Relative Distance: the Key to the Shape of Hepatic Building Blocks

The delineation and the shape of the smallest structural units of the liver is still the subject of debate. However, the blood flow from an upstream terminal branch of the portal vein to a downstream central vein is thought to induce a functional zonation in hepatocyte gene expression. This property was used to determine boundary conditions for the shape of the hepatic building blocks. Histochemical techniques that specifically label periportally or pericentrally expressed enzymes can be used to distinguish periportal and pericentral areas in a liver section. Pairs of images from aligned serial sections, one stained for a portal and the next for a central enzyme, are used. Segmentation and skeletonisation of these images results in the skeletons of the portal and central areas. Distance transformation with respect to these skeletons gives for each point in the image pair the distance to the nearest terminal branches of the portal vein and the central vein. For each point the relative position on the porto-central radius can then be calculated as its distance to a portal vein divided by the sum of its portal and its central distance. In the resulting relative radius image, the area occupied by ‘zones’ of equivalent relative radius can be measured. According to the principle of Delesse the relative area of a zone in the image is equal to the relative volume of that zone in the tissue. For structural units of plate-like, cylindrical or spherical shape, the relative volume of a zone is equal to the relative radius of that zone to the power 1, 2 or 3, respectively. Thus, the exponent in the relative area relative radius relation gives information on the shape of the structural unit. Measurement of the areas of each relative radius zone and determination of the area radius relation in images of random sections of adult mouse liver results in an exponent of 1.1. This suggests that the smallest structural unit of the mouse liver has the shape of a needle.