Modeling Tissue Perfusion Using a Homogenized Model with Layer-wise Decomposition

Abstract The proposed two-scale model of perfused tissues enables to reduce the computational complexity by converting a 3D problem with heterogeneous structure into several 2D problems. The model is developed using the homogenization method applied to upscale the Darcy flow problem for each layer featured by the dual porosity. The multi-layer model involves 2D pressure fields for different channel types within each layer and inter-layer fluxes for multiple compartments. The approach combining homogenization and the layer-wise domain decomposition is convenient for an efficient simulation of perfusion in complex branching structures at lower hierarchies of perfusion trees.