Computational techniques for biological fluids: From blood vessel scale to blood cells

Simulation of flows in the cardiovascular system faces many challenges. Chief among these is the issue of treatment of blood flow at disparate scales. For blood flows through large vessels a Newtonian homogeneous fluid model can be adequate, while in the capillaries and in orifices and constrictions individual blood cells and interactions among blood cells assume importance. Another important feature of flows in the cardiovascular system or in the presence of cardiovascular prostheses is the interaction of blood with moving boundaries (e.g. arterial walls, heart, heart valves, and ventricular assist devices). Computational fluid dynamics has made significant progress in tackling these challenges to the extent that it is now feasible to calculate flows through parts of the cardiovascular system with a great degree of fidelity and physiological realism. This chapter presents fundamental aspects of the demands on and capabilities of numerical solution techniques for solving a variety of blood flow phenomena. Large scale flows with significant fluid inertia and small scale flows with individual blood cells are covered. Applications of the methods and sample results are shown to illustrate the state-of-the-art of computations in cardiovascular biofluid dynamics.