The reported allometric constant for blood
The reported allometric constant for blood flow in the portal vein is, with 0.76, lower than that for the hepatic artery (0.86; ), implying that the contribution of the hepatic artery to lobular perfusion increases with increasing size of the mammal. A change in the relative contribution of the hepatic artery and portal vein to liver perfusion will affect the extrapolation of pharmacological data from small to large animal models and humans, if metabolic activity in the liver is determined with the Fick principle, which states that the product of blood flow to an organ and the arteriovenous concentration difference of a substance determine uptake or release of a substance by that organ. Since just one study was available to underscore this hypothesis and since this study compiled data on mice, rats, dogs and humans only , we have reviewed the pertinent literature for paired samples of liver perfusion (portal and hepatic vein, or portal vein and hepatic artery). Our review includes mice, rats, rabbits, dogs, pigs, sheep, macaque monkeys, humans, and cattle, that is, mammals with a 10,000-fold range in body mass. Liver blood flow was determined with indicator dilution methods (para-aminohippuric Methoctramine (PAH), microspheres, or clearance of indocyanine green or bromosulphtalein), ultrasound or electromagnetic probes, MRI or CT imaging. The PAH-based assay is used in both small and large mammals, but many of these studies in rodents do not provide quantitative data on transhepatic blood flow, so that our PAH sample is somewhat biased to larger mammals. The microsphere technique is, on the other hand, often used in small and intermediate size mammals. The collected data revealed a pronounced difference between liver perfusion as determined with the PAH-dilution method and all other methods (Fig. 4C–F). The allometric constant of blood flow in the hepatic artery was 1.00–1.09 with all methods used (Fig. 4C; not significantly different), but that in the portal vein was 1.11 for PAH and only 0.79 for all other methods (P < 0.001) and similar to that reported earlier . The numbers for the hepatic vein followed that of the portal vein (P < 0.001). Fig. 4F, finally, shows that the allometric constant of the ratio of the contribution of the hepatic artery and portal vein to hepatic perfusion is zero for PAH and 0.29 for all other assays (P = 0.001). The differences persist when we compare PAH with all other indicator-dilution methods only. We do not know the reason for the observed difference, except that it appears to arise from the portal-vein data. Good correspondence was reported between microsphere- and electromagnetic probe-based estimates of liver perfusion in rats , between microspheres- and MRI-based estimates of portal blood flow in rabbits , and between electromagnetic probe- and indocyanine-green clearance-based estimates of liver perfusion in dogs . Because the allometric constant for hepatic perfusion via the portal vein as determined with the PAH dilution method is ~0.3 units higher than the previously  and presently collected values for all other, technically diverse techniques combined, we tentatively conclude that the PAH data are not representative. Because the regression lines (Fig. 4D) crossed, the PAH-based estimates of portal blood flow in small mammals like mice and rats were low and those in large mammals like cows high relative to reference values. Since the perfusion pressure and flow rate are low in the portal vein and since plasma is a viscous fluid, a potential explanation is incomplete mixing of the injected PAH in between the mesenteric-vein injection site and the portal vein in the smaller mammals (distance >10-fold longer in cattle than in mice). In large ruminants like cattle, on the other hand, often more than one (frequently two) of the three large tributaries to the portal vein (gastrosplenic, gastroduodenal, anterior mesenteric veins) are cannulated  to optimize mixing in the portal vein. Since cannulation of one tributary should suffice according to theory, this protocol suggests that portal blood flow in ruminants can be overestimated.