A Mathematical Model of Blood Circulation in the Liver Lobule

Abstract

The liver has a specialized circulation. It is supplied by two main vessels: the hepatic portal vein, carrying nutrient-rich deoxygenated blood, and the hepatic artery, carrying oxygenated blood. The hepatic portal vein supplies up to 80% of the blood. Within the liver, both the portal vein and the hepatic artery undergo a series of successive bifurcations, which end at the portal tracts. Each portal tract contains three vessels: a portal vein, an artery and a bile duct. Blood drains out from the portal tracts into the sinusoidal space and from there into the central veins. The central veins, after a series of converging bifurcations, end at the hepatic veins, which carry blood out of the liver. The sinusoidal space consists of a network of tortuous, interconnected channels called sinusoids. One of the most common and widely accepted descriptions of the primitive units of the liver is the “classic lobule”. A diagram of an idealized arrangement of liver lobules is shown in Figure 1. Each lobule has the shape of a hexagonal prism with a portal tract running along each of the parallel edges and a central vein on the central axis. The remainder of the space is made up of sinusoids.