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.
Department of Mathematical Sciences, Loughborough University, Loughborough, Leics LE11 3TU, UK. Electronic address: d.reddyhoff@lboro.ac.uk.
Dennis
D
Reddyhoff
Department of Mathematical Sciences, Loughborough University, Loughborough, Leics LE11 3TU, UK.
John
J
Ward
Translational Safety, Drug Safety and Metabolism, Darwin Building, Cambridge Science Park, Milton Road, Cambridge, Cambs CB4 0FZ, UK.
Dominic
D
Williams
MRC Centre for Drug Safety Science, Department of Molecular and Clinical Pharmacology, Institute of Translational Medicine, University of Liverpool, Sherrington Building, Ashton Street, Liverpool L69 3GE, UK.
Sophie
S
Regan
MRC Centre for Drug Safety Science, Department of Molecular and Clinical Pharmacology, Institute of Translational Medicine, University of Liverpool, Sherrington Building, Ashton Street, Liverpool L69 3GE, UK.
Steven
S
Webb
D000082:Acetaminophen / Q000009:adverse effects / Q000493:pharmacokinetics*; D000465:Algorithms; D018712:Analgesics, Non-Narcotic / Q000009:adverse effects / Q000493:pharmacokinetics*; D056486:Chemical and Drug Induced Liver Injury / Q000209:etiology / Q000378:metabolism; D062787:Drug Overdose / Q000150:complications / Q000378:metabolism; D006801:Humans; D008954:Models, Biological; D012680:Sensitivity and Specificity
D018712:Analgesics, Non-Narcotic; D000082:Acetaminophen
Acetaminophen; Analysis; Metabolism; Modelling; Toxicology