A computational model for hepatotoxicity by coupling drug transport and acetaminophen metabolism equations

Abstract

The spatial distributions of cytochrome P450 (CYP450) and glutathione (GSH) in liver lobules determine the heterogeneous hepatotoxicity of acetaminophen (APAP). Their interplay in conjunction with blood flow is not well understood. In this paper, we integrate a cellular APAP metabolism model with a sinusoidal blood flow to simulate the temporal‐spatial patterns of APAP‐induced hepatotoxicity. The heterogeneous distribution of CYP450 and GSH is modeled by linearly varying their reaction rates along the portal triad to the central vein axis of a sinusoid. We found that the spatial distribution of GSH, glutathione S‐transferases (GSTs), and CYP450 all contributes to the high acetaminophen protein adduct formation at zone 3 of the lobules. The reversed spatial gradients of CYP450 and GSH cause quick depletion of GSH, which is further accelerated by the distribution of GST. The hepatic flow congestion and hyperperfusion however do not seem to play a significant role in the zonal hepatotoxicity. The simulation results may be useful for understanding the APAP‐induced hepatotoxicity and associated pharmaceutical treatment.

Virtual Lobule Models Are the Key for Multiscale Biomechanical and Pharmacological Modeling for the Liver

“…From a mathematical modeling's perspective, the sinusoidal flow may be modeled with a partial differential equation (PDE), where the spatial variable x transverses a sinusoid, and the temporal variable t spans a designated time. The dependant variable c is the concentration of a drug in the blood, while c Tissue is the drug concentration in hepatocytes or liver tissue (Franiatte et al, 2019 ). The influx and efflux of drug molecules across the sinusoidal wall are modeled by the two terms inside the red block in the listed equation in Figure 1 .…”

“…The influx and efflux of drug molecules across the sinusoidal wall are modeled by the two terms inside the red block in the listed equation in Figure 1 . When the spatial dimension is not considered but the temporal profile is critical, such as the time course of drug concentration in the liver, ordinary differential equations (ODEs) are used to quantify the drug metabolism in hepatocytes or liver tissues (Reddyhoff et al, 2015 ; Franiatte et al, 2019 ). In this way, cellular and intra-cellular dynamics are coupled.…”

“…Spatial heterogeneity in metabolism can be simulated by arranging the compartments in a series with different metabolism and clearance parameters (Meyer et al, 2017 ). In the drug-transport equation, the influx/efflux of drug molecules across the sinusoidal wall are included inside the red block (Franiatte et al, 2019 ). PT, portal triad; CV, central vein; Cl m , drug clearance through metabolism; CCO, constructive constrained optimisation; PBPK, pharmacokinetics based pharmacokinetic modeling.…”

“…An even simpler lobule representation is a series of compartments arranged according to the above mentioned metabolic zones along the PT-CV axis (Fan et al, 2010 ; Schwen et al, 2016 ), as shown in Figure 1E . This zonal representation has been adopted by several pharmacokinetic (PK) studies dealing with metabolic heterogeneity (Fu et al, 2018 ; Franiatte et al, 2019 ). Putting together, simulations for the blood and drug flow, uptake, excretion, and metabolism of drugs in hepatocytes constitute a typical example of multiscale modeling, as illustrated in Figure 1 .…”

Mathematical Modeling for Hepatitis B Virus: Would Spatial Effects Play a Role and How to Model It?

“…Differing densities for immune cells (Kupffer, NK) at key spatial locations as well as cell-level transporter distributions (e.g., the NTCP) are natural inclusions for investigation. With a continuum model for fluid transport and tissue-level dynamics (e.g., a convection-diffusion equation for the sinusoidal flow) and discrete cell models (e.g., cellular dynamics models of ordinary differential equation systems) over a suite of spatially heterogeneous sample regions, a multi-scaled, detailed and computationally tractable model of the hepatic HBV-immune dynamic is possible (Cangelosi et al, 2017;Franiatte et al, 2019). Low densities of innate immune cells at key spatial locations (e.g., Kupffer near portal-triads), the polarity of cellular distributions of sinusoid-facing transporters (e.g., NTCP), and metabolic roles along the portal-central axis (e.g., hepatic zones I-III) have yet to be investigated for their impact on the HBV infection dynamic.…”