'42 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



tube. If the pressure head is sufficiently large, and 

 the mean shearing stress within the tube (equation 2) 

 is greater than about 50 dynes per cm-, the plotted 

 points will lie closely about a straight line (the kinetic 

 energy correction must be applied, of course, if 

 necessary, and the correction must be small, owing 

 to the vmcertainty in its exact value). This straight 

 line, if extrapolated, will appear to indicate that the 

 rate of flow would be zero when the applied pressure 

 is such that the mean shearing stress is about 10 

 dynes per cm^ (the exact figure varies greatly in 

 different samples of blood). This, however, is only 

 apparent, since if the extrapolated "intercept" 

 pressure is applied to the tube, the blood will be 

 found to flow quite readily, and will continue to 

 flow even when the pressure is reduced well below 

 this value (5, 23). In this region, the plotted points 

 indicating the relation between the rate of flow and 

 the applied pressure lie on a smooth curve, which is 

 convex to the pressure axis. 



Now according to the Poiseuille equation, the 

 relation between the rate of flow of a Newtonian 

 fluid (Q,) and the applied pressure head (P) should be 

 represented by a straight line passing through the 

 origin of the flow and pressure axes (equation 4). 

 Blood, therefore, is not a Newtonian fluid. If the red 

 cells are separated from the plasma or serum, and 

 resuspended in a simple saline solution, the plasma 

 or serum is found to behave as a Newtonian fluid, 

 whereas the suspension of cells is non-Newtonian; 

 the anomalous behavior of blood is due, therefore, 

 to the presence of the red cells. In studying these 

 properties, we are thus concerned primarily with the 

 effects produced by the presence of the red cells; 

 and we are concerned with the relative viscosity of 

 the blood with respect to that of the plasma. In a tube 

 of given dimensions, we may write the Poiseuille 

 equation for the flow of plasma in the form: 



a. 



G„-P 



(.2) 



where the quantity G',, (which may he called the 

 "conductance" of the tui)e for plasma) replaces the 

 quantity ira-'/'ST/p-T),,,/, where r;,, is the relative viscosity 

 of the plasma, r;,,, is the absolute viscosity of water, / 

 is the length of the tube, and a is its radius. Similarly, 

 for the flow of blood, in the same tube, wc may write: 



Qj, = {G,/n*)-P 



(13) 



where r;* is the apparent viscosity of the blood, 

 relative to that of the plasma, in the particular 

 condiiions of measurement; its value depends not 

 onlv on the \olume fraction of the red cells (the 



hematocrit value) as already discussed, but also on 

 the shearing stress applied, on the radius of the tube, 

 as will be discussed later, and on other factors, some 

 of which have not been precisely defined. As is 

 obvious from equation 13, the apparent relative 

 viscosity of the blood at any particular value of the 

 applied pressure and rate of flow is proportional to 

 the ratio P/Qj,. Owing to the curvature of the pres- 

 sure-flow line, this ratio falls steadily towards an 

 asymptotic value as P and Qt are made larger. 



When the shearing stress is large, and the pressure- 

 flow line sensibly straight, we may write equation 13 

 in the form: 



d" = (.Gp/vl){P - P*) 



(13a) 



where 77^ is defined by the slope of the straight line 

 to which the observed pressure-flow line approxi- 

 mates — i.e., by the ratio dP'dQj, when P approaches 

 infinity — and P* is the intercept of this line on the 

 axis of pressure. If P is made very large compared 

 with P*, the mean shearing stress being not less than 

 about 150 dynes per cm-, and provided that the 

 flow remains laminar, the ratio P/Qj, will be nearly 

 constant; in these limiting conditions blood will 

 appear to behave as a Newtonian fluid. 



The reduction in the apparent viscosity of blood 

 with increase in the shearing stress and rate of shear 

 has been observed chiefly when the blood is made to 

 flow through a tube; it appears to have been noticed 

 first by Ewald (17). Brunclage (9), however, observed 

 it when blood was sheared in a rotating cylinder 

 (Couette) viscometer; in this apparatus the shear 

 occurs in the annular space between two concentric 

 cylinders, the outer one being rotated at different 

 but constant speeds, and the torque produced on the 

 inner one being measured by means of a torsion wire. 

 Copley et al. (11), again, oliservcd it in an apparatus 

 in which relati\e viscosities were measured in terms 

 of the rate at which a sphere rolled down an inclined 

 tube filled with blood; the shearing stress and rate of 

 shear being varied by altering the inclination of the 

 tube. It is not to be expected, however, that the 

 change in apparent viscosity with a given change in 

 shearing stress or rate of shear will be the same in all 

 these types of viscometer. Several different factors 

 are responsible for the effects observed. 



Orifnlatiori of the Red Cells 



If the particles of a suspension are not splierical, 

 and in the limit are either tiiin rods or flat discs, they 

 may become orientated when the suspension is 



