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

TL;DR

This paper presents a new mathematical model of blood hemostasis that incorporates LDL cholesterol levels, revealing conditions for self-organization, oscillations, and chaos, which influence thrombophilia development.

Contribution

It introduces the first model including LDL influence on hemostasis and analyzes complex dynamic behaviors like chaos and bifurcations in blood metabolism.

Findings

Identification of conditions for self-organization and chaos in hemostasis

Discovery of bifurcations and transition to chaotic oscillations

Calculation of Lyapunov exponents and strange attractors

Abstract

A mathematical model of the metabolic process of formation of the hemostasis in a blood-carrying 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.