MODELLING OF ELECTRODYNAMIC, HYDRODYNAMIC, AND DEFORMATION PROCESSES IN THE SYSTEM «MUSCLE TISSUE OF THE HEART - VESSELS - BLOOD» - Vasserman, I.N.; Shestakov, A.P. (Perm Federal Research Centre Journal, 2016)
A mathematical model, describing the electromagnetic processes in the human heart, is proposed. It represents a system of nonlinear partial differential equations. A numerical algorithm and its implementation, based on FEniCS, a finite element library, are developed for this model. The interaction between a wave of action potential and an additional source of excitation in a two-dimensional case is simulated. As a result it was shown that the generation of a spiral wave occurs only if the additional excitation is localized sharply on the «tail» of the wave (in the vicinity behind the wave). The generation of a spiral wave in the three-dimensional model of the human heart is also considered. The process of propagation of the excitation wave in the field of heterogeneous electrodynamic parameters, which cause unidirectional blocking of the wave propagation, is considered. The inhomogeneous conductivity and action potential duration were considered. By using the combination of such domains, one can simulate heterogeneity, leading to self-excitation and formation of a spiral wave. The influence of anisotropy of the electrical properties on the propagation of the excitation wave is shown for ventricle segments of the heart. A model of the evolution of active myocardial stresses, based on the HMT-model, is developed. To test it a series of numerical experiments, including myocardial reaction to a change in intracellular calcium concentration, is carried out. To join the fibers in the three-dimensional structure, a model of myocardial is formed on the basis of solid mechanics.