A numerical method for determining the localized initial condition for some mathematical models of the heart excitation
Matematičeskoe modelirovanie, Tome 24 (2012) no. 7, pp. 59-66.

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A numerical method for determining the localized initial conditions for some mathematical models of the heart excitation is proposed. In the direct problem the process of changing field potential in two domains, corresponding to a heart and a torso, is modelled. A change of the potential in the heart is described by FitzHugh–Nagumo model or Aliev–Panfilov model for 2D domain. The inverse problem consists in determining the localized initial excitation of the heart from potential measurements on the boundary of the torso. The results of numerical experiments are presented.
Keywords: inverse problem, FitzHugh–Nagumo model, Aliev–Panfilov model, numerical method.
Mots-clés : excitation source
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A. M. Denisov; I. A. Pavelchak. A numerical method for determining the localized initial condition for some mathematical models of the heart excitation. Matematičeskoe modelirovanie, Tome 24 (2012) no. 7, pp. 59-66. http://geodesic.mathdoc.fr/item/MM_2012_24_7_a4/

[1] FitzHugh R., “Mathematical models of threshold phenomena in the nerve membrane”, Bull. Math. Biophysics, 1955, no. 17, 257–278 | DOI

[2] FitzHugh R., “Impulses and physiological states in theoretical models of nerve membrane”, Biophysical J., 1961, no. 1, 445–466 | DOI | MR

[3] Nagumo J., Arimoto S., Yoshizawa S., “An active pulse transmission line simulating nerve axon”, Proc. IRE, 1962, no. 50, 2061–2070 | DOI

[4] Aliev R. R., Panfilov A. V., “A simple two-variable model of cardiac excitation”, Chaos Solutions and Fractals, 7:3 (1996), 293–301 | DOI

[5] Sundnes J., Lines G. T., Cai X. et al., Computing the Electrical Activity in the Heart, Springer, 2006, 311 pp. | MR | Zbl

[6] Elkin Yu. E., Moskalenko A. V., Starmer Ch. F., “Spontannaya ostanovka dreifa spiralnoi volny v odnorodnoi vozbudimoi srede”, Matematicheskaya biologiya i bioinformatika, 2:1 (2007), 73–81 | MR

[7] Medvedinskii A. B., Rusakov A. V., Moskalenko A. V. i dr., “Issledovanie avtovolnovykh mekhanizmov variabelnosti elektrokardiogramm vo vremya vysokochastotnykh aritmii: rezultaty matematicheskogo modelirovaniya”, Biofizika, 48:2 (2003), 314–323

[8] He Y., Keyes D. E., “Reconstructing parameters of the FitzHugh–Nagumo system from boundary potential measurements”, J. Comput. Neurosci., 23:2 (2007), 251–264 | DOI | MR

[9] Pavelchak I. A., Tuikina S. R., “Metod chislennogo resheniya obratnoi zadachi dlya modifitsirovannoi modeli Fitts-Khyu–Nagumo”, Prikladnaya matematika i informatika, 2011, no. 37, 98–106

[10] Pavelchak I. A., “Chislennyi metod opredeleniya lokalizovannogo nachalnogo usloviya v modelyakh Fitts-Khyu–Nagumo i Alieva–Panfilova”, Vestnik MGU. Vychislitelnaya matematika i kibernetika, 2011, no. 3, 7–13 | MR

[11] Titomir L. I., Kneppo L., Matematicheskoe modelirovanie bioelektricheskogo generatora serdtsa, Nauka, M., 1999, 447 pp.

[12] Denisov A. M., Kalinin V. V., “Obratnaya zadacha dlya matematicheskikh modelei vozbuzhdeniya serdtsa”, Zhurnal vychisl. matem. i matem. fiziki, 50:3 (2010), 539–543 | MR | Zbl