Excitable membranes are an important type of nonlinear dynamical system, and their study can be used to provide a connection between physical and biological circuits. We discuss two models of excitable membranes important in cardiac and neural tissues. One model is based on the Fitzhugh–Nagumo equations, and the other is based on a three-transistor excitable circuit. We construct a circuit that simulates reentrant tachycardia and its treatment by surgical ablation. This project is appropriate for advanced undergraduates as a laboratory capstone project or as a senior thesis or honors project and can also be a collaborative project, with one student responsible for the computational predictions and another for the circuit construction and measurements.

1.
D. U.
Silverthorn
,
W. C.
Ober
,
C. W.
Garrison
, and
A. C.
Silverthorn
,
Human Physiology, An Integrated Approach
(
Prentice-Hall
,
Upper Saddle River, NJ
,
1998
).
2.
R.
Fitzhugh
, “
Impulses and physiological states in theoretical models of nerve membrane
,”
Biophys. J.
1
,
445
466
(
1961
).
3.
J.
Nagumo
,
S.
Arimoto
, and
S.
Yoshizawa
, “
An active pulse transmission line simulating nerve axon
,”
Proc. IRE
50
,
2061
2070
(
1962
).
4.
P. H.
Bunton
,
W. P.
Henry
, and
J. P.
Wikswo
, “
A simple integrated circuit model of propagation along an excitable axon
,”
Am. J. Phys.
64
,
602
606
(
1996
).
5.
G. Y.
Yuan
,
S. G.
Chen
, and
S. P.
Yang
, “
Eliminating spiral waves and spatiotemporal chaos using feedback signal
,”
Eur. Phys. J. B
58
,
331
336
(
2007
).
6.
R.
Cassia-Moura
,
F. G.
Xie
, and
H. A.
Cerdeira
, “
Effect of heterogeneity on spiral wave dynamics in simulated cardiac tissue
,”
Int. J. Bifurcation Chaos Appl. Sci. Eng.
14
,
3363
3375
(
2004
).
7.
I. B.
Schwartz
,
I.
Triandaf
,
J. M.
Starobin
, and
Y. B.
Chernyak
, “
Origin of quasiperiodic dynamics in excitable media
,”
Phys. Rev. E
61
,
7208
7211
(
2000
).
8.
M. H.
Ross
and
W.
Pawlina
,
Histology A Text and Atlas
(
Lippincott, Williams and Wilkins
,
Baltimore, MD
,
2006
).
9.
A.
Patel
and
S. M.
Markowitz
, “
Atrial tachycardia: Mechanisms and management
,”
Expert Rev. Cardiovasc. Ther.
6
,
811
822
(
2008
).
10.
A. L.
Hodgkin
and
A. F.
Huxley
, “
A quantitative description of membrane current and its application to conduction and excitation in nerve
,”
J. Physiol. (London)
117
,
500
544
(
1952
).
11.
B.
van der Pol
and
J.
van der Mark
, “
The heartbeat considered as a relaxation oscillator, and an electrical model of the heart
,”
Philos. Mag.
6
,
763
775
(
1928
).
12.
R. C.
Hilborn
,
Chaos and Nonlinear Dynamics
, 2nd ed. (
Oxford U.P.
,
New York
,
2003
), pp.
97
99
.
13.
J. C.
Comte
and
P.
Marquié
, “
Generation of nonlinear current-voltage characteristics. A general method
,”
Int. J. Bifurcation Chaos Appl. Sci. Eng.
12
,
447
449
(
2002
).
14.
P.
Marquié
,
J. C.
Comte
, and
S.
Morfu
, “
Analog simulation of neural information propagation using an electrical Fitzhugh–Nagumo lattice
,”
Chaos, Solitons Fractals
19
,
27
30
(
2004
).
15.
J. J.
Ebers
and
J. L.
Moll
, “
Large signal behavior of junction transistors
,”
Proc. IRE
42
,
1761
1772
(
1954
).
16.
J. D.
Irwin
and
D. V.
Kerns
, Jr.
,
Introduction to Electrical Engineering
(
Prentice-Hall
,
Upper Saddle River, NJ
,
1995
), p.
333
.
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.