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.

• Klíčová slova
• Bernoulli equation, Darcy flow, Dynamic contrast-enhanced computed tomography, Liver perfusion, Porous media, Transport equation,
• MeSH
• analýza metodou konečných prvků MeSH
• biologické modely MeSH
• jaterní oběh * fyziologie   MeSH
• játra krevní zásobení   diagnostické zobrazování   MeSH
• kontrastní látky farmakokinetika   MeSH
• lidé MeSH
• matematické pojmy MeSH
• počítačová rentgenová tomografie statistika a číselné údaje   MeSH
• počítačová simulace MeSH
• poréznost MeSH
• vylepšení rentgenového snímku metody   MeSH
• zobrazování trojrozměrné statistika a číselné údaje   MeSH
• Check Tag
• lidé MeSH
• Publikační typ
• časopisecké články MeSH
• práce podpořená grantem MeSH
• Názvy látek
• kontrastní látky MeSH