Modeling of the contrast-enhanced perfusion test in liver based on the multi-compartment flow in porous media

Abstract

The paper deals with modeling the liver perfusion intended to improve quantitative analysis of the tissue scans provided by the contrast-enhanced computed tomography (CT). For this purpose, we developed a model of dynamic transport of the contrast fluid through the hierarchies of the perfusion trees. Conceptually, computed time-space distributions of the so-called tissue density can be compared with the measured data obtained from CT; such a modeling feedback can be used for model parameter identification. The blood flow 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 correction terms to respect the local 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. The contrast fluid saturation is governed by transport equations adapted for the 1D and 3D flow models. The complex perfusion model has been implemented using the finite element and finite volume methods. We report numerical examples computed for anatomically relevant geometries of the liver organ and of the principal vascular trees. The simulated tissue density corresponding to the CT examination output reflects a pathology modeled as a localized permeability deficiency.

A 3D‐1D coupled blood flow and oxygen transport model to generate microvascular networks

“…Finally, the performance of the numerical model could be further tested by considering CT scans showing the saturation distribution of a contrast fluid. 16 Besides the transport of oxygen further convection-diffusion equations modelling the injection of a contrast fluid could be added and the resulting simulation data could be compared with the image data.…”

“…14 In order to account for the vessel hierarchy, multi-compartment flow models have been considered. 15,16 A challenge in this context is to estimate the permeability tensors and porosities for each compartment and to derive suitable coupling conditions between the different compartments. Other types of models directly simulate vascular growth taking optimality principles like the minimisaton of building material or the minimisation of energy dissipation into account.…”

A computational model applied to myocardial perfusion in the human heart: From large coronaries to microvasculature

“…This idea is based on the heterogeneous Domain Decomposition approach for multi-physics problems, see [56]. Examples of splitting algorithms in such context are given, e.g., by [18,5] for the fluidstructure interaction problem, [20] for the Stokes-Darcy coupling, [10] for the 3D-1D geometric multiscale coupling, [57] for the liver perfusion coupled problem. In particular, the idea is to equip the fluid problem with a Neumann boundary condition coming from the Robin interface condition (3c), and to provide to the first (most upstream) Darcy problem a mass term coming from (3d).…”

“…After operating an homogenization procedure, the blood flow in the myocardium is treated as the flow through a porous medium. In this respect, a straight Darcy model has been considered in [42], whereas a moresophisticated multi-compartment Darcy model has been proposed in [15,47,34,35,41], see also [57] for an application to the perfusion in the liver. 2.…”

A new framework for assessing subject-specific whole brain circulation and perfusion using MRI-based measurements and a multi-scale continuous flow model

“…A model of perfusion should be in accordance with the physiological interpretation of perfusion being considered as a feeding arterial flow of oxygenated blood into the tissue or an organ. As a solution, we adopt a continuous flow model in which perfusion is regarded as the volume flux of oxygenated blood, which transits from arterial to the venous side in a two-compartment (2C) model [16–19]. This understanding of perfusion is both mathematically strict and physiologically sound.…”