Sub-voxel perfusion modeling in terms of coupled 3d-1d problem

We study perfusion by a multiscale model coupling diffusion in the tissue and diffusion along the one-dimensional segments representing the vasculature. We propose a block-diagonal preconditioner for the model equations and demonstrate its robustness by numerical experiments. We compare our model to a macroscale model by [P. Tofts, Modelling in DCE MRI, 2012].