Mathematical modelling of oxygen gradients in stem cell-derived liver tissue.

A major bottleneck in the study of human liver physiology is the provision of stable liver tissue in sufficient quantity. As a result, current approaches to modelling human drug efficacy and toxicity rely heavily on immortalized human and animal cell lines. These models are informative but do possess significant drawbacks. To address the issues presented by those models, researchers have turned to pluripotent stem cells (PSCs). PSCs can be generated from defined genetic backgrounds, are scalable, and capable of differentiation to all the cell types found in the human body, representing an attractive source of somatic cells for in vitro and in vivo endeavours. Although unlimited numbers of somatic cell types can be generated in vitro, their maturation still remains problematic. In order to develop high fidelity PSC-derived liver tissue, it is necessary to better understand the cell microenvironment in vitro including key elements of liver physiology. In vivo a major driver of zonated liver function is the oxygen gradient that exists from periportal to pericentral regions. In this paper, we demonstrate how cell culture conditions for PSC-derived liver sphere systems can be optimised to recapitulate physiologically relevant oxygen gradients by using mathematical modelling. The mathematical model incorporates some often-understated features and mechanisms of traditional spheroid systems such as cell-specific oxygen uptake, media volume, spheroid size, and well dimensions that can lead to a spatially heterogeneous distribution of oxygen. This mathematical modelling approach allows for the calibration and identification of culture conditions required to generate physiologically realistic function within the microtissue through recapitulation of the in vivo microenvironment.

Multiscale modelling of drug transport and metabolism in liver spheroids.

In early preclinical drug development, potential candidates are tested in the laboratory using isolated cells. These in vitro experiments traditionally involve cells cultured in a two-dimensional monolayer environment. However, cells cultured in three-dimensional spheroid systems have been shown to more closely resemble the functionality and morphology of cells in vivo. While the increasing usage of hepatic spheroid cultures allows for more relevant experimentation in a more realistic biological environment, the underlying physical processes of drug transport, uptake and metabolism contributing to the spatial distribution of drugs in these spheroids remain poorly understood. The development of a multiscale mathematical modelling framework describing the spatio-temporal dynamics of drugs in multicellular environments enables mechanistic insight into the behaviour of these systems. Here, our analysis of cell membrane permeation and porosity throughout the spheroid reveals the impact of these properties on drug penetration, with maximal disparity between zonal metabolism rates occurring for drugs of intermediate lipophilicity. Our research shows how mathematical models can be used to simulate the activity and transport of drugs in hepatic spheroids and in principle any organoid, with the ultimate aim of better informing experimentalists on how to regulate dosing and culture conditions to more effectively optimize drug delivery.