Continuous mathematical models of blood flow and their applications

Simulating the movement of blood flow through the cardiovascular system has important applications in biomedicine such as improving our understanding of cardiovascular diseases, designing new therapeutics and medical devices, and planning surgical interventions. Several modelling approaches were developed to describe blood flow, ranging from continuous single-phase and multi-phase models, to particle-based methods such as the Lattice Boltzmann and the Dissipative Particle Dynamics methods. In this talk, we will discuss some of the continuous modelling methods that are commonly used to simulate blood flow. We begin by presenting the physiological and physical characteristics of blood flow in different conditions and locations of the cardiovascular system. Next, we introduce blood flow rheology models, including the ones that capture complex blood flow behavior such as shear thinning and discuss the effect of the hematocrit. Then, we present some multi-phase models of blood flow and discuss their derivation from the mixture theory and numerical implementation. We illustrate the advantage of the multi-phase models by showing their ability to model platelet margination and clot formation due to blood cell stagnation. After that, we discuss the challenges related to validation against experiments and the numerical implementation of these models.