Optimal control of the immune response synchronizing the various regulatory compartments of the immune system. I. Mathematical analysis of the risk of pathological disorders in the organism

Abstract

This article is a continuation of a series of papers that build on the scientific heritage of academicians V. M. Glushkov and V. S. Mikhalevich in the field of application of the system approach and optimization methods to the study of regulation mechanisms of the immune status of the organism and development of theoretical tools for quantitative evaluation of the functional state of the organism [1][2][3][4].The new class of integro-functional models of evolving systems proposed by V. M. Glushkov has allowed a deeper study of regulation mechanisms responsible for maintaining effective viability of the organism and has provided a theoretical substantiation of the observed phenomenon of adaptive redistribution and regenerative accumulation of lymphocytes [1], These models also have been used to solve a number of optimization problems that suggest an optimal strategy for treatment of patients with some forms of acute leucosis [5][6][7]. This direction has received further development in the work of Academician V. S. Mikhalevich and his collaborators, who have studied mathematical models of regulation in blood-formation systems [2], system analysis of regulation mechanisms of the defensive functions of the organism [3], and the effect of some intracellular factors and biologically active agents on immune response dynamics [4].Because of the essential variability in immune system parameters, the existence of alternative regulation mechanisms and competing cell populations, as well as the synergism and antagonism of interacting lymphocyte populations [8][9][10], which have been both observed experimentally and noted in these studies, it is apprently impossible to use the levels of various functional indicators (cell concentration, rate of fermentation reactions, etc.) in the complex hierarchical structure representing the immune system as an integral characteristic of the functional state of the organism. Mathematical models for the determination of dynamic invariants have been developed in [11][12][13][14]. These models make it possible to assess the degree of balance among the various regulation systems, which may characterize the functional capabilities of the organism.The purpose of the present study is to develop the theoretical principles for optimal control of the immune response. The objective of optimal control is to normalize the defensive functions of the organism by synchronizing the various regulatory compartments of the immune system.The present study focuses on the following topics: 1) creation of mathematical models for various compartments of the immune system and determination of optimal control of the immune response ensuring prevalence of the normalizing effect of immunocorrectors; 2) missing data recovery and prediction of the dynamics of the functional state of the organism in the presence of certain imbalances in the regulation systems; 3) estimation of the probability of prepathotological and pathological states in individuals subjected to negative environmental factors, A MODEL OF THE INTERACT...