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# Mathematical model of oxygen consumption for healthy man during physical work

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A.V. Demin – Research Scientist, State Scientific Center of Russian Federation – Institute of Biomedical Problems of Russian Academy of Sciences (SSC RF IBMP RAS, Moscow). E-mail: a_demin2005@mail.ru
A.I. Ivanov – Ph.D. (Eng.), Associate Professor of St. Petersburg Branch of the National Research University «Higher School of Economics». E-mail: ai_wald@mail.ru
A.V. Suvorov – Dr.Sc. (Med.), Head of the Laboratory of Physiology and Biomechanics of Cardi-orespiratory System (SSC RF IBMP RAS, Moscow). E-mail: suvalex@imbp.ru

In this experiment we measured the oxygen consumption for each respiratory cycle («breath-by-breath») of 17 healthy sub-jects breathing air during dosed physical work on a ergo metric bicycle. We had found a non-linear mathematical model of oxygen consumption change by human in the discharge of an increasing load in the air. The model is the solution of the differential equation describing changes in the oxygen consumption rate with increasing load. The individual model’s coefficients can be found using numerical methods of using measurement results. The model provides an accuracy, including prognostic accuracy, with an error not exceeding 23% of actual measurements performed during maximum load. The model was tested in a number of experimental studies of the SSC RF - IBMP RAS, which allows us to recommend using it for people with different levels of physical development and fitness. Quite interesting is the following model property (hence the physiological properties of test organisms) we found that: the value of the load corresponding to the maximum rate of oxygen consumption, oxygen consumption is half of the maximum possible consumption. Another property of the found model: the independence of the law increasing the consumption of oxygen during physical work, increasing the power of the initial oxygen consumption without load. That means that mood, tension or muscle relaxation, calmness and excitement at the start state has no effect on oxygen consumption process during increasing physical activity. In turn, the independence of the solutions on the initial load means no physiological sense in the initial load changes in the test for maximum oxygen consumption. Based on the performed numerical comparisons we came to the conclusion that the resulting mathematical model can be successfully used to describe the physiological characteristics of the efficiency of gas exchange, and for people of different ages and different levels of fitness. Model properties allow easier selection of the initial values of the power levels of physical work and to simplify the requisition for maximum oxygen consumption test. Found model allows to determine whether the level reached maximal oxygen consumption in a particular case, that may be useful to overcome the subjectivity of as-sessment of tolerability load.
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