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

Abstract. In this study, we explore the mechanism of macrophage polarization and its significance in the development of large-scale infarction with favorable outcomes, using a minimal mathematical model of aseptic inflammation dynamics. The problem is considered in the local approximation and in the two-dimensional non-stationary formulation. The study aims to address the pertinent problem of analyzing general principles governing macrophage polarization in the context of devising therapeutic strategies and refining the "therapeutic window". Key trends are identified to enhance the effectiveness of macrophage polarization for therapeutic purposes, along with providing approximate estimations of optimal macrophage interventions that yield organ-preserving and regenerative effects. Our findings reveal that M1/M2 macrophage polarization results from an additive interplay of at least two mechanisms - cytokine-dependent activation and reprogramming of activated macrophages. Furthermore, our modeling data demonstrate the pivotal role of macrophage reprogramming as a direct response to microenvironmental changes, facilitating favorable disease progression and its outcomes. Moreover, we establish that the process of macrophage polarization plays a crucial role in localizing focal inflammation, leading to the formation of the infarction core within finite dimensions and  quasi-stationary structure at the periphery, comprising immune cell clusters. The modeling results exhibit qualitative and quantitative agreement with the experimental data. Importantly, the computational experiments results align with the majority of laboratory and clinical studies, emphasizing the therapeutic potential of macrophage polarization management as a promising treatment strategy. The paper is a follow-up of the previously published work series, devoted to the study of spatial and temporal aspects of the  inflammation and death processes development in heart muscle cells.

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