PubMed1992
Optimality in branching structure of the hepatic arterial vessel in 16 patients with liver cirrhosis was studied. The controls used in this study were 14 patients with gastric or colonic cancer not accompanied by liver dysfunction. Optimality principle was based on the concept that blood vessel size and arrangement provided for blood flow with minimum energy loss. Measurements were made of parent and branch vessel diameters from selective celiac arteriogram. After that we measured the included angles of the branch-points of portal vein using ultrasonography. The branch-points of interest were the third bifurcations of right intrahepatic portal vein and artery. The following results are presented in terms of three parameters (r2(2)/r1(2), r1/r0, and r2/r0). The theoretical equations have been shown by several authors. The curve representing these equations was shown by Zamir. We analyzed the scatter of the data points and compare the theoretical and actual results with them. The extent of the scatter is studied making a comparison between control patients and patients with cirrhosis. The data points in control patients were plotted near the theoretical curve. In patients with cirrhosis, the data points show a definite tendency to be plotted far away from the theoretical curve, when we take account of both vessel diameters and branching angles. This discrepancy between theoretical values and actual data in patients with cirrhosis is considered to be caused by the following factors which may influence the vascular structure; hemodynamic change caused by increase of intrahepatic shunt, and morphological change caused by increased fibrosis or/and parenchymal nodules of the liver.