The use of numerical simulation in the study of the cardiovascular system (with its inherent pathologies) has greatly increased in the past few years. Blood flow interacts mechanically and chemically with vessel walls producing a complex fluid-structure interaction problem, which is practically impossible to simulate in its entirety.

Several reduced models have been developed which may give a reasonable approximation of averaged quantities, such as mean flow rate and pressure, in different sections of the cardiovascular system. They are, however, unable to provide the details often needed for understanding a local behavior, such as the effect on the shear stress distribution due a modification in the blood flow following a partial stenosis.

The derivation of these heterogeneous models, and their coupling, will be presented together with schemes for their numerical solution. These techniques may be extended by including models for chemical transport. Several numerical results on cases of real life interest will be presented.