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Vanderbilt University

Living State Physics Group

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Novel Insights on the Virtual Electrode Response

John P. Wikswo, Jr. Shien-Fong (Marc) Lin

Bradley Roth Franz Baudenbacher

David Latimer Living State Physics

Vanderbilt University, TN

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• Review of bidomain model • Excitation with a point electrode

• Virtual cathodes and anodes • Make/break stimulation • Quatrefoil reentry

•Endocardial Shock Response •Field Shock Response

OUTLINE

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The Cardiac Bidomain Model

• Homogeneous syncytium • Separate intra- and

extracellular spaces • Differing electrical

anisotropies • Non-linear membrane • Fiber curvature,

heterogeneities, and discontinuities???

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“Virtual Electrodes”

• The Virtual Cathode is the region of tissue adjacent to a stimulating electrode that is depolarized rapidly by electrotonic spread.

• The Virtual Anode is the region of tissue adjacent to a stimulating electrode that is hyperpolarized rapidly by electrotonic spread.

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Phenomena unique to the cardiac bidomain with unequal intracellular and extracellular anisotropies

• Extended, quatrefoil current loops exist outside an expanding, activation wave front.

• Measurable, quatrefoil magnetic fields are produced by the extended current loops.

• The virtual cathode from strong, point stimulation has a dog bone shape.

• The virtual cathode exists in three dimensions, and rotates with depth due to the differing fiber orientations.

• The shape of the virtual cathode is altered pharmacological agents that block ion channels.

• Fiber rotation can alter the shape of the virtual cathode recorded on the epicardium.

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• Point stimulation produces longitudinal hyperpolarization. • Point anodal stimulation can produce adjacent depolarization. • Simultaneous virtual cathodes and anodes explain make and break

stimulation. • Bipolar stimulation produces complex areas of depolarization and

hyperpolarization. • Directionally-dependent time constant of the action potential foot. • Uniform field defibrillation of hearts with curved fibers can

polarize membranes deep within the myocardium. • Strong point stimulation can produce quatrefoil spiral-wave reentry.

Phenomena unique to the cardiac bidomain with unequal intracellular and extracellular anisotropies, con’t

Optical Imaging Setup

Ca me ra M 1

M 2

B S D 1

D 2

F L T T o

F r a m e - G r a b b e r

So li d- St at e L as er ( 53 2 nm ) I s o l a t e d h e a r t

s t a i n e d w i t h d i - 4 - A N E P P S

M1,M2: Mirrors BS: Beam Splitter D1, D2: Diffusers FLT: Long-Pass Filter (590 nm) TL129 s4608 6/6/2000 TL129 8

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Vanderbilt Cardiac Imaging System

300 frames/sec 128x128 pixels or 1200 frames/sec 64x64 pixels

12-bit Resolution

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Information from Imaging Data

Structure Function Dynamics

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Point-Electrode Excitation of Refractory Tissue

Cathodal Current Anodal Current 1 mm

Fiber Direction

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Long-Standing Puzzle Why can the heart be stimulated electrically in four

different ways?

• Turning-on of negative current (cathodal make) • Turning-on of positive current (anodal make) • Turning-off of negative current (cathodal break) • Turning-off of positive current (anodal break)

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Four Modes of Cardiac

Activation F i b e r D i r e c t i o n

D e p o l a r i z e d

H y p e r p o l a r i z e d

A

B C

D E

C a t h o d a l M a k e

C a t h o d a l B r e a k

A n o d a l M a k e

A n o d a l B r e a k

R e s t i n g

2 m m

Cathode Anode

Make Break

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0 ms 2 4 6 8

0 ms 3 6 9 12

0 ms 2 4 6 8

1 mm

0 ms 3 6 9 12

Cathode Make

-10 mA

Anode Make +10 mA

Cathode Break

-2 mA

Anode Break +3mA

Depolarized

Hyperpolarized

<-2 -1 0 1

>2

∆F/F (%)

