THE SIMULATION OF ELECTRICAL SIGNALS PROPAGATION IN THE HEART MUSCLE OF THE HUMAN USING SOFTWARE PACKAGE COMSOL

Abstract

This paper is devoted to the modeling of the electrical system of the man’s cardiac tissue. The paper aims creating of the model, that geometrical structure is close to the actual geometry of the human heart. The processes occurring in the heart muscle are modeling by solving a system of nonlinear differential equations. In the first stage, the conceptual problem can be formulated as follows: to create a model of the transmission of electrical signals, the geometrical structure of which is close to the actual geometry of the heart muscle. The next stage of the technology cycle is a mathematical formulation of the problem. In this paper, it can be formulated as a solution to a system of nonlinear differential equations with given initial and boundary conditions. At the stage of constructing a mathematical model it is necessary to resort to some assumptions. In particular, you should consider the fact that the geometry created by the heart muscle will be enough simplified with the average size of a real heart and will be 54 × 54 × 70 mm. At the stage of construction of computing algorithms to the mathematical model mathematical methods to its algorithmization was used. As considered in this paper, the system of nonlinear differential equations has no analytic solution, so to get the results it was decided to use a numerical method – the finite element method. To implement the finite element method mathematical modeling package COMSOL was selected. In the next stage model was built using the COMSOL Multiphysics, including input of the physical parameters, initial and boundary conditions, the finite element mesh generation. As a result, a visual solution of the system FitzHugh–Nagumo has been received; graphs are showing the propagation of the electrical signal in the heart. In the fifth stage, the representation, processing, analysis and interpretation of the results are given. Thus, the task can be broken down by stages of computational experiment. Forecasting based on the constructed model at this stage is not possible due to the simplifications in the model, but a more detailed study of the problem can be done.