A Parametric Study of Blood Flow in the Microvessels

Program year: 1975/1976Digitized from print original stored in HDRSince blood is the transport medium for the materials to be exchanged, the understanding of the flow of blood is essential to the understanding of the materials exchange. The nature of the blood flow varies considerably throughout the cardiovascular system. The flow is typically pulsatile in the large vessels and arterioles, but is quite irregular within the capillaries where the diameter of the erythrocytes corresponds to that of the vessels themselves. The characteristics of blood flow in any given vessel are related to the pressure difference and the resistance involved. Two factors are largely responsible for the resistance to flow: 1. The vessel geometry (length, diameter) 2. The flow properties of blood (viscosity) Especially at the level of the microcirculation, the vessel diameter is important. Because the diameters of the vessels within the microcirculation are small compared with those of the arteries and veins, the microvessels offer the largest resistance to flow. The resistance to flow is roughly proportional to the reciprocal of the fourth power of the vessel diameter (Guyton, 1971). Thus, as the diameter of a vessel decreases, the resistance increases, but at a much faster rate. The contribution of the viscosity of blood to the resistance is also significant. Blood viscosity is dependent upon three factors: 1. Hematocrit 2. Erythrocyte geometry 3. Types and concentrations of proteins in the plasma Of these, the hematocrit, or the concentration of the red blood cells, is the most important. The hematocrit for a given volume of blood, defined as the ratio of the volume of the red blood cells to the volume of the whole blood, is most commonly determined clinically by centrifuging a column of whole blood for a standard length of time. During the centrifugation, the erythrocytes are packed at the bottom of the column (erythrocytes are more dense than plasma). The hematocrit is then expressed as the quotient of the red blood cell column height and the total column height. As shown in Figure 1, an increase in the hematocrit results in an exponential increase in the blood viscosity. In addition to the local variations in hematocrit within the microvessels, there is an apparent reduction in hematocrit in vessels smaller than about 0.3 mm (300um) in inner diameter. This phenomenon was first documented by Fahraeus in 1929 after a series of studies using small glass capillary tubes ranging from 47- 507 um in inside diameter. The magnitude of this reduction is important phisiologically because the hematocrit of a volume of blood affects flow properties, as indicated above, and this, in turn, affects erythrocyte distribution and thus oxygen distribution at branch points. The viscosity decrease which accompanies the hematocrit reduction, called the Fahraeus Effect, allows the heart to pump blood through the small vessels with less effort than it might otherwise have to exert