Simulation of a detoxifying organ function: Focus on hemodynamics modeling and convection‐reaction numerical simulation in microcirculatory networks

Abstract

When modeling a detoxifying organ function, an important component is the impact of flow on the metabolism of a compound of interest carried by the blood. We here study the effects of red blood cells (such as the Fahraeus‐Lindqvist effect and plasma skimming) on blood flow in typical microcirculatory components such as tubes, bifurcations and entire networks, with particular emphasis on the liver as important representative of detoxifying organs. In one of the plasma skimming models, under certain conditions, oscillations between states are found and analyzed in a methodical study to identify their causes and influencing parameters. The flow solution obtained is then used to define the velocity at which a compound would be transported. A convection‐reaction equation is studied to simulate the transport of a compound in blood and its uptake by the surrounding cells. Different types of signal sharpness have to be handled depending on the application to address different temporal compound concentration profiles. To permit executing the studied models numerically stable and accurate, we here extend existing transport schemes to handle converging bifurcations, and more generally multi‐furcations. We study the accuracy of different numerical schemes as well as the effect of reactions and of the network itself on the bolus shape. Even though this study is guided by applications in liver micro‐architecture, the proposed methodology is general and can readily be applied to other capillary network geometries, hence to other organs or to bioengineered network designs.

In vitro to in vivo acetaminophen hepatotoxicity extrapolation using classical schemes, pharmacodynamic models and a multiscale spatial-temporal liver twin

“…Poiseuille-flow is considered, which relates the volume flow rate to the pressure difference along each sinusoid of the sinusoidal network. To account for the dependence of the effective blood viscosity with the sinusoid diameter (Fahraeus-Lindqvist effect) an empirical effective blood viscosity model was chosen ( Boissier et al, 2021 ).…”

In silico modeling for the hepatic circulation and transport: From the liver organ to lobules

“…Models for liver lobules (a) liver lobules modeled as hexagonal prism; (b) histological image‐based algorithm for inter‐lobular boundaries (Ahmadi‐Badejani et al, 2020); (c) the liver model incorporating vascular imaging (Hammad et al, 2014); (d) liver lobule where sinusoids are graphs (Boissier et al, 2021); (e) and (f) liver lobules models for damage and regeneration of hepatocytes after perfusion of ammonia in CCl 4 intoxication mice models (Schliess et al, 2014). The necrotic region occurs at the peri‐CV zone after CCl 4 intoxication for 1 day.…”

“…These include particle models that simulate the interaction of RBCs with capillary wall (Fedosov et al, 2010; Sun & Munn, 2005), and the models that use empirical laws (e.g., for the Fahraeus–Lindqvist effects) to represent the blood viscosity in micro‐vessels (Pries et al, 1994; Pries & Secomb, 2005). In a recent work for sinusoidal flow (Boissier et al, 2021), the sinusoidal network was extracted from confocal laser scanning micrographs of mice (Hoehme et al, 2010). The sinusoidal network is defined as a graph containing nodes and edges (Figure 4c), where a governing convection reaction equation is solved (Boissier et al, 2021).…”

Automated Detection of Portal Fields and Central Veins in Whole-Slide Images of Liver Tissue

“…Such quantitative parameters are particularly interesting for parameterizing models of hepatic metabolic processes involving the sinusoidal or lobular scale. 23 , 26 , 27 , 28 , 29 , 30 , 31 …”