A numerical method of parameter reconstruction in the FitzHugh-Nagumo and Aliev-Panfilov models

Authors

  • I.A. Pavelchak

Keywords:

FitzHugh-Nagumo and Aliev-Panfilov models
inverse problem
numerical methods

Abstract

An inverse problem for the FitzHugh-Nagumo and Aliev-Panfilov models describing the wave propagation in excitable media is considered. The problem consists in the reconstruction of model parameters using the measurements performed on the boundary of a plane domain. Various sets of the parameters can be considered as unknown. A numerical method for solving the inverse problem is proposed. The numerical results are discussed.

New computational technologies

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Published

2012-02-20

Issue

Vol. 13 (2012): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biography

I.A. Pavelchak

Lomonosov Moscow State University,
Faculty of Computational Mathematics and Cybernetics
• PhD Student

References

  1. FitzHugh R. Mathematical models of threshold phenomena in the nerve membrane // Bull. Math. Biophysics. 1955. 17, N 4. 257-278.
  2. FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane // Biophysical J. 1961. 1, N 6. 445-466.
  3. Nagumo J., Arimoto S., Yoshizawa S. An active pulse transmission line simulating nerve axon // Proc. IRE. 1962. 50, N 10. 2061-2070.
  4. Aliev R.R., Panfilov A.V. A simple two-variable model of cardiac excitation // Chaos Solutions and Fractals. 1996. 7, N 3. 293-301.
  5. Sundnes J., Lines G.T., Cai X. et al. Computing the electrical activity in the heart. Berlin: Springer, 2006.
  6. Елькин Ю.Е., Москаленко А.В., Стармер Ч.Ф. Спонтанная остановка дрейфа спиральной волны в однородной возбудимой среде // Математическая биология и биоинформатика. 2007. 2, № 1. 73-81.
  7. Медвединский А.Б., Русаков А.В., Москаленко А.В. и др. Исследование автоволновых механизмов вариабельности электрокардиограмм во время высокочастотных аритмий: результаты математического моделирования // Биофизика. 2003. 48, № 2. 314-323.
  8. He Y., Keyes D.E. Reconstructing parameters of the FitzHugh-Nagumo system from boundary potential measurements // J. Comput. Neurosci. 2007. 23, N 2. 251-264.
  9. Moreau-Villeger V., Delingette H., Sermesant M. et al. Building maps of local apparent conductivity of the epicardium with a 2-D electrophysiological model of the heart // IEEE Trans. on Biomedical Engineering. 2006. 53, N 8. 1457-1466.
  10. Cox S.J., Wagner A. Lateral overdetermination of the FitzHugh-Nagumo system // Inverse Problems. 2004. 20, N 5. 1639-1647.