Department of Mechanics, Faculty of Applied Sciences, NTIS - New Technologies for Information Society, University of West Bohemia, Pilsen, Czech Republic.
Biomedical Center, Faculty of Medicine, Charles University Pilsen, Pilsen, Czech Republic.
PLoS One. 2021 Dec 2;16(12):e0260068. doi: 10.1371/journal.pone.0260068. eCollection 2021.
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.
为了对肝脏灌注、代谢和其他生理过程进行计算效率高的数学建模，需要对微血管网络进行方便的几何描述。目前使用的组织模型基于小叶水平上被普遍接受的实质结构的示意性结构，假设其具有完美的规则结构和几何对称性。肝小叶、门小叶或肝腺泡通常被认为是独立的功能单元，其上研究特定的生理问题。我们提出了一种新的周期单元——肝代表性周期细胞（LRPC），并建立了其几何参数化。LRPC 由两个门小叶组成，因此它包含了肝腺泡作为子结构。与经典的唯象建模方法相比，LRPC 的一个显著优点是能够基于周期均匀化方法进行多尺度建模。导出的宏观方程涉及所谓的有效介质参数，例如组织渗透性，它反映了 LRPC 的几何形状。通过这种方式，可以尊重宏观现象（如不均匀灌注）与小叶（介观）水平上相关的局部过程之间的相互影响。基于 LRPC 的模型旨在用于整个肝脏的完整分层模型中。使用通过均匀化得到的双渗透率达西模型，我们说明了基于 LRPC 的建模在描述实质内血液灌注中的有用性。
