The detailed mechanisms by which re-entry and ventricular fibrillation are initiated in the heart remain poorly understood because they are difficult to investigate experimentally. We have used a simplified excitable media computational model of action potential propagation to systematically study how re-entry can be produced by diffuse regions of inexcitable tissue. Patterns of excitable and inexcitable tissue were generated using a genetic algorithm. The inexcitable tissue was modeled in two ways: (i) diffusive, electrically connected but inexcitable tissue, or (ii) zero-flux, areas of tissue electrically disconnected in the same way as zero-flux boundary conditions. We were able to evolve patterns of diffuse inexcitable tissue that favored re-entry, but no single structure or pattern emerged. Diffusive inexcitable regions were inherently less arrhythmogenic than zero-flux inexcitable ones.

1.
D. P.
Zipes
and
H. J.
Wellens
, “
Sudden cardiac death
,”
Circulation
98
,
2334
2351
(
1998
).
2.
M. J.
Davies
, “
Pathological view of sudden cardiac death
,”
Br. Heart J.
45
,
88
96
(
1981
).
3.
S.
Goldstein
,
J. R.
Londis
,
R.
Leighton
,
G.
Ritter
,
C. M.
Vasu
, and
A.
Lantis
, “
Characteristics of the resuscitated out-of-hospital cardiac arrest victim with coronary heart disease
,”
Circulation
64
,
977
984
(
1981
).
4.
V. I.
Krinsky
, “
Spread of excitation in an inhomogeneous medium
,”
Biophysics (Engl. Transl.)
,
11
,
676
683
(
1966
).
5.
A. V.
Panfilov
and
J. P.
Keener
, “
Effects of high frequency stimulation on cardiac tissue with an inexcitable obstacle
,”
J. Theor. Biol.
163
,
439
448
(
1993
).
6.
K. I.
Agladze
,
J. P.
Keeper
,
S. C.
Müller
, and
A. V.
Panfilov
, “
Rotating spiral waves created by geometry
,”
Science
264
,
1746
1748
(
1994
).
7.
C.
Cabo
,
A. M.
Pertsov
,
W. T.
Baxter
,
J. M.
Davidenko
,
R. A.
Gray
, and
J.
Jalife
, “
Wavefront curvature as a cause of slow conduction and block in isolated cardiac muscle
,”
Circ. Res.
75
,
1014
1028
(
1994
).
8.
C.
Cabo
,
A. M.
Pertsov
,
J. M.
Davidenko
,
W. T.
Baxter
, and
R. A.
Gray
, “
Vortex shedding as a precursor of turbulent electrical activity in cardiac muscle
,”
Biophys. J.
70
,
1105
1111
(
1996
).
9.
A.
Pertsov
, in “
Scale of Geometric Structures Responsible for Discontinuous Propagation in Myocardial Tissue Conduction in the Heart
,” edited by
P. M.
Spooner
,
P. W.
Jayner
, and
J.
Jalife
(
Futura Publishing Co.
,
Armonk, NY
,
1997
).
10.
B. I.
Jugdutt
, “
Remodelling of the myocardium and potential targets in the collagen synthesis pathways
,”
Curr. Drug Targets Cardiovasc Haematol. Disord
3
,
1
30
(
2003
).
11.
B.
Swynghedauw
, “
Molecular mechanisms of myocardial remodeling
,”
Physiol. Rev.
79
,
215
262
(
1999
).
12.
J. M.
De Bakker
,
F. J. L.
Van Capelle
, and
M. J.
Janse
, “
Re-entry as a cause of ventricular tachycardia in patients with chronic ischemic heart diseases: Electrophysiologic and anatomic correlation
,”
Circulation
68
,
518
533
(
1988
).
13.
T. J.
Wu
,
J. J. C.
Ong
,
C.
Hwang
,
J. J.
Lee
,
M. C.
Fishbein
,
L.
Czer
,
A.
Trento
,
C.
Blanche
,
R. M.
Kass
,
W. J.
Mandel
,
H.
Karagueuzian
, and
P.
Chen
, “
Characteristics of wave fronts during ventricular fibrillation in human hearts with dilated cardiomyopathy: Role of increased fibrosis in the generation of re-entry
,”
J. Am. Coll. Cardiol.
32
,
187
196
(
1998
).
14.
