Geodesic
Algorithms for the intraoperative modeling of the dynamics of atrial excitation
Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 2, pp. 3-11.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem is studied of the modeling of atrial excitation in clinical conditions. The basic model requirements and the existing methods are considered for modeling the excitation dynamics of the contractile myocardium. The cellular automaton theory serves as the basis of a model. The calculations are carried out on a rectangular grid. For each pair of the cellular automaton elements, the time delay of the excitation transfer is computed. Such an approach allows us to adapt the model to the particular data obtained by electrophysiological tests. 
@article{SJIM_2005_8_2_a0,
     author = {S. I. Andreev and V. A. Kochegurov},
     title = {Algorithms for the intraoperative modeling of the dynamics of atrial excitation},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {3--11},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2005_8_2_a0/}
}
TY  - JOUR
AU  - S. I. Andreev
AU  - V. A. Kochegurov
TI  - Algorithms for the intraoperative modeling of the dynamics of atrial excitation
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2005
SP  - 3
EP  - 11
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2005_8_2_a0/
LA  - ru
ID  - SJIM_2005_8_2_a0
ER  - 
%0 Journal Article
%A S. I. Andreev
%A V. A. Kochegurov
%T Algorithms for the intraoperative modeling of the dynamics of atrial excitation
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2005
%P 3-11
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2005_8_2_a0/
%G ru
%F SJIM_2005_8_2_a0
S. I. Andreev; V. A. Kochegurov. Algorithms for the intraoperative modeling of the dynamics of atrial excitation. Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 2, pp. 3-11. http://geodesic.mathdoc.fr/item/SJIM_2005_8_2_a0/

[1] Holden A. V., Biktashev V. N., “Computational biology of propagation in excitable media models of cardiac tissue”, Chaos. Solitons Fractals, 2000, no. 8, 1643–1658 | MR

[2] Simelius K., Nenonen J., Horácek M., “Modeling cardiac ventricular activation”, Internat. J. Bioelectromagnetism, 2001, no. 2, 51–58

[3] Kaplan D. T., Smith J. M., Saxber B. E. H., Cohen R. J., “Nonlinear dynamics in cardiac conduction”, Math. Biosci., 1988, no. 90, 19–48 | DOI | MR | Zbl

[4] Wienier N., Rosenblueth A., “The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle”, Arch. Inst. Cardiology (Mexico), 1946, no. 16, 205–265 | MR

[5] Luo C. H., Rudy Y., “A model of the ventricular cardiac action potential: depolarization, repolarization, and their interaction”, Circ. Res., 1991, no. 6, 1501–1526

[6] Luo C. H., Rudy Y., “A dynamicmodel of the cardiac ventricular action potential. I: Simulations of ionic currents and concentration changes”, Circ. Res., 1994, no. 6, 1071–1096

[7] Luo C. H., Rudy Y., “A dynamic model of the cardiac ventricular action potential. II: Afterdepolarizations, triggered activity, and potentiation”, Circ. Res., 1994, no. 6, 1097–1113

[8] Ivanitskii G. R., “Biofizika na rubezhe stoletiya: avtovolny”, Biofizika, 1999, no. 5, 773–795

[9] Vang V. K., “Issledovanie prostranstvenno raspredelennykh dinamicheskikh sistem metodami veroyatnostnogo kletochnogo avtomata”, Uspekhi fiz. nauk, 1999, no. 5, 481–505 | DOI