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Introduction to Biomedical Engineering

Kung-Bin Sung

Device/Instrumentation I – bioelectric phenomena

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Outline

• Chapter 11: bioelectric phenomena– Origin of potential across cell membrane– Quantitative derivation and calculation of

resting membrane potential– Action potential

• Measuring biopotential– ECG– EMG, EEG, etc.

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Origin of membrane potential

• Cell membrane– permeable to some but not all ions– Consists of a lipid bilayer and has capacitive

properties• Different concentrations of ions inside

and outside of the cell membrane– Ion channels– Active ion pumps

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What ions are there?

Cytoplasm ExtracelluarIon (mM) fluid (mM)

K+ 400 20Na+ 50 440Cl– 52 560

Data obtained from squid giant axon

Note:There are also negatively charged proteins inside cell membrane

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Driving forces of ion movement• Diffusion – particles move from high-

concentration to low-concentration

• Drift – flow of charged particles due to electric fields

dxKdDdiffusionJK][)(

+

−=

dxdvKZdriftJ K ][)( +−= µ

D: diffusivity constant (m2/s)

µ: mobility (m2/sV)Z: ionic valence = +1 for K+

v: voltage across membrane

Electric field

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Resting potential – one ion

0)()( =+ diffusionJdriftJ KK

0][][ =−−+

+

dxKd

qkT

dxdvKZ µµ

qkTD µ

=

Now consider K+ only, and in the case of steady state

k: Boltzmann’s constantT: absolute temperatureq: charge of electron

][][

+

+

−=KKd

qkTdv

i

ooiK K

KqkTvvE

][][ln +

+

=−= Nernst equation

= 26mV at room temperatureNernst potential

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Resting potential – two ions

o

iCl

i

oK Cl

ClqkTE

KK

qkTE

][][ln

][][ln −

−

+

+

===

Suppose membrane is permeable to K+ and Cl-, and in the case of steady state

o

i

i

o

ClCl

KK

][][

][][

−

−

+

+

=

Space charge neutrality: the number of cations in a given volume (both inside and outside of the membrane) is equal to the number of anions

Donnan equilibrium

Example 3.1: determine steady-state concentrations using the Donnan equilibrium and space charge neutrality

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Example 3.1

1000][][

500][][

=+

=+−−

++

oi

oi

ClCl

KK

oo

ii

ClK

ClK

][][

][500][−+

−+

=

=+

o

i

i

o

ClCl

KK

][][

][][

−

−

+

+

=

mVEClClKK Koioi 18333][667][333][167][ ===== −−++

Inside cell :[KCl] = 100 mM[RCl] = 500 mM

Outside cell :[KCl] = 400 mM

Initial condition:

Donnan equilibriumSpace charge neutrality

Steady-state concentrations

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Goldman equation

⎟⎟⎠

⎞⎜⎜⎝

⎛++++

= +−+

+−+

iNaoCliK

oNaiCloKm NaPClPKP

NaPClPKPqkTV

][][][][][][ln

Concentrations of ions of squid giant axonThe resting potential is -60 mV

PK is the permeability of K+

δK

KDP = δ is the thickness of the membrane

Each ion’s contribution to the membrane potential depends on its relative permeability

Goldman equation

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Resting potential and ion pumps• Resting potential must be maintained at a

relatively stable level• Na+ ions tend to move into the cell due to

electric field (resulting from resting potential) and diffusion along the concentration gradient

• K+ ions tend to move out of the cell• Active Na-K pump prevents change in

concentration and hence maintains the resting potential (3 Na+ out and 2 K+ in)

• Concentration of other ions (Cl-) is determined by the resting potential

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Ion channelsChannels: - Made of trans-membrane proteins- Water-filled passages allow ions and very small molecules (water and urea) to pass through the cell membrane

Open channel: depends on size and charge

Gated channel: Usually closed; the opening of such channels is controlled chemically, electrically, or mechanically

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Na-K Ion pumpActive transport protein (pump) moves molecules against their concentration gradient ⇒ needs energy (provided by ATP)

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Origin of action potential• Neuron’s ability to conduct “signal”• Voltage-gated Na+ channels open once the

membrane potential is raised (stimulated) to certain threshold

• Further increase in membrane potential is achieved by an influx of Na+ (positive feed back)

• The membrane is “depolarized”• Opening of voltage-gated K+ channels lowers

the membrane potential (back to resting potential)

• Propagation of the action potential

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Action potential (cont.)Nernst potential of Na+