H. H.
Hsia
and
F. E.
Marchlinski
, “
Characterization of the electroanatomic substrate for monomorphic ventricular tachycardia in patients with non-ischemic cardiomyopathy
,”
PACE
25
,
1114
1127
(
2002
).
15.
A. M.
Varnava
,
P. M.
Elliott
,
N.
Mahon
,
M. J.
Davies
, and
W. J.
McKenna
, “
Relation between myocyte disarray and outcome in hypertrophic cardiomyopathy
,”
Am. J. Cardiol.
88
,
275
279
(
2001
).
16.
H.
Hayashi
,
C.
Wang
,
Y.
Miyauchi
,
C.
Omichi
,
H.-N.
Pak
,
S.
Zhou
,
T.
Ohara
,
W. J.
Mandel
,
S.-F.
Lin
,
M. C.
Fishbein
,
P.-S.
Chen
, and
H. S.
Karagueuzian
, “
Ageing-related increase to inducible atrial fibrillation in the rat model
,”
J. Cardiovasc. Electrophysiol.
13
,
801
808
(
2002
).
17.
K. H. W. J.
Ten Tusscher
and
A. V.
Panfilov
, “
Influence of non-excitable cells on spiral breakup in two-dimensional and thee-dimensional excitable media
,”
Phys. Rev. E
68
,
062902
(
2003
).
18.
K. H. W. J.
Ten Tusscher
and
A. V.
Panfilov
, “
Wave propagation in excitable media with randomly distributed obstacles
,”
Multiscale Model. Simul.
3
,
265
282
(
2005
).
19.
H. W.
Vliegen
,
A.
van der Laarse
,
C. J.
Cornelisse
, and
F.
Eulderink
, “
A study on tissue composition, polyploidization and multinucleation
,”
Eur. Heart J.
12
,
488
494
(
1991
).
20.
P.
Camelliti
,
T. K.
Borg
, and
P.
Kohl
, “
Structural and functional characterization of cardiac fibroblasts
,”
Cardiovasc. Res.
65
,
40
51
(
2005
).
21.
W. A.
Hsueh
,
R. E.
Law
, and
Y. S.
Do
, “
Integrins, adhesion and cardiac remodeling
,”
Hypertension
31
,
176
180
(
1998
).
22.
K. T.
Weber
, “
Cardiac interstitium in health and disease: The Fibrillor Collagen Network
,”
J. Am. Coll. Cardiol.
13
,
1637
1652
(
1989
).
23.
V.
Pelouch
,
I. M. C.
Dixon
,
L.
Golfman
,
R. E.
Beamish
, and
N. S.
Dhalla
, “
Role of extracellular matrix proteins in heart function
,”
Mol. Cell. Biochem.
129
,
101
120
(
1994
).
24.
C. E.
Squires
,
G. P.
Escobar
,
J. F.
Payne
,
R. A.
Leonardi
,
D. K.
Goshorn
,
N. J.
Sheats
,
I. M.
Mains
,
J. T.
Mingoia
,
E. C.
Flack
, and
M. L.
Lindsey
, “
Altered fibroblast function following myocardial infarction
,”
J. Mol. Cell. Cardiol.
39
,
699
707
(
2005
).
25.
M. J.
Davies
and
A.
Pomerance
, “
Quantitative study of ageing changes in the human sinoartrial mode and internodal tracts
,”
Br. Heart J.
34
,
150
152
(
1972
).
26.
C. P.
Alder
,
W. P.
Ringdale
, and
N.
Böhm
, “
DNS-gehalt und zellzahl in hertz und leber von kindern
,”
Pathol. Res. Pract.
172
,
25
41
(
1981
).
27.
I.
Shiraishi
,
T.
Takamatsu
,
T.
Minanikawa
,
Z.
Onouchi
, and
S.
Fujita
, “
Quantitative histological analysis of the human sinoatrial node during growth and ageing
,”
Circulation
85
,
2176
2184
(
1992
).
28.
J. M. T.
de Bakker
,
M.
Stein
, and
V. M.
van Rijen
, “
Three-dimensional anatomic structures as substrate for ventricular tachycardia/ventricular fibrillation
,”
Heart Rhythm
2
,
777
779
(
2005
).
29.
G.
Bub
,
A.
Shrier
, and
L.
Glass
, “
Spiral wave generation in heterogeneous excitable media
,”
Phys. Rev. Lett.
88
,
058101
(
2002
).
