CIRCULATION TIMES AND THEORY OF INDICATOR-DILUTION METHODS 597 



from measured plasma flow is \alid, but whole blood 

 volume cannot be estimated I'rom plasma volume 

 and venous hematocrit (19). 



Let the rate at which erythrocytes flow through a 

 vein be Fe and the rate at which plasma flows be 

 Fp . Consider that the entire outflow from a vein is 

 collected In one unit of time the collecting vessel 

 will contain a voknne equal to Fe of erythrocytes 

 and a \olume equal to Fp of plasma, a total blood 

 volume, Fb = Fk + Fp . When the collecting vessel 

 is subjected to centrifugation, it will be found that 

 the hematocrit ratio (as percentage) is 



and 



Ht = [Fe/(Fe + Fp)yjoo = (Fe/Fb) 100 



Ht 



(Fp/Fb) 100 



Whence Fb = 100 Fp/(ioo — Ht), \'erifying that 

 blood flow can be calculated from plasma flow and 

 venous hematocrit ratio. 



To calculate the relation between volumes, sub- 

 stitute the appropriate ('//for F. It will be found that 



■■-■>[(i)t"«,) 



where subscripts B, P, and E refer to values for whole 

 blood, plasma, and erythrocytes, respectively. There- 

 fore, a single hematocrit correction factor is insuffi- 

 cient to convert plasma volume to blood volume. The 

 ratio of mean transit time of erythrocytes to that of 

 plasma must be known. By independent labeling of 

 plasma albumin and erythrocytes, Ie and tp have 

 been measured simultaneously in several vascular 

 beds (6, 9). 



The equation Ht = {Fe/Fb)/ 100 states that the 

 venous hematocrit ratio is a function of erythrocyte 

 flow and of plasma flow. Therefore, it should be 

 possible to change the hematocrit ratio by changing 

 the ratio of erythrocyte flow to total blood flow. A 

 preliminary examination of this prediction has been 

 made. In a group of eight determinations on four 

 normal men, when forearm blood flow was occluded, 

 the antecubital venous hematocrit ratio was always 

 less, on the average by 1.5 per cent (unpublished 

 observations). 



RECIRCULATION 



Recirculation of indicator is of practical importance 

 when it occurs before all indicator particles have 

 completed the first transit. For the case of sudden- 

 injection, this means that before the concentration 

 of indicator at outflow has returned to zero it is 



augmented by some indicator particles which have 

 already been counted once; and for the case of con- 

 stant-injection, this means that before the plateau 

 concentration C,„^^ is reached there is an increase in 

 the slope of the curve C{t) vs. /, owing to reappearance 

 of old indicator particles. There are two reasons for 

 trying to understand recirculation. One is that, in 

 most cases, recirculation is a nuisance which confuses 

 interpretation of the primar\- circulation curve, 

 making it difficult to perform proper calculation of 

 F and V. The other is that the concentration-time 

 curve during recirculation may give some informa- 

 tion about the channels through which recirculation 

 occurs, as in the case of abnormal shunts. 



There are two ways to handle the problems created 

 b>- the presence of recirculation. One is to extend the 

 treatment of the concentration of indicator as a 

 function of flow and volume to include the case of 

 recirculation. The other is to treat formally the con- 

 centration of indicator during first circulation as a 

 separate event from the observed concentration in 

 the presence of recirculation and, by some means, 

 extract from the over-all concentration-time curve the 

 concentration-time curve which applies onlv to the 

 first circulation. Both of these treatments have been 

 advanced. 



Let us first examine the po.ssibility of including con- 

 centration due to recirculation in our fundamental 

 equations for flow and \olume. 



A general formal expression for an indicator-dilu- 

 tion curve which includes recirculation can be ob- 

 tained simply by extending the argument from which 

 equation 17 was developed. The important equation 

 which follows, and its de\elopment, is according to 

 Stephenson (30) as modified by Meier & Zierler (19). 

 Introduce indicator into the inflow of the system 

 at rate /(/), where the function is completely unspeci- 

 fied for the moment. During the interval s to s -\- ds 

 time units before /, the amount of indicator introduced 

 is / (/ — s) ds. The fraction of this amount eliminated 

 per unit time at time /, or s time units later, is h{s). 

 Therefore, the contribution to the rate at which 

 indicator leaves the system at time / made by indi- 

 cator introduced between s and j + ds time units 

 earlier is the product [his)] [i (t — s) ds]. Summing 

 for all such time intervals before /, the rate at which 

 indicator leaves at time / is JJ / (/ — s) h(s) ds. 

 But this rate is also equal to F C(t), where C(t) is the 

 concentration at outflow. Therefore, 



C{t) 



F Jo 



i (t - s) h(s) ds 



(24) 



Equation i 7, which was developed for the case of 



