Geometrical model of lobular structure and its importance for the liver perfusion analysis

Abstract

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.

In vitro construction of liver organoids with biomimetic lobule structure by a multicellular 3D bioprinting strategy

“…All these factors are involved in regulating the phenotype and function of hepatocytes. [22][23][24] ECMs distributed around cells not only provide mechanical support for tissues and organs, but also participate in a variety of cell signalling pathways. 7,25 Therefore, the mimicking of cell heterogeneity, ECM composition and structural features of native liver organ is essential for the functional expression of the in vitro constructed models.…”

“…From a physiological point of view, hepatocytes are located in a complex but well‐organized microenvironment provided by the lobules, including various types of non‐parenchymal (such as endothelial, stellate and Kupper) cells, insoluble ECMs and soluble cytokines. All these factors are involved in regulating the phenotype and function of hepatocytes 22–24 . ECMs distributed around cells not only provide mechanical support for tissues and organs, but also participate in a variety of cell signalling pathways 7,25 .…”

Reduced order modeling of blood perfusion in parametric multipatch liver lobules

“…Our goal is to enable the efficient modeling of blood perfusion in the liver at the mesoscale level of functional units with varying geometries. Most existing work idealizes liver lobules as perfect two-dimensional hexagons [15,16], but there is a need to give up this idealization in order to be able to generate lobule structures that fill more complex domains [17]. The blood circulation in the liver is a complex process involving the entry of blood through two primary vessels: the hepatic artery and the portal vein, and discharge through one vessel: the hepatic vein.…”