596 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



the limiting concentration will reflect altered flow 

 appropriately. If the changes in flow are rapid and 

 phasic and if the mean transit time of the system is 

 always relatively long, the limiting concentration will 

 alter sluggishly and will measure the average flow. 



Although if flow and \olume vary independently, 

 the system cannot be stationary; it is possible for flow 

 and volume to vary together so that '"stationarity" 

 is maintained. 



Flow of Indicator Particles Is not Representative 

 of Flow of Total Fluid 



If an indicator is used to measure flow and volume 

 of distribution of biological fluids, it must be estab- 

 lished that the distribution of transit times of the 

 indicator is that of the fluid under study. Indicators 

 are used frequently to estimate blood or plasma flow 

 and volume, and both blood and plasma are heter- 

 ogeneous. 



In practice only one of the components of plasma 

 is tagged, usually. For example, it is common to use 

 as indicator certain dyes which bind chiefly to scrum 

 albumin or to use tracer amounts of albumin labeled 

 with I'^'. In these cases the transit times measured are 

 those of serum albumin which may or may not be 

 representative of blood or plasma. 



Nonrepresentative behavior also arises from the 

 fact that some substances, such as water, leave vascular 

 systems by dififusing across capillaries. If indicator is 

 attached to serum albumin, which diffuses across 

 capillaries only \'ev\ slowly compared to water, then, 

 insofar as there is net water loss from the arteriolar 

 end of capillaries, indicator will be concentrated. 

 For the case of constant-injection, indicator leaves 

 arterioles at concentration = 1/ F. In proximal por- 

 tions of the capillaries its concentration will exceed 

 I/F. If all water returns to the capillaries at their 

 venular ends, concentration of indicator entering 

 venules will again be I/F. If the water does not return 

 completely to the venular end of the capillaries, as 

 in edema formation, prominent lymphatic flow, or 

 renal glomeruli, concentration of indicator in the 

 veins will exceed I/F, where F is arterial inflow, but 

 it will equal / divided by the venous outflow. There- 

 fore, if there is net water movement into or out of 

 the vascular bed under study, and indicator is 

 albumin, the flow which is measured by the equa- 

 tions developed here is the venous outflow and not 

 the arterial inflow. 



The fact that water moves out of capillaries, yield- 

 ing a concentration of indicator which exceeds I/F, 

 even if only transiently (i.e., even if all the water 



returns to the vascular bed), means that the methods 

 must underestimate the volume. By the sudden- 

 injection method, the mean transit time of the indi- 

 cator is less than that of water which has an extra- 

 vascular circuit. In the constant-injection method, 

 the mass of indicator in the system is estimated cor- 

 rectly from the equation M = F J" [Cmax ~" C'(<)] 

 dt, but it is no longer true that this M divided by 

 volume is C„,nx because some portion of M exists at 

 a concentration greater than Cmax • Some bound on 

 the error may be calculable if there is sufficient 

 information about the system. 



For example, consider that the volume, V, is com- 

 posed of a subvolume f'l , containing a mass A/j of 

 indicator at equilibrium concentration Cmax = I/F, 

 and a subvolume I'o , containing a mass A/2 of indi- 

 cator at an average concentration C'supemiax , w'here 

 M = My + Mo. Then V = \\ + V. = 



(Afi/Cn,a.) + (Afs/Qupermax) = (M/C^ax) - 

 A/2 ( I /Cmax — l/Csupermax)- TllUS, if 3 boUnd On M -j 



is known, for example from the fact that the \olume 

 of plasma in capillaries is only, say, i per cent of the 

 plasma volume of the system under study, then the 

 error may be neglected for certain purposes. For the 

 case of systems containing a large capillary volume 

 the error may be important. For example, in the 

 kidney, the concentration of tagged albumin exceeds 

 I/F in the glomerular capillaries and in the efferent 

 arterioles, returning almost to I/F in the peritubular 

 capillaries. 



For the case of substances which diffuse out of 

 capillaries, flow cannot be measured by the sudden- 

 injection method if the indicator does not flow out of 

 the effluent sampling site. Flow can be measured by 

 the constant-injection method and, for vascular beds, 

 the measured flow is, in fact, plasma flow (or blood 

 flow, depending on the analytical procedure). How- 

 ever, the volume measured is the \olume in which 

 indicator is distributed and therefore exceeds the 

 plasma volume. The mean transit time, t = V/F, 

 calculated from transients of the constant-injection 

 curve is, of course, that of indicator and not of 

 plasma. 



INHOMOGENEITY OF BLOOD AND SIONIFICANCE 

 OF VENOUS HEM.\TOCRIT 



An error may occur when an indicator which tags 

 an element of plasma is used to estimate whole 

 blood flow and \olume. The distributions of traversal 

 times of plasma aliumiin and of erythrocytes are 

 diflerent (6, 9). Computation of whole blood flow 



