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Research program


Review of mathematical models of physiological systems and the bases of physiological avatar technology. The report is presented based on the report "Physiological Avatar technology in problems of sports" on the III-th interdisciplinary scientific and practical seminar "Mathematical Methods and Models in Sport", held on 12.16.2015 at the Center for Sports Technology at Moscomsport.

Main directions

Mathematical modeling and identification provides new possibilities in a wide variety of tasks research and applied. The proposed further review of the applications is the main directions of development of PhA research program.

  • Control of devices and artificial circulatory support

    Development of algorithms for control devices and artificial circulatory support is one of the main research directions for the PhA program.

    More about: Overview of applications in medicine and physiology .

  • Physiology and practical medicine

    In medical research and pharmacology of the implementation of this research program provides a powerful tool of computer simulation of classical statistical health experiment.

    More about: Overview of applications in medicine and physiology .

  • Sports medicine and training process

    In the field of professional sports and fitness development research program of FA is in the direction of development of new efficient methods to assess the quantities of the individual anaerobic threshold, maximal oxygen consumption, the development of methods to quantify and controls the volume of training load.

    The most promising area of ​​applied research for the PhA program is to develop advanced features sports training and, in particular, methods and algorithms for optimal planning of the volume of training load based on the concept of training impulse (TRIMP).

    More about: Implementation of the method of training impulse .

Our publications

Solodyannikov, Yu.V., Elementy matematicheskogo modelirovaniya i identifikatsii sistemy krovoobrashcheniya (Elements of Mathematical Modeling and Identification of Blood Circulation System), Samara: Samar. Univ., 1994.

The book addresses the construction of mathematical models of the circulatory system, the identification of its parameters and conditions, analysis of the constructed models, and offers the appropriate software for the personal computer, designed in a Windows environment. The book is intended for psychologists, researchers, mathematicians, applied scientists in the field of computer medicine.

A. P. Proshin and Yu. V. Solodyannikov. Mathematical Modeling of Blood Circulation System and Its Practical Applications // Automation and Remote Control, Vol. 67, No. 2, 2006, pp. 329-341.

The human blood circulation system is represented by a nonlinear oscillation system for computer-aided digital modeling in real time scale. A parametric identification problem is formulated and its numerical solution algorithm is designed. A computer-aided blood circulation modeling and identification system is designed. The new approaches to construct real control systems for artificial and auxiliary blood circulation elements are based on neurocomputer technologies.

T.I. Ostapenko, A.P. Proshin, Yu. V. Solodyannikov. Research on blood circulation system identifiability // Automation and Remote Control, Vol. 68, No. 7, 2007, 1239-1255.

The problem of identifiability by periodic-motion measurements is formulated and solved by a simplest two-circuit mathematical model of blood circulation system. By computeraided symbolic mathematics, the initial point of periodic motion is computed and properties of this motion are studied. The measuring system, which makes enables solving the problem of blood circulation system parametric identification unambiguously, is mathematically strictly defined. Recommendations for practical implementation of this measuring system are given.

A. P. Proshin and Yu. V. Solodyannikov. Identification of the parameters of blood circulation system // Automation and Remote Control, Vol. 71, No. 8, 2010, pp. 1629-1647.

A formulation of the problem of parametric identification from measurements of periodic motion was considered using a mathematical model of the blood circulation system. A method for its numerical solution on the basis of the random global search algorithm was proposed. A software realization of the identification procedure as parallel computation processes in the symmetrical multiprocessor computer systems and the distributed computation environment was described. Practical applications were considered using the example of factor analysis of the origins of arterial hypertension and also medical and sport applications, including the noninvasive monitoring of the level of blood hemoglobin and some kinds of stimulants.

A. P. Proshin and Yu. V. Solodyannikov. Mathematical modeling of lactate metabolism with applications to sports // Automation and Remote Control, Vol. 74, No. 6, 2013, pp. 1004-1019.

Based on a mathematical model of the blood circulatory system, we construct a mathematical model for lactate metabolism in a human body. We pose the identification problem for lactate metabolism parameters by measurements. We develop the method, algorithm, and software for solving this identification problem. We also consider practical applications in sports medicine and the training process, in particular in our studies of the anaerobic threshold phenomenon and propose new methods for estimating the individual anaerobic threshold and maximal oxygen consumption for athletes.


The article presents a method of mathematical modeling and identification of parameters of the circulatory system for the measurement of the absolute value of circulating volume blood.