Fundamentals of vascular bio-fluid and solid mechanics

Abstract

While considering the circulatory system, a mechanical view point provides the basis for understanding various physiological and pathophysiological phenomena. In this section, we introduce the fundamentals of fluid and solid mechanics in relation to the circulatory system. In the first part on fluid mechanics, we start by introducing the concepts of Newtonian and non-Newtonian fluids, viscosity, and apparent viscosity. Then, the rheological properties of blood are described, and the universal mechanical law for flow through cylindrical tubes is derived. Based on that law, we consider the characteristics of tube flow for Newtonian and non-Newtonian fluids and present several representative examples of mathematical models for blood flow through vessels. These models have a close relationship with important physiological phenomena. In the second part, we first discuss the concept of continuum mechanics for a large deformation of the vascular wall. Then, we introduce passive hyperelastic models, an active smooth muscle model, and incorporations of residual strain and smooth muscle contractions. We demonstrate typical axisymmetric solutions of arterial wall stress for a tube model under physiological loading conditions, i.e., longitudinal stretch and intraluminal pressure. We also show some approaches for arterial diseases such as atherosclerosis, aortic aneurysm, and aortic dissection.