MATHEMATICAL MODELING OF THE PHYSIOLOGICAL PROCESS OF MUSCLE CONTRACTION

The article discusses improved mathematical models for the physiological process of muscle contraction based on the well-known hypotheses of the functioning of the musculoskeletal system of the human body. In particular, according to the first phenomenological hypothesis of A. Hill, on the basis of rheological models of the components of muscle tissue, a mathematical model was developed for changing the power load of muscle tissue for isometric tetanus and muscle contraction (lengthening) at a constant rate. It has been established that a common drawback of A. Hill's approach is the assumption that the force-speed ratio must be fulfilled instantly after changing the power load. This is inconsistent with the experimental data on the recovery of strength tension after a stepwise change in muscle length. To overcome these disadvantages, A. Huxley's hypothesis was chosen. It is based on the principles of kinetics of the distribution of the binding sites of actin (monomer) with the protein filament (cross bridges). It is assumed that the binding sites on actin are far enough from each other so that only one such binding site is available to each bridge. On the basis of A. Huxley's hypothesis, a mathematical model of muscle tissue strength load was developed, which depends on the distribution function of the number of cross bridges. The results of the comparison of theoretical and experimental studies of the power load on the muscle, based on the developed mathematical models in the form of differential equations, confirmed the adequacy of the use of known theoretical provisions to describe the course of biological processes in muscle tissues.