SALT LAKE CITY -- University of Utah mathematicians developed a set of calculus equations to make it easier for doctors to save Tylenol overdose patients by quickly estimating how much painkiller they took, when they consumed it and whether they will require a liver transplant to survive.
"It's an opportunity to use mathematical methods to improve medical practice and save lives," says Fred Adler, a professor of mathematics and biology and coauthor of a study that developed and tested the new method.
The study of acetaminophen - the generic pain and fever medicine sold as Tylenol and in many other nonprescription and prescription drugs - was set for publication within a week in Hepatology, a journal about liver function and disease.
Adler, math doctoral student Chris Remien and their colleagues showed that using only four common medical lab tests - known as AST, ALT, INR and creatinine - the equations can quickly and accurately predict which Tylenol overdose patients will survive with medical treatment and which will die unless they receive a liver transplant.
The researchers analyzed the records of 53 acetaminophen overdose patients treated at the University of Utah's University Hospital to test the equations and show they quickly and accurately predicted, in retrospect, which patients survived and which died.
Speed is essential in listing acute liver failure patients as candidates for transplant, says study coauthor Norman Sussman, a former University of Utah liver doctor now at the Baylor College of Medicine in Houston.
If a doctor is uncertain and starts to treat an acetaminophen-poisoning patient with the antidote to combat liver failure - even though the patient may not survive with such medicine - their odds for getting a new liver are reduced.
"If I wait another day until I list them for transplant, the chance of getting a liver is that much lower," Sussman says. "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. They become too sick and can't stand the transplant."
The new method using calculus equations will let doctors rapidly determine if a patient can survive with antidote treatment or will die unless they get a transplant.
The study urges another clinical trial to prove the new method's usefulness.
Sussman plans to start a one-year prospective trial testing the method on 50 patients at the University of Utah and three hospitals in Houston.
If that trial proves the method can accurately predict ahead of time how Tylenol-poisoning patients will fare, "we believe we could create a tool available and immediately useful to clinicians," Sussman says. Adler foresees a smartphone application.
Adler, Remien and Sussman conducted the study with University of Utah hepatologist Terry Box and Lindsey Waddoups, clinical research coordinator for the University of Utah's gastroenterology division. The research was funded by a National Science Foundation grant to the University of Utah's program in mathematical biology.