A convenient geometrical description of the microvascular network is necessary for computationally efficient mathematical modelling of liver perfusion, metabolic and other physiological processes. The tissue models currently used are based on the generally accepted schematic structure of the parenchyma at the lobular level, assuming its perfect regular structure and geometrical symmetries. Hepatic lobule, portal lobule, or liver acinus are considered usually as autonomous functional units on which particular physiological problems are studied. We propose a new periodic unit-the liver representative periodic cell (LRPC) and establish its geometrical parametrization. The LRPC is constituted by two portal lobulae, such that it contains the liver acinus as a substructure. As a remarkable advantage over the classical phenomenological modelling approaches, the LRPC enables for multiscale modelling based on the periodic homogenization method. Derived macroscopic equations involve so called effective medium parameters, such as the tissue permeability, which reflect the LRPC geometry. In this way, mutual influences between the macroscopic phenomena, such as inhomogeneous perfusion, and the local processes relevant to the lobular (mesoscopic) level are respected. The LRPC based model is intended for its use within a complete hierarchical model of the whole liver. Using the Double-permeability Darcy model obtained by the homogenization, we illustrate the usefulness of the LRPC based modelling to describe the blood perfusion in the parenchyma.
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.
- 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
1st edition 541 stran : ilustrace (převážně barevné), portréty, tabulky ; 24 cm
- Konspekt
- Ortopedie. Chirurgie. Oftalmologie
- NLK Obory
- chirurgie
- experimentální medicína
- NLK Publikační typ
- kolektivní monografie
PURPOSE: Quantitative description of hepatic microvascular bed could contribute to understanding perfusion CT imaging. Micro-CT is a useful method for the visualization and quantification of capillary-passable vascular corrosion casts. Our aim was to develop and validate open-source software for the statistical description of the vascular networks in micro-CT scans. METHODS: Porcine hepatic microvessels were injected with Biodur E20 resin, and the resulting corrosion casts were scanned with 1.9-4.7 [Formula: see text] resolution. The microvascular network was quantified using newly developed QuantAn software both in randomly selected volume probes (n = 10) and in arbitrarily outlined hepatic lobules (n = 4). The volumes, surfaces, lengths, and numbers of microvessel segments were estimated and validated in the same data sets with manual stereological counting. Calculations of tortuosity, radius histograms, length histograms, exports of the skeletonized vascular network into open formats, and an assessment of the degree of their anisotropy were performed. RESULTS: Within hepatic lobules, the microvessels had a volume fraction of 0.13 [Formula: see text] 0.05, surface density of 21.0 [Formula: see text] 2.0 [Formula: see text], length density of 169.0 [Formula: see text] 40.2 [Formula: see text], and numerical density of 588.5 [Formula: see text] 283.1 [Formula: see text]. Sensitivity analysis of the automatic analysis to binary opening, closing, threshold offset, and aggregation radius of branching nodes was performed. CONCLUSION: The software QuantAn and its source code are openly available to researchers working in the field of stochastic geometry of microvessels in micro-CT scans or other three-dimensional imaging methods. The implemented methods comply with reproducible stereological techniques, and they were highly consistent with manual counting. Preliminary morphometrics of the classical hepatic lobules in pig were provided.
- MeSH
- interpretace obrazu počítačem metody MeSH
- játra krevní zásobení diagnostické zobrazování MeSH
- koroze MeSH
- mikrocévy diagnostické zobrazování MeSH
- prasata MeSH
- rentgenová mikrotomografie metody MeSH
- software MeSH
- zobrazování trojrozměrné metody MeSH
- zvířata MeSH
- Check Tag
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
