Mathematicians from the University of Utah have developed a set of calculus equations, which simplifies diagnosing and therefore saving lives of Tylenol overdose patients. The study of acetaminophen, generic pain and fever medicine sold as Tylenol, that is also in many other nonprescription and prescription drugs, is published in Hepatology, a journal about liver function and disease, and estimates quickly how much and when individuals have taken painkillers and if a liver transplant is necessary for their survival.
Acetaminophen is the primary generic name for drugs known generically as APAP and paracetamol. It is present in prescription medicines, for example, Tylenol with Codeine, Percocet or Vicodin, and numerous over-the-counter drugs, such as Tylenol, Anacin, Pediacare, Triaminic as well as in combination cold medications like Nyquil.
The majority of people are unaware that a common analgesic is able to destroy the liver and can cause death at only about five times the recommended dose, which, in medical terms, is a narrow margin. The current maximum dose of acetaminophen is 4 grams, i.e. 4,000 milligrams or eight 500 mg tablets in 24 hours, which leaves no margin for error between the 4-gram maximum and the 6 grams that can cause liver damage, or the 20 grams that can potentially destroy 70% of liver cells and cause death.
Adler and his team state:
"Acetaminophen is the leading cause of acute liver injury in the United States, accounting for some 56,000 emergency room visits, 26,000 hospital admissions and about 500 deaths annually."Treatment for acetaminophen overdoses can be successful if doctors administer an antidote called N-acetylcysteine (N-Ac or "nack") within approximately 24 hours. However, after a certain time limit the treatment becomes ineffective and patients will die without a transplant.
Norman Sussman, a former University of Utah liver doctor, now at the Baylor College of Medicine in Houston, says that speed is of the essence when enlisting acute liver failure patients for a transplant. In incidents where the doctor is unsure whether a patient survives and starts administering the antidote to combat liver failure to acetaminophen-poisoning patients', their chances 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. 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 fact that many overdose patients are confused or comatose and unable to communicate how much acetaminophen they took or when they took it makes predicting their prognosis difficult.
Fred Adler, a professor of mathematics and biology and coauthor of a study that developed and tested the new method declared:
"It's an opportunity to use mathematical methods to improve medical
practice and save lives."
Adler and his team demonstrated that using just four common medical lab tests, i.e. AST, ALT, INR and creatinine, allows doctors to quickly equate and predict precisely which Tylenol overdose patients will survive with medical treatment, and which require a liver transplant in order to survive. Dying liver cells release enzymes called AST (aspartate aminotransferase) and ALT (alanine aminotransferase), which means that higher levels of these enzymes indicate liver damage. INR (prothrombin time/international normalized ratio) measures the speed in which the blood clots. Given that the liver cells produce clotting factors, clotting will be slower if the liver malfunctions. Creatinine is a measure of kidney dysfunction, in this case secondary to liver damage.
They developed a new method using eight main "differential equations", i.e. basic calculus equations that describes the effect of changes in one variable affecting changes in another variable over time. According to the equations, the "model" demonstrates step-by-step how the liver metabolizes acetaminophen and the production of NAPQI, a liver-destroying substance.
The calculus is the first known "dynamical" model that is based on real biology, unlike existing "statistical" methods that determine how overdose patients get along. For instance, the statistical method, the King's College Criteria (KCC), estimates acetaminophen overdose patients' likely chances of survival or death by using correlations between INR and creatinine lab tests combined with which patients actually lived or died in the past. According to the KCC, liver failure is predicted if the INR exceeds 6.4, creatinine levels are higher than 3.4 and the patients show confusion, altered consciousness or coma due to liver damage.
Sussman considers the KCC to be outdated, stating that it has proven less beneficial over time. He says that as a doctor:
"...your first decision has to be, 'Do I list this patient for transplant?'" when a patient is diagnosed with liver failure. "That was the purpose of the King's College Criteria.
You need to make an immediate decision: Do I think this patient will live or die? If I think they'll live, I'm going to treat them [with the antidote]. If they're going to die, the next question is, are they a candidate for transplant? Our goal was to try to trace it back to: when did the damage start? Once you know that and the peak damage reflected in the ALT, then you have the tools to predict survival or death."
Sussman states that liver transplant candidates, whose acute liver failure is half due to acetaminophen poisoning, are placed at the top of the transplant list, overriding most candidates with chronic liver failure like alcoholism. At present, around 16,000 people are on the transplant waiting list in the U.S. with approximately 5,000 to 6,600 liver transplants performed each year.
Adler adds that the problem is that the criteria "look at the statistical relationship between lab test results and patient outcome without understanding what's happening inside the liver. It's just statistics," whilst the new method "tracks how the liver's health changes over time."
To test their equations for speed and accuracy, the researchers retrospectively evaluated records of 53 acetaminophen overdose patients treated at the University of Utah's University Hospital to confirm, which patients survived and which died. They assessed the records of all 53 patients for the new study for alcohol use, malnutrition status and if an overdose of acetaminophen was taken in an attempt to commit suicide or whether it was an accidental single overdose or a chronic, multiple-day overdose.
Two patients received a liver transplant but were excluded from the evaluation "because we don't know if they would have died or recovered without transplant." Eight of the remaining 51 patients died and 43 survived. After calculating AST, ALT and INR tests on admission and when creatinine levels were higher than 3.4, the findings demonstrated that the equation was extremely precise in retrospectively predicting the survival or death of an overdose patient.
The findings revealed that the equation demonstrated a sensitivity of 100%, i.e. it accurately predicted the death of all eight patients as compared to the KCC, which predicted just one of the eight death. It also showed a 67% "positive predictive value," given