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Mathematical model

Base technology PhA is a mathematical model of the physiological systems of the human body. The development of this model started under the leadership of Yu.V.Solodyannikov in 70-90-ies of XX century. This model was developed as part of research on artificial heart, led V.I.Shumakov. The original version of the model described only the systemic circulation. As a result of development in the 90's model was included in the approach to the formalization of the regulation of contractile ability of the heart, which was developed in Amosov's School.

On the basis of this model, complex experiments was carried out in the Kuibyshev State University confirmed its agreement with the experimental data. In this model have been carried out research questions of identifiability, observability, controllability, stability.

Numerous medical and technical tests digital model (based on the Institute of Transplantation and Artificial Organs Medical Sciences of the USSR and the Samara Medical Institute) were carried out by simulating the various stationary and transient modes of the circulatory system of animals and man /Solodyannikov, Yu.V., Elementy matematicheskogo modelirovaniya i identifikatsii sistemy krovoobrashcheniya (Elements of Mathematical Modeling and Identification of Blood Circulation System), Samara: Samar. Univ., 1994 /. These tests have proved that the model has quite adequate homeostatic properties of a real body (the stability of the periodic motion, sensitivity to changes in the parameters, transients, etc.). All these properties of the model are well interpreted in the conventional terms of physiology and medicine. Digital model (normal avatar) is protected by the state registration certificates.

In the modern version of a mathematical model of the physiological systems of the body including the ideas and methods of the theory homeostatic systems, theory allometric parameters depending on the weight of the body (Allometric laws) intensively developed at present the theory of neural networks. Neural network analogy atrioventricular node of the heart, wire His-Purkinje system and the autonomic nervous system that controls the tone of the blood vessels used to build the model of neuro-humoral regulation.

Extending the model constructed by incorporating the equations describing the dynamics of metabolism (in particular the lactate and carbohydrates) in the human body. Also included is a mathematical model ergoreflektornyh control actions. Ergorefleksom skeletal muscle physiology is called the mechanism of regulation of the body, carried out through metabolic muscle receptors that respond to the accumulation of incompletely oxidized metabolites in muscle.

The modern version of the model and its a fairly complete description is available on the Internet in Russian and English languages. Meaningful description of the model equations, its classification and properties as a dynamic system in a strict mathematical form given in the recommended links.

Recommended references

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.

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.

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