Multiscale modelling of liver perfusion

Abstract

We compare two homogenized models of the microcirculation which rely on different assumptions. The first model has been derived by the homogenization of the mesoscopic structure with the double-porosity medium represented by the Biot model with large contrasts in the permeability coefficients constituting the Darcy law. The newly developed so-called Biot-Darcy-Brinkman (BDB) model is described in the paper; it arises from a two-stage homogenization of the fluid-structure interaction problem which requires geometric representations of the sinusoidal and the inter-lobular vasculatures associated with venous compartments, the portal and the hepatic veins. An illustrative example shows a good correspondence between the two models.