1156 
MONITORING 
cer recirculation. (Even when there is no 
convective recirculation of tracer to D, the tra- 
cer input rates x (t) need not be zero since there 
may still be diffusive input fluxes.) When there 
is no recirculation of tracer in our model, then 
Qv (t) = 0 and q = 0, and a single arterial 
injection suffices. This is the model considered 
by Zierler.i Thus it may be seen that Equation 
(7) reduces, as expected, to the form given by 
Zierler^ for measuring the mean transit time t 
by residue detection in the absence of tracer re- 
circulation, viz.. 
00 
00 
t = q 
MEAN BLOOD FLOW 
(t)dt. (8) 
By the general volume theorem (or central- 
volume principle) of indicator dilution 
theory,!'^'^ the first moment mi of the transit- 
time distribution, i.e., the mean transit time t of 
traced substance, is related to the geometric vol- 
ume V of the system of interest and the flow 
rate F of traced substance through the system 
by the equation 
mi = t = XV/F. 
(9) 
Here, X is the average^'^** tissue-to-blood parti- 
tion coefficient, defined as the steady-state ratio 
of the volume-average concentration of tracer 
in V to its concentration in traced fluid (e.g., 
blood plasma). Hence, on combining Equations 
(7) and (9), we obtain for the ratio of flow 
rate of traced substance to the volume of the 
system 
■p X(l - ) 
= — z, . (10) 
[qa(t) - qv(t)]dt 
The above result holds when there is recircu- 
lation of tracer to the system of interest h(t) 
and to adjacent perfused tissues within the field 
of view of a radiation detector used in residue 
detection, independently of the complexities of 
the recirculation paths and of the flow patterns 
within the detector field. Equation (10) is 
equally valid when the only system within the 
detector field is h (t) , since in this case any re- 
circulating tracer in adjacent perfused tissues 
will not infiuence the detector response. 
DUAL-INJECTION ANIMAL EXPERIMENTS 
At Washington University School of Medi- 
cine, numerous animal experiments designed on 
the basis of our dual-injection theory have been 
performed. Specific numerical results will ap- 
pear in future publications as more data are ac- 
cumulated and as we refine the computational 
procedures for implementing our equations. 
Here, we describe briefly the essential features 
of these experiments and give some indication 
of the agreement between blood-flow values pre- 
dicted on our theory with those measured di- 
rectly. 
Figures 5-7 represent, schematically, some 
specific examples of the general configuration of 
Figure 2. Each diagram shows a particular vas- 
cular system of interest, h(t), (renal, my- 
ocardial, and cerebral) within the detector field 
of view, which also encompasses other vascular 
systems from which interfering radiations due 
to recirculating tracer may emanate. Recircula- 
tion, of course, also carries radiotracer into the 
systems of interest. In each of these situations, 
the system for which the transit-time distribu- 
RENAL 
ARTERY 
SYSTEMIC 
CIRCULATION 
OUTSIDE 
DETECTOR FIELD 
PULMONARY 
CIRCULATION 
Figure 5. — Residue Detection with Recirculation for 
the Kidney. 
