Development of methods for mathematical modeling of endothelium. In silico modeling of the structures of the cardiovascular system (CSS) based on a model from the theory of automatic control (TAU)

Abstract

Purpose. On the basis of the model from the theory of automatic control (TAU) and the development of an adequate and effective mathematical model of the endothelium, to simulate in silico the structures of the cardiovascular system (CCC), as elements of the physico-biological system of automatic regulation (FBSAR). The article is aimed at researchers in the field of fundamental pharmacology and medicine. Materials and methods. We introduce the mathematical model "nozzle-damper-bellows" - as a theoretical and experimental justification for the construction and development of a mathematical model: endotheliocyte, endothelium, smooth muscle cells (MMC) and the vessel wall. On this basis, we will draw up a structural and functional scheme of the physico-biological control object (FBOU), as a dynamic link in the composition of the physico-biological system of automatic regulation (FBSAR). Outcomes. The conclusions of the mathematical model have been reformulated and the in-silico modeling of the structures of the cardiovascular system (CCC) based on the model from the theory of automatic control (TAU), gives us the possibility of adapted processes into automatic control systems (CAP) on processes in physico-biological automatic control systems (FBSAR). Scientific contributions. Based on the automatic control system (CAP) of the physical process, structured from the regulator (R) and the control object (OC) (Figure 4), we have created a physico-biological automatic control system (FBSAR) and the corresponding physico-biological control objects (FBOU). The tuning coefficients introduced by the mathematical model of the control object (OC) and the regulator (R) in automatic control systems (CAP) are similar to the tuning coefficients of homeostasis for real physical and biological control objects (FBOU), and physico-biological automatic control systems (FBSAR). Conclusion. The main effects on the pharmacological target of the cardiovascular system, like physico-biological automatic control systems (FBSAR) are the coefficients of adjustment of practical implemented connections in automatic control systems (ATS), from the theory of automatic control (TAU)