Dual continuum upscaling of liver lobule flow and metabolism to the full organ scale

Abstract

The liver is the body’s primary metabolic organ and its functions operate at multiple time and spatial scales. Here we employ multiscale modelling techniques to describe these functions consistently, based on methods originally developed to describe reactive fluid flow processes in naturally-fractured geological sediments. Using a fully discretized idealized lobule model for flow and metabolism, a dual continuum approach is developed in two steps: 1) Two interacting continua models for tissue and sinusoids properties, followed by 2) further upscaled dual continua models leading to an averaged lobule representation. Results (flows, pressures, concentrations, and reactions) from these two approaches are compared with our original model, indicating the equivalences and approximations obtained from this upscaling for flow, diffusion, and reaction parameters. Next, we have generated a gridded dual continuum model of the full liver utilizing an innovative technique, based on published liver outline and vasculature employing a vasculature generation algorithm. The inlet and outlet vasculature systems were grouped into five generations each based on radius size. With a chosen grid size of 1 mm3, our resulting discretized model contains 3,291,430 active grid cells. Of these cells, a fraction is occupied vasculature, while the dominant remaining fraction of grid cells approximates liver lobules. Here the largest generations of vasculature occupy multiple grid cells in cross section and length. The lobule grid cells are represented as a dual continuum of sinusoid vasculature and tissue. This represents the simplest gridded dual continuum representation of the full liver organ. With this basic model, numerous full liver drug metabolism simulations were run. A non-reactive PAC (paclitaxel) injection case including only convective transfer between vasculature and tissue was compared with including an additional diffusive transfer mechanism. These two cases were then rerun with tissue reaction, converting injected PAC to PAC-OH (6-hydroxypaclitaxel). There was little transfer of PAC from vasculature to tissue without the addition of diffusive transfer, and this had a significant observable effect on internal PAC distribution in the absence of reaction, and also on the distribution of PAC-OH for the reactive cases.