A mathematical model of the metabolic process of atherosclerosis

Abstract

I n the present work with the help of a mathe matical modeling, we continue the study of a prostacyclinthromboxane system of blood. We will investigate how low density lipoproteins (LDL) influence the dynamics of this metabolic process. In the construction of equations (Eqs.) of our model and the determination of its parameters, we used the re sults obtained by Prof. S.D. Varfolomeev and Prof. A. T. Mevkh. Their book and the fruitful collabo ration with them [13] allow Prof. V.P. Gachok and the author to obtain calculation results similar to the experimental ones in the case where the system is in a stable state of hemostasis [49], which state charac terizes a healthy blood vessel. It is the ideal state, which is attained by synchronization of the systems of thrombosis and antithrombosis. The dynamical stationary equilibrium arises. The desynchroniza tion of these systems results in the appearance of autooscillatory modes in the metabolic process of a prostacyclinthromboxane system. If the stationary kinetics is broken so that the level of thromboxane increases, then the coagulability of blood grows as well, and the appearance of thrombosis becomes possible in the circulatory system. On the contrary, if the level of prostacyclin increases, then the coagu lability of blood decreases, and hemophilia occurs. If the autooscillatory mode arises, then the appearance of a thrombus as a result of increased coagulabil ity on some time interval and its abruption under a decrease of the coagulability in the following time interval are possible. The actions of external and in ternal factors induce various modes in the system.The metabolic process of coagulability of blood is considered by the author of the article as an open nonlinear system. The study was conducted using methods of nonlinear dynamics.The kinetic model [49] 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 thrombo cytes and endothelium, to analyze the influence of parallel processes running with the participation of arachidonic acid on kinetics of changes and on sta tionary levels of prostanoids, and to find the struc turalfunctional connections of selforganization in the biosystem.

Spectral Analysis and Invariant Measure in Studies of the Dynamics of the Hemostasis of a Blood Vessel

“…In the present work, we continue the investigation of the autooscillatory modes in the metabolic process of a b hemostasis of a blood vessel. The obtained dynamical modes [22,23] indicate the dependence of the dynamics of the process on a change in the level of cholesterol in blood.…”

“…Here, the overall scheme of the metabolic process of hemostasis of a blood vessel [22,23] is generalized by including the influence of cytokines on the formation of atherosclerotic plaques (see Fig. 1).…”

“…In the frame of this approach, a mathematical model of blood vessel with regard for the presence of low-density lipoproc ○ V.I. GRYTSAY, 2021 teins (LDLs) such as "poor cholesterol" in blood and the formation of atherosclerotic plaques in blood vessels was constructed in [22,23], and the influence of LDLs on the self-organization of the hemostasis of a blood vessel and the formation of dynamical chaotic modes in the system was studied. The interval of a level of the dissipation of cholesterol from blood, where chaotic autooscillations can arise, was determined.…”

Structural Instability of a Biochemical Process

“…A mathematical model of the process under flow conditions in a bioreactor was developed by the general scheme of metabolic processes in Arthrobacter globiformis cells at a transformation of steroids [8][9][10][11][12][13][14][15][16][17][18].…”

“…Works [8][9][10][11][12][13][14][15][16][17][18] considered the mathematical model of a bioreactor transforming steroids [19] under flow conditions depending on a change of the dissipation, the kinetic membrane potential of cells, and the input flows of a substrate and oxygen. Various scenarios of the transition from stationary modes to selfoscillatory modes with different multiplicities were presented, and the regions of the formation of strange attractors were determined.…”