gnabar, gkbar, gl, ena, ek, el
RANGE mp_inf, m_inf, h_inf, s_inf
RANGE tau_mp, tau_m, tau_h, tau_s
RANGE localtemp
}
UNITS {
(mA) = (milliamp)
(mV) = (millivolt)
}
PARAMETER {
142
gnapbar = 0.01 (mho/cm2)
gnabar = 3.0 (mho/cm2)
gkbar = 0.08 (mho/cm2)
gl = 0.007 (mho/cm2)
ena = 50.0 (mV)
ek = -90.0 (mV)
el = -90.0 (mV)
:celsius (degC)
localtemp (degC)
dt (ms)
v (mV)
vtraub=-80
ampA = 0.01
ampB = 27
ampC = 10.2
bmpA = 0.00025
bmpB = 34
bmpC = 10
amA = 1.86
amB = 21.4
amC = 10.3
bmA = 0.086
bmB = 25.7
bmC = 9.16
ahA = 0.062
ahB = 114.0
ahC = 11.0
bhA = 2.3
bhB = 31.8
bhC = 13.4
asA = 0.3
asB = -27
asC = -5
bsA = 0.03
bsB = 10
bsC = -1
}
STATE {
mp m h s
}
ASSIGNED {
inap (mA/cm2)
ina (mA/cm2)
ik (mA/cm2)
il (mA/cm2)
mp_inf
m_inf
h_inf
s_inf
tau_mp
143
tau_m
tau_h
tau_s
q10_1
q10_2
q10_3
}
BREAKPOINT {
SOLVE states METHOD cnexp
inap = gnapbar * mp*mp*mp * (v - ena)
ina = gnabar * m*m*m*h * (v - ena)
ik = gkbar * s * (v - ek)
il = gl * (v - el)
}
DERIVATIVE states { : exact Hodgkin-Huxley equations
evaluate_fct(v)
mp'= (mp_inf - mp) / tau_mp
m' = (m_inf - m) / tau_m
h' = (h_inf - h) / tau_h
s' = (s_inf - s) / tau_s
}
UNITSOFF
INITIAL {
:
: Q10 adjustment
:
: q10_1 = 2.2 ^ ((celsius-20)/ 10 )
: q10_2 = 2.9 ^ ((celsius-20)/ 10 )
: q10_3 = 3.0 ^ ((celsius-36)/ 10 )
q10_1 = 2.2 ^ ((localtemp-20)/ 10 )
q10_2 = 2.9 ^ ((localtemp-20)/ 10 )
q10_3 = 3.0 ^ ((localtemp-36)/ 10 )
evaluate_fct(v)
mp = mp_inf
m = m_inf
h = h_inf
s = s_inf
}
PROCEDURE evaluate_fct(v(mV)) { LOCAL a,b,v2
a = q10_1*vtrap1(v)
b = q10_1*vtrap2(v)
tau_mp = 1 / (a + b)
mp_inf = a / (a + b)
144
a = q10_1*vtrap6(v)
b = q10_1*vtrap7(v)
tau_m = 1 / (a + b)
m_inf = a / (a + b)
a = q10_2*vtrap8(v)
b = q10_2*bhA / (1 + Exp(-(v+bhB)/bhC))
tau_h = 1 / (a + b)
h_inf = a / (a + b)
v2 = v - vtraub : convert to traub convention
a = q10_3*asA / (Exp((v2+asB)/asC) + 1)
b = q10_3*bsA / (Exp((v2+bsB)/bsC) + 1)
tau_s = 1 / (a + b)
s_inf = a / (a + b)
}
FUNCTION vtrap(x) {
if (x < -50) {
vtrap = 0
}else{
vtrap = bsA / (Exp((x+bsB)/bsC) + 1)
}
}
FUNCTION vtrap1(x) {
if (fabs((x+ampB)/ampC) < 1e-6) {
vtrap1 = ampA*ampC
}else{
vtrap1 = (ampA*(x+ampB)) / (1 - Exp(-(x+ampB)/ampC))
}
}
FUNCTION vtrap2(x) {
if (fabs((x+bmpB)/bmpC) < 1e-6) {
vtrap2 = -bmpA*bmpC
}else{
vtrap2 = (bmpA*(-(x+bmpB))) / (1 - Exp((x+bmpB)/bmpC))
}
}
FUNCTION vtrap6(x) {
if (fabs((x+amB)/amC) < 1e-6) {
vtrap6 = amA*amC
}else{
vtrap6 = (amA*(x+amB)) / (1 - Exp(-(x+amB)/amC))
}
}
FUNCTION vtrap7(x) {
145
if (fabs((x+bmB)/bmC) < 1e-6) {
vtrap7 = -bmA*bmC
}else{
vtrap7 = (bmA*(-(x+bmB))) / (1 - Exp((x+bmB)/bmC))
}
}
FUNCTION vtrap8(x) {
if (fabs((x+ahB)/ahC) < 1e-6) {
vtrap8 = -ahA*ahC
}else{
vtrap8 = (ahA*(-(x+ahB))) / (1 - Exp((x+ahB)/ahC))
}
}
FUNCTION Exp(x) {
if (x < -100) {
Exp = 0
}else{
Exp = exp(x)
}
}
UNITSON
Ca_track.mod COMMENT
NEURON implementation to keep track of cai based on injected
calcium (handled in another mechanism)
ENDCOMMENT
NEURON {
SUFFIX ca_track
USEION ca READ ica WRITE cai
RANGE tau, C0
}
UNITS {
(mA) = (milliamp)
(mol) = (1)
(molar) = (mol/liter)
(mM) = (millimolar)
(uM) = (micromolar)
(um) = (micrometer)
FARADAY = (faraday) (coulombs)
}
PARAMETER {
tau = 303 (ms) : AB soma; 300 ms for PD soma
C0 = 0.5 (uM)
146
}
ASSIGNED {
ica (mA/cm2)
diam (um)
}
STATE {
cai (mM)
}
INITIAL {
cai = (1e-3)*C0
}
BREAKPOINT {
SOLVE states METHOD cnexp
}
COMMENT
Surface area of a cyl of length len is PI*len*diam
so net ca influx is -(ica/(2*FARADAY))*PI*len*diam
Volume is PI*len*diam^2/4
so in the absence of buffering or transport
rate of change of conc is -(ica/(2*FARADAY))*4/diam
ENDCOMMENT
DERIVATIVE states {
cai' = -(1e4)*2*ica/(FARADAY*diam) : remove buffering and
transport + (1e-3)*(C0 - (1e3)*cai)/tau
}
Cagk.mod
Cagk.mod was obtained from the model database for NEURON:
http://senselab.med.yale.edu/ModelDB/ShowModel.asp?model=3509
CaSquare.mod
This mod file implements a rectangular intracellular calcium release given delay, duration
, and amplitude variables.
NEURON {
POINT_PROCESS CaSquare
USEION ca WRITE ica
RANGE del, dur, amp
}
UNITS {
(nA) = (nanoamp)
147
}
PARAMETER {
del (ms)
dur (ms)
amp (nA) : negative is inward
}
ASSIGNED {
ica (nA)
}
BREAKPOINT {
at_time(del)
at_time(del + dur)
if (t > del && t < del + dur) {
ica = amp
}else{
ica = 0
}
}
CaTherm.mod
This mod file implements an intracellular calcium release that follows the temperature
change profile caused by infrared light pulses.
NEURON {
POINT_PROCESS CaTherm
USEION ca WRITE ica
RANGE del, dur, amp
RANGE tau
}
UNITS {
(nA) = (nanoamp)
}
PARAMETER {
del (ms)
dur (ms)
amp (nA) : negative is inward
tau = 90 (ms) < 1e-9, 1e9 > : exponential thermal relaxation
time
}
ASSIGNED {
ica (nA)
}
148
BREAKPOINT {
if (t < del) {
ica = 0 : no activity before the delay has passed
}
if (t >= del && t <= del+dur) { : energy deposition phase
ica = amp * (t-del)/dur : linear ramp during
deposition
}
if ( t > del+dur ) { : thermal relaxation phase
ica = amp * exp(-(t-(del+dur))/tau) * -1/tau
}
}
Spatially-Lumped Membrane Models
HHMembrane.hoc
/*---------------------------------------------------------
--------------------
Written by: Erik J. Peterson
Updated: Dec 2012
Implements a spatially-lumped membrane with HH channels,
applies a transient temperature and membrane capacitance
change. Meant to replicate results observed by Shapiro et
al. in "Infrared light excites cells by changing their
electrical capacitance"
(data supplied in supplemental material)
-----------------------------------------------------------
------------------*/
second_order = 2 //0 - reverse Euler; 1 - Crank-Nicholson
(CN); 2- 2nd order CN
cvode_active(0)
///////////////////////////////////////////////////////////
////////////////////////////////////////////////////////
// Define all of the model global variables
proc model_globals() {
//print "-D- Entered Model Globals"
celsius = 6.3 // degC
basetemp = celsius
mxtmpjmp = 15 // maximum temperature jump that takes
place during pulse
v_init=-65 //mV
dt=0.005 //msec
tstop=50 //msec
149
del = 10 //msec
// EDIT HERE for model differences
fiberD = 10 // um (initial value)
pulsedur = 1 // ms
tmpdelta = 15 // temperature increase per ms of
applied pulse
capdelta = 0.08 // cm increase factor
k1 = 1 // capacitance change scale factor
k2 = 1 // temperature change scale factor
coupled_T_C = 1 // when 1, capacitance changes are
scaled with temperature changes 8%Cm/15degC. When 0,
temperature peak is constant, and k only affects Cm
// IR pulse paramters
therm_relax = 90 //[ms] - thermal relaxation time
constant
//define the membrane capacitance
cmem = 1 //[uF/cm2]
//print "-D- Leaving Model Globals"
}
model_globals()
create node
// Calculate the dependent variables
///////////////////////////////////////////////////////////
////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////
////////////////////////////////////////////////////////
proc createall() {
//create the single node for this model
create node
node{
nseg=1
diam=fiberD
L=1
cm=cmem //[uF/cm2]
insert hh // insert HH based channel dynamics
ena_hh = 55 //[mV]
el_hh = -55 //10.59892-60
ek_hh =-72
insert extracellular // initialize extracellular
voltage source
150
e_extracellular = 0 // set extracellular voltage
source to ground
// insert the capacitive current element
insert memcap
del_memcap(0.5) = del // delay to
stimulation
dur_memcap(0.5) = pulsedur // pulse
duration
cd_memcap(0.5) = k1* capdelta * cmem // peak
capacitance delta that occurs over the pulse duration
}
finitialize(v_init)
fcurrent()
}
///////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////
/////////////////////////////////////////////////////////
//advance() is a NEURON function that is called at every
time step
proc advance(){
// changes in membrane capacitance appear to follow a
thermal relaxation curve, implement this here
// increases tend to be about 0.8%/mJ deposited or
0.008*power[W]*time applied[ms]
// the tmprl_scale value computed below needs to be
multiplied by the intensity of power below to give the
final capacitance increase
if (t <= del ) {
cap_scale = 0 // no increase in base
capacitance
tmp_scale = 0 // no increase in temperature
} else if (t > del && t <= del + pulsedur) { //
energy deposition phase
// tmprl scale is the fraction of the deposition
time
cap_scale = (t - del)/pulsedur * capdelta
tmp_scale = (t - del)/pulsedur * tmpdelta
} else if (t > del+pulsedur) { //
thermal relaxation phase
// temporal scale is the exponential decay term
cap_scale = capdelta * exp(-(t-
(del+pulsedur))/therm_relax)
151
tmp_scale = tmpdelta * exp(-(t-
(del+pulsedur))/therm_relax)
}
// assign the temperature, membrane capacitance, and
capacitive current
node.cm(0.5) = cmem + k1 * cmem * cap_scale
celsius = basetemp + k2 * tmp_scale
fadvance()
}
///////////////////////////////////////////////////////////
////////////////////////////////////////////////////////
proc main() {
// simulation time
tstop = del + pulsedur + 20
celsius = basetemp
// create axon
createall()
access node
}
main()
xpanel("variables")
xvalue("Capacitive Change Scale (*8%)", "k1", 1,
"main()", 1)
xvalue("Temperature Change Scale (*15degC)", "k2", 1,
"main()", 1)
xvalue("Pulse Duration", "pulsedur",1, "main()", 1)
xvalue("Baseline Temperature", "basetemp", 1,
"main()",1)
xpanel()
FHMembrane.hoc /*---------------------------------------------------------------
--------------
Written by: Erik J. Peterson
Updated: Mar 2012
Implements a single node with HH channels, applies a temperature
and membrane
capacitance change. Meant to replicate results observed by
Shapiro et al. in
152
"Infrared light excites cells by changing their electrical
capacitance"
(data supplied in supplemental material)
NOTE: currently the membrane capacitance is zeroed out. this
needs to be switched back for a proper model.
