Modeling the perfusion characteristics of liver tissue may provide information useful in surgical treatment which require resection of the pathological tissue regions or for drug delivery.
At the macro-scale the whole organ may be modeled as a porous medium with nonuniform, non isotropic permeability. At an intermediate scale, the tissue can be seen as composed of small units known as “lobules”. At the micro-scale flow within each lobule occurs in a complicated network of micro-vessels known as “sinusoids”.
The macro-scale permeability tensor may be estimated via a set of simulations at the micro-scale
where the flow velocity in response to a given hydraulic load over a small sample of tissue is calculated.
We perform numerical simulations over geometries obtained from in-vivo micro-images, using an unfitted tensor-product cartesian mesh and a penalization strategy to enforce boundary conditions at the vessel boundaries.
 Taffetani, M., de Falco, C., Penta, R., Ambrosi, D., Ciarletta, P.
Biomechanical modelling in nanomedicine: multiscale approaches and future challenges
(2014) Archive of Applied Mechanics
 E. Bulgarello, S. Frizziero, Isogeometric Simulation of the Perfusion Characteristic in the Liver Tissue, M.Sc. Thesis in Mathematical Engineering, Politecnico di Milano, 2014