INDICATOR SUBSTANCES AND FLOW ANALYSIS 



641 



the difiiculties of various techniques and opine that 

 tlie new tools will eventually furnish a workable 

 method for the determination of coronarv blood flow- 

 in man. 



Hepatic Flow 



The ijlood flow throui^h tlie liver has been measured 

 by Dobson & Jones (2 1 ) by observing the rate of dis- 

 appearance of intravenously injected particulate 

 matter from the blood stream. 



In the dog and in mice, up to 90 per cent of intra- 

 venously injected colloidal chromic phosphate 

 (labeled with P'-) can be recovered in the liver, and 

 most of the balance in the spleen. For the first few 

 minutes the disappearance curve is essentially ex- 

 ponential, with C, = Cue"'", where C, is the concen- 

 tration at any time, /, Co is the initial concen- 

 tration, and k is the disappearance constant. 



For longer time intervals (30 min or more) the 

 disappearance curve is not a single exponential but 

 may be resolved into three exponential components. 

 Of these the slowest component, or "tail"' of the curve, 

 is attributed to the presence of noncentrifugable small 

 particles in the colloidal suspension injected. At time 

 zero this component contributes only 0.16 per cent of 

 the radioactivity in the l:)lood. 



The two fast components of a representative curve 

 in mice have half-times of 20 and 73 sec. The fastest 

 component is regarded as being dependent on the 

 liver blood flow. Since the splenic venous blood goes 

 through the liver, the splenic blood flow is part of the 

 hepatic blood flow. If the liver and spleen were 100 

 per cent efficient in removing the labeling agent from 

 the blood, the disappearance constant, k, would 

 measure the fraction of the circulating blood which 

 passes through the liver in a unit time interval, but if 

 only some fraction, rj, is removed in one passage, k is 

 the product of r] and the perfusion factor. If ri is low, 

 a correction is needed to take into account the double 

 uptake in the splenic-liver flow. In anesthetized mice, 

 dogs, and rabbits, the efficiency factor, -q, in the liver 

 was found to be 80 to 90 per cent and in mice the 

 spleen circulation was found to average ai)out 4 per 

 cent of the liver circulation, so in general the correc- 

 tion for splenic plus hepatic uptake is not significant 

 in these studies. In any event, k gives the minimum 

 perfusion factor. 



A theoretically possible but unprox-en explanation 

 for the second fast component involves the different 

 rates of time required for transit of the extrahepatic 

 portions of the circulation. Alternatively, the particles 



may fall into two discrete groups on the basis of the 

 efficiency of their removal by the liver. 



The above considerations justify the idealization of 

 the system as comprising a one-compartment open 

 system, with the blood being regarded as a uniformly 

 mixed compartment and the liver as the only output 

 route. Studies of the mixing times in the blood with 

 similar but more slowly disappearing colloids con- 

 taining yttrium [Gofman, cited in (21)] indicate 

 that in rabbits the colloid is mi.xed with 95 per cent 

 of the circulating blood in one-half to one minute. 



The maximum and minimum blood-liver perfusion 

 factors found with the above method in anesthetized 

 animals were: dog 1.2 to 1.4, rabbit 1.12 to 1.3, and 

 mouse 1 .7 to 2.2 volumes of blood per minute per vol- 

 ume of tissue. 



Tlie minimum values in nonanesthetized rabJDits 

 and mice were lower, but the efficiency factors were 

 not determined. Epinephrine and irradiation (19,000 

 to 26,000 rad delivered from radioactive yttrium) were 

 found to lower the liver circulation. 



With mice it is possible to check the results obtained 

 using the blood-disappearance curve by comparing it 

 with the liver-appearance curve obtained by in vivo 

 measurements with an external counter. For animals 

 larger than small rats, the absorption of P^- 0- par- 

 ticles in thick layers of tissue renders in vivo counting 

 too inaccurate, but similar procedures involving 

 gamma-emitting labels would make the in vivo tech- 

 nique applicable in man. 



Parker & Finney (46) agree that the liver blood 

 flow is the rate-limiting step in the removal of certain 

 colloids from the blood for small doses of injected ma- 

 terial, but with larger doses find it necessary to express 

 the rate dependence on dose as follows, where C is 

 the concentration in the plasma: 



dc 



= ,tc«33 



dl 



The doses above a critical dose are removed from the 

 blood with a very low efficiency in a single passage 

 through the liver, and in this circumstance blood flow 

 is not the rate-limiting step. 



Flow Rates Measured hy Tissue Uptake of K*- 



In contrast with the method described above for the 

 liver blood flow, Sapirstein (55, 56) has capitalized 

 on the extreme rapidity with which potassium and 

 related ions penetrate almost all tissues [Walker & 

 Wilde (71), Ginsburg& Wilde (28)]. Studies with K^ 

 indicated that at least during the first minute after an 



