Abstract
The Fenton-Karma model is a simplification of complex ionic models of cardiac membrane that reproduces quantitatively many of the characteristics of heart cells; its behavior is simple enough to be understood analytically. In this paper, a map is derived that approximates the response of the Fenton-Karma model to stimulation in zero spatial dimensions. This map contains some amount of memory, describing the action potential duration as a function of the previous diastolic interval and the previous action potential duration. Results obtained from iteration of the map and numerical simulations of the Fenton-Karma model are in good agreement. In particular, the iterated map admits different types of solutions corresponding to various dynamical behavior of the cardiac cell, such as 1:1 and 2:1 patterns.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1034-1042 |
| Number of pages | 9 |
| Journal | Chaos |
| Volume | 12 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 2002 |
Fingerprint
Cite this
Analysis of the Fenton-Karma model through an approximation by a one-dimensional map. / Tolkacheva, E. G.; Schaeffer, D. G.; Gauthier, D. J.; Mitchell, C. C.
In: Chaos, Vol. 12, No. 4, 12.2002, p. 1034-1042.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Analysis of the Fenton-Karma model through an approximation by a one-dimensional map
AU - Tolkacheva, E. G.
AU - Schaeffer, D. G.
AU - Gauthier, D. J.
AU - Mitchell, C. C.
PY - 2002/12
Y1 - 2002/12
N2 - The Fenton-Karma model is a simplification of complex ionic models of cardiac membrane that reproduces quantitatively many of the characteristics of heart cells; its behavior is simple enough to be understood analytically. In this paper, a map is derived that approximates the response of the Fenton-Karma model to stimulation in zero spatial dimensions. This map contains some amount of memory, describing the action potential duration as a function of the previous diastolic interval and the previous action potential duration. Results obtained from iteration of the map and numerical simulations of the Fenton-Karma model are in good agreement. In particular, the iterated map admits different types of solutions corresponding to various dynamical behavior of the cardiac cell, such as 1:1 and 2:1 patterns.
AB - The Fenton-Karma model is a simplification of complex ionic models of cardiac membrane that reproduces quantitatively many of the characteristics of heart cells; its behavior is simple enough to be understood analytically. In this paper, a map is derived that approximates the response of the Fenton-Karma model to stimulation in zero spatial dimensions. This map contains some amount of memory, describing the action potential duration as a function of the previous diastolic interval and the previous action potential duration. Results obtained from iteration of the map and numerical simulations of the Fenton-Karma model are in good agreement. In particular, the iterated map admits different types of solutions corresponding to various dynamical behavior of the cardiac cell, such as 1:1 and 2:1 patterns.
UR - http://www.scopus.com/inward/record.url?scp=0036921378&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036921378&partnerID=8YFLogxK
U2 - 10.1063/1.1515170
DO - 10.1063/1.1515170
M3 - Article
C2 - 12779627
AN - SCOPUS:0036921378
VL - 12
SP - 1034
EP - 1042
JO - Chaos
JF - Chaos
SN - 1054-1500
IS - 4
ER -