Mathematical modelling of chronic acetaminophen metabolism and liver injury (Q2922514)

The model of this paper, extends the model of acetaminophen (APAP) metabolism and associated liver damage [\textit{C. H. Remien} et al., ``Mathematical modeling of liver injury and dysfunction after acetaminophen overdose: early discrimination between survival and death'', Hepatology 56, No. 2, 727--734 (2012; \url{doi:10.1002/hep.25656. Epub 2012})] by including an APAP intake term \(\sigma\) in the APAP equation and an additional small leak term \(\delta_NN\) in the \(N\)-acetyl-\(p\)-benzoquinoneimine (NAPQI) equation. The decay in the NAPQI equation ensures that levels remain bounded even when the number of liver cells approaches zero. NEWLINENEWLINENEWLINEThe authors consider five time-variant scenarios. Three scenarios involve constant APAP use, followed by a dose of APAP in the form of a pulse of size \(A_{\mathrm{over}}\), and two scenarios involve decreased GSH production. NEWLINENEWLINENEWLINEThese scenarios are explored with some time-depending parameters for a range of chronic intake level, size of overdose amount and decrease in GSH production rate. NEWLINENEWLINENEWLINEThe biological interpretation of the model is: the chronic use of APAP increases hepatic necrosis risk associated with a single (over)dose. Continued APAP intake leads to more hepatocyte damage than when APAP use is eventually discontinued. APAP intake after the damage has begun results in greater damage than typical for that dose because there are fewer hepatocytes to process the APAP. Even when the APAP use is discontinued immediately following overdose, the damage from an overdose over a background of chronic use is greater than from a single time overdose because GSH levels are lower. NEWLINENEWLINENEWLINETo determine the ability of a single overdose model to accurately predict the outcome from liver injury, marker measurements against a background of chronic use are analyzed and, synthetic AST, ALT and INR values are generated from five scenarios for the single time overdose model MALD. The synthetic data points are fit to MALD using weighted least squares to estimate the overdose amount and timing.NEWLINENEWLINEThe authors found that the rapid binding of glutathione (GSH) to NAPQI leads to a relatively simple threshold, which means that the liver is either being injured rapidly, or it is not being injured. In spite of that, other parameters may vary with time, and APAP intake can follow virtually any time course. The threshold nature of the system combined with the improbability of balance of NAPQI production with hepatocyte regeneration, gives the possibility to predict that APAP-induced liver injury is generally acute, and thus predictions of the extent of liver injury are robust, even with chronic use.NEWLINENEWLINEThe dynamics of the presented model exhibit threshold behavior, giving insight into why chronic APAP use leads to acute, rather than chronic, liver damage. The dynamics suggest that fits to MALD, which are based on a values of measurable markers at admission assuming a single overdose, can accurately estimate the level of hepatocyte damage and thus the patient outcome, even when the overdose occurs against a background of chronic use.