Mathematical Modeling of Blood Flow in the Cardiovascular System

This chapter gives a short overview of the mathematical modeling of blood flow circulation at different resolutions, from the large vessel scale (three-dimensional, one-dimensional, and zero-dimensional modeling) to microcirculation, including aspects related to the biomechanics of vascular tissues and tissue perfusion. The chapter focuses first on the different mathematical formulations, discussing the underlying physical laws, the link to clinical data, and related challenges. Next, recent applications related to medical imaging are then discussed, highlighting the potential of computer simulation and of the interplay between modeling, imaging, and experiments in order to improve clinical diagnosis and treatment. The chapter ends presenting some current challenges and perspectives.