Mathematical modeling of liver injury and dysfunction after acetaminophen overdose: early discrimination between survival and death

Acetaminophen is the leading cause of acute liver injury in the developed world. Timely administration of N-Acetylcysteine (N-Ac) prevents the progression of serious liver injury and disease, while failure to administer N-Ac within a critical time frame allows disease progression and in the most severe cases may result in liver failure or death. In this situation, liver transplantation may be the only life-saving measure. Thus, the outcome of an acetaminophen overdose depends upon the size of the overdose and the time to first administration of N-Ac. We developed a system of differential equations to describe acute liver injury due to acetaminophen overdose. The Model for Acetaminophen-induced Liver Damage (MALD) uses a patient's AST, ALT, and INR measurements on admission to estimate overdose amount, time elapsed since overdose, and outcome. The mathematical model was then tested on 53 patients from the University of Utah. With the addition of serum creatinine, eventual death was predicted with 100% sensitivity, 91% specificity, 67% PPV, and 100% NPV in this retrospective study. Using only initial AST, ALT, and INR measurements, the model accurately predicted subsequent laboratory values for the majority of individual patients. This is the first dynamical rather than statistical approach to determine poor prognosis in patients with life-threatening liver disease due to acetaminophen overdose. Conclusion: MALD provides a method to estimate overdose amount, time elapsed since overdose, and outcome from patient laboratory values commonly available on admission in cases of acute liver failure due to acetaminophen overdose and should be validated in multicentric prospective evaluation.