Blood Flow and Thrombus Formation

Abstract

BLOOD RHEOLOGY To analyze blood fl ow and stresses that develop in it, and its interaction with the blood constituents, we traditionally consider blood as a continuously deformable continuum in motion. Using this approach, we can characterize blood as a Newtonian fl uid (in which the fl uid deforms linearly as a function of the stress imposed) or a non-Newtonian fl uid (in which the fl uid deforms nonlinearly as a function of the stress). The Newtonian behavior of blood fl ow is relevant to most of the larger arteries in the vasculature. However, blood possesses a unique non-Newtonian viscosity behavior, which becomes apparent when it fl ows through the smaller vessels, such as arterioles and capillaries. This behavior is also observed when blood fl ow forms vortical structures, as may be found in fl ow through cardiovascular prostheses or in cardiovascular disease processes such as stenoses and aneurysms ( 1 ). In analyzing other aspects of hemodynamics such as the apparent reduction of viscosity and the migratory tendency of blood cells in the smaller scale vessels (i.e., the microcirculation), it is found that blood may be treated as a suspension of cells in plasma. The non-Newtonian behavior exhibited by whole blood is due to fi brinogen molecules on the surface of red blood cells (RBC) that cause them to stack together in the rouleaux formation. This phenomenon is most pronounced during pregnancy, under pathological conditions, and when a large number of fi brinogen molecules are present on RBC surfaces. Such aggregation of cells in arterioles and small arteries is responsible for blood’s deviation from Newtonian behavior ( 1 ). From a mechanics point of view, this behavior is a combination of Bingham and pseudoplastic fl uid characteristics. That is, it has a yield stress; however even above this yield stress, the shear stress to shear rate relationship is nonlinear ( Fig. 1 ). A well-accepted, heuristic non-Newtonian model of blood is the Casson model. This behavior is most apparent in shear rates that are below 20 s −1 , with the region 20–100 s −1 being the transition region. Above a shear rate of 100 s −1 blood behaves as a Newtonian fl uid. However, in the non-Newtonian range, the shear stress does not exceed the yield stress in the central core fl ow region, and the core is merely carried along by the fl uid in the annular region. Thus, the central core has a fl at velocity profi le (plug fl ow), which is carried by the annular region surrounding it, sustaining the bulk of the shear stress ( 1 ). As blood consists of various kinds of cells such as erythrocytes (RBC), white blood cells (WBC or leukocytes), and platelets (thrombocytes) suspended in plasma, there is often a need to analyze its rheological properties in relation to its nature and to its cell-suspension properties. RBCs outnumber the other cells and assume major AQ01