Homogenization of the Perfusion and Contrast Fluid Transport in the Liver Lobules

We present a two-scale model of the contrast fluid (CF) transport in liver tissue derived using the asymptotic homogenization using an idealized representative periodic cell established as a segment of the liver lobulus. The micromodel is based on the double porosity concept with a strong heterogeneity in the permeability and the diffusion coefficients to distinguish the capillary vessels in the microporosity. The resulting macromodel incorporates the double Darcy model of the blood perfusion which provides the local advection velocity field involved in the coupled advection-diffusion problem. This modelling approach enables to capture non-uniformity of the perfusion and CF saturation within a “macroscopic” tissue sample whereby the geometrical specification of the lobulus, i.e. the tissue microstructure, is respected.