30.
B. E.
Steinberg
,
L.
Glass
,
A.
Shrier
, and
G.
Bub
, “
The role of heterogeneities and intercellular coupling in wave propagation in cardiac tissue
,”
Philos. Trans. R. Soc. London, Ser. A
364
,
1299
1231
(
2005
).
31.
P.
Kuklik
and
J.
Zebrowski
, “
Reentry wave formation in excitable media with stochastically generated inhomogeneities
,”
Chaos
15
,
033301
033307
(
2005
).
32.
J. H.
Holland
,
Adaptation in Natural and Artificial Systems
(
University of Michigan Press
,
Ann Arbor, MI
,
1992
).
33.
L.
Davis
,
Handbook of Genetic Algorithms
(
Van Nostrand Reinhold
,
New York
,
1991
).
34.
J.
McCall
, “
Genetic algorithms for modelling and optimization
,”
J. Comput. Appl. Math.
184
,
205
272
(
2005
).
35.
R. H.
Clayton
, “
Computational models of normal and abnormal action potential propagation in cardiac tissue: Linking experimental and clinical cardiology
,”
Physiol. Meas
22
,
R15
R34
(
2001
).
36.
R. A.
FitzHugh
, “
Impulses and physiological states in theoretical models of nerve membrane
,”
Biophys. J.
1
,
445
466
(
1961
).
37.
J.
Nagumo
,
S.
Arimoto
, and
S.
Yoshizawa
, “
Active pulse transmission line simulating nerve axion
,”
Proc. IRE
50
,
2061
(
1962
).
38.
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
).
39.
P. M.
Sutcliffe
and
A. T.
Winfree
, “
Stability of knots in excitable media
,”
Phys. Rev. E
68
,
016218
(
2003
).
40.
A. T.
Winfree
, “
Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media
,”
Chaos
1
,
1054
1500
(
1991
).
41.
I.
Rechenberg
,
Evolutionsstrategie: Optimierung Technischer Systeme nach Prinzipien der Biologischen Evolution
(
Frommann-Holzboog Verlag
,
Stuttgart
,
1973
).
42.
H. P.
Schwefel
,
Numerical Optimization for Computer Models
(
John Wiley
,
Chichester, UK
,
1981
).
43.
Z.
Michalewicz
,
Genetic Algorithms+Data Structures=Evolution
(
Springer-Verlag, Berlin
,
1996
).
44.
L. M.
Schmitt
, “
Fundamental study theory of genetic algorithms
,”
Theor. Comput. Sci.
259
,
1
61
(
2001
).
45.
P.
Camelliti
,
C. R.
Green
,
I.
LeGrice
, and
P.
Kohl
, “
Fibroblast network in rabbit sinoatrial node: Structural and functional identification of homogeneous and heterogeneous coupling
,”
Circ. Res.
94
,
828
835
(
2004
).
46.
K.
Goshima
and
Y.
Tonomura
, “
Synchronized beating of embryonic mouse myocardial cells mediated by FL cells in monolayer culture
,”
Exp. Cell Res.
56
,
387
392
(
1969
).
47.
G.
Gaudesius
,
M.
Miragoli
,
S. P.
Thomas
, and
S.
Rohr
, “
Coupling of cardiac electrical activity over extended distances by fibroblasts of cardiac origin
,”
Circ. Res.
93
,
421
428
(
2003
).
48.
L.
Brown
, “
Cardiac extracellular matrix a dynamic entity
,”
Am. J. Physiol. Heart Circ. Physiol.
289
,
H973
H974
(
2005
).
49.
M.
Bär
,
E.
Meron
, and
C.
Utzny
, “
Pattern formation on anisotropic and heterogeneous catalytic surfaces
,”
Chaos
12
,
204
214
(
2002
).
50.
J.
Sielewiesick
and
J.
Górecki
, “
Pinwheel-like structures resulting from interactions of plane pulses of excitation
,”
Phys. Rev. E
66
,
067101
(
2002
).
51.
A. V.
Panfilov
, “
Spiral breakup in an array of coupled cells: The role of the intercellular conductance
,”
Phys. Rev. Lett.
88
,
118101
(
2002
).
52.
G.
Pruessner
and
H. J.
Jensen
, “
Efficient algorithm for the forest fire model
,”
Phys. Rev. E
70
,
066707
(
2004
).
You do not currently have access to this content.