Optimal structural and functional organization of the circulatory and respiratory systems

In this article, mathematical models dealing with the structure and steady functional states of the circulatory and respiratory systems, based on the solving of optimization problems with different optimality criteria are reviewed. As a result of mathematical modeling, the principal structural and functional parameters of the circulatory (vessel diameters of the arterial tree, end-diastolic and stroke volume of the isolated left ventricle, left ventricular ejection as a function of time, hemodynamic vascular resistance for the isolated left ventricle) and respiratory (branch diameters of the bronchial tree, breathing frequency, inspiratory and expiratory phase duration, air flow as a function of time) systems are determined. The best agreement between the optimal and observed parameters is obtained by using mathematical models based on the minimum energy consumption criterion.