Mathematical models for blood flow

This thesis deals with the mathematical modelling of hemorheology that consists in the study of blood flow either as a homogeneous fluid or as suspension of cells in plasma. we will look at a few areas of hemorheology. In particular, we will deal with microcirculation, the part of the circulatory system that includes venules, arterioles, and capillaries. The microcirculation plays a fundamental role in the circulatory system, as it is the part of the system responsible for trans- porting blood to the periphery. Specifically, in this thesis we will analyze the blood flow that occurs in vessels whose diame- ter is between about 100 and 500 micrometers. In this “segment”two important phenomena occur that are not yet fully explained. The first fundamental phenomenon is the F ̊ahraeus-Lindqvist effect, which is observed in vessels with diameter less than about 500μm. It consists in a variation in blood viscosity according to the vessel’s diameter through it flows. The second phenomenon of greatest importance to the physiology of the microcir- culatory system is the vasomotion, a rhythmical contraction-relaxation mechanism of microvessels, that regulates fluid and nutrient exchange between the vascular system and peripheral tissues. This thesis is devoted to the mathematical modeling of these two phenomena, for which, as already mentioned, there are even nowadays no exhaustive theoretical explanations.