590 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



V. 



u 



c 



3 



cr 



1/.- 



^4 



^ v^ 







3- 



:: 2- 



c 



(J 



c 

 o 



FIG. 5 



cone. X At X 

 2 X 



X 



4 

 3 

 2 

 I 



t 

 3 

 4 

 5 

 6 

 7 



6 



16 

 15 

 12 



7 



r =56 



Area = E cAt » 12 

 X . Ec • At • t 



56 

 12 



Ec • At 

 * 4.7 



time 



— r- 

 



I 



-r- 

 2 



3 



1^ 

 4 



-r- 

 5 



-r- 

 6 



-T- 



7 



FIG. 4- A frequency histogram of times. [From Zierler (38).] 



FIG. 5. Variation of concentration of indicator withi time plotted as a frequency histogram. 

 Distribution of transit times same as in fig. 4. [From Zierler (38).] 



and leave it is F. The rate at which the particles 

 making up dV leave the system is therefore F h{t) dt. 

 Some of these particles leave at time zero, and parti- 

 cles of this traversal time continue to leave the system 

 untU time t, at which instant all such particles will 

 have been eliminated. 



The volume of such particles, d\\ is the time re- 

 quired for them to leave, t, multiplied by the rate at 

 which they leave, F h{t) dt, or dV = t F h{t) dt = 

 F I h{t) dt. 



To find the volume of the system, simply add up 

 all elements dV, or 



Since h(t) is the frequency function of traversal 

 times, \^ t h{t) dt is the mean of traversal times, or 

 the mean transit time or mean circulation time, 

 denoted by t. Therefore, 



I- = Ft 



(10) 



= '/" 



Jo 



/ h(i) dt 



(9) 



which states the fundamental fact that volume = 

 flow multiplied by mean transit time. 



Those indicator particles requiring times between t 

 and t -\- dt to leave the system can be regarded as 

 pushing out ahead of them all fluid particles char- 

 acterized by the same traversal time. Thus, when 

 indicator appears at Q.) 3^ fluid particles / F li{t) dt 

 ha\e left the system. In terms of the observed con- 



