Mathematical modeling of blood flow in the cardiovascular system

Abstract

This chapter gives a short overview of the mathematical modeling of blood flow at different resolutions, from the large vessel scale (three-dimensional, one-dimensional, and zero-dimensional modeling) to microcirculation and tissue perfusion. The chapter focuses first on the formulation of the mathematical modeling, discussing the underlying physical laws, the need for suitable boundary conditions, and the link to clinical data. Recent applications related to medical imaging are then discussed, in order to highlight 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.