Information Technologies and Computer Engineering

The article deals with the improved mathematical models of the physiological process of muscle contraction based on the known hypotheses of the functioning of the musculoskeletal system of the human body. In particular, according to the first phenomenological hypothesis of A. Hill, a mathematical model of changes in the force load of muscle tissue for the modes of isometric tetanus and contraction (lengthening) of a muscle at a constant speed was developed on the basis of rheological models of muscle tissue components. It has been established that the general disadvantage of A. Hill's approach is the assumption that the force-velocity relationship should be performed instantly after a change in force load, which does not correspond to experimental data on the recovery of force stress after a step change in muscle length. To overcome these shortcomings, the Huxley hypothesis was chosen, which is based on the principles of the kinetics of the distribution of actin (monomer) binding sites with protein filaments (cross-bridges). It is assumed that the binding sites on actin are far enough apart that only one such binding site is available to each filament. Based on A. Huxley's hypothesis, a mathematical model of the force load of muscle tissue was developed, which depends on the distribution function of the number of transverse bridges. The results of the comparison of theoretical and experimental studies of force loading on the muscle, based on the developed mathematical models in the form of differential equations, confirmed the adequacy of using known theoretical positions to describe the course of biological processes in muscle tissue

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