Abstract
A mathematical model of the metabolic process of atherosclerosis is constructed. The functioning of the polyenzymatic prostacyclin-thromboxane system of blood and the influence of a level of “bad cholesterol”, namely low density lipoproteins (LDL), on it are studied. With the help of the numerical experiment, we analyze the influence of the concentration of molecules of fat on hemostasis of blood in blood vessels. The kinetic curves for components of the system, phase-periodic bifurcation diagrams, attractors for various modes, and Poincaré cross-section and image of a strange attractor are constructed. The complete spectra of Lyapunov’s exponents, divergencies, KS-entropies, predictability horizons, and Lyapunov dimensions of the fractality of strange attractors are calculated. Conclusions about the structural-functional connections, which determine the dependence of hemostasis of a circulatory system on the level of cholesterol in blood are drawn.
Highlights
The kinetic model [4,5,6,7,8,9] allowed us to trace the effect of various levels of activities of phospholipases and concentrations of prostacyclin and thromboxane on properties of a biosystem, to determine the role of the arachidonic acid exchange between thrombocytes and endothelium, to analyze the influence of parallel processes running with the participation of arachidonic acid on kinetics of changes and on stationary levels of prostanoids, and to find the structural-functional connections of self-organization in the biosystem
We will study the influence of concentration of “bad cholesterol” (LDL) on the metabolism of a hemostasis of blood vessels
Studies of the oscillatory dynamics of the given metabolic process will allow one to investigate the process of self-organization of the metabolic process of hemostasis of a circulatory system under changes in blood cholesterol level
Summary
A mathematical model of the metabolic process of atherosclerosis is constructed. The functioning of the polyenzymatic prostacyclin-thromboxane system of blood and the influence of a level of “bad cholesterol”, namely low density lipoproteins (LDL), on it are studied. The desynchronization of these systems results in the appearance of autooscillatory modes in the metabolic process of a prostacyclin-thromboxane system. We will study the influence of concentration of “bad cholesterol” (LDL) on the metabolism of a hemostasis of blood vessels. The excessive content of fat in organism causes formation of atheromatous plaques They are aggregates of LDL on internal walls of blood vessels, causing stenosis. Studies of the oscillatory dynamics of the given metabolic process will allow one to investigate the process of self-organization of the metabolic process of hemostasis of a circulatory system under changes in blood cholesterol level. This will allow one to study the regularity of metabolic processes in human organism from a single physical viewpoint of synergetics
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