Nernst potential of K+

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Action potential – experimental resultsVoltage clamp experiments by Hodgkin and Huxley in 1952- Apply a fixed voltage (above threshold) across the membrane of a squid giant axon- There are only two types of voltage-time-dependent permeable channels (Na+ and K+) in a squid giant axon- Study the time-dependent characteristics of these channels

Sodium and Potassium currents due to a −20mV voltage clamp

into cell

out of cell

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Action potential (cont.)What happens if voltage clamp is turned off immediately after the membrane potential reaches the threshold? (similar to natural activation of neurons)

- Na+ channels close quickly and K+ channels remain open and then close slowly- Net current becomes outward (due to K+)- Membrane potential decreases to Nernst potential of K+

(the membrane is now hyperpolarized)- Na+ channels cannot be reopened until the membrane has been hyperpolarized ⇒ refractory period- The Na-K pump restore the membrane potential to its resting level and “recycle” the ions involved in the action potential

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Action potential (cont.)

Depolarization propagates in one direction – refractory period prevents the back-propagation of the action potential

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Action potential of muscle cells

- Muscle cells are also excitable- Similar mechanism involving ion channels-Depolarization results in contraction of the muscle

Action potential of neuron

Action potential of muscle fiber

Force of muscle contraction

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Action potential (cont.)

Different excitable cells (note the difference in time-scale)

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Refractory periods in cardiac muscle

Refractory period: determines how fast the cell can be excited repeatedly

Skeletal muscle

Cardiac muscle

Repeated stimulationAction potential (red) and muscle contraction (blue)

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Pacemaker (autorhythmic) tissueSpontaneous action potential without input from the nervous system

Some “leaking” channels allow Na+ and K+ to pass the membrane at negative membrane potentialSince flow of Na+ > K+, the net effect is an increase in membrane potential

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Electrocardiogram (ECG)

PQRST pattern

Period = 1/heart rate

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ECG

• Measure the electrical activity of the heart (myocardium)

• Non-invasive – potential measured on body surface

• Human body can be considered as a conductor (ions in cells and body fluids)

• Measured potential is the total effect

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From action potential to ECG

VA-C

VC-B

Conceptually, action potential propagates and measurements from different locations can tell you the direction of propagation

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From action potential to ECG

VA-B

Differential potential between A and B

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ECG measures integrated signal from the heart

Representative electric activity from various regions of the heart

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ECG measures direction and relative magnitude of action potential

Cardiac vector of the QRS complex using Einthoven’s triangle

The direction of the mean vector at any time can be obtained from signals of two of the three leads

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Example ECG pre-amplifier

Differential signal between two arms, with right-leg feed back to reduce common-mode interference (more on circuits later)

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More ECG measurements

3 leads (left arm, right arm, and left leg), using right leg as commonChest leads

V1-V6

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Electrode: ion-metal interface

C

C

C

C+

C+

C+A–

A–

e–

e–

e–

Electrolyte (human body)Electrode (metal)

Coupling of biopotential to electronic circuit

C C+ + e− A− A + e−

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Electrode for ECGElectrolyte soaked foam provides good electrical contact with the skin, and reduces motion artifacts

Ag-AgCl electrode: Ag base coated with a thin layer of AgCl

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Electrode: half-cell potential

Results in a DC offset in measured signal; can be removed by high pass filtering

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ECG circuitBlock diagram

High pass filter

Low pass filter

pre-amp

V+

V-

amp A/D converter

Signal ground

Block DC component

Cut-off 100~200Hz

Isolation

More on instrumentation later

Rg

Total gain >1000

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Electromyogram (EMG)

Electrodes for EMG- Non-invasive, disk electrodes (similar to ECG)- Percutaneous needle electrodes for direct recording of electrical signals from nerves and muscle fibers

Bipolar Unipolar

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Electroencephalogram (EEG)

Non-invasive electrode: cup electrodes- Made of platinum or tin- 5-10mm in diameter- Filled with conducting electrolyte gel- Attached to the scalp

Invasive electrode: subdermal needle electrodes- Made of platinum or stainless-steel- 10mm long and 0.5mm wide- Inserted under the skin to provide better electrical contact

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Electroencephalogram (EEG)Example of EEG signals

8-13 Hz

14-30 Hz

4-7 Hz

<3.5 Hz

Frequency of EEG signal increases with higher degrees of cerebral activity.During period of metal activity, the signal becomes asynchronous and measured magnitude decreases

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Microelectrodes

Tip formed by drawing, diameter 0.1-10µm

Tip formed by etching, diameter a few microns

Micromachined silicon substrate with openings

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References

• Medical Instrumentation: Application and Design, edited by John G. Webster

• Human Physiology: an Integrated Approach (2nd edition), by D.U. Silverthorn