Timescale analysis of a mathematical model of acetaminophen metabolism and toxicity

Acetaminophen is a widespread and commonly used painkiller all over the world. However, it can cause liver damage when taken in large doses or at repeated chronic doses. Current models of acetaminophen metabolism are complex, and limited to numerical investigation though provide results that represent clinical investigation well. We derive a mathematical model based on mass action laws aimed at capturing the main dynamics of acetaminophen metabolism, in particular the contrast between normal and overdose cases, whilst remaining simple enough for detailed mathematical analysis that can identify key parameters and quantify their role in liver toxicity. We use singular perturbation analysis to separate the different timescales describing the sequence of events in acetaminophen metabolism, systematically identifying which parameters dominate during each of the successive stages. Using this approach we determined, in terms of the model parameters, the critical dose between safe and overdose cases, timescales for exhaustion and regeneration of important cofactors for acetaminophen metabolism and total toxin accumulation as a fraction of initial dose

Mathematical modelling of a liver hollow fibre bioreactor

A mathematical model has been developed to assist with the development ofa hollow fibre bioreactor (HFB) forhepatotoxicity testing of xenobiotics; specifically, to informthe HFBoperating set-up, interpret data from HFB outputsand aid in optimizingHFBdesign to mimic certain hepatic physiological conditions. Additionally,the mathematical model has been used to identify the key HFB and compound parameters that will affect xenobiotic clearance. The analysis of this model has produced novel results that allow the operating set-up to be calculated,and predictions of compound clearanceto begenerated.The mathematical modelpredictsthe inlet oxygen concentration and volumetric flow ratethat gives a physiological oxygen gradient in the HFB to mimic a liver sinusoid. It has also been used to predict the concentration gradients and clearanceof a test drug and paradigm hepatotoxin, paracetamol (APAP).The effect of altering theHFBdimensions and fibre propertieson APAP clearance under the condition of a physiological oxygen gradientis analysed.These theoretical predictions can be usedto design the most appropriateexperimental set upand data analysis toquantitatively compare the functionality of cell types that are cultured within the HFB to those in other system

Mathematical modelling of a liver hollow fibre bioreactor

A mathematical model has been developed to assist with the development ofa hollow fibre bioreactor (HFB) forhepatotoxicity testing of xenobiotics; specifically, to informthe HFBoperating set-up, interpret data from HFB outputsand aid in optimizingHFBdesign to mimic certain hepatic physiological conditions. Additionally,the mathematical model has been used to identify the key HFB and compound parameters that will affect xenobiotic clearance. The analysis of this model has produced novel results that allow the operating set-up to be calculated,and predictions of compound clearanceto begenerated.The mathematical modelpredictsthe inlet oxygen concentration and volumetric flow ratethat gives a physiological oxygen gradient in the HFB to mimic a liver sinusoid. It has also been used to predict the concentration gradients and clearanceof a test drug and paradigm hepatotoxin, paracetamol (APAP).The effect of altering theHFBdimensions and fibre propertieson APAP clearance under the condition of a physiological oxygen gradientis analysed.These theoretical predictions can be usedto design the most appropriateexperimental set upand data analysis toquantitatively compare the functionality of cell types that are cultured within the HFB to those in other system