Fig 1.
Schematic views of the hepatic lobule.
Three classic schematics of the liver lobule are; central vein (CV)-centered, portal triads (PT)-centered and acinus. Despite different descriptive views of a liver lobule, the components and functions are the same. PT (blue) consists of hepatic artery, portal vein and bile duct. Blood enters a liver lobule via both hepatic arteries and portal veins, flows across network of liver sinusoids (red), and empties into central vein (CV). During transit, blood-borne substances are absorbed by and metabolized within hepatocytes (green), the major parenchymal cells of the liver, which make up most of liver mass. A liver lobule has three sub-regions (zones) that carry out different metabolic functions. Although definitions for zones vary slightly dependent on the descriptive view, generally, zone I refers to the periportal region; zone II refers to mid-lobular region; zone III refers to pericentral region. Due to both local local microdosimetry and different metabolic functions, the three zones exhibit different types and extents of damage under pathological conditions.
Fig 2.
Schematics of model representations of the liver.
Representations of the liver as BOX (A), PIPE (B), or NET (C) models. BOX models represent liver as either a single PBPK compartment representing both the blood and tissue of the organ (left in (A)) or separate blood and tissue compartments (right in (A)). PIPE models represent liver tissue as a linear chain of hepatocyte (or perhaps zonal) compartments and model blood as either a chain of blood compartments (left in (B)) or as a continuous medium for substance transport solved using convection-diffusion equation (right in (B)). NET models represent liver sinusoid network as spatially defined anastomotic chains of compartments and represent hepatocytes as individual compartments lining the sinusoid network (C).
Fig 3.
(A) Micrograph of sinusoids in a deep section of a rat liver. A central vein is located near the upper right. The scale bar is 100μm and the width of the individual sinusoids is ≈ 8μm. (B) Two-dimensional view of the virtual mouse liver lobule showing the sinusoid network. Hepatocytes, sinusoids, central vein and portal triads are colored green, red, yellow and blue, respectively. (C) Partial cut-away three-dimensional view of the virtual mouse liver lobule. (D) Schematics and equations for transport and metabolism. For more details on the advection model see Section 1.5 in S1 Text.
Table 1.
Anatomical parameters of the simulated and real liver lobules.
Fig 4.
Spatial map and quantitative analysis of calculated flow velocities within the virtual sinusoid network.
(A) Spatial map of flow velocities. Warmer color represents greater flow velocity. Color bar units are μm/s. (B) Calculated flow velocities in individual sinusoids segments with respect to their distances to central vein. Color codes angular positions with black indicating axial (vertex/PT to CV) and white facial (center of lobule face to CV) flows. (C) Histogram of calculated flow velocities.
Table 2.
Xenobiotic dependent simulation parameters for transport and metabolism.
Fig 5.
Transient xenobiotic and metabolite concentrations at t = 20 s in select PERSISTENT simulations.
(α, β) pairs are (0.01, 0.1/s) and (10, 10/s) in upper and lower panels, respectively. In each panel, CLint, from top to bottom row, are 0/s, 0.1/s, and 1/s, respectively. Ds, from left to right column, are 10−7, 10−6, and 10−5 cm2/s, respectively. Color scale has units mmol/L. See Section 3 in S1 Text and S1 Animations for animations of these simulations.
Fig 6.
Spatial maps of select steady-state quantities within the virtual liver lobule.
(A) xenobiotic concentration; (B) metabolic rate; (C) time for the xenobiotic concentration to reach half of steady-state value. Solid circles indicate the positions of individual hepatocytes in the virtual liver lobule slice. These three simulations have the same transport parameters (α = 1, β = 1/s and D = 1 × 10−6 cm2/s) and only differ in metabolism parameters (from left to middle to right column, CLint = 0.01/s, 0.1/s, 1/s, respectively).
Fig 7.
Spatial and temporal characteristics of xenobiotic distribution within the virtual liver lobule.
(A) Time course of radially zonal average xenobiotic concentration in the first 20 seconds of simulation; (B) Steady-state xenobiotic concentrations in individual hepatocytes; (C) time for the xenobiotic concentration to reach half of steady-state value in individual hepatocytes. Color codes radial location of cells/zones from central to peripheral. These three simulations have the same transport parameters (α = 1, β = 1/s and D = 1 × 10−6 cm2/s) and only differ in metabolism parameters (from left to middle to right column, CLint = 0.01/s, 0.1/s, 1/s, respectively).
Fig 8.
Heat maps of central-to-peripheral ratios at steady state in PERSISTENT simulations with various strengths of transport and metabolism.
The complete heat map consists of 25 smaller heat maps, termed constituent heat maps. A constituent heat map contains 12 different (α, β) pairs (indicated on the upper-left most heat map), each of which represents varying strength of active transport. Diffusive trans-membrane rate constants, increase from left to right increasing passive transport. Intrinsic clearance CLint, increases from top to bottom which represents increasing metabolism. Warmer color reflects greater central-to-peripheral ratio, “PP” and “PC” refer to periportal and pericentral, respectively.
Fig 9.
Heat maps of axial-to-facial ratios at steady state in PERSISTENT simulations with various strengths of transport and metabolism.
The complete heat map consists of 25 smaller heat maps, termed constituent heat maps. A constituent heat map contains 12 different (α, β) pairs, each of which represents varying strength of active transport (refer to Fig 8 for details on the range of (α, β) pairs). Diffusive trans-membrane rate constants, increase from left to right, which represents increasing passive transport. Intrinsic clearance CLint, increase from top to bottom, which represents increasing metabolism. Warmer color reflects greater axial-to-facial ratio, “FA” and “AX” refer to facial and axial, respectively.
Fig 10.
Schematics of the three emergent patterns of hepatic exposure at steady state in PERSISTENT simulations and corresponding parameter domains of transport and metabolism.
Schematics of exposure patterns are shown in gray scale, qualitatively indicating high or low steady state xenobiotic concentrations. Parameter domains, colored region in “AT” (active transport), “PT” (passive transport) and “M” (metabolism) strength bars, define the range of transport and metabolism parameters that give rise to the corresponding spatial exposure patterns.
Fig 11.
Heat maps of extraction fractions of the xenobiotic at steady state in PERSISTENT simulations with various strength of transport and metabolism.
The complete heat map consists of 25 smaller heat maps, termed constituent heat maps. A constituent heat map contains 12 different (α, β) pairs, each of which represents varying strength of active transport (refer to Fig 8 for details on the range of (α, β) pairs). Diffusive trans-membrane rate constants increase from left to right, which represents increasing passive transport. Intrinsic clearance CLint increases from top to bottom, which represents increasing metabolism. Darker color reflects greater extracted fraction.
Fig 12.
Summary map of appropriate in silico model representation of the liver.
Two criteria determine if a liver lobule representation is appropriate: Precision of describing microdosimetry and computational efficiency. Five colored maps correspond to different strengths of passive transport, increasing from left to right column. In each colored map, direction from left to right corresponds to increasing metabolism and direction from top to bottom refers to increasing active transport. Color codes the appropriate model representation: blue–BOX; red–PIPE; green–NET. Since this is a three parameter space with color, individual slices of the space are shown horizontally and the colored maps are rotated for better visualization. The conditions for the model choices are as follows: If azimuthal discrepancy is greater than 25% (A) or 100% (B), NET is appropriate (green regions). If azimuthal discrepancy is smaller than 25% (A) or 100% (B) and radial discrepancy is larger than 25% (A) or 100% (B), PIPE is appropriate (red regions). Otherwise, BOX is appropriate (blue regions). Predicted parameter domains for oxygen (“O2”) and acetaminophen (“APAP”) are marked.