**Eduard ROHAN**, University of West Bohemia, Czech Republic:

*Multicompartment and multiscale models of blood flow in liver for simulation of the CT perfusion test*

The talk is devoted to a multiscale approach to modelling the tissue blood perfusion which should enable for an improved quantitative analysis of the tissue scans provided by the standard computed tomography (CT). For this purpose we developed a model of dynamic transport of the contrast fluid through the hierarchies of the perfusion trees. The research is aimed at developing a complex model which would assist in planning the liver surgery. Recently we proposed a multicompartment model of the blood perfusion in liver which serves as the feedback for simulations of the dynamic perfusion CT investigation. The flow can be characterized at several scales for which different models are used. Flow in larger branching vessels is described using a simple 1D model based on the Bernoulli equation with correction terms respecting the pressure losses associated with the dissipation. This model is coupled through point sources/sinks with a 3D model describing multicompartment flows at the lower hierarchies of the perfusion trees penetrating to the parenchyma. For modelling the microcirculation at the level of liver lobules, the homogenization technique can be used. Two models are presented. The first one is based on upscaling the Darcy flow in the porous material with large contrasts in the permeability coefficients. The second one is based on two-level upscaling of the Stokes flow with rescaled viscosities in the microvessels, or capillaries. This leads to a Brinkman-Darcy system of equations governing the flow at the mesoscopic level. Numerical examples are presented.

**Tuesday, February 2, 10:30 a.m. to 11:30 a.m., Jacques-Louis Lions lecture hall, building C, Paris center. Coffee from 10:15 a.m.**