Dynamics of Pulsatile Blood Flow I

Abstract

Solutions of fluid flow problems, to fully determine the dynamics of the fluid, including a mapping of the velocity field and of the relation between the prevailing pressure and flow fields, are possible only in the most simply constructed cases and mostly in the physical sciences. Fluid flow problems in biology, by contrast, are rarely simply constructed and can rarely be solved directly. The problem of flow in a tube, for example, has a simple so called “Poiseuille flow” solution when the tube is rigid, its cross section is perfectly circular, the tube is long enough for the flow to be fully developed, and the fluid is a smooth “continuum” that has the simple rheological properties of a “Newtonian” fluid in which the shear stress is related linearly to the velocity gradients. Barely any of these ideal conditions is met in biological problems involving flow in tubes, most notably the problem of blood flow in arteries which is the subject of this book. Here the fluid is not a smooth continuum but a suspension in plasma of discrete red and other blood cells and, as we saw in the previous chapter, the system does not consist of a single tube but of many millions of tube segments that are joined together in a hierarchical tree structure. The segments are rarely long enough or perfectly circular to support fully developed Poiseuille flow, and the details of flow at their junctions are highly complicated and depend strongly on the exact geometry of each junction. Furthermore, the precise branching structure of the arterial tree or sub-trees within the cardiovascular system can rarely be mapped to the last detail so as to allow a mathematical solution of the flow problem based on a given tree structure as was done in the previous chapter.