¹Federal Research Center for Information and Computational Technologies, Novosibirsk, Russia
²Novosibirsk National Research State University, Novosibirsk, Russia

Abstract. The results of numerical modelling of the necrotic death of myocardial cells and immune response dynamics in type II ischemic infarction are presented. The initial conditions were consistent with the experimental data. The adopted minimal mathematical model focused on the balance of pro- and anti-inflammatory factors of aseptic inflammation and their influence on the process of cardiomyocyte death. The issue of the formation of nonlinear dynamic structures in the adopted reaction-diffusion system of equations in the absence of convective terms has been examined. It is shown that a stable localization of the solution of the initial-boundary value problem within the spatial region of practically unchanged size is observed in a fairly wide range of parameters of the initial conditions set in the form of bell-shaped finite functions. 

Qualitative properties of solutions allow biological interpretation. Within the framework of the adopted model, we considered several important examples and, on this basis, described a typical scenario of a heart attack with a favorable outcome. We have studied the most general patterns of the formation of demarcation inflammation near a large necrosis focus in a typical acute infarction scenario, taking into account individual differences in the topology of the coronary vascular network and the topography of the infarction. The adequacy of the results is confirmed by quantitative and qualitative agreement with a fairly wide range of experimental data on the dynamics of infarction in the left ventricle of the mouse heart.

Key words: mathematical model, reaction–diffusion equations, method of fractional steps, acute myocardial infarction, local injury, biochemistry, cardiomyocytes, cytokines, macrophages, demarcation inflammation, structures.