Simulating microdosimetry in a virtual hepatic lobule

Abstract

The liver plays a key role in removing harmful chemicals from the body and is therefore often the first tissue to suffer potentially adverse consequences. To protect public health it is necessary to quantitatively estimate the risk of long-term low dose exposure to environmental pollutants. Animal testing is the primary tool for extrapolating human risk but it is fraught with uncertainty, necessitating novel alternative approaches. Our goal is to integrate in vitro liver experiments with agent-based cellular models to simulate a spatially extended hepatic lobule. Here we describe a graphical model of the sinusoidal network that efficiently simulates portal to centrilobular mass transfer in the hepatic lobule. We analyzed the effects of vascular topology and metabolism on the cell-level distribution following oral exposure to chemicals. The spatial distribution of metabolically inactive chemicals was similar across different vascular networks and a baseline well-mixed compartment. When chemicals were rapidly metabolized, concentration heterogeneity of the parent compound increased across the vascular network. As a result, our spatially extended lobule generated greater variability in dose-dependent cellular responses, in this case apoptosis, than were observed in the classical well-mixed liver or in a parallel tubes model. The mass-balanced graphical approach to modeling the hepatic lobule is computationally efficient for simulating long-term exposure, modular for incorporating complex cellular interactions, and flexible for dealing with evolving tissues.

Figure 1. Hepatic lobules receive nutrient-rich blood from the gut through the portal venule and oxygen-rich blood from the lungs through arterioles.

Blood flows past sheets of hepatocytes through the sinusoids and into the central vein. Image adapted from an original by Amber Goetz, first published in .

Figure 2. The virtual lobule morphology is constructed iteratively.

First, sinusoids outward from the central vein (i). In addition to small random variations in the direction of propagation, the sinusoids branch into two sinusoids pointed away from the central vein with probability P_br (ii). Multiple sinusoids are started from the central vein in an attempt to fill space (iii). Portal “triads” consisting of arterioles and venules through which blood enters the lobule are added to the perimeter of the lobule and connected to the vasculature (iv). Finally, the sinusoids are lined with hepatocytes as space allows (v).

Figure 3. Five different lobule morphologies were examined.

They are: a) one portal triad, no branching or noise, b) six portal triads with noise and additional sinusoids, c) six portal triads, 10% chance of branching, d) three portal triads with 10% branching, and e) six portal triads with 5% chance of branching. Though the overall layout (middle column) can be compared qualitatively with physiology, we evaluate these geometries by comparing the flow (left-hand column) predicted for a rat with in vivo measurements of flow in rat sinusoids (Komatsu et al. (1990) [31]). We also compare (right-hand column) the radial dependence of concentration at t_max with the prediction for a well-mixed compartment with equivalent metabolic clearance (heavy dashed line). Comparison of profiles b-e with profile a provides an approximate comparison to a parallel tubes prediction. The solid line indicates the mean for multiple lobules and sinusoids, while the shading indicates the 95% quantile (variability).

Figure 4. Sinusoid connectivity was represented with a graph.

Spatial proximity between sinusoids within simulated lobule (a) was used to generate connectivity graphs (b), which are aggregated (c) in order to solve for flow from the portal triads to the central vein using ODEs.

Figure 5. Similar nodes were aggregated to reduce the complexity of the sinusoid connectivity graph.

Figure 6. A physiologically-based pharmacokinetic model was used to relate oral and inhalation exposure to blood flow into the liver.

Figure 7. A physiologic lobule is a three-dimensional polyhedron with a volume between 0.1 and 0.9 µL .

Our (quasi-)two-dimensional simulated lobule is assumed to have a thickness equal to a sinusoidal diameter (23.5 µm [29]). Therefore many identical simulated lobules in parallel are needed to fill the volume of one physiologic lobule. Blood flow to the simulated lobules is divided by R_liv∶lob, the ratio of the volume of the whole liver to the volume of single lobule.

Figure 8. Average concentration throughout lobule for the five morphologies depicted in Figure 3.

The ensemble average for all five lobules is very similar to the well-mixed lobule prediction (indicated by the dashed line) however the different morphologies produce different whole-liver clearances because the number of hepatocytes as a fraction of the volume of the simulated lobule is geometry-dependent.

Figure 9. The distribution of the number of molecules at each hepatocyte following a total dose of 10 µMol.

Figure 10. The distribution of maximum concentration experienced by hepatocytes relative to the prediction of a well-mixed PBPK model (solid line).

Figure 11. The breadth of the distribution of maximum exposure received by individual hepatocytes, i.e. variability in exposure, grows with the clearance rate.

The shaded region indicates the 95% interval.

Figure 12. The predicted number of apoptotic cells, caused by locally exceeding a threshold of 110% of the maximum average liver concentration, is negligible for a spatially-extended lobule when the metabolism rate is low (lower curve).

For a rapidly metabolized compound (upper curve) variability in exposure causes some apoptosis in the spatially-extended lobule. The shaded region indicates the 95% interval.