The localized inverse problem of electrocardiography is formulated and a solution method is proposed. The method allows determining the potential of the cardiac electric field on one of the heart sections.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. C. Barr and M. S. Spach, Inverse Solutions Directly in terms of Potentials [Russian translation], Med-itsina, Moscow (1979).
J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, K.-A. Mardal, and A. Tveito, Computing the Electrical Activity of the Heart, Springer, Berlin (2006).
A. M. Denisov, E. V. Zakharov, A. V. Kalinin, and V. V. Kalinin, “Application of Tikhonov’s regulatization method to solving the electrocardiographic inverse problem,” Vestnik MGU, Ser. 15: Vychisl. Matem. Kibern., No. 2, 5–10 (2008).
A. M. Denisov, E. V. Zakharov, A. V. Kalinin, and V. V. Kalinin, “Numerical methods for some inverse problems of the electrophysiology of the heart,” Diff. Uravn., 45, No. 7, 1014–1022 (2009).
E. V. Zakharov and A. V. Kalinin, “Numerical solution of the three-dimensional Dirichlet problem in a piecewise-homogeneous medium by the boundary integral equation method,” Zh. Vychisl. Mat. Matem. Fiz., 49, No. 7, 1197–1206 (2009).
A. M. Denisov, E. V. Zakharov, A. V. Kalinin, and V. V. Kalinin, “Numerical solution of the inverse electrocardiographic problem for a medium with piecewise-constant electrical conductivity,” Zh. Vychisl. Mat. Matem. Fiz., No. 7, 1233–1239 (2010).
A. V. Kalinin, “Iteration algorithm for solving the inverse electrocardiographic problem for a medium with a piecewise-constant electrical conductivity,” Prikl. Mat. Informat., MGU, No. 34, 35–40 (2010).
A. M. Denisov, E. V. Zakharov, and A. V. Kalinin, “A method to determine a point arrhythmia focus on the cardiac surface by solving the inverse electrocardiographic problem,” Mat. Modelirovanie, 24, No. 4, 22–30 (2012).
M. M. Lavrent’ev, V. G. Romanov, and S. P. Shishatskii, Ill-Posed Problems in Mathematical Physics and Analysis [in Russian], Nauka, Moscow (1980).
E. M. Landis, “Some issues of qualitative theory of elliptical and parabolic equations,” UMN, 14, No. 2, 21–85 (959).
R. Lattes and J.-L. Lions, Quasi-Reversibility Method and Its Applications [Russian translation], Mir, Moscow (1970).
V. A. Kozlov, V. G. Maz’ya, and A. V. Fomin, “An iteration method for the Cauchy problem for ellipti-cal equations,” Zh. Vychil. Mat. Matem. Fiz., 31, No. 1, 64–74 (1991).
A. A. Samarskii and P. N. Vabishchev, Numerical Methods for Inverse Problems of Mathematical Physics [in Russian], Editorial URSS, Moscow (2004).
A. N. Tikhonov and V. Ya. Arsenin, Methods of Solution for Ill-Posed Problems [in Russian], Nauka, Moscow (1986).
G. R. Mirams, C. J. Arthurs, M. O. Bernabeu, R. Bordas, and others, “Chaste: An open source C++ library for computational physiology and biology,” PLoS Comput. Biol., 9, No. 3, e1002970 (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Matematika i Informatika, No. 45, 2014, pp. 47–54.
Rights and permissions
About this article
Cite this article
Denisov, A.M., Zakharov, E.V. & Kalinin, A.V. Numerical Solution of the Localized Inverse Problem of Electrocardiography. Comput Math Model 26, 168–174 (2015). https://doi.org/10.1007/s10598-015-9265-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-015-9265-2