-----------------------------------------------------------------
------------*/
second_order = 2 //0 - reverse Euler; 1 - Crank-Nicholson (CN);
2- 2nd order CN
cvode_active(0)
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
// Define all of the model global variables
proc model_globals() {
//print "-D- Entered Model Globals"
celsius = 20 // 20
basetemp = celsius //degC
mxtmpjmp = 15 // maximum temperature jump that takes
place during pulse
v_init=-70 //mV
dt=0.0005 //msec
tstop=50 //msec
del = 10 //msec
// EDIT HERE for model differences
fiberD = 10 // um (initial value)
pulsedur = 1 // ms
tmpdelta = 15 // temperature increase per ms of applied
pulse
capdelta = 0.08 // cm increase factor
// IR pulse paramters
therm_relax = 90 //[ms] - thermal relaxation time constant
//define the membrane capacitance
cmem = 1 //[uF/cm2]
//print "-D- Leaving Model Globals"
}
model_globals()
create node
// Calculate the dependent variables
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
proc createall() {
//create the single node for this model
153
//print "-D- Entered Createall"
create node
node{
nseg=1
diam=fiberD
L=10
cm=cmem //[uF/cm2]
insert fh
//insert extracellular // initialize extracellular
voltage source
//e_extracellular = 0 // set extracellular voltage
source to ground
// insert the capacitive current
insert memcap
del_memcap(0.5) = del
dur_memcap(0.5) = pulsedur
cd_memcap(0.5) = capdelta * cmem * pulsedur // this
is the total change in membrane capacitance in [uF/cm2] per ms of
pulse deposited
//cd_memcap(0.5) = capdelta * 1 * pulsedur // this is
the total change in membrane capacitance in [uF/cm2] per ms of
pulse deposited
}
finitialize(v_init)
fcurrent()
//print "-D- Leaving Createall"
}
/////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////
//advance() is a NEURON function that is called at every time
step
proc advance(){
// changes in membrane capacitance appear to follow a
thermal relaxation curve, implement this here
// increases tend to be about 0.8%/mJ deposited or
0.008*power[W]*time applied[ms]
// the tmprl_scale value computed below needs to be
multiplied by the intensity of power below to give the final
capacitance increase
if (t <= del ) {
cap_scale = 0 // no increase in base
capacitance
tmp_scale = 0 // no increase in temperature
} else if (t > del && t <= del + pulsedur) { // energy
deposition phase
// tmprl scale is the fraction of the deposition time
154
cap_scale = (t - del) * capdelta
tmp_scale = (t - del) * tmpdelta
} else if (t > del+pulsedur) { // thermal
relaxation phase
// temporal scale is the exponential decay term
cap_scale = capdelta * pulsedur * exp(-(t-
(del+pulsedur))/therm_relax)
tmp_scale = tmpdelta * pulsedur * exp(-(t-
(del+pulsedur))/therm_relax)
}
// assign the temperature, membrane capacitance, and
capacitive current
node.cm(0.5) = cmem + cmem * cap_scale
//node.cm(0.5) = cmem + cmem * cap_scale *0
celsius = basetemp + tmp_scale
fadvance()
}
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
proc main() {
// simulation time
tstop = del + pulsedur + 20
// printf("-D- tstop is: %0.3f\n", tstop)
// printf("-D- pulsedur is is: %0.3f\n", pulsedur)
// create axon
createall()
access node
}
main()
xpanel("variables")
xvalue("Cm increase factor (per ms of IR pulse)
[uF/cm2/ms]", "capdelta", 1, "main()", 1)
xvalue("Temperature increase (per ms of IR pulse)
[degC/ms]", "tmpdelta", 1, "main()", 1)
xvalue("Pulse Duration", "pulsedur",1, "main()", 1)
xvalue("FiberDiameter", "fiberD",1, "main()", 1)
xvalue("Base Temperature", "basetemp",1, "main()", 1)
xpanel()
HHMembrane_Looped.hoc
This hoc file uses a binary search algorithm to loop through and determine minimum
calcium current necessary to activate the membrane.
155
/*---------------------------------------------------------------
--------------
Written by: Erik J. Peterson
Updated: Nov 2012
Implements a single node with HH channels, applies a temperature
and membrane
capacitance change. Meant to replicate results observed by
Shapiro et al. in
"Infrared light excites cells by changing their electrical
capacitance"
(data supplied in supplemental material)
NOTE: currently the membrane capacitance is zeroed out. this
needs to be switched back for a proper model.
-----------------------------------------------------------------
------------*/
second_order = 0 //0 - reverse Euler; 1 - Crank-Nicholson (CN);
2- 2nd order CN
cvode_active(0)
objref Int_file, out1, out2
// Input file handles - Input is the intensity of stimulation
along an axon
Int_file = new File()
// Output file handles - Two output files
out1 = new File() // Maximum intracellular calcium (cai) reached
out2 = new File() // Max depolarization near the end of the axon
// create the pulsedur and temperature data vectors (simulaiton
loops on these)
objref dur_data, delay_data, temp_data
dur_data = new Vector()
temp_data = new Vector()
delay_data = new Vector()
dur_data.append(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1,
2, 5, 10 )
//dur_data.append(1, 2, 5, 10 )
temp_data.append(6.3, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28,
30, 32, 34, 36, 38)
delay_data.append(0, 0.5, 1, 1.5, 2)
strdef work, cai_output
sprint(work,"/home/erik/DATA/FNI_Lab/LaserStim/ModelingOpticalAct
ivation/IntracellularCalciumRelease/HHMembrane/")
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
// Define all of the model global variables
proc model_globals() {
//print "-D- Entered Model Globals"
celsius = 6.3 // degC
156
basetemp = celsius
mxtmpjmp = 15 // maximum temperature jump that takes
place during pulse
v_init=-65 //mV
dt=0.005 //msec
tstop=50 //msec
del = 10 //msec
// Calcium release parameters
i_calcium = 0 // [nA]
calc_dur = 1 // [ms]
cai_base = 0 // [mM] baseline intracellular calcium value
cai_max = 0 // [mM] variable to store the maximum value
of cai achieved
response_delay = 0
// Capacitive change parameters
pulsedur = 1 // ms
tmpdelta = 15 // temperature increase per ms of applied
pulse
capdelta = 0.08 // cm increase factor
k = 1 // capacitance and temperature change scale
factor
therm_relax = 90 //[ms] - thermal relaxation time constant
//define the membrane capacitance
cmem = 1 //[uF/cm2]
//print "-D- Leaving Model Globals"
}
model_globals()
objectvar calcium_release
create node
// Calculate the dependent variables
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
proc createall() {
//create the single node for this model
create node
node{
nseg=1
diam=10
L=10
cm=cmem //[uF/cm2]
insert hh // insert HH based channel dynamics
ena_hh = 55 //[mV]
el_hh = -55 //10.59892-60
ek_hh =-72
157
// insert the capacitive current element
insert memcap
del_memcap(0.5) = del // 10ms delay to
stimulation
dur_memcap(0.5) = pulsedur // pulse duration
cd_memcap(0.5) = k* capdelta * cmem // peak
capacitance delta that occurs over the pulse duration
// insert intracellular calcium injection
insert ca_track // mechanism for tracking changes in
intracellular calcium based on injected currents
if (cagk_enable == 1) { // run with and without this
hyperpolarizing channel activated
insert cagk // calcium-gated potassium current
}
// insert an intracellular calcium current with either a
square or ramp and exp. decay current pulse
if (square == 0) {
calcium_release = new CaTherm(0.5) //inserted in the
center of the segment
calcium_release.del = del + response_delay
calcium_release.dur = calc_dur
calcium_release.amp = -i_calcium // [nA], negative is
inward
calcium_release.tau = 600 // [ms], exponential decay
at the end slow this down a lot
} else {
calcium_release = new CaSquare(0.5) //inserted in the
center of the segment
calcium_release.del = del + response_delay
calcium_release.dur = calc_dur
calcium_release.amp = -i_calcium // [nA], negative is
inward
}
}
finitialize(v_init)
fcurrent()
}
/////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////
/////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////
//advance() is a NEURON function that is called at every time
step
proc advance(){
// changes in membrane capacitance appear to follow a
thermal relaxation curve, implement this here
// increases tend to be about 0.8%/mJ deposited or
0.008*power[W]*time applied[ms]
158
// the tmprl_scale value computed below needs to be
multiplied by the intensity of power below to give the final
capacitance increase
if (t <= del ) {
cap_scale = 0 // no increase in base
capacitance
tmp_scale = 0 // no increase in temperature
} else if (t > del && t <= del + pulsedur) { // energy
deposition phase
// tmprl scale is the fraction of the deposition time
cap_scale = (t - del)/pulsedur * capdelta
tmp_scale = (t - del)/pulsedur * tmpdelta
} else if (t > del+pulsedur) { // thermal
relaxation phase
// temporal scale is the exponential decay term
cap_scale = capdelta * exp(-(t-
(del+pulsedur))/therm_relax)
tmp_scale = tmpdelta * exp(-(t-
(del+pulsedur))/therm_relax)
}
// assign the temperature, membrane capacitance, and
capacitive current
node.cm(0.5) = cmem + k * cmem * cap_scale
celsius = basetemp + k * tmp_scale
// keep track of the intracellular calcium
if (t < del) {
cai_base = node.cai(0.5)
}
if (node.cai(0.5) > cai_max) {
cai_max = node.cai(0.5)
}
if (node.v(0.5) > vmax) {
vmax = node.v(0.5)
}
fadvance()
}
////////////////////////////////////////////////// FILE I/O
///////////////////////////////////////////////////////
proc print_headers() {
//print "-D- entered print header\n"
// Open the two output files and write out the headers
if (square == 1) {
sprint(cai_output,
"%s/Results/IntracellularCalcium_Square_Delay%.2f_CaGkEn_%d.csv",
work, response_delay, cagk_enable)
} else {
159
sprint(cai_output,
"%s/Results/IntracellularCalcium_Ramp_Delay%.2f_CaGkEn_%d.csv",
work, response_delay, cagk_enable)
}
out1.wopen(cai_output)
out1.printf("%s\n", "Ca++Duration,6.3 C,8.0 C,10.0 C,12.0
C,14.0 C,16.0 C,18.0 C,20.0 C,22.0 C,24.0 C,26.0 C,28.0 C,30.0
C,32.0 C,34.0 C,36.0 C,38.0 C")
out1.close()
}
proc print_calcdur() {
// write out the calcium duration into the first column of
each output file
out1.aopen(cai_output)
out1.printf("%.1f", calc_dur)
out1.close()
}
proc print_results() {
// print each line of results into the above file
out1.aopen(cai_output)
out1.printf(",%.6f",cai_max)
out1.close()
}
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
proc main() {
for square = 0,1 { // test with square calcium pulse and with
ramp to expoentially decreasing
for cagk_enable = 0, 1{ // test with and without calcium
gated potassium channels engaged
for delay_no = 0, delay_data.size()-1{ // add different
delays between capacitive/thermal change and calcium change
response_delay = delay_data.x[delay_no]
print_headers() // Open the output file and write out
the header
for dur_no = 0, dur_data.size-1{ // loop through all
pulse durations
// simulation timing parameters
calc_dur = dur_data.x[dur_no] // [ms] - duration
of the calcium release
tstop = del + calc_dur + response_delay + 20
//set the simulation run time
// write out the fiber diameter into the first
column of each output file
print_calcdur()
for temp_no = 0, temp_data.size()-1 { // execute
sim at many different temperature values
// reset model parameters
// simulation variables
160
celsius = temp_data.x[temp_no]
basetemp = celsius
// Adjust "i_calcium" in a binary search to
find the threshold for the rest of the model parameters
last_amp = 0
current_amp = 0.1 // current value to use for
amplitude
current_result = 0
loop_counter = 0
cap = 1e9 // upper limit on the
amplitude, this is replaced to prevent oscillations
while (abs(last_amp-current_amp) > (.001
*current_amp) ) {
//(re) initialize for the next iteration
vmax = -100
cai_max = 0
i_calcium = current_amp // negative
current is inward
// create membrane and simulate
createall()
access node
run()
//printf("-D- vmax is: %f\n", vmax)
if (vmax > 0) {
//print "-D- found a case that fired!
