THE HEPATIC CIRCULATION 



i4°3 



sec). The amount leaving is the product of the blood 

 flow and the average hepatic venous radioactivity 

 (F) at the same time. Since blood flow can be meas- 

 ured by the BSP method and average arterial and 

 venous radioactivities can be obtained by "integrated 

 sampling" the amount of tracer distributed within the 

 splanchnic bed is easily determined following intra- 

 venous injection of I 131 HSA and divided by the 

 arterial concentration at equilibrium (A eq ) to yield a 

 value for splanchnic blood volume: 



SBV = 



(A-V)x EHBF x t e 



(A.a) 



where EHBF is expressed in milliliters of blood flow 

 per second. Since splanchnic blood volume is equal to 

 the product of the hepatic blood flow per second and 

 the mean splanchnic circulation time (MCT) in 

 seconds, 



it follows, 



SBV -" EHBF x MCT 



MCT'^^L- 



(A.a) 



It will be recognized that the Hamilton-Stewart and 

 Kety-Schmidt methods alluded to above are applica- 

 tions of the same principle which has been treated at 

 greater length mathematically by Stephenson and 

 others (284, 315). [See also Chapters 18 and 19 of 

 this Handbook^ Radioactive phosphate or chromium- 

 labeled erythrocytes have been used to determine 

 splanchnic red cell mass and erythrocyte circulation 

 time (94). Any other relatively nondiffusible sub- 

 stance should yield equally reliable results, provided 

 the major assumptions upon which the method is 

 based are valid. 



All the difficulties implicit in the measurement of 

 hepatic blood flow pertain with equal force to the 

 determination of the splanchnic blood volume. Of 

 added importance is the assumption of "representa- 

 tive hepatic venous sampling," because the distribu- 

 tion of tracer within splanchnic blood flow varies 

 from time to time during equilibration, appearing 

 first in the hepatic arterial inflow and later in other 

 parts of the bed. Thus the various splanchnic pathways 

 must be represented within each outflow tract to an 

 equivalent degree. In view of the anatomical arrange- 

 ments and the data yielded by study of circulation 

 time (see below) this assumption seems to be valid 

 in normal man and animals. Local changes within 

 the liver will certainly interfere and the effects of 



streamlining (to be dealt with later) may also in- 

 troduce inequalities by predisposing to predominance 

 of splenic and gastrointestinal vascular routes within 

 the left and right hepatic venous outflows, respectively. 

 The fact that similar values are obtained with 

 sampling from right and left lobes suggests that this 

 possibility is not important, but further work is 

 necessary to settle the matter. Uniform and diffused 

 admixture of tracer throughout all the blood filling 

 the splanchnic blood vessels must have been com- 

 pleted by the "equilibrium time." Since equilibra- 

 tion appears to be attained within 3 min or less, it 

 seems most unlikely that volumes of blood held rela- 

 tively motionless, in contact with but not actively a 

 part of the circulating blood, are included in the 

 final value. Tracer undoubtedly must find its way 

 into the splenic pulp, but largely by diffusion rather 

 than by active mixing, thus probably accounting for 

 the lack of change in splanchnic blood volume (SBY) 

 noted following splenectomy. For this reason the 

 value should be referred to as the "circulating 

 splanchnic blood volume." Although the term specif- 

 ically indicates the volume of whole blood, the tracer 

 usually employed (I 131 HSA) is actually distributed 

 within the plasma. Blood volume must therefore be 

 computed from the estimated plasma volume and 

 the arterial hematocrit. But the latter is not strictly 

 applicable because the phenomena of "lamination" 

 and "plasma skimming" result in a lower hematocrit 

 in blood flowing through the capillaries than in 

 arterial blood. The resulting error may be relatively 

 large and must be borne in mind in interpreting 

 shifts, particularly in association with a changing 

 hematocrit. Simultaneous determinations of red cell 

 mass and plasma volume should yield a more accurate 

 estimate of the total volume, though measurement of 

 the red cell mass is undoubtedly more seriously limited 

 by the difficulty of complete admixture. Blood flow 

 and volume must remain relatively constant during 

 the period of determination — at least 10 min — to 

 permit estimation of hepatic blood flow. Owing to 

 the limits of accuracy imposed by the analytical 

 procedures, blood flow must not be so large relative to 

 volume as to minimize critically the difference be- 

 tween the mean values for arterial and hepatic 

 venous radioactivities. Experiments with model sys- 

 tems in which the blue dye, T-1824, has been used 

 have demonstrated the validity of the method pro- 

 vided flow per minute is not greater than three times 

 the volume (63). A higher ratio may be compatible 

 with sufficiently accurate measurement of the arterio- 



