MATHEMATICAL MODEL FOR THE INVESTIGATION OF HYPOXIC STATES IN THE HEART MUSCLE AT VIRAL DAMAGE

Abstract

The main complications of organism damaged by SARS-CoV-2 virus are various cardiovascular system lesions. As a result, the secondary tissue hypoxia is developed and it is relevant to search the means for hypoxic state alleviation. Mathematical modeling of this process, followed by the imitation of hypoxic states development, and subsequent correction of hypoxia at this model may be one of the directions for investigations. Aim. The purpose of this study was to construct mathematical models of functional respiratory and blood circulatory systems to simulate the partial occlusion of blood vessels during viral infection lesions and pharmacological correction of resulting hypoxic state. Methods. Methods of mathematical modeling and dynamic programming were used. Transport and mass exchange of respiratory gases in organism, partial occlusion of blood vessels and influence of antihypoxant were described by the systems of ordinary nonlinear differential equations. Results. Mathematical model of functional respiratory system was developed to simulate pharmacological correction of hypoxic states caused by the complications in courses of viral infection lesions. The model was based on the theory of functional systems by P. K. Anokhin and the assumption about the main function of respiratory system. The interactions and interrelations of individual functional systems in organism were assumed. Constituent parts of our model were the models of transport and mass exchange of respiratory gases in organism, selforganization of respiratory and blood circulatory systems, partial occlusion of blood vessels and the transport of pharmacological substance. Conclusions. The series of computational experiments for averaged person organism demonstrated the possibility of tissue hypoxia compensation using pharmacological substance with vasodilating effect, and in the case of individual data array, it may be useful for the development of strategy and tactics for individual patient medical treatment.