- amplitude should go down"
last_result = current_result
current_result = 1
} else {
last_result = current_result
current_result = 0
}
// Binary search
if (last_result == 0 && current_result ==
0) {
// last was 0, current is 0 -> double
current amplitude
last_amp = current_amp
current_amp = current_amp * 2
if (current_amp > cap){ // don't
allow this to exceed the cap
current_amp = cap
}
//print "-D- Low Low Going up"
} else if (last_result == 0 &&
current_result == 1) {
//last was 0, current is 1 -> split
amplitude difference
161
//print "-D- amplitude is going down
by a bit"
if (current_amp < cap ){ // set a new
upper limit
cap = current_amp
}
difference = abs(current_amp -
last_amp)
last_amp = current_amp
current_amp = current_amp -
difference/2
//print "-D- Low Hi Going down"
} else if (last_result == 1 &&
current_result == 0) {
// last was 1, current is 0 -> split
amplitude difference up
difference = abs(last_amp -
current_amp)
last_amp = current_amp
current_amp = current_amp +
difference/2
//print "-D- Hi Low Going up"
} else if (last_result == 1 &&
current_result == 1) {
// last was 1, current is 1 -> divide
amplitude of lowest by 2
//print "-D- amplitude is going down
by 1/2"
if (current_amp < cap ){ // set a new
upper limit
cap = current_amp
}
last_amp = current_amp
current_amp = current_amp/2
//print "-D- Hi Hi going down"
}
difference = abs(last_amp - current_amp)
//printf ("-D- check: difference= %.9f
c_amp = %.9f\n", difference, current_amp)
loop_counter = loop_counter +1
} // close the while loop, then print the
results
printf("-D- final amplitude: %f %f %f\n",
current_amp, cai_max, node.cai(0.5))
// write final results to the output file
print_results()
} // end temperature loop
printf ("-I- Completed Ca++ pulse duration:
%.1f\n", calc_dur)
// finish writing the output file lines for each
output file
out1.aopen(cai_output)
162
out1.printf("\n")
out1.close()
} // end duration loop
printf ("-I- Completed Delay: %.1f\n",
response_delay)
} // end delays loop
printf ("-I- Completed CaGk State: %.1f\n", cagk_enable)
}// end cagk loop
printf ("-I- Completed Square State: %.1f\n", square)
}// end pulse shape loop
}
main()
quit()
Spatially-Distributed Axon Models
HHAxon_DiamAndTempSweep.hoc /*---------------------------------------------------------------
--------------
Written by: Erik J. Peterson
Updated: Oct 2012
A single axon expressing Hodgkin & Huxley-described squid giant
axon dynamics.
Output is printed out to the user-selected directory. Results
include:
1) whether each simulation resulted in an action potential
(depolarized above zero)
2) vector of transmembrane voltages for the user-specified
segments (otherwise default = center node)
This extends the model used by Shapiro et al. in
"Infrared light excites cells by changing their electrical
capacitance"
(data supplied in supplemental material)
-----------------------------------------------------------------
------------*/
// set the numerical engine used for solving
second_order = 0 //0 - reverse Euler; 1 - Crank-Nicholson (CN);
2- 2nd order CN
cvode_active(0)
objref Int_file, out1, out2
// Input file handles - Input is the intensity of stimulation
along an axon
Int_file = new File()
// Output file handles - Two output files
163
out1 = new File() // Max depolarization at the center of the axon
out2 = new File() // Max depolarization near the end of the axon
// create the pulsedur, diameter, and temperature data vectors
(simulaiton loops on these)
objref dur_data, diam_data, temp_data
dur_data = new Vector()
diam_data = new Vector()
temp_data = new Vector()
dur_data.append(1, 0.5, 0.1)
diam_data.append(5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20)
temp_data.append(6.3, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28,
30, 32, 34, 36, 38)
strdef work, center_max_result, end_max_result
sprint(work,"~/DATA/FNI_Lab/LaserStim/ModelingOpticalActivation/M
embraneCapacitance/SingleAxonSimulations/HodgkinHuxley_Axon/")
//////////////////////////////-SUBROUTINES-
//////////////////////////////////////////////
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
// Define all of the model global variables
proc model_globals () {
initialT = 6.3 // [degC]
celsius = initialT // [degC], global temperature value
dt=0.001 //msec
tstop=50 //msec
delay=10 //msec
del = delay //msec
// number of 20[um] axon segments (not to be confused with
nseg of each compartment)
axon_segs = 81
deltax = 20 // [um]
cmem = 1 //[uF/cm2] - baseline membrane capacitance
rhoa=1.1e6 //[Ohm-um] specific axoplasmic resistance
(McNeal Model)
v_init=-65.3 //mV - initial resting potential
pi=3.141592654
// EDIT HERE for model differences
fiberD = 10 //um (initial value)
pulsedur = 1 // [ms] - duration of laser pulse used
// depolarization max variables
base_v = v_init
center_max = v_init
end_max = v_init
// define capacitance change per ms pulse
164
deltaC = 8 // [%]
deltaT = 15 // [degC]
pulsedur = 1 // [ms] - duration of laser pulse used
// electrical stimulus parameters
epw = 0 // [ms] - duration of electrical stimulus used
amp = 0 //[mA] amplitude
e_del = 10.9 // [ms] electrical delay to end a 100us
electrical pulse at the same time as a 1ms IR pulse
// IR pulse paramters
therm_relax = 90 //[ms] - thermal relaxation time constant
//electrical parameters
rhoa=1.1e6 //[Ohm-um] specific axoplasmic resistance
rhoe=3e6 //[Ohm-um] specific extracellular
resistance
//print "-D- Leaving Model Globals"
}
model_globals ()
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
//calculate extracellular voltage and infrared light intensity
applied to each node based on position
objref Vext, Intensity, xvec // voltage and light intensity
vectors used for scaling stimulation
Vext=new Vector(axon_segs,0) //extracellular voltage applied
to nodes
xvec=new Vector(axon_segs,0) //x-coordinate for all the nodes
Intensity = new Vector(axon_segs,0)
//calculate xy position of every node
//center of middle node is at the origin
proc xypos(){
xvec.x[0]=-((axon_segs-1)/2)*deltax
for i=1, axon_segs-1 {
xvec.x[i]=xvec.x[i-1]+deltax
//print "node ", i, " x=", x.x[i], " y=", y.x[i]
}
}
//point source extracellular electrode --> V=I*rhoe/(4*pi*r)
proc volt(){
for k=0, axon_segs-1 {
r = sqrt((400)^2 + (xvec.x[k])^2) //[um] distance
from electrode to node[i]. Electrode is 400um from the axon
Istim = amp
Vext.x[k]=(Istim*rhoe)/(4*pi*r) //[mV]
}
}
165
// Include the following to simulate a single Gaussian profile
// intensity follows gaussian distribution along x direction of
axon: y = exp(-0.5 .* x.^2./34000). Designed for 400um 1/e^2
beam size in [um]
proc intensity(){
for k=0, axon_segs-1 {
Intensity.x[k]= exp(-0.5 * xvec.x[k]^2/34000)
//[unitless]
//print "node ", k, " x=", xvec.x[k], " intensity = ",
Intensity.x[k]
}
}
// Include the following to simulate two Gaussian profiles,
offset by the same value “separation”
//// intensity follows gaussian distribution along x direction of
axon
//proc intensity(){
// for k=0, axon_segs-1 {
// //Intensity.x[k]= exp(-0.5 * xvec.x[k]^2/34000)
////[unitless]
// Intensity.x[k]= 1/1.13 (exp(-0.5 * (xvec.x[k] +
separation/2)^2/34000) + exp(-0.5 * (xvec.x[k] -
separation/2)^2/34000))
//print "node ", k, " x=", xvec.x[k], " intensity = ",
Intensity.x[k]
// }
//}
// Include the following to simulate the flat beam profile,
offset by the same value “separation”
//// intensity follows gaussian distribution along x direction of
axon
//proc intensity(){
// for k=0, axon_segs-1 {
// if (xvec.x[k] < -separation/2) { // intensity below
the first peak
// Intensity.x[k] = exp(-0.5 * (xvec.x[k] +
separation/2)^2/34000)
// } else if (xvec.x[k] > separation/2) {
// Intensity.x[k] = exp(-0.5 * (xvec.x[k] -
separation/2)^2/34000)
// } else {
// Intensity.x[k] = 1
// }
//print "node ", k, " x=", xvec.x[k], " intensity = ",
Intensity.x[k]
// }
//}
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
166
create ax_seg[axon_segs]
proc createall() {
//print "-D- Entered Createall"
xypos() // calculate positioning of all nodes
intensity() // calculate gaussian beam distribution
volt() // calculate voltages as a funciton of position
// (re)create the individual segments
create ax_seg[axon_segs]
for a=0,axon_segs-1 {
ax_seg[a]{
nseg=1
diam=fiberD
L=deltax
cm=cmem //[uF/cm2]
Ra=4*(rhoa/10000)/pi * L/(diam*diam) //[Ohm-cm]
specific axoplasmic resistance (From Chiel paper). (Convert Ohm-
um to Ohm-cm)
insert extracellular // enable application of
extracellular voltage later
//printf("-D- Illuminated Segment: %d\n", a)
// insert a current source that replicates the
capacitive current
insert memcap
del_memcap(0.5) = del
dur_memcap(0.5) = pulsedur
cd_memcap(0.5) = deltaC/100 * cmem *
Intensity.x[a] // this is the total change in membrane
capacitance in [uF/cm2] achieved during stim pulse, scaled to
reflect gaussian distribution
vr_memcap(0.5) = 130 //[mV] - value used in Shapiro
et al. model, reversal potential due to surface charges
therm_relax_memcap(0.5) = 90 //[ms] - thermal
relaxation time of bulk nerve tissue, meas. by Wells et al. 2007
// insert HH dynamics that accept a local temperature
increase on top of celsius
insert hh_t
ena_hh_t = 55 // [mV]
ek_hh_t = -72 // [mV]
el_hh_t = 10.59892-60 // leakage current reversal
potential used by Shapiro et al. 2012
}
}
// connect all of the segments to create an axon
for a=0, axon_segs-2 {
connect ax_seg[a+1](0), ax_seg[a](1)
}
167
finitialize(v_init)
fcurrent()
//print "-D- Leaving Createall"
}
/////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////
//advance() is a NEURON function that is called at every time
step.
