Math Model Gauges Potential Tylenol Overdose, Liver Damage

Chris Remien, left, and Fred Adler (Lee J. Siegel, University of Utah)

Researchers at University of Utah and Baylor College of Medicine have devised a set of calculus equations to quickly estimate the amount of Tylenol ingested by a patient, and if the patient may need a liver transplant. Their work is scheduled to appear in an upcoming issue of the journal Hepatology.

Acetaminophen is the generic name for the compound used in over-the-counter pain-killers, such as Tylenol, Anacin, Pediacare, and Triaminic and combination cold medications like Nyquil. It is also found in prescription pain-killers such as Tylenol with Codeine, Percocet, and Vicodin.

Yet despite its popularity, acetaminophen can cause liver damage with as little as five times the recommended dosage. The FDA cites studies showing acetaminophen as the leading cause of acute liver failure, with almost half of acetaminophen-related cases associated with accidental overdose.

Fred Adler, a Utah professor of mathematics and biology, and mathematics doctoral student Chris Remien (pictured at top) identified four common lab tests to estimate overdose amount, time elapsed since overdose, and outcome. With the results of these tests, Adler, Remien, and colleagues then developed a set of differential equations from calculus to predict which Tylenol overdose patients will survive with medical treatment and which will die unless they receive a liver transplant.

The researchers’ Model for Acetaminophen-induced Liver Damage uses equations that describe the changes in a variable that can affect changes in another variable over time. In this case, the model simulates the step-by-step metabolizing of acetaminophen in the liver, including production of NAPQI, a liver-destroying substance.

The researchers tested their model by analyzing the records of 53 acetaminophen overdose patients treated at the University of Utah’s University Hospital to test the equations. The results showed the model predicted between 67 and 100 percent of the eventual deaths caused by liver failure from the individual test results, indicating which acetaminophen overdose patients will survive with treatment and which will require a liver transplant to avoid death.

The model of the liver’s biology, say the authors, is considered an improvement over current statistical models. The problem, says Adler, is the criteria in the statistical model “look at the statistical relationship between lab test results and patient outcome without understanding what’s happening inside the liver. It’s just statistics.”

Coauthor and physician Norman Sussman, now at now at the Baylor College of Medicine in Houston, plans a one-year prospective trial testing the method on 50 patients at the University of Utah and three hospitals in Houston. If the trial proves the method can accurately predict ahead of time how Tylenol-poisoning patients will fare, says Sussman, “we believe we could create a tool available and immediately useful to clinicians.”

Read more: Medication Poisoning of Young Children Rising Sharply

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