How to Explain Why "Unequal Anisotropy

Ratios" is Important Using Pictures but No

MathematicsBradley J. Roth

Dept. Physics, Oakland University

1) Rotation

2) Distribution

Two Mechanisms

R o t a t i o n

E

J

U n e q u a l A n i s o t r o p y R a t i o s

Ei

Ji

Ee

Je

x

yEi

Ee

Je

Ji

Ji+ J

e

Holzer et al., “High Resolution Magnetic Images of Planar Wave Fronts Reveal Bidomain Properties of Cardiac Tissue”Biophys. J., 87:4326–4332, 2004.

x

y

E i E e

+ + + ++

- - - - -

+ +

- -

J eJ i

J i + J e

D

H

DD

H H

x

y

Ei

Ee

Ji

Je

Ei

Ee

Ji

Je

Ei

Ee

Ji

Je

D

H

D

H

D

H

x

y

Ei

Ee

Ji

Je

Ee

Ei

Ji

Je

r

θ

Ji

Je

Ei E

e

D

H

Wikswo et al., “Virtual Electrodes in Cardiac Tissue: A CommonMechanism for Anodal and Cathodal Stimulation” Biophys. J., 69:2195-2210, 1995.

D i s t r i b u t i o n

Ji

Je

U n e q u a l A n i s o t r o p y R a t i o s

Ji

Je

Ji

Je

x

y

Ji

Je

Je

Ji

H

H

H

+ V - V

x

y

Ji

Je

Ji

Je

Ji

Je

DH

Ji

Ji

Je

Je

D H

+ V - V

Ji

Je

x

y

x

y

Ji

Je

Ji

Je

Ji

Je

D

H

Woods et al., “Virtual electrode effects around an artificial heterogeneity during field stimulation of cardiac tissue” Heart Rhythm, 3:751-751, 2006

x

y

Ji

Je

Ji

Je

Ji

Je

D

H

Woods et al., “Virtual electrode effects around an artificial heterogeneity during field stimulation of cardiac tissue” Heart Rhythm, 3:751-751, 2006

Roth and Langrill Beaudoin, “Approximate analytical solutions of the Bidomain equations for electrical stimulation of cardiac tissue with curving fibers.” Phys Rev E, 67: 051925, 2003.

Quiz

Roth and Langrill Beaudoin, “Approximate analytical solutions of the Bidomain equations for electrical stimulation of cardiac tissue with curving fibers.” Phys Rev E, 67: 051925, 2003.

Supported by the National Institutes of Healthand the American Heart Association--Midwest Affiliate