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FIGURE 11 If the same three tubes described in Fig. 10 are arranged in parallel, the reciprocal of the resistance offered by the combination of tubes is equal to the sum of the reciprocals of their individual resistances. Note that this total resistance will always be less than the smallest single resistance.

0 10 20 30 40 50 60 70 80 Hematocrit

FIGURE 12 The viscosity of blood (relative to water) is a function of hematocrit. Note that at 0 hematocrit (plasma), viscosity due to plasma proteins is about twice that of water. For a normal hematocrit of 45-50%, blood viscosity is about three times that of water.

0 10 20 30 40 50 60 70 80 Hematocrit

FIGURE 12 The viscosity of blood (relative to water) is a function of hematocrit. Note that at 0 hematocrit (plasma), viscosity due to plasma proteins is about twice that of water. For a normal hematocrit of 45-50%, blood viscosity is about three times that of water.

function of hematocrit (the percent of total blood volume comprised of red blood cells). Even with no cells present, blood plasma is about twice as viscous as water because of the presence of proteins, mainly albumin; however, at a normal hematocrit of 45%, blood is about three times as viscous as water. Viscosity will increase in conditions in which the number of red blood cells is increased above normal (polycythemia) and will decrease in conditions in which the hematocrit is decreased below normal (anemia).

Unlike water, which is a newtonian fluid, the viscosity of blood changes with flow. This can be seen by observing the difference in driving pressure that it takes to maintain flows at various rates through a rigid glass tube (Fig. 13). For a newtonian fluid, flow would

FIGURE 13 When a newtonian fluid flows through a rigid tube, the flow is proportional to the pressure gradient across the tube. With blood, however, the viscosity appears to increase at low flow rates, causing a nonlinear pressure flow curve. The formed elements in the blood are responsible for this anomalous viscosity.

FIGURE 13 When a newtonian fluid flows through a rigid tube, the flow is proportional to the pressure gradient across the tube. With blood, however, the viscosity appears to increase at low flow rates, causing a nonlinear pressure flow curve. The formed elements in the blood are responsible for this anomalous viscosity.

always be exactly proportional to AP. A doubling of AP would double Q no matter what the rate of flow. For blood, however, the pressure flow curve becomes quite nonlinear at low flow rates. Pure plasma is a solution, and therefore, fact newtonian. The variable viscosity of blood occurs because at low flow rates the formed elements, including the red cells and platelets, begin to stick to one another. This non-newtonian property of blood, referred to as anomalous viscosity, in practice causes only a small deviation from Ohm's law at normal blood flow rates and usually can be ignored. Nevertheless, anomalous viscosity can significantly increase resistance to flow when perfusion pressure is low, as occurs in shock and other hypotensive states, and can exacerbate low blood flow state. This is sometimes referred to as blood sludging.

In the microcirculation, the formed elements cause the viscosity of blood to be dependent on the diameter of the vessel through which it is flowing. This phenomenon is known as the Fahraeus-Lindquist effect. As shown in Fig. 14, the viscosity of blood appears to actually decrease as the vessel diameter decreases below 50 mm, which is just opposite of what might be imagined. The explanation for the Fahraeus-Lindquist effect appears to be due to the proclivity of red cells to concentrate in the center of the blood vessel in a process termed axial streaming. Because the velocity is highest in the center of the vessel, the pressure is lowest in that region and the cells are literally sucked into the center. On the other hand, it can be shown that the geometry of a round tube causes most of the viscous drag to be concentrated nearest to the vessel wall. In the small vessels where axial streaming is pronounced, the blood in the critical region near the vascular wall is left with a low hematocrit and thus a low viscosity. The net result is that overall viscosity appears to drop. Another consequence of the axial streaming of blood cells is that they literally pass through an organ faster than the plasma. This causes the intra-organ hematocrit always to be somewhat lower than that of the central circulation.

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