S. I. Mukhin

Studying the influence of gravitational overloads on the parameters of blood flow in vessels of greater circulation

The paper is devoted to the numerical modeling of the blood flow in the human cardiovascular system with allowance for gravitational action. A model of the operation of the heart and an equation of state are proposed and studied. Modifications of the graph of the cardiovascular system for the simulation of possible positions of the object in conditions of multifold gravitational overloads are considered.

Mathematical modeling of quasi-one-dimensional hemodynamics

New unpublished results of research conducted under the guidance of Prof. Favorskii at the Chair of Computational Methods of Moscow State University are presented. Justification and implementation of a quasi-one-dimensional approximation for mathematical modeling of hemodynamics are discussed.

Conservative schemes of matter transport in a system of vessels closed by the heart

We suggest a conservative model and the corresponding conservative numerical method for analyzing the motion of matter in a branched vessel system closed by the heart. The efficiency of the algorithm is justified by test computations.

Mathematical Modeling of Some Applied Problems in Haemodynamics

The present study discusses some basic issues of mathematical modeling in medicine and describes examples of specific results of analytical and numerical investigations in haemodynamics. It briefly describes a method for constructing exact solutions of the linearized equations of haemodynamics on a graph, an analysis of these solutions, and a particular application of the proposed theory for solving practical medical problems. A number of nonspecific aortoarteritis syndromes are simulated. Examples of mathematical modeling of blood flow in the systemic circulatory circuit under the action of a periodically contracting heart are presented. These examples reproduce some of the main physiological regularities of the circulatory system as a whole. One of the applications of mathematical modeling in haemodynamics includes the “stealing” of cerebral blood supply during a temporary occlusion of the subclavian artery.