Mathematical modelling of blood circulation in the liver

Blood flow in the liver has several unique features compared with other organs in the body. The liver is made up of functional units called lobules, and blood flows across the lobules from the portal tracts to the central veins travelling through small vessels called sinusoids. Vascular septae are vessels running between neighboring portal tracts. Rather than all the blood entering the lobule directly from the portal tracts, some goes from the portal tracts into the vascular septae, and is then distributed into the lobule. In this paper we present a model of the flow in a lobule. We consider an idealized geometry and treat the sinusoids as a porous medium. In the model the portal tracts and vascular septae act as sources of flux of blood and the central veins as sinks. Our results suggest that the vascular septae decrease extreme values of the pressure that could be achieved near to the portal tracts and result in a flow that could distribute nutrients more evenly to all the functional cells of the liver. We conclude with a discussion of extensions of the model.