Relating function to branching geometry: a micro-CT study of the hepatic artery, portal vein, and biliary tree.

Utilizing micro-computed tomography images, the hierarchical structure, interbranch segment lengths and diameters of a hepatic artery, a portal vein, and two biliary trees from intact rat liver lobes were characterized. The data were investigated by analyzing the geometric properties of the vascular structures, such as how interbranch segment diameters change at bifurcation points. In the case of the hepatic artery and portal vein trees (in which the flow rate is high by comparison with that in the biliary tree), the vascular geometry is consistent with a fluid transport system which aims to simultaneously minimize both the power loss of laminar flow, and a cost function proportional to the total volume of material needed to maintain the system (lumenal contents). In comparison, the biliary tree (which has a low flow rate and an opposite flow direction to that of the hepatic artery and portal vein) was found to have a geometry in which the lumen cross-sectional area is maintained at bifurcations. These findings imply that the histological makeup and therefore the pathophysiology of biliary tree vasculature are likely very different from that of the vasculature within the systemic arterial tree. The extent to which the characteristic variability/scatter in the data may have resulted from imaging and/or measurement errors was examined by simulating such errors in a theoretical tree model and comparing the results with the measured data.