Towards image-based analysis of the liver perfusion using a hierarchical flow model

Abstract

The paper summarizes our activities in modelling tissue perfusion using a multilevel approach which is based on information retrievable form CT and micro CT images. We focus on the liver tissue for which the perfusion modelling is of great interest for both medical research and clinical practice. The blood flow in liver is characterized at several scales for which different models are used. Flows in upper hierarchies represented by larger branching vessels are described using simple 1D models based on the Bernoulli equation extended by the Poiseuille correction terms to respect the viscous pressure losses. To describe flows in smaller vessels and in the tissue parenchyma, we propose a 3D continuum model of porous medium defined in terms of hierarchically matched compartments characterized by hydraulic permeabilities. The 1D models corresponding to the portal and hepatic veins are coupled with the 3D model through point sources, or sinks. For the lowermost level representing the quasi-periodic lobular structure we apply the homogenization method which provides the permeability features of the hepatic sinusoids considered as the double porosity. In the paper we discuss several approaches how to determine the flow model parameters which can be combined. Also the model validation using the realistic geometries reconstructed using the CT scans is discussed.