Multiscale models of the vascular system

Abstract

As we have illustrated in the previous chapters, there are essentially three classes of models for the vascular system: fully three dimensional models, based on the Navier-Stokes (NS) equations, one dimensional models, including the space dependence on the vessel axial coordinate, based on the Euler (E) equations, and the lumped parameter or zero-dimensional models, based on the Kirchhoff laws (K) for hydraulic networks. Navier-Stokes based models can account for many different features of blood flow problems, such as the blood rheology (Chapter 6), the vascular wall dynamics (Chapter 3), the interaction between blood flow and wall deformation (Chapters 8 and 9). These models are perfectly adequate for investigating qualitatively and quantitatively the effects of the geometry on the blood flow (Chapters 5) and the possible relations between local haemodynamics and the development of some pathologies (Chapter 1). On the other hand, the high computational costs (Chapters 2, 3 and 9) restrict their use to cover few contiguous vascular districts only.