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

Abstract

A mathematical model of atherosclerosis of a blood vessel is advanced with regard for the entry of low-density lipoproteins (LDLs) into blood. For the first time, the influence of cytokines on the inflammation of a blood vessel at the formation of atherosclerotic plaques is taken into account. With the help of the expansion in a Fourier series and the calculation of an invariant measure, the scenario of the appearance of strange attractors depending on a change in the parameter of the dissipation of cholesterol is studied. The conclusion is made about the interconnection of the dynamics of the metabolic process in a blood vascular system and its physical state.