// this one modifies the membrane capacitance and temperatuer
proc advance(){
// changes in membrane capacitance appear to follow a
thermal relaxation curve, implement this here
// increases tend to be about 0.8%/mJ deposited or
0.008*power[W]*time applied[ms]
// the tmprl_scale value computed below needs to be
multiplied by the intensity of power below to give the final
capacitance increase
if (t <= del ) {
cap_scale = 0 // no increase in base
capacitance
tmp_scale = 0 // no increase in
temperature
} else if (t > del && t <= del + pulsedur) { // energy
deposition phase
// tmporal scale is the fraction of the deposition
time
cap_scale = (t - del)/pulsedur * deltaC/100
tmp_scale = (t - del)/pulsedur * deltaT
} else if (t > del+pulsedur) { // thermal
relaxation phase
// temporal scale is the exponential decay term
cap_scale = deltaC/100 * exp(-(t-
(del+pulsedur))/therm_relax)
tmp_scale = deltaT * exp(-(t-
(del+pulsedur))/therm_relax)
}
if (t > e_del && t <= e_del + epw) { // Monophasic square
pulse is applied
volt_scale = 1
} else {
volt_scale = 0
}
// adjust the temperature, membrane capacitance, and
capacitive current to the illuminated axon segments
for i=0,axon_segs-1 {
newTemp = initialT + tmp_scale * Intensity.x[i]
if (max_temp < newTemp) {
max_temp = newTemp
168
}
// apply extracellular voltage
ax_seg[i].e_extracellular(0.5)=amp * volt_scale *
Vext.x[j] //[mV]
// apply membrane capacitance and temperature change
with time, scaled in space
ax_seg[i].cm(0.5)= cmem * ( 1 + cap_scale *
Intensity.x[i] )
ax_seg[i].localtemp_hh_t(0.5) = newTemp
// apply temperature-dependent change in axoplasmic
resistance
ax_seg[i].Ra = 4*(rhoa/10000)/pi * L/(diam*diam) *
(1/1.3)^((newTemp - initialT)/10) // Q10 from Frijns et al., same
as that of ionic solution
}
// keep track of the maximum membrane depolarization
throughout the simulation (center and distant nodes)
if (t < delay ) {
base_v = ax_seg[10].v(0.5)
} else {
//printf("-D- at time: %f voltage is: %f ", t,
ax_seg[(axon_segs-1)/2].v(0.5))
if (ax_seg[(axon_segs-1)/2].v(0.5) > center_max) {
center_max = ax_seg[(axon_segs-1)/2].v(0.5)
//printf("reassigned center_max to %f", center_max)
}
if (ax_seg[3].v(0.5) > end_max) {
end_max = ax_seg[3].v(0.5)
}
//printf("\n")
}
fadvance()
}
////////////////////////////////////////////////// FILE I/O
///////////////////////////////////////////////////////
proc print_headers() {
//print "-D- entered print header\n"
// Open the two output files and write out the headers
sprint(center_max_result,
"%s/Results/CenterNode_MaxDepolarization_PD%.2f.csv", work,
pulsedur)
out1.wopen(center_max_result)
out1.printf("%s\n", "Diameter,6.3 C,8.0 C,10.0 C,12.0 C,14.0
C,16.0 C,18.0 C,20.0 C,22.0 C,24.0 C,26.0 C,28.0 C,30.0 C,32.0
C,34.0 C,36.0 C,38.0 C")
out1.close()
169
sprint(end_max_result,
"%s/Results/DistantNode_MaxDepolarization_PD%.2f.csv", work,
pulsedur)
out2.wopen(end_max_result)
out2.printf("%s\n", "Diameter,6.3 C,8.0 C,10.0 C,12.0 C,14.0
C,16.0 C,18.0 C,20.0 C,22.0 C,24.0 C,26.0 C,28.0 C,30.0 C,32.0
C,34.0 C,36.0 C,38.0 C")
out2.close()
}
proc print_diameters() {
// write out the fiber diameter into the first column of each
output file
out1.aopen(center_max_result)
out1.printf("%.1f", fiberD)
out1.close()
out2.aopen(end_max_result)
out2.printf("%.1f", fiberD)
out2.close()
}
proc print_results() {
//print "-D- Entered print_results"
// print each line of results into the above file
out1.aopen(center_max_result)
out1.printf(",%.4f",center_max-v_init) // tempresults is
1 if axon did fire, 0 otherwise
out1.close()
// print each line of results into the above file
out2.aopen(end_max_result)
out2.printf(",%.4f",end_max-v_init) // tempresults is 1
if axon did fire, 0 otherwise
out2.close()
//print "-D- Leaving print_results"
}
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
proc main() {
for dur_no = 0, dur_data.size()-1{
// simulation timing parameters
pulsedur = dur_data.x[dur_no] // [ms] - duration of laser
pulse used
tstop = delay + pulsedur + 50 //set the simulation run time
//printf("-D- tstop is: %0.3f\n", tstop)
//printf("-D- pulsedur is is: %0.3f\n", pulsedur)
print_headers() // Open the two output files and write out
the headers
170
for diam_no = 0, diam_data.size()-1{ // execute once per
diameter
fiberD = diam_data.x[diam_no]
deltax = 20 //[um]
// write out the fiber diameter into the first column of
each output file
print_diameters()
for temp_no = 0, temp_data.size()-1 { // execute sim at
many different temperature values
// reset model parameters
// depolarization max variables
base_v = v_init
center_max = v_init
end_max = v_init
// simulation variables
celsius = temp_data.x[temp_no]
initialT = temp_data.x[temp_no]
max_temp = celsius
tmpdelta = 15 // temperature increase per ms of
applied pulse
capdelta = 8 // [%] percent capacitance change
// create axon
createall()
finitialize(v_init)
// run the model created
access ax_seg[0]
run()
printf("-D- max_temp was: %f initial temp was: %f
\n", max_temp, initialT)
// output the final max voltage values
print_results()
} // end temperature loop
printf ("-I- Completed diameter: %.1f\n", fiberD)
// finish writing the output file lines for each output file
out1.aopen(center_max_result)
out1.printf("\n")
out1.close()
out2.aopen(end_max_result)
out2.printf("\n")
out2.close()
} // end diameter loop
printf ("-I- Completed Pulse Duration: %.1f\n", pulsedur)
} // end pulse duration loop
}
main() // auto-execute main
quit() // exit when done
171
MRGAxon_Interactive_LoadBeamShape.hoc /*---------------------------------------------------------------
--------------
Written by: Erik J. Peterson
Updated: Jan 2010
Reads voltage data for all segments of the axon simulated and
determines whether an
Action Potential would have occurred under those conditions.
The model dynamics are described in detail in:
McIntyre CC, Richardson AG, and Grill WM. Modeling the
excitability of
mammalian nerve fibers: influence of afterpotentials on the
recovery
cycle. Journal of Neurophysiology 87:995-1006, 2002.
-----------------------------------------------------------------
------------*/
second_order = 0 //0 - reverse Euler; 1 - Crank-Nicholson (CN);
2- 2nd order CN
cvode_active(1)
objref Int_file, out1, out2
// Input file handles - Input is the intensity of stimulation
along an axon
Int_file = new File()
// Output file handles - Two output files
out1 = new File() // Max depolarization at the center of the axon
out2 = new File() // Max depolarization near the end of the axon
// Delcare objects for Matrices
objref intensity_data
intensity_data = new Matrix(1,221) // 1 is nrow, 221 is the
number for voltage points for a 21 node axon model (ncol)
// Declare string definitions
strdef intensity_to_read, work, center_max_result, end_max_result
sprint(work,"~/DATA/FNI_Lab/LaserStim/ModelingOpticalActivation/M
embraneCapacitance/SingleAxonSimulations/MRG_Axon/")
/// SUBROUTINES ///
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
// Define all of the model global variables
proc model_globals() {
//print "-D- Entered Model Globals"
initialT = 37 // [degC]
celsius = initialT // [degC], global temperature value
v_init=-80 //mV
dt=0.0005 //msec
172
tstop=50 //msec
delay=10 //msec
// depolarization max variables
base_v = v_init
center_max = v_init
end_max = v_init
// EDIT HERE for model differences
fiberD = 10 //um (initial value)
pulsedur = 1 // [ms] - duration of laser pulse used
zshift_no = 0 // control which shifted Ve value is used
amps = 1 // amplitude scaling factor
//Axon topological parameters//
nodes = 21
paranodes1 = 40
paranodes2 = 40
segs_per_internode = 10
internodes = (nodes-1)*(segs_per_internode) - paranodes1 -
paranodes2
num_of_total_segs = nodes + paranodes1 + paranodes2 +
internodes
// define capacitance change per ms pulse
deltaC = 8 // [%]
deltaT = 15 // [degC]
tmpdelta = 15 // temperature increase per ms of applied
pulse
capdelta = 8 // cm increase factor (8% comes from
Shapiro et al. 2012)
// IR pulse paramters
del = delay //[ms] delay to application of laser pulse
therm_relax = 90 //[ms] - thermal relaxation time constant
//define the membrane capacitance
cmem = 2 //[uF/cm2]
//morphological parameters//
paralength1=3 //um
nodelength=1.0 //um
space_p1=0.002 //um
space_p2=0.004 //um
space_i=0.004 //um
//electrical parameters//
rhoa=0.7e6 //Ohm-um
mycm=0.1 //uF/cm2/lamella membrane
mygm=0.001 //S/cm2/lamella membrane
//print "-D- Leaving Model Globals"
}
173
model_globals()
//defaults and initializations
create node[nodes]
create MYSA[paranodes1]
create FLUT[paranodes2]
create STIN[internodes]
// Calculate the dependent variables
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
/*
Originally McIntyre had a number of if statements here such as:
if (fiberD==5.7) {g=0.605 axonD=3.4 nodeD=1.9 paraD1=1.9
paraD2=3.4 deltax=500 paralength2=35 nl=80}
In this version, these values are based equations.
Relationships:
g = 0.0172(FiberDiameter)+0.5076; R^2 =
0.9869
AxonDiameter = 0.889(FiberDiameter)-1.9104; R^2 =
0.9955
NodeDiameter = 0.3449(FiberDiameter)-0.1484; R^2 =
0.9961
paraD1 = 0.3527(FiberDiameter)-0.1804; R^2 =
0.9846
paraD2 = 0.889(FiberDiameter)-1.9104; R^2 =
0.9955
deltax = 969.3*Ln(FiberDiameter)-1144.6; R^2 =
0.9857
paralength2 = 2.5811*(FiberDiameter)+19.59; R^2 =
0.9874
nl = 65.897*Ln(FiberDiameter)-32.666; R^2 =
0.9969
The following equations are techniqually only good for fiber
diameters between 5.7 and 16.0 because
the equations were determined (in Excel) to fit the data over
that range only (y-intercept was not forced).
Matlab randomly chooses fiber diameters and they can range from 3
to 16. Diameters of 3, 4, or 5 may not result
in the correct values here.
LATER NOTE: Diameters of 3 produce negatvie values for deltax.
Therefore, any fiber with a 3um diameter will be
changed to a 4 um diameter fiber.
