Math equations could save drug-overdose patients

SALT LAKE CITY - The ubiquitous pain medicine acetaminophen is a leading cause of poisoning, claiming about 500 U.S. lives a year. Rapid detection and early treatment are key to preventing lethal liver damage or securing an organ transplant if the patient's liver is too far gone.

Now University of Utah mathematicians have devised simple equations, using results from standard blood tests, that could improve the way doctors assess patients who have overdosed on acetaminophen, which is found in Tylenol, Nyquil, Anacin and many other over-the-counter brands and prescription pain relievers.

The findings provide further evidence that math has relevance in clinical settings with the potential to improve medicine and save lives, according to Fred Adler, a math professor and co-author of a forthcoming study.

"Math helps you see the invisible," Adler said. "You can't observe liver damage, which matters the most, but you can observe biomarkers and use math to connect backward, in this case to determine how much (acetaminophen) they took and when they took it."

Holding a cross-appointment in the biology department, Adler specializes in using mathematical equations to characterize complex biological processes.

"I absolutely love this paper. It's a whole new way of looking at this," said former University of Utah hepatologist Norman Sussman, who initiated the study. "There are other areas where it could apply, where you have an acute injury, but nothing as common as Tylenol poisoning."

Adler is hardly alone in using math to understand maladies. Mathematicians can focus on the mechanisms at play and develop equations that capture their essence, said Utah State University professor Jim Powell. A mathematician-biologist himself, Powell builds models that predict how chronic wasting disease spreads in wildlife populations and pine beetles spread through forests.

According to Adler's paper, acetaminophen is the most common cause of acute liver failure, sending 56,000 Americans to the emergency room every year and resulting in 26,000 hospital admissions. Physicians currently use a statistical model to determine how to treat overdose patients. The new method could be a big improvement because it's based on well-established knowledge of how the body metabolizes the drug and how the toxicity plays out, according to lead author Chris Remien, a doctoral student in math.

Tylenol itself is not poisonous, but the liver produces a toxin while clearing it from the bloodstream. Four grams, or eight tablets, a day is about the maximum the body's clearing mechanism can safely handle.

"Five times the recommended dose can kill you. I don't know of any other drug like this," Adler said. But patients can be effectively treated with an antidote within 24 hours. The trouble is, symptoms take a day to appear.

"(Overdose victims) will show up confused or comatose so patient information is not very reliable," Remien said. Late treatment with the antidote wastes precious time.

"If I wait another day until I list them for transplant, the chance of getting a liver is that much lower," said Sussman, now a professor at Texas' Baylor College of Medicine. "If you're going to get someone transplanted, you have to do it fast or you miss the boat. The patient may pass the window when transplants can be done."

The method takes measurements of standard biomarkers in the blood: AST and ALT are released by dying cells; INR is a measure of the liver's clotting factors; and creatinine is a measure of kidney function. Adler envisions an iPhone app in which physicians input these values and receive estimates for the overdose's timing and severity.

The team applied the method retrospectively to 53 cases treated at University Hospital, and correctly predicted eight cases that ended in death and 39 where the patient survived. The four cases they got wrong were survivors they predicted would die.

Sussman plans to test the method on future cases arising at the University of Utah and three Texas hospitals. Until its reliability is proven, however, it cannot be used to guide any patient's treatment.

The study appears in Hepatology, a journal devoted to liver function and disease. Co-authors include University of Utah hepatologist Terry Box and Lindsey Waddoups, clinical research director of the School of Medicine's gastroenterology division.

Distributed by Scripps Howard News Service, www.scrippsnews.com.

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