Mathematical Modeling of the Innate Immune Response Dynamics in Myocardial Infarction. Part I. Hierarchy of Mathematical Models

Abstract

In this work, a hierarchy of six mathematical models of a mechanistic type, previously focused on the description of aseptic inflammation in a surgical skin wound, is used for the first time to describe events in the core of ischemic injury in myocardial infarction. Computational experiments have shown that all simplified models of this hierarchy, obtained in the process of reducing one of the most complete models, inherit its qualitative properties in a biologically significant range of parameters. Two strategies for calibrating models based on data on the dynamics of inflammation in the infarct nucleus caused by ligation of the left coronary artery in mice are considered. In the first strategy, the optimal set of parameters is defined for each model, and in the second strategy, «universal» set of parameter values is found, common to all models of the hierarchy. It is shown that the changes in parameters during the transition to a new, more simplified level of idealization, which resulted from the implementation of the first calibration strategy, should be considered not as random variations, but as belonging to a single «global» distribution of data combining information about all models of the hierarchy. The dependence of the solution of the initial problem on the parameters and initial conditions is investigated, biological interpretations of the results obtained in the context of a heart attack are given. The presented data demonstrate that the scenario observed both in vivo and in a computational experiment is one of the typical scenarios of an innate immune response to local tissue damage, realized in myocardial infarction and in a surgical skin wound, and all the results of numerical modeling obtained using this hierarchy of models for aseptic inflammation in surgical wound injury are valid and in case of myocardial infarction. One of the biological mechanisms associated with the chronicity of inflammation, which determines the severe course of a heart attack or a high risk of a terminal scenario, has been demonstrated. Some options for managing inflammation to reduce the severity of a heart attack have been identified. A more detailed study of the patterns of development of the immune response in heart attack against the background of concomitant pathologies, including the most common dysfunctions of blood cells or disorders of its cellular composition, is the subject of upcoming research.