26 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



\/. VoA„-V|,A,'V,Ay 



A - A 

 CV 593 CC = 101.5% 

 PV 996 CC ■ loco's 



10 30 50 70 90 110 130 



FIG. 2. Distribution volumes of P^' cells and T-1824 in a 

 barbitalized dog. Labels injected simultaneously at time o in a 

 femoral vein, samples from a femoral artery. Values for CV 

 and PV by equation i, using time o intercepts shown, are given 

 above on left. A simultaneous infusion-withdrawal procedure 

 was begun at 62 min and completed at 70 min. During this 

 period 700 ml of previously prepared autologous whole blood 

 containing neither cell nor plasma label was infused, while at 

 the same time 700 ml of blood was withdrawn from the circu- 

 lation. The distribution spaces of the infused unlabeled cells 

 and plasma were calculated by equation 2, modified as shown 

 above on the right. All volumes V and activities A refer either 

 to cells or to plasma, and have the following definitions: Vj 

 is the volume drawn, V, the volume infused. A^ is the label 

 activity in the pooled drawn blood; A,^ is the activity circu- 

 lating at the completion of the exchange, obtained by backward 

 extrapolation of the second-hour curve to an intercept at 70 

 min; and .4, is the activity circulating before the e.xchange, read 

 at the 70-min intercept of the first-hour curve, extrapolated 

 forward. The distribution spaces of the unlabeled cells and 

 plasma, corrected for sampling, are shown below the working 

 equation, and are also given as percentages of the previously 

 measured label distribution volumes. 



an exponential disappearance rate suggests, the 

 amount cleared from plasma is dependent upon the 

 plasma concentration, loss during the mixing period 

 must be excessive, since plasma concentration is 

 excessive at this time. It is difficult to see how the loss 

 during the periodic phase of the mixing period, in 

 particular, could be predictably related to the rate at 

 any subsequent time. Unless special clearing mecha- 

 nisms operate during the mixing period alone, which 

 seems unlikely, the uncorrected loss of plasma label 

 during this period should be greater for labels which 

 have a high postmixing disappearance rate, than for 

 those with lower rates. Uncorrected loss during the 

 mixing period probably accounts for the overestima- 

 tion of plasma volume which is obtained with rapidly 

 disappearing plasma labels (94). 



Criteria of Uniform Mixing 



From the point of view of semantics, mixing is not 

 complete until the concentration of label is the same 



throughout the circulatory system. Sampling the 

 venous effluent from individual circuits is a direct ap- 

 proach from this point of view, but yields data which 

 are difficult to interpret because of the time lapse in 

 transit of the local circuits. If the time-concentration 

 curve for venous blood is periodic, the intersection of 

 its rising limb with the arterial time-concentration 

 curve is not predictably related to label concentration 

 within the local circuit. If, on the other hand, the 

 local venous curve is aperiodic because of nonuni- 

 formity of individual transit times, and the mean 

 transit lime is long, equalization of arterial and venous 

 label concentrations mav be indefinitcK' delayed 

 (182, 237). 



Study of tissues for their label content has shown 

 that in some tissues label concentrations do not stabi- 

 lize until long after stable concentrations have been 

 achie\ed in blood. In mice, the Fe*^ activity of circu- 

 lating cells does not change after 15 min. But the 

 activity of spleen and kidney continues to rise for an 

 hour, whereas that of the liver rises excessively during 

 the first few minutes and then declines (74). 



From the operational point of view, it is immaterial 

 wiiether a uniform concentration of label has actually 

 been achieved throughout the cardiovascular system. 

 The only rec|uircment is that label activity in the 

 sampled blood represent the mean for the system. If 

 permanent labels are injected, the finding of constant 

 activity in the central circulation o\er a reasonably 

 long period is the most reliable indication that this 

 requirement has been met. When temporary labels 

 are used, the best indication is the achievement of a 

 constant rate of disappearance. 



Tlie Predicted Time Requirement for Mixing 



Equations for mixing ha\e been formulated in terms 

 of the concentration of injected label, the fractional 

 concentration returning to the sampling site after one 

 circulation, and the transit time for the latter (214). 

 Tiiese are of limited applicability to the cardiovascu- 

 lar system because of the impossibility of defining 

 transit time in a quantitatively useful way. The mini- 

 mal mixing time may be defined with confidence, 

 albeit with some naivete, as the time required for a vol- 

 ume equivalent to the blood volume to pass once 

 through the heart. Using approximate values for 

 cardiac output and blood volume, the minimal time 

 in man is about i min, in medium-sized dogs al)out 20 

 sec, and in rats about 10 sec (53). In these and other 

 species for which data are available, the actual mixing 

 requirement appears to be man\' times the minimal 



