Spatial Architecture of Biliary Tree in Mammals: Fractal and Euclidean Geometric Features

The study of the fractal architecture of various organs and structures expanded the possibilities for determining the ranges of their functioning and structural arrangement, which, as a result, was reflected in the development of new approaches to diagnostics and therapeutic impacts. The architecture of the excretory duct systems, similar to the hemo- and lymph- circulatory beds and the bronchial tree, is considered fractal. At the same time, information about hitherto unknown structures of the biliary tree continues to appear in the literature. We aimed to study the features of the spatial geometry of the biliary tree and assess the significance of both its fractal and Euclidean characteristics for the development of approaches that facilitate comprehensive description of intrahepatic biliary tract architecture. We investigated the architecture of the biliary trees of six men, seven male canines, and seven male Wistar rats using the corrosion casting method. Corrosion casts were prepared by injecting solidifying latexes into the bile ducts. The preparations were studied using a light stereomicroscope and a scanning electron microscope. Biliary tree branching is of various types. In addition, the correlation between variations in the caliber and length of the bile ducts and their order is not significant. Therefore, the biliary tree should not be considered as a classical fractal and it consists of the main modules, represented by the network of the bile canaliculi (first nonfractal module) and a biliary tree with a fractal branching (second module) that drains the bile canaliculi mesh and the additional modules represented by the mucosal biliary glands (in mammals with the gallbladder) or the periportal biliary plexus (in mammals without a gallbladder) and the aberrant biliary ducts. Such a configuration of the biliary bed should optimally ensure the smooth implementation of the physiological function of the liver, as well as its adaptation to different pathologies accompanied by biliary hypertension. It also might be considered in the diagnosis and assessment of ductular reaction, biliary regeneration, and/or carcinogenesis.