Timescale analysis of a mathematical model of acetaminophen metabolism and toxicity

Journal of Theoretical Biology
Dennis ReddyhoffSteven Webb

Abstract

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.

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Citations

Aug 24, 2016·Scientific Reports·Thomas SchreiterAli Canbay
Apr 19, 2018·CPT: Pharmacometrics & Systems Pharmacology·Chantelle L MasonSteven D Webb
Dec 19, 2017·Frontiers in Physiology·Bruno ChristNavina Waschinsky
Jun 30, 2019·International Journal for Numerical Methods in Biomedical Engineering·Sylvain FraniatteHarvey Ho
Aug 3, 2019·The Journal of Pharmacology and Experimental Therapeutics·Rob C Van WijkPiet H van der Graaf
May 18, 2019·Journal of Theoretical Biology·Ian SorrellSteven Webb

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