Analysis of compartments-in-series models of liver metabolism as partial differential equations: the effect of dispersion and number of compartments.

Non-alcoholic fatty liver disease is the most common cause of chronic liver disease. Precipitated by the build up of extra fat in the liver not caused by alcohol, it is still not understood why steatosis occurs where it does in the liver microstructure in non-alcoholic fatty liver disease. It is likely, however, that the location of steatosis is due, at least in part, to metabolic zonation (heterogeneity among liver cells in function and enzyme expression). Recently, there has been an influx of computational and mathematical models in order to investigate the relationship between metabolic zonation and steatosis in non-alcoholic fatty liver disease. Of interest among these models are "compartments-in-series" models. Compartments-in-series models include the spatial distribution of metabolite concentrations via series of compartments that are connected through some representation of blood flow. In this paper, we analyze one such model, focusing specifically at how the number of compartments and inclusion of dispersion in the flow affect simulation results. We find the number of compartments to have a much larger effect than the inclusion of dispersion, however this is likely due to numerical artifacts. Overall, we conclude that considering partial differential equations that are equivalent to compartments-in-series models would be beneficial both in computation and in theoretical analyses.