Additional file 2: Figure S5. of A physiologically-based flow network model for hepatic drug elimination III: 2D/3D DLA lobule models

Non-reactive PAC profiles across the lobule without diffusion in 3D – block view. (a) PAC at 0.01 min, (b) PAC at 0.05 min, (c) PAC at 0.1 min (d) PAC at 1 min. Color bar is in molfrac. (PPTX 613 kb

Additional file 3: Figure S2. of A physiologically-based flow network model for hepatic drug elimination III: 2D/3D DLA lobule models

Non-reactive PAC profiles across the lobule with diffusion in 3D – block view. (a) PAC at 0.01 min, (b) PAC at 0.05 min, (c) PAC at 0.1 min (d) PAC at 1 min. Color bar is in molfrac. (PPTX 431 kb

DataSheet1_Dual continuum upscaling of liver lobule flow and metabolism to the full organ scale.docx

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.</p

Additional file 5: Figure S6. of A physiologically-based flow network model for hepatic drug elimination III: 2D/3D DLA lobule models

Reactive (6 × 10-3 min-1) PAC and PAC-OH profiles across the lobule without diffusion effects and base case metabolism in 3D – block view. (a) PAC at 0.01 min, (b) PAC at 0.05 min, (c) PAC at 0.1 min, (d) PAC at 1 min, (e) PAC-OH at 0.01 min, (f) PAC-OH at 0.05 min, (g) PAC-OH at 0.10 min, (h) PAC-OH at 1 min. Color bar is in molfrac. (PPTX 1050 kb

Additional file 6: Figure S4. of A physiologically-based flow network model for hepatic drug elimination III: 2D/3D DLA lobule models

Reactive (6 × 10-3 min-1) PAC and PAC-OH profiles across the lobule with diffusion effects and base case metabolism in 3D – sliced view. (a) PAC at 0.1 min, (b) PAC at 0.5 min, (c) PAC at 1 min, (d) PAC-OH at 0.1 min, (e) PAC-OH at 0.5 min, (f) PAC-OH at 1 min. Color bar is in molfrac. (PPTX 378 kb

Additional file 1: Figure S1. of A physiologically-based flow network model for hepatic drug elimination III: 2D/3D DLA lobule models

Non-reactive PAC profiles across the lobule with diffusion. (a) PAC at 0.01 min, (b) PAC at 0.1 min, (c) PAC at 0.2 min (d) PAC at 0.5 min. Color bar is in molfrac. (PPTX 206 kb

Input parameters used in the CCO generation of the vasculature structures shown in Fig 1.

Input parameters used in the CCO generation of the vasculature structures shown in Fig 1.</p

Building a 3D Virtual Liver: Methods for Simulating Blood Flow and Hepatic Clearance on 3D Structures - Fig 8

Non-reactive PAC profiles through the cross-section of the hepatic vein vasculature at (a) 0.1 minutes and (b) 1.5 minutes.</p

Parameters based on the Strahler ordering of vasculature in 2D.

Parameters calculated based on the method of CCO (results from this paper) and GCO [31].</p

An example of Strahler ordering.

Here, black segments are of order 1, green order 2, blue order 3, and red order 1.</p