Fiber Direction

Synchronous Imaging of Point Activation Patterns --- Virtual Electrodes ---

(Wikswo, Lin and Abbas. Biophys. J . 69 :2195-2210, 1995)

10,000 pixel/frame

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Prediction In tissue with differing intracellular and extracellular anisotropies, a second, strong stimulus, delivered at the same location and during the vulnerable phase of the first wave front, results in a reentrant wave with four phase singularities. • Thick line - depolarization phase • Thin line - repolarization “ The formation of a re-entrant action potential wave front in tissue with unequal anisotropy ratios,” B.J. Roth and J.M. Saypol, International J. of Bifurcation and Chaos, 1: 927-928 (1991)

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Prediction of Quatrefoil Reentry

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Quatrefoil Reentry Predicted by the Bidomain Model

Fiber Direction

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Activation Sequence S1

S2 (CI: 140 ms) Cathode-break

S2 (CI: 180 ms) Cathode-make

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Quatrefoil Reentry from Cathodal Stimulation

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Isochronal Map of Quatrefoil Reentry (Cathodal S2)

Fiber Direction

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Functional Block is Characterized by Low-Amplitude Oscillation of Vm

T

L B

100 ms

-∆F/F 5 %

L

T

B

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Isochronal Map of Quatrefoil Reentry (Anodal S2)

Fiber Direction

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Prediction • The heart-medium interface, e.g., air versus

a conducting bath, affects the distribution of stimulus and action currents

• The epicardial transmembrane potential distribution will differ greatly for endocardial stimulation of a heart in air or in a bath.

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Endocardium

Epicardium

air bath

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Heart Free in the Bath

A monophasic anodal shock (100 V/5 ms, CI: 500 ms) is delivered from the apex of LV with the heart in the bath WITHOUT against the frontal glass plate. The response is dramatically different. TL129 S4625

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Heart Pressed against the Front Window

A monophasic anodal shock (100 V/5 ms, CI: 160 ms) is delivered from the apex of LV with the heart in the bath and pressed against the frontal glass plate. TL129 S4626

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Propagationless, Post-Shock

Charge-Diffusion

Low-amplitude oscillation at the border

37 ms after the Shock Excitation Pattern

dVm/dt Vm Distribution

(180 ms Coupling Interval) TL129 S4627

S1 S2

Frame interval: 0.8 ms (1200 frames/sec)

Response during a 200-V/5-ms Shock Cathodal shock

Anodal shock

Cathodal shock, heart against the plate

Anodal shock, heart against the plate

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Preservation of Endocardial Response with Insulating Plate

A.

B.

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The Problem of Defibrillation

If the heart is a cable with a length constant of 1-3 mm, the trans-membrane potential will fall below threshold within several length constants of the electrodes.

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Possible Answers • Discrete mechanisms Intracellular junctions Uncoupled bundles Patches of fat or collagen

“Cardiac tissue in an electrical field: A study in electrical stimulation,” N.A. Trayanova and B.J.Roth, Computers in Cardiology 1992, (IEEE Computer Society Press, 1992) pp. 695-698.

• Continuous mechanisms Cardiac surfaces Fiber ends Tissue anisotropy Fiber curvature Fiber branching Strand taper Fiber rotation

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Tissue Response to Field Shock

90 -10

45 -10

0 -10

O

O

O

0 +10

O

45 +10

O

90 +10

O

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Conclusion • Excitation with point electrode produces complex

patterns of virtual electrodes • Monophasic endocardial shocks elicit bipolar response

through the heart wall • Field shock produces initial bidomain response

independent of fiber orientation • Epicardial response from endocardial shock depends

on the heart-medium interface • Break excitation may be significant in defibrillation

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Future Studies

• Biphasic shock

• Heterogeneous bidomain

• Knockout mice

• “Break” defibrillation mechanism