0.60 6 5 4 3 2 1 0.50.20.1 0.40.3 Tube diameter (mm) Relative viscosity •Fig. 17.8 Therelativeviscosityofbloodrelativetothatofwaterincreasesasafunctionoftubediameteruptoadiameterofapproximately0.3mm.(RedrawnfromFåhraeusR,LindqvistT.Am J Physiol. 1931;96:562.) therefore reduces the resistance to flow in blood vessels that possess the greatest resistance. The influence of tube diameter on apparent viscosity is explained in part by the actual change in blood composition as it flows through small tubes. The composition of blood changes because the red blood cells tend to accumulate in the faster axial stream, whereas plasma tends to flow in the slower marginal layers. Because the axial portions of the bloodstream contain a greater proportion of red cells and this axial portion moves at greater velocity, the red blood cells tend to traverse the tube in less time than plasma does. Furthermore, the hematocrit of the blood contained in small blood vessels is lower than that in blood in large arteries or veins.
The physical forces responsible for the drift of erythrocytes toward the axial stream and away from the vessel walls when blood is flowing at normal rates are not fully understood. One factor is the great flexibility of red blood cells. At low flow rates, like those in the microcirculation, rigid particles do not migrate toward the central axis of a tube, whereas flexible particles do. The concentration of flexible particles near the tube’s central axis is enhanced by an increase in the shear rate.
The apparent viscosity of blood diminishes as the shear rate is increased (
Fig. 17.9 ), a phenomenon called shear thinning. The greater the amount of flow, the greater the rate that one lamina of fluid shears against an adjacent lamina. The greater tendency for erythrocytes to accumulate in the axial laminae at higher flow rates is partly responsible for this nonnewtonian behavior. However, a more important factor is that at very slow flow rates, the suspended cells tend to form aggregates; such aggregation increases blood viscosity. As flow is increased, this aggregation decreases, and so does the apparent viscosity of blood (see
Fig. 17.9
The tendency for erythrocytes to aggregate at low flow rates depends on the concentration of the larger protein molecules in plasma, especially fibrinogen. For this reason, changes in blood viscosity with flow rate are much more pronounced when the concentration of fibrinogen is high. In addition, at low flow rates, leukocytes tend to adhere to the endothelial cells of the microvessels and thereby increase the apparent viscosity of the blood.
•Fig. 17.9 Decreaseintheviscosityofblood(cp,centipoise)atincreasingratesofshear(sec−1).Theshearrateisthevelocityofonelayeroffluidinrelationtothatoftheadjacentlayersandisdirectionallyrelatedtotherateofflow.(RedrawnfromAminTM,SirsJA.Q J Exp Physiol. 1985;70:37.)2400 7 6 5 4 3 18060 120 Shear rate/sec–1 Viscosity (cp) •Fig. 17.10 Effectoftheplasmafibrinogenconcentrationontheflexibilityofhumanerythrocytes.(RedrawnfromAminTM,SirsJA.Q J Exp Physiol. 1985;70:37.)40 8 6 4 2 0 31 2 Fibrinogen concentration (mg/mL) Erythrocyte flexibility (% min–1)