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

Authors

  • I.A. Pavelchak Lomonosov Moscow State University

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.

Author Biography

I.A. Pavelchak

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.

Published

20-02-2012

How to Cite

Павельчак И. A Numerical Method of Parameter Reconstruction in the FitzHugh-Nagumo and Aliev-Panfilov Models // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2012. 13. 172-176

Issue

Section

Section 1. Numerical methods and applications