*/
proc calc_dependents() {
//print "-D- Entering calc_dependents"
g = 0.0172*(fiberD)+0.5076 //??
axonD = 0.889*(fiberD)-1.9104 //diameter of the
axon
174
nodeD = 0.3449*(fiberD)-0.1484 //diameter of the
node
paraD1 = 0.3527*(fiberD)-0.1804 //diameter of
paranode 1
paraD2 = 0.889*(fiberD)-1.9104 //diameter of
paranode 2
deltax = 969.3*log(fiberD)-1144.6 //total length
between nodes (including 1/2 the node on each side)
paralength2 = 2.5811*(fiberD)+19.59 //length of paranode2
nl = 65.897*log(fiberD)-32.666 //number of lamella
Rpn0=(rhoa*.01)/(PI*((((nodeD/2)+space_p1)^2)-
((nodeD/2)^2)))
Rpn1=(rhoa*.01)/(PI*((((paraD1/2)+space_p1)^2)-
((paraD1/2)^2)))
Rpn2=(rhoa*.01)/(PI*((((paraD2/2)+space_p2)^2)-
((paraD2/2)^2)))
Rpx=(rhoa*.01)/(PI*((((axonD/2)+space_i)^2)-((axonD/2)^2)))
interlength=(deltax-nodelength-(2*paralength1)-
(2*paralength2))/6
//print "-D- Leaving calc_dependents"
}
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
proc createall() {
//(re)build the actual axon
//print "-D- Entered Createall"
create node[nodes]
create MYSA[paranodes1]
create FLUT[paranodes2]
create STIN[internodes]
//print "-D- got past creation"
forall insert extracellular // initialize extracellular
voltage source
forall e_extracellular = 0 // set extracellular voltage
source to ground
//print "-D- got past extracellular"
for i=0,nodes-1 {
node[i]{
nseg=1
diam=nodeD
L=nodelength
Ra=rhoa/10000
cm=cmem
insert axnode_t
// the nodes are always assumed affected by the
laser (at least for now)
insert memcap // membrane dynamics that
account for laser induced current
175
del_memcap(0.5) = delay // [ms] delay before
laser pulse
dur_memcap(0.5) = pulsedur // [ms] duration of
laser pulse
cd_memcap(0.5) = 0 // irradiance [W/cm2] of
the laser (it will be overwritten later)
xraxial=Rpn0
xg=1e10
xc=0
}
}
for i=0, paranodes1-1 {
MYSA[i]{
nseg=1
diam=fiberD
L=paralength1
Ra=rhoa*(1/(paraD1/fiberD)^2)/10000
cm=cmem*paraD1/fiberD
insert pas
g_pas=0.001*paraD1/fiberD
e_pas=v_init
insert memcap // membrane dynamics that
account for laser induced current
del_memcap(0.5) = delay // [ms] delay before
laser pulse
dur_memcap(0.5) = pulsedur // [ms] duration of
laser pulse
cd_memcap(0.5) = 0 // irradiance [W/cm2] of
the laser (it will be overwritten later)
xraxial=Rpn1
xg=mygm/(nl*2)
xc=mycm/(nl*2)
}
}
for i=0, paranodes2-1 {
FLUT[i]{
nseg=1
diam=fiberD
L=paralength2
Ra=rhoa*(1/(paraD2/fiberD)^2)/10000
cm=cmem*paraD2/fiberD
insert pas
g_pas=0.0001*paraD2/fiberD
e_pas=v_init
insert memcap // membrane dynamics that
account for laser induced current
del_memcap(0.5) = delay // [ms] delay before
laser pulse
176
dur_memcap(0.5) = pulsedur // [ms] duration of
laser pulse
cd_memcap(0.5) = 0 // irradiance [W/cm2] of
the laser (it will be overwritten later)
xraxial=Rpn2
xg=mygm/(nl*2)
xc=mycm/(nl*2)
}
}
for i=0, internodes-1 {
STIN[i]{
nseg=1
diam=fiberD
L=interlength
Ra=rhoa*(1/(axonD/fiberD)^2)/10000
cm=cmem*axonD/fiberD
insert pas
g_pas=0.0001*axonD/fiberD
e_pas=v_init
insert memcap // membrane dynamics that
account for laser induced current
del_memcap(0.5) = delay // [ms] delay before
laser pulse
dur_memcap(0.5) = pulsedur // [ms] duration of
laser pulse
cd_memcap(0.5) = 0 // irradiance [W/cm2] of
the laser (it will be overwritten later)
xraxial=Rpx
xg=mygm/(nl*2)
xc=mycm/(nl*2)
}
}
for i=0, nodes-2 {
connect MYSA[2*i](0), node[i](1)
connect FLUT[2*i](0), MYSA[2*i](1)
connect STIN[6*i](0), FLUT[2*i](1)
connect STIN[6*i+1](0), STIN[6*i](1)
connect STIN[6*i+2](0), STIN[6*i+1](1)
connect STIN[6*i+3](0), STIN[6*i+2](1)
connect STIN[6*i+4](0), STIN[6*i+3](1)
connect STIN[6*i+5](0), STIN[6*i+4](1)
connect FLUT[2*i+1](0), STIN[6*i+5](1)
connect MYSA[2*i+1](0), FLUT[2*i+1](1)
connect node[i+1](0), MYSA[2*i+1](1)
}
finitialize(v_init)
fcurrent()
//print "-D- Leaving Createall"
177
}
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
proc set_power() {
// assign Cm changes to memcap to control capacitive
current
// to each axon segment (depending on the beam profile)
dummycount = 0
nc = 0
mc = 0
fc = 0
sc = 0
for data_block = 0, nodes-2 {
for dummycount = 0, segs_per_internode {
col =
(data_block*(segs_per_internode+1)+dummycount) // column counter
if (dummycount == 0) {
node[nc].cd_memcap(0.5)= capdelta/100 *
cmem * intensity_data.x[zshift_no][col]
nc = nc+1
}
if (dummycount == 1 || dummycount == 10) { //must
be at MYSA
MYSA[mc].cd_memcap(0.5)= capdelta/100 *
cmem * intensity_data.x[zshift_no][col]
mc = mc+1
}
if (dummycount == 2 || dummycount == 9) { //must
be at FLUT
FLUT[fc].cd_memcap(0.5)= capdelta/100 *
cmem * intensity_data.x[zshift_no][col]
fc = fc+1
}
if (dummycount > 2 && dummycount < 9) { //must be
at STIN
STIN[sc].cd_memcap(0.5)= capdelta/100 *
cmem * intensity_data.x[zshift_no][col]
sc = sc+1
}
}
}
// assignment of the final node
node[nc].cd_memcap(0.5) = capdelta/100 * cmem
*intensity_data.x[zshift_no][col+1]
}
/////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////
//advance() is a NEURON function that is called at every time
step
proc advance(){
178
// the memcap current source does not change the membrane
capacitance variable for each segment
// Cm and the temperature of each segment are changed in
advance() instead
// changes in membrane capacitance appear to follow a
thermal relaxation curve
// increases tend to be about 0.8%/mJ deposited or
0.008*power[W]*time applied[ms]
// the tmprl_scale value computed below needs to be
multiplied by the intensity of power below to give the final
capacitance increase
if (t <= delay ) {
cap_scale = 0
tmp_scale = 0
} else if (t > delay && t <= delay + pulsedur) { // energy
deposition phase
cap_scale = (t - delay)/pulsedur * capdelta/100
tmp_scale = (t - delay)/pulsedur * tmpdelta
} else if (t > delay+pulsedur) { // thermal
relaxation phase
// temporal scale is the exponential decay term
cap_scale = capdelta/100 * exp(-(t-
(delay+pulsedur))/therm_relax)
tmp_scale = tmpdelta * exp(-(t-
(delay+pulsedur))/therm_relax)
}
// assign the membrane capacitance to each segment
(depending on the type of stimulation)
// also assign the amount of capacitance delta
dummycount = 0
nc = 0
mc = 0
fc = 0
sc = 0
for data_block = 0, nodes-2 {
for dummycount = 0, segs_per_internode {
col =
(data_block*(segs_per_internode+1)+dummycount) // column counter
// proportional temperature and capacitance
increases are calculated
prop_cap_increase = cap_scale *
intensity_data.x[zshift_no][col]
prop_temp_increase = tmp_scale *
intensity_data.x[zshift_no][col]
if (dummycount == 0) {
// apply the cell membrane capacitance increase
node[nc].cm(0.5) = cmem * (1 +
prop_cap_increase)
// apply the local temperature increase
179
node[nc].localtemp_axnode_t(0.5) = celsius
+ prop_temp_increase
// adjust the axial resistance based on the new
temperature
node[nc].Ra = rhoa/10000 * (1/1.3)^((celsius +
prop_temp_increase - initialT)/10)
nc = nc+1
}
if (dummycount == 1 || dummycount == 10) { //must
be at MYSA
// apply the cell membrane capacitance
increase
MYSA[mc].cm(0.5) = paraD1/fiberD * cmem * (1 +
prop_cap_increase)
// adjust the axial resistance based on the new
temperature
MYSA[mc].Ra = Ra=rhoa*(1/(paraD1/fiberD)^2)/10000
* (1/1.3)^((celsius + prop_temp_increase - initialT)/10)
mc = mc+1
}
if (dummycount == 2 || dummycount == 9) { //must
be at FLUT
// apply the cell membrane capacitance
increase
FLUT[fc].cm(0.5) = paraD2/fiberD * cmem * (1 +
prop_cap_increase)
// adjust the axial resistance based on the new
temperature
FLUT[fc].Ra = rhoa*(1/(paraD2/fiberD)^2)/10000 *
(1/1.3)^((celsius + prop_temp_increase - initialT)/10)
fc = fc+1
}
if (dummycount > 2 && dummycount < 9) { //must be
at STIN
// apply the cell membrane capacitance
increase
STIN[sc].cm(0.5) = axonD/fiberD * cmem * (1 +
prop_cap_increase)
// adjust the axial resistance based on the new
temperature
STIN[sc].Ra = rhoa*(1/(axonD/fiberD)^2)/10000 *
(1/1.3)^((celsius + prop_temp_increase - initialT)/10)
sc = sc+1
}
}
}
//compute capacitance change at the final node
// apply the cell membrane capacitance increase
node[nc].cm(0.5) = cmem * (1 + cap_scale *
intensity_data.x[zshift_no][col+1] )
// apply the local temperature increase
180
node[nc].localtemp_axnode_t(0.5) = celsius + (tmp_scale *
intensity_data.x[zshift_no][col+1])
// adjust the axial resistance based on the new temperature
node[nc].Ra = rhoa/10000 * (1/1.3)^((celsius + (tmp_scale *
intensity_data.x[zshift_no][col+1]) - initialT)/10)
// keep track of the maximum membrane depolarization
throughout the simulation (center and distant nodes)
if (t < delay ) {
base_v = node[10].v(0.5)
} else {
if (node[10].v(0.5) > center_max) {
center_max = node[10].v(0.5)
}
if (node[2].v(0.5) > end_max) {
end_max = node[2].v(0.5)
}
}
fadvance()
}
////////////////////////////////////////////////// FILE I/O
///////////////////////////////////////////////////////
proc determine_intensity_file() {
sprint(intensity_to_read,
"%s/BeamProfilesByDiameter/NRN_InfraredIrradiance_%.1f.txt",
work, fiberD)
//printf ("-D- reading %s\n", intensity_to_read)
}
/*proc print_results() {
//print "-D- Entered print_results"
// Filename is specified to include the diameter and
pulse width used. No need to print these constants every time
sprint(results_to_write,"%sNRN_output/Diam_%.1f_PW_%.3f_NRNoutput
.dat",work,diam_data.x(diam_no), pws.x(pw_no))
// print each line of results into the above file
out1.aopen(results_to_write)
out1.printf("%.1f\t%.1f\t%.0f",volt_data.x[zshift_no][0],volt_dat
a.x[zshift_no][1],tempresults) // tempresults is 1 if axon did
fire, 0 otherwise
out1.printf("\n")
out1.close()
//print "-D- Leaving print_results"
}*/
/////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////
proc main() {
celsius = initialT
tstop = delay + pulsedur + 50 //set the simulation run time
181
//printf("-D- tstop is: %0.3f\n", tstop)
//printf("-D- pulsedur is is: %0.3f\n", pulsedur)
// read in Gaussian intensity (HH and FH models are simpler
and so Gaussian is computed within the simulation)
determine_intensity_file()
Int_file.ropen(intensity_to_read)
intensity_data.scanf(Int_file) // EJP - loading
intensity_data (matrix) loads the entire matrix from Ve_file
Int_file.close()
// Calculate dependent variables
calc_dependents()
// create axon
createall()
finitialize(v_init)
set_power() // set the incident IR power
levels
access node[0]
// output the final max voltage values
}
main()
xpanel("variables")
xvalue("Transient Capacitance Increase [%Baseline]",
"capdelta", 1, "main()", 1)
xvalue("Transient Temp Increase", "tmpdelta", 1, "main()", 1)
xvalue("Pulse Duration [ms]", "pulsedur",1, "main()", 1)
xvalue("FiberDiameter [um]", "fiberD",1, "main()", 1)
xvalue("Initial Temp [degC]", "initialT", 1, "main()", 1)
xpanel()
xopen("Interactive_MRG.ses")
182
APPENDIX III: MATLAB CODE
Recruitment Curve Plotting
AnalyzeAndPlotOpticalRecruitmentCurves.m
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
% Goal: plot optical recruitment versus optical pulse
duration in a way
% that minimizes the effect of dropped response
% Output:
% 1) individual for a given position with two subfigures
% a) rectified and integrated recruitment, with
missed pulses removed
% b) percentage of pulses yielding response across
all pulse
% durations
% 2) Recruitment across all muscles and all positions in
.fig format (for
% configuring and plotting subsets of data to be saved in
other formats
% later. These graphs will be a mess without pre-work, so
other formats
% are worthless)
% 3) Gompertz sigmoidal fits will be applied to each
recruitment curve,
% wih the parameters and R^2 written out for each muscle
and recruitment
% curve. No need for upper and lower estimates on
parameters for this
% case.
