Rohan Eduard, Lukeš Vladimír, Jonášová Alena
NTIS - New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8, 30614, Pilsen, Czech Republic.
J Math Biol. 2018 Aug;77(2):421-454. doi: 10.1007/s00285-018-1209-y. Epub 2018 Jan 24.
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.
本文致力于对肝脏灌注进行建模，旨在改进对对比增强计算机断层扫描（CT）所提供的组织扫描图像的定量分析。为此，我们开发了一种造影剂在灌注树层级结构中动态传输的模型。从概念上讲，可以将所谓组织密度的计算时空分布与从CT获得的测量数据进行比较；这种建模反馈可用于模型参数识别。血液流动在多个尺度上进行表征，针对不同尺度使用了不同的模型。由较大分支血管代表的高层级结构中的血流，使用基于伯努利方程并通过修正项进行扩展以考虑局部压力损失的简单一维模型来描述。为了描述较小血管和组织实质中的血流，我们提出了一种多孔介质的三维连续介质模型，该模型根据具有水力渗透率特征的层级匹配隔室来定义。与门静脉和肝静脉相对应的一维模型通过点源或汇与三维模型耦合。造影剂饱和度由适用于一维和三维流动模型的传输方程控制。复杂的灌注模型已使用有限元和有限体积方法实现。我们报告了针对肝脏器官和主要血管树的解剖学相关几何形状计算的数值示例。对应于CT检查输出的模拟组织密度反映了一种被建模为局部渗透率缺陷的病理情况。
