In analyzing blood flows, one is generally interested in how the blood responds to forces (e.g., pressure gradients, shear stresses). The general fluid mechanical procedure used to predict how a fluid flows in response to forces involves three steps:

(1) Consideration of all the forces being exerted on an infinitesimally small volume of fluid. This is done by use of the physical principle known as the conservation of momentum, and results in equations which relate the forces to velocity gradients.

(2) Introduction of rheological (“constitutive”) equations which are specific to the fluid being analyzed. These equations indicate how the fluid responds to forces, and relate the forces to the resulting velocity gradients. The rheological equations contain fluid specific characteristics (e.g., apparent viscosity as a function of shear rate).

(3) Substitution of the rheological equations into the conservation of momentum equations, and integration of the resultant differential equations to obtain macroscopic relationships, such as between flow rates and pressure gradients.

In this chapter, this procedure will be illustrated for specific applications to blood.