Three-Chamber Model of Human Vascular System for Explanation the Quasi-Regular and Chaotic Dynamics of the Blood Pressure and Flow Oscillations
N. Kizilova
Dec 7, 2015
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Key Takeaway Key Takeaway: The three-chamber model of the human vascular system explains the quasi-regular and chaotic dynamics of blood pressure and flow oscillations, highlighting the importance of material parameters within physiological limits.
Abstract
Arterial blood pressure P(t) and flow V(t) curves measured by ultrasound or other technique exhibit quasi-regular dynamics with clear patterns of the P(V) loops. In this paper, the curves measured in central aorta, upper, and low extremities of young healthy volunteers and patients with cardiovascular disorders are studied. Both quasi-regular and chaotic dynamics of the P(t) and V(t) signals are found. A mathematical model of a series connection of three nonlinear viscoelastic chambers representing central (1) and peripheral arterial (2) and peripheral venous (3) compartments are proposed. The pressure and flow oscillations in each compartment are computed at different model parameters such as resistivity of the microcirculatory bed, elastic and viscous parameters of the arterial and venous walls. It was found the quasi-regular dynamics with different patient-specific patterns of the P(V) attractor are proper to variations of the material parameters within the physiological limits, while the chaotic dynamics appear when wall compliance and/or resistivity of the chambers (2) or (3) are too high. Those variations are proper to deep vein thrombosis, microcirculatory disorders, and age-related degradation of the blood vessel wall.