% Algorithm for identifying data to plot:
% EMG detection will be enabled, with a detection window
of 15ms
% -> most all EMG response starts 4-5ms after the
trigger, and does
% not last a very long time
% Cases where less than 30% of the applied pulses yield
detectable EMG
% will be treated in one of two ways:
% For stimulation below the minimum pulse duration
with >=30%
% activation, a rectified and integrated result of
the noise will be
% used
183
% For cases above the minimum pulse duration with
>=30% activation,
% the response is removed from the graph if less than
30% of the
% pulses at this duration fired. This is assumed to
be a case of
% reduced INS sensitivity. If >=30% of the pulses
fired, these fired
% pulses are rectified and integrated and the
response is included in
% the final graph.
% To improve runtime performance, all graphing will be
saved until the end
% of analyzing a given work area, with results saved in
structs. Results
% include plot labels and lines, etc.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
function AnalyzeAndPlotOpticalRecruitmentCurves (basework)
% base work area is provided to the script.
fontsize = 14;
% read the work directory for the side data available
side_list = dir(basework);
for sl = 1:numel(side_list) % iterate once for each side,
should be LeftSide or RightSide (within Hybrid Stimulation)
if (~strcmp(side_list(sl).name, 'RightSide') &&
~strcmp(side_list(sl).name, 'LeftSide'))
continue; % don't try to work in this directory if
it is empty
elseif side_list(sl).isdir == 0 % skip if this is not a
directory
continue
end
side = side_list(sl).name;
% iterate on each position/combination within the
OpticalStimulation
% directory (skipping politely if there are none)
new_work = [basework '/' side '/OpticalStimulation/'];
if ~exist(new_work, 'file')
disp(['-I- Did not find OpticalStimulation
directory in ' side_list(sl).name])
184
continue; % Hybrid Stimulation was not run on this
side
end
% read the analog input map, define trigger and other
muscle labels
% (this is constant for a given side, so only do it
once)
% trigger channel here needs to be the optical trigger
ir_stim = 1;
[inputs, trigger_chan] = ParseAnalogInputMapFile
([basework '/' side], ir_stim);
% read the Optical Stimulation directory for different
cases to analyze
position_list = dir(new_work);
analyze = 0; % flag used to skip plotting if no
recruitment data found
pl = 0;
for p_idx = 1:numel(position_list)
if (isempty(strfind(position_list(p_idx).name,
'Recruit')) || position_list(p_idx).isdir == 0)
continue % skip if this is not recruitment
data, or not a directory
end
analyze = 1; % found at least one directory to
analyze
pl = pl+1; % keep track of the number of positions
that actually count
% this directory is where "RawData", "Plots", and
"SummaryData" are
% stored (or configure it to have them)
line_label = position_list(p_idx).name;
work = [new_work '/' position_list(p_idx).name
'/'];
summarydir = [work '/SummaryData/'];
if ~exist(summarydir, 'file') % Create necessary
folders if they do not already exist
mkdir(summarydir);
end
% Make a copy of the currently executing m file to
the location specified in "work"
copyfile([mfilename('fullpath') '.m'],
sprintf('%s', summarydir));
185
% read the selected directory for all filenames,
returning experiment trial
% variables
% filename structure
PulseDuration_1.00_ms_X_0.00_um_Y_0.00_um_Pulse_0.lvm
[ irpulses, ~, ~, ~] = ParseDirectoryForPulses
([work 'RawData/']);
% temporary fix, if the sampling rate is too slow,
0.2ms pulses are not
% caught.
% cycle through each pulse duration and add the
result to the final
% vector to be plotted
for pd = 1:numel(irpulses)
% current IR pulse duration
irpulse = irpulses(pd);
% define the basic filename that will be used,
%
PulseDuration_1.00_ms_X_0.00_um_Y_0.00_um_Pulse_0.lvm
str_ir = sprintf('%.2f', irpulse);
file_template = ['PulseDuration_' str_ir
'_ms_X_' sprintf('%.2f', 0) '_um_Y_' sprintf('%.2f', 0)
'_um_Pulse_*.lvm'];
blank_time = 2e-3; % time to blank after
optical trigger [ms]
window_time= 15e-3; % time after the trigger to
look for emg [ms]
filter_time= 12e-3; % filter time is not used
when emg detect is true
emg_detect = 1; % ExtractAndAnalyze should
use EMG detection algorithms
thresh_mult = 6; % Threshold detection
occurs at thresh_mult*rms of each signal
% extract data for all files matching the file
template
[recruitment, values] =
ExtractAndAnalyzeLVMData...
([work 'RawData/'], trigger_chan, inputs,
file_template, ...
window_time, filter_time, blank_time,
emg_detect, thresh_mult);
% organize results in a struct for later
graphing and
% manipulation. Saving data for all channels
186
idx = 0;
for ai = 1:numel({recruitment.Label}) % each
channel
if (isempty(strfind(recruitment(ai).Label,
'LG')) && ...
isempty(strfind(recruitment(ai).Label, 'MG')) && ...
isempty(strfind(recruitment(ai).Label, 'TA')) && ...
isempty(strfind(recruitment(ai).Label, 'Sol')))
continue % skip if this is not muscle
data, or not a directory
end
idx = idx + 1;
alldata.Position(pl).name = line_label;
alldata.Position(pl).Channel(idx).Label
= recruitment(ai).Label;
alldata.Position(pl).Channel(idx).PulseDur(pd) = irpulse;
alldata.Position(pl).Channel(idx).MeanPosEMG(pd) =
recruitment(ai).MeanPosEMG;
alldata.Position(pl).Channel(idx).SDPosEMG(pd) =
recruitment(ai).SDPosEMG;
alldata.Position(pl).Channel(idx).ErrPosEMG(pd) =
recruitment(ai).ErrPosEMG;
alldata.Position(pl).Channel(idx).MeanNoEMG(pd) =
recruitment(ai).MeanNoEMG;
alldata.Position(pl).Channel(idx).SDNoEMG(pd) =
recruitment(ai).SDNoEMG;
alldata.Position(pl).Channel(idx).ErrNoEMG(pd) =
recruitment(ai).ErrNoEMG;
alldata.Position(pl).Channel(idx).Percent(pd) =
recruitment(ai).Percent;
alldata.Position(pl).Channel(idx).EMG(pd).Values = ...
[irpulse*ones(numel(values(ai,:)),1)
values(ai,:)']; % horizontal concat.
end
187
% clear out the recruitment structure before
the next loop
clearvars recruitment
end % done cycling through the pulse durations
end % done cycling through positions
if analyze == 0
continue; % no analyzable data was found on this
side. move on
end
% time to organize the results into the output figures.
This is where
% matlab will go a little crazy making plots and will
hijack the
% computer it is run on for a while as graphs are
opened and closed
% open a figure for results across this experiment (on
this side)
fh_master = figure;
for p = 1:numel(alldata.Position) % plot for each
position
fh_pos = figure;
fh_pct = figure;
position_id = alldata.Position(p).name;
work = [new_work '/' position_id '/'];
% open a figure for this position
for c = 1:numel(alldata.Position(p).Channel(:)) %
plot for each channel
fit_vec = [];
plot_vec = [];
pct_vec = []; % store percent of pulses
activated for every duration
% first look at percentages, and ID the first
index with >=30%
thresh_idx =
find(alldata.Position(p).Channel(c).Percent(:) >= 0.3, 1);
if isempty(thresh_idx)
thresh_idx =
numel(alldata.Position(p).Channel(c).Percent(:)) +1;
end
% now extract the recruitment curve data for
the fired cases
188
for d =
1:numel(alldata.Position(p).Channel(c).Percent) % cycle
through durations
pct_vec(d,1) =
alldata.Position(p).Channel(c).PulseDur(d); %#ok<AGROW>
pct_vec(d,2) =
alldata.Position(p).Channel(c).Percent(d); %#ok<AGROW>
if d < thresh_idx
% include the non-fired results
vec_idx = size(plot_vec, 1)+1;
plot_vec(vec_idx,1) =
alldata.Position(p).Channel(c).PulseDur(d); %#ok<AGROW> %
pulse duration
plot_vec(vec_idx,2) =
alldata.Position(p).Channel(c).MeanNoEMG(d); %#ok<AGROW>%
mean
plot_vec(vec_idx,3) =
alldata.Position(p).Channel(c).SDNoEMG(d); %#ok<AGROW>%
sd
plot_vec(vec_idx,4) =
alldata.Position(p).Channel(c).ErrNoEMG(d); %#ok<AGROW>%
err
fit_vec = [fit_vec;
alldata.Position(p).Channel(c).EMG(d).Values]; %#ok<AGROW>
else
% include the fired cases, only if
percent is high enough
current_pct =
alldata.Position(p).Channel(c).Percent(d);
if current_pct < 0.3 && ... % check if
the response is less than 30 -OR-
current_pct <
max(alldata.Position(p).Channel(c).Percent(d:end)) % see if
response returns, skip this
continue; % skip this case
end
vec_idx = size(plot_vec, 1)+1;
plot_vec(vec_idx,1) =
alldata.Position(p).Channel(c).PulseDur(d); %#ok<AGROW> %
pulse duration
plot_vec(vec_idx,2) =
alldata.Position(p).Channel(c).MeanPosEMG(d); %#ok<AGROW> %
mean
plot_vec(vec_idx,3) =
alldata.Position(p).Channel(c).SDPosEMG(d); %#ok<AGROW> %
sd
189
plot_vec(vec_idx,4) =
alldata.Position(p).Channel(c).ErrPosEMG(d); %#ok<AGROW> %
err
fit_vec = [fit_vec;
alldata.Position(p).Channel(c).EMG(d).Values]; %#ok<AGROW>
end
end
% Plot vec now contains the x and y data, and
error bars to
% plot.
% First: fit it to a gompertz sigmoid and write
out the results
% Establish directories to save gompertz fit
data
% fits_dir = [work
'/SummaryData/FitOptRecruitment/'];
% if ~exist(fits_dir, 'file') % Create
necessary folders if they do not already exist
% mkdir(fits_dir);
% end
% [ params, Rsquared, error, curve_x, curve_y]
= FitSigmoid (plot_vec(:,1), plot_vec(:,2));
% if error == 0
% filename =
sprintf('%s_FitParameters_Rsq%.2f.txt', ...
% alldata.Position(p).Channel(c).Label,
Rsquared);
% dlmwrite([fits_dir filename], params, '
');
% end
% % plot the sigmoid fits, too
% PlotData (fh_pos, curve_x, curve_y, c+18, ...
% [alldata.Position(p).Channel(c).Label '-
Fit'])
% Second: plot all muscle recruitment data for
this position in
% a single graph
PlotDataWErrBars (fh_pos, ...
plot_vec(:,1), plot_vec(:,2),
plot_vec(:,4), ...
c, alldata.Position(p).Channel(c).Label)
PlotData (fh_pct, pct_vec(:,1), pct_vec(:,2),
c, ...
190
alldata.Position(p).Channel(c).Label)
% Third: add all muscle recruitment data to the
master plot for
% this directory
PlotDataWErrBars (fh_master, ...
plot_vec(:,1), plot_vec(:,2),
plot_vec(:,4), ...
c, [alldata.Position(p).Channel(c).Label '-
' position_id])
end % done cycling through channels
% Establish directories to save plots for this
position
plots_dir = [work
'/Plots/OpticalRecruitmentCurves/'];
if ~exist(plots_dir, 'file') % Create necessary
folders if they do not already exist
mkdir(plots_dir);
end
% save and close the plot across muscles in this
position
figure(fh_pct)
title('Pulses with EMG Response [%]', 'FontSize',
fontsize);
xlabel('Optical Pulse Duration', 'FontSize',
fontsize);
SaveGCF2Filename ([plots_dir
'OpticalPercentage_AcrossMuscles'])
close(gcf)
figure(fh_pos)
title('Rectified and Integrated Recruitment -
Optical Stimulation', 'FontSize', fontsize);
xlabel('Optical Pulse Duration', 'FontSize',
fontsize);
SaveGCF2Filename ([plots_dir
'OpticalRecruitment_AcrossMuscles'])
close(gcf)
end % done cycling through positions
plots_dir = [new_work
'/CommonPlots/OpticalRecruitmentCurves/'];
if ~exist(plots_dir, 'file') % Create necessary folders
if they do not already exist
mkdir(plots_dir);
191
end
% save and close the plot across muscles and positions
(just in .fig
% format)
figure(fh_master)
title('Rectified and Integrated Recruitment - Optical
Stimulation', 'FontSize', fontsize);
xlabel('Optical Pulse Duration', 'FontSize', fontsize);
saveas(gcf, [plots_dir
'OpticalRecruitmentCurves_All.fig'], 'fig') % for reading
values directtly from graph
close(gcf)
end % done cycling through sides
end
%%% SUBROUTINES %%%
function [ irpulses, Xvec, Yvec, index_order] =
ParseDirectoryForPulses (work)
% read the directory for all lvm files
files = dir([work '/*Pulse*.lvm']); % pulses are repeat
measures
% cycle through all files storing all of the pulse,
amplitude, and position
% data
for f = 1:length(files)
% file should follow:
PulseDuration_<n.nn>_ms_X_<n.nn>_um_Y_<n.nn>_um_Pulse_<n>.l
vm
% split the filename into segments
params = regexp(files(f).name, '_', 'split');
% get the stimulus duration and coordinates
irpulses(f) = str2double(params{2}); %#ok<AGROW>
Xvec(f) = str2double(params{5}); %#ok<AGROW>
Yvec(f) = str2double(params{8}); %#ok<AGROW>
% store the timetamps
timestamps(numel(unique(irpulses)),2) = irpulses(f);
%#ok<AGROW>
timestamps(numel(unique(irpulses)),1) =
files(f).datenum; %#ok<AGROW>
end
% sort the timestamps order
[pulse_order, index_order] = sortrows(timestamps,1);
192
% reduce each vector to the unique values
irpulses = sort(unique(irpulses));
Xvec = unique(Xvec);
Yvec = unique(Yvec);
end
function [ params, Rsquared, error, curve_x, curve_y] =
FitSigmoid (x, y)
% data is passed as a 2-D matrix. Col 1 is pulse
amplitudes, the other
% columns are the values on the recorded channels for each
pulse amplitude
% (rectified and integrated)
error = 0;
% 4-parameter Gompertz (from Matt, modified to include a DC
offset
f = @(p,x) p(4) + p(1) .* exp( 100*p(2) .* exp( p(3) .* x
));
lb = [-1e6 -1e6 -1e6];
ub = [ 1e6 1e6 1e6];
options = optimset('Display','off');
saved.mse=inf;
a=max(y); % set the top asymptote inital guess
d=min(y); % set the bottom asymptote initial guess
for b=0:-100:-500
for c=0:-1:-5
p0=[a b c d]';
DOF = numel(x)-numel(p0); % calculate Degrees of
Freedom
if DOF == 0 % cannot compute if there are not
enough DOF
error = 1;
return;
end
% performed with least squares curve fit
% [p,sse,r,~,~,~,J] = lsqcurvefit(f, p0, x,
y, lb, ub, options);
% mse = sse/(DOF); % Mean square error
% performed with non-linear fit
[p,r,J,~,mse] = nlinfit(x,y,f,p0);
% dbug_fit1 = [mse saved.mse]
193
if (mse<saved.mse)
saved.p = p;
saved.mse = mse;
saved.J = J;
saved.r = r;
saved.sse = sse;
end
end
end
% determine the saved parameter values
params = saved.p;
% compute R^2
sstot=sum((y-mean(y)).^2);
Rsquared=1-saved.sse/sstot;
% return a smooth fit of the curve
curve_x = linspace( max(x), min(x));
curve_y = f(saved.p, curve_x);
end
function PlotDataWErrBars (h, X, Y, E, idx, line_label)
[line_formats] = LineStyleLibrary;
% make full screen figures
% screen_size = 0.9.*get(0, 'ScreenSize');
% call up the figure or create it if it does not exist
figure(h)
hold on;
h1 = errorbar(X, Y, E, line_formats{idx});
set(h1, 'LineWidth', 1.0 );
set(h1, 'DisplayName', line_label);
legend('Location', 'Best')
hold off;
end
function PlotData (h, X, Y, idx, line_label)
[line_formats] = LineStyleLibrary;
% make full screen figures
% screen_size = 0.9.*get(0, 'ScreenSize');
figure(h);
hold on;
h1 = plot(X, Y, line_formats{idx});
set(h1, 'LineWidth', 1.0 );
set(h1, 'DisplayName', line_label);
legend('Location', 'Best')
194
hold off;
end
function [line_formats] = LineStyleLibrary
% set up figure plot styles
line_formats = {'-b', '-r', '-k', '--b', '--r', '--k', ...
'-.b', '-.r', '-.k', ':b', ':r', ':k',...
'-ob', '-or', '-ok', '-+b', '-+r', '-+k',...
'-xb', '-xr', '-xk', '-^b', '-^r', '-^k',...
'-<b', '-<r', '-<k', '-vb', '-vr', '-vk',...
'-sb', '-sr', '-sk','-db', '-dr', '-dk',...
'-pb', '-pr', '-pk','-hb', '-hr', '-hk'};
end
ExtractAndAnalyzeLVMData.m
% work - The work area for for this particular data set.
Contains "RawData" "SummaryData" and "Plots" directories
for this
% trigger_chan - analog input channel with the electrical
or laser trigger
% inputs - list of names for the analog inputs
% file_template - basic name of the file that will be
analyzed. May contain
% * wildcard to include many files with the same general
name structure.
% Returned 'analysis' data will include data aggregated
across all of
% the files specified by file_template
% window_time is the time past the trigger over which data
is summarized
% fileter_time is the length of time over which the sliding
average is
% performed
% stim_type is 0 if electrically triggered or 1 if
optically triggered
% (impacts the search for a triggered event)
function [analysis, values, start_times, stop_times, peaks]
= ...
ExtractAndAnalyzeLVMData(work, trigger_chan, inputs,
file_template, window_time, filter_time, blank_time,
EMG_detect, thresh_mult)
% Make a copy of the currently executing m file to the
location specified in "work"
195
copyfile([mfilename('fullpath') '.m'], sprintf('%s', [work
'/../SummaryData/']));
% define the return data structure. Each label will hold a
vector based on
% the analog input channel it represents
analysis = struct('Mean', {}, 'Err', {}, 'SD', {},...
'MeanRmOutlier', {}, 'ErrRmOutlier', {}, 'SDRmOutlier',
{}, ...
'MeanPosEMG', {}, 'ErrPosEMG', {}, 'SDPosEMG', {}, ...
'MeanNoEMG', {}, 'ErrNoEMG', {}, 'SDNoEMG', {}, ...
'Label', {}, 'Maximum', {}, 'Percent', {});
%%%% Reading Input Files %%%%
% Multiple trials have the same name except for the pulse
or trial
% number. Using dir at this point will grab all of them
with the
% same pulse duration and coordinates. This gives a small
grouping
% of like files to analyze.
% search the working directory for all data files matching
the pattern
filebase = [work file_template];
file_list = dir(filebase);
% then cycle through each file that matched, aggregating
the data to
% provide a mean for the electrical and hybrid stimulation
across all trials
rectandint = [];
twitch_detect = [];
start_times = [];
stop_times = [];
peaks = [];
values = [];
if numel(file_list) == 0
return
end
% % debugging %
% dbug_filebase = filebase;
% dbug_found = numel(file_list);
for i = 1: numel(file_list)
% skip this file if it is empty
if file_list(i).bytes == 0
196
continue;
end
% extract trailing pulse or trial number from this
file, return zero if
% not found
% optical stim base:
PulseDuration_2.30_ms_X_0.00_um_Y_0.00_um_Pulse_2.lvm
% hybrid stim base:
Position1C1Cath_IRPW2.00_Ch1_0.00_Ch2_0.00_Ch3_0.00_Ch4_0.0
0_PW_0_IRE_1_Pulses_0_Freq_0.00_Trial_1.lvm
if ~isempty(strfind(file_list(i).name, 'Trial_'))
idx1 = strfind(file_list(i).name, 'Trial_') + 6;
idx2 = strfind(file_list(i).name, '.lvm') - 1;
iter = str2double(file_list(i).name(idx1:idx2));
elseif ~isempty(strfind(file_list(i).name, 'Pulse_'))
idx1 = strfind(file_list(i).name, 'Pulse_') + 6;
idx2 = strfind(file_list(i).name, '.lvm') - 1;
iter = str2double(file_list(i).name(idx1:idx2));
else
iter = 0;
end
% read in all the data from the current file, remove DC
offset,
% rectify, and integrate
[data, ~, ~] = ExtractLVMData ...
(work, file_list(i).name, window_time, filter_time,
blank_time, trigger_chan, inputs, EMG_detect, thresh_mult);
% check whether the appropriate trigger was detected
and valid data was
% collected
if data(1).Triggered == 1
% record the result across all channels, appending
the result to
% the end
rectandint(:, end+1) = [data(:).Result];
%#ok<AGROW>
twitch_detect(:,end+1) = [data(:).Fired];
%#ok<AGROW>
% record the EMG stats for each pulse and store
them, adding a new
% column for each iteration of the trial
start_times(:,end+1) = [iter; [data(:).Start]'];
%#ok<AGROW>
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stop_times(:,end+1) = [iter; [data(:).Stop]' ];
%#ok<AGROW>
%%% this is currently broken %%% peaks(:,end+1) =
[iter; [data(:).Peak]']; %#ok<AGROW>
end
end
% for each analog input channel, compute the mean and
confidence across
% all files and store them in the recruitment structure
% check that there is valid data (need a trigger to be
detected)
if data(1).Triggered == 1
for j = 1:numel({data.Label})
analysis(j).Label = data(j).Label;
% compute mean and error bars with all data
[analysis(j).Mean, ~, MuCI, ~] =
normfit(rectandint(j, :));
analysis(j).Err = (MuCI(2)-MuCI(1))/2; % enable
this for standard error of the mean
analysis(j).SD = sqrt(var(rectandint(j, :))); %
enable this for standard deviation from the mean
% compute results with outliers removed with
Thompson Tau method
if numel(rectandint(j, :)) > 2
% removal can only happen if there are more
than 3 data points
cleaned = removeoutliers(rectandint(j, :));
else
cleaned = rectandint(j, :);
end
[analysis(j).MeanRmOutlier, ~, MuCI, ~] =
normfit(cleaned);
analysis(j).ErrRmOutlier = (MuCI(2)-MuCI(1))/2; %
enable this for standard error of the mean
analysis(j).SDRmOutlier = sqrt(var(cleaned)); %
enable this for standard error of the mean
% compute the response, with fired and non-fired
responses
% separated.
% fired
[analysis(j).MeanPosEMG, ~, MuCI, ~] =
normfit(rectandint(j, twitch_detect(j,:) > 0));
198
analysis(j).ErrPosEMG = (MuCI(2)-MuCI(1))/2; %
enable this for standard error of the mean
analysis(j).SDPosEMG = std(rectandint(j,
twitch_detect(j,:) > 0)); % enable this for standard
deviation from the mean
% not fired
[analysis(j).MeanNoEMG, ~, MuCI, ~] =
normfit(rectandint(j, twitch_detect(j,:) == 0));
analysis(j).ErrNoEMG = (MuCI(2)-MuCI(1))/2; %
enable this for standard error of the mean
analysis(j).SDNoEMG = std(rectandint(j,
twitch_detect(j,:) == 0)); % enable this for standard
deviation from the mean
% computethe maximum response
analysis(j).Maximum = max(rectandint(j, :));
% compute the percentage of cases fired
analysis(j).Percent = mean(twitch_detect(j,:));
% provide the individual values as well
values(j,:) = rectandint(j, :); %#ok<AGROW> %
include outliers
end
end
% debugging %
% dbug_triggered = data(1).Triggered
end
ExtractEMGStartAndStopTime2.m
% this function reads through a list of files supplied to
it, and extracts
% the EMG start and stop time, relative to the trigger
% the algorithm is as follows:
% compute the standard deviation of the EMG signal, and set
the detection
% threshold as an integer number of the standard deviation.
Look for the
% first threshold crossing after the trigger, then progress
back until the
% signal crosses zero. This will be the "start" time.
Thresholding will be
% checked against the rectified signal, but the zero
crossing time will be
199
% detected from the raw signal.
% stop time is more complex, because ringing, multiple
pulses, and drifting
% complicate the detection of the end of a pulse. The
algorigthm looks for
% regions where constant polarity is maintained for at
least 1ms and less
% than 5ms
% The start and stop times will be reported for each input
file as vectors.
% Zeros in the start and stop matrices indicate where stim
was not detected.
% start and stop times are given with respect to the
trigger time.
% blank_time (in [ms]) provides a set blanking time after
the trigger to ignore
% window (in [ms]) sets an upper limit on the window of
time to investigate
function [start, stop] = ExtractEMGStartAndStopTime2
(rawdata, sample_time, std_dev, thresh_mult, window)
% extract sample rate and calculate the number of samples
for this window
limit = floor(window/sample_time); % number of samples to
limit the analysis to
% initalize vectors
start = zeros(size(rawdata,2));
stop = zeros(size(rawdata,2));
for col = 1:size(rawdata,2) % operate on each column
(separate channel)
% for col = 4:4 % operate on each column (separate channel)
% construct a time vector that begins at the end of the
% blanking phase and extends to the end of the signal
time = (1:numel(rawdata(:,col))) * sample_time;
% set the initial detection threshold
detect_thresh = std_dev(col) * thresh_mult;
% % debug plotting - plotting the detection threshold
% dbugmaxtime = max(time);
% dbugmintime = min(time);
% figure
200
% hold on
% plot(time, rawdata(:,col))
% plot(time(1:end-1), diff(rawdata(:,col)), 'r--')
% s1 = line([dbugmintime dbugmaxtime],
[detect_thresh detect_thresh]);
% set(s1, 'Color', 'g');
% perform thresholding on rectified data. returns
vector
% that is 1 at each index where the statement is true
if numel(rawdata(1:end,col)) < (limit -1)
above_thresh = abs(rawdata(:,col)) >
(detect_thresh);
else
above_thresh = abs(rawdata(1:limit-1,col)) >
(detect_thresh);
end
indices = find(above_thresh == 1);
if ~isempty(indices)
% index of first threshold crossing after the
trigger
first = indices(1);
% s1 = line([time(first) time(first)], [-1 1]);
% set(s1, 'Color', 'c');
% find the next zero crossing as an intermediate
point
first = first + BlockSize(rawdata(first:end,col),
0) -2;
if first<0
first = 0;
end
% s1 = line([time(first) time(first)], [-1 1]);
% set(s1, 'Color', 'k');
% analyze the response before the threshold
crossing, looking for the start of the EMG response
max_phase = 0.004; %[s]
min_phase = 0.0005; %[s]
min_peak = 0.5*thresh_mult*std_dev(col);
leadin = FindResponseEnd
(fliplr(rawdata(1:first,col)'), sample_time, min_phase,
max_phase, min_peak);
% leadin = BlockSize(fliplr(rawdata(1:first,col)'),
2* std_dev(col));
201
% repeat for the signal after the threshold
crossing, looking for
% the end of the response
max_phase = 0.004; % [s]
min_phase = 0.0005; % [s]
min_peak = 0.5*thresh_mult*std_dev(col);
% disp(['-D- dbug: ' num2str(first) ' '
num2str(col)])
signal_length =
FindResponseEnd(rawdata(first+1:end,col), sample_time,
min_phase, max_phase, min_peak);
% calculate start and stop values
start(col) = time(first - leadin+2); % reported
relative to the trigger
stop(col) = start(col) + (signal_length+ first) *
sample_time;
%
% % continue debug plot - plot the adjusted
start and stop
% % times
% s1 = line([(start(col) ) start(col)], [-
1 1]);
% set(s1, 'Color', 'b');
% s1 = line([(stop(col)) stop(col)], [-1
1]);
% set(s1, 'Color', 'k');
% hold off
end
end
end
%%%%%%%%%% SUBROUTINES %%%%%%%%%%%%%%%
% BlockSize computes the number of indices to the next
transition below
% threshold
function [index, indices] = BlockSize (signal, threshold)
if ~isempty(signal)
% take the polarity of the current signal
ref_polarity = sign(signal(1)); % set the first
reference polarity
% determine the polarity of each point, offset by the
threshold value
polar_sig = sign(signal - (threshold * ref_polarity));
% compute the number of indices to the transition to
the next polarity
202
indices = find(polar_sig ~= ref_polarity);
if ~isempty(indices)
index = indices(1);
else
index = 0;
indices = [];
end
else
index = 0;
indices = [];
end
end
% FindResponseEnd analyzes the waveform to detect EMG start
or stop
function signal_length = FindResponseEnd (signal,
sample_time, min_phase, max_phase, min_peak)
% signal_length - the returned index from the beginning of
the supplied
% waveform where the EMG supposedly ends
% signal - the waveform to be analyzed
% sample_time - time step at which data was collected
% min_phase - shortest time to consider for a single
positive or negative
% phase of the signal.
% max_phase - longest time to consider a single positive or
negative phase
% before breaking it up by slope
% % compute the zero crossings from start to the signal's
end, idx is the
% % first zero crossing, all_crossings contains all of the
crossings
% [idx all_crossings] = BlockSize (signal, 0);
%
% if isempty(all_crossings)
% signal_length = 0;
% return;
% end
%
% % perform an initial check to the next polarity change:
% if idx * sample_time < max_phase
% idx = all_crossings(2); % start at the next zero
crossing
% end
203
% signal_length = 1;
% done = 0;
% while done ==0 && idx ~=0
% if idx*sample_time >= max_phase
% % this signal maintains polarity too long to be
part of the EMG
% % response, break it up based on derivativea and
stop when the
% % derivative pieces get too small.
% deriv = diff(signal);
% [~, deriv_crossings] = BlockSize(deriv, 0);
% d_counter = 1;
% if deriv_crossings(d_counter) * sample_time <
0.002 % shorter than max deriv. move to the next one
% d_counter = 2;
% end
% deriv_time = (deriv_crossings(d_counter + 1) -
deriv_crossings(d_counter)) * sample_time;
% while deriv_time < 0.002 && deriv_time > 0.0004
% d_counter = d_counter + 1;
% deriv_time = (deriv_crossings(d_counter + 1)
- deriv_crossings(d_counter)) * sample_time;
% end
% signal_length = deriv_crossings(d_counter)
% done = 1;
% elseif idx*sample_time < min_phase
% % the last length before transition was very
short,
% % look at the polarity over the next ms
% check2 = BlockSize (signal(signal_length +
idx:end), 0);
% % check that the signal returns to a state of
% % maintained polarity for at least 1ms
% if (check2*sample_time) > min_phase
% % signal returns to maintain polarity for
more
% % than min limit, increase the signal length
and loop
% % again
% signal_length = signal_length + idx + check2;
% idx = BlockSize (signal(signal_length:end),
0);
% else
% % signal return is too short, complete the
loop
% done = 1;
% end
204
% else
% % signal is within the max/min limits. now check
that it at least
% % reaches threshold, or do not include it
% if max(signal(signal_length:signal_length+idx-1))
> detect_thresh
% signal_length = signal_length + idx;
% idx = BlockSize (signal(signal_length:end),
0);
% else
% signal_length = signal_length + idx;
% done = 1;
% end
% end
% end
done = 0; % this will end the loop when the analysis is
done
signal_length = 1; % index offset from start of the signal
% find the first change in polarity from the reference
[idx ~] = BlockSize (signal, 0);
while done == 0 && idx ~= 0
% check whether the time until the first polarity
% change is too long (8ms)
if (idx * sample_time) >= max_phase % phase is too
long, analyze further
% this signal maintains polarity too long to be
part of the EMG
% response, break it up based on derivativea and
stop when the
% derivative pieces get too small.
deriv = diff(signal);
[~, deriv_crossings] = BlockSize(deriv, 0);
d_counter = 1;
if deriv_crossings(d_counter) * sample_time < 0.002
% shorter than max deriv. move to the next one
d_counter = 2;
end
deriv_time = (deriv_crossings(d_counter + 1) -
deriv_crossings(d_counter)) * sample_time;
while deriv_time < 0.003 && deriv_time > 0.0004
d_counter = d_counter + 1;
deriv_time = (deriv_crossings(d_counter + 1) -
deriv_crossings(d_counter)) * sample_time;
end
signal_length = deriv_crossings(d_counter);
done = 1;
205
% dbug1 = [idx signal_length]
% % if the block is too long, start looking at the
derivative
% deriv = diff(signal);
% [~, deriv_crossings] = BlockSize(deriv, 0);
% % determine the derivative zero crossing right
before the currently
% % indexed point. zeros of the derivative are
peaks of the orignal
% % signal
% peaks = find(deriv_crossings < idx);
% dc_idx = peaks(end) % index for navigating
through the array of derivative crossing indexes
% dbug_dc = deriv_crossings(dc_idx)
% % find out how long the current slope polarity is
maintained,
% % slope_pol_idx holds the number of samples at a
given polarity
% slope_pol_idx = deriv_crossings(dc_idx+1) -
deriv_crossings(dc_idx)
% while slope_pol_idx * sample_time < 0.002 &&
slope_pol_idx * sample_time > 0.0004
% % deivative changes fast enough, keep dicing
up
% % until it does not
% dc_idx = dc_idx + 1;
% % repeat the derivative check on the next
segment of the signal
% slope_pol_idx = deriv_crossings(dc_idx+1) -
deriv_crossings(dc_idx)
% end
% % stop the loop here when the derivative changes
% % get too long. complete the loop
% signal_length = deriv_crossings(dc_idx)
% done = 1
% % check whether the time until the first polarity
% % change is too short (1ms)
elseif (idx * sample_time) < min_phase % check if this
phase is too short
% the last length before transition was very short,
% look at the polarity over the next ms
check2 = BlockSize (signal(signal_length +
idx:end), 0);
% check2 = BlockSize
(signal(signal_length + idx+check1:end));
% check that the signal returns to a state of
206
% maintained polarity for at least 1ms
if (check2*sample_time) > min_phase
% signal returns to maintain polarity for more
% than 0.5ms, increase the signal length and
loop
% again
signal_length = signal_length + idx + check2;
idx = BlockSize (signal(signal_length:end), 0);
else
% signal return is too short, complete the loop
done = 1;
end
else
% this phase falls within the max/min window, check
whether it
% exceeds the phase detection threshold as well
if signal_length+idx <= numel(signal)
% check whether the current phase exceeds the
threshold
if max(signal(signal_length:signal_length+idx))
> min_peak
signal_length = signal_length + idx;
idx = BlockSize (signal(signal_length:end),
0);
else
signal_length = signal_length + idx;
done = 1;
end
else
% there are not enough samples left finish
done = 1;
end
end
end
end
207
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