Self-Organization and Chaos in the Metabolism of Hemostasis in a Blood Vessel

Abstract

A mathematical model of the metabolic process of formation of the hemostasis in a bloodcarrying vessel is constructed. As distinct from the earlier developed model of the multienzyme prostacyclin-thromboxane system of blood, this model includes, for the first time, the influence of the level of "bad cholesterol", i.e., low-density lipoproteins (LDLs), on the hemostasis. The conditions, under which the self-organization of the system appears, and the modes of autooscillations and chaos in the metabolic process, which affects the formation of hemostasis and the development of thrombophilia, are found. With the aid of a phase-parametric diagram, the scenario of their appearance is studied. The bifurcations of doubling of a period and the transition to chaotic oscillations as a result of the intermittence are found. The obtained strange attractors are formed due to a mixing funnel. The full spectra of Lyapunov's indices, KS-entropies, "predictability horizons", and Lyapunov's dimensions of strange attractors are calculated. The reasons for a change in the cyclicity of the given metabolic process, its stability, and the physiological manifestation in the blood-carrying system are discussed. The role of physiologically active substances in a decrease in the level of cholesterol in blood vessels is estimated. K e y w o r d s: hemostasis, LDLs, self-organization, strange attractor, phase-parametric diagram, Lyapunov's indices, KS-entropy.Multicellular organism is a holistic system, whose cells are specialized for the execution of various functions. Their structural-functional connections form the self-organization in the system. The interaction inside organism is realized via complex regulating, coordinating, and correcting mechanisms with participation of neural, humoral, exchanging, and other processes. Many separate mechanisms, which regulate internal cellular and intercellular mutual relations, form opposite (antagonistic) actions, by balancing one another. This leads to the establishment of a variable physiological equilibrium in organism, which allows an alive system to hold a relative dyc ○ V.I. GRYTSAY, 2016 namical stationary state, despite the changes in the environment and the variations arising in the process of vital activity of organism. From the viewpoint of biophysics, it is a state, in which all processes responsible for the energetic transformations in organism are in a dynamical equilibrium. Such state is called the homeostasis.The blood composition steadiness has a special meaning for the vital activity of organism. Two antagonistic systems exist in blood vessels: those responsible for the coagulation and anticoagulation of blood. Due to their presence, the functional equilibrium, which hampers the coagulation of blood inside vessels, is formed. This state is called the hemostasis [1][2][3][4].arXiv:1707.05372v1 [q-bio.TO]

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

“…3, d ). The given chaotic mode of the strange attractor 1 × 2 arises by the Feigenbaum scenario due to the intermittence at 0 = 0.437 [22]. In Figs.…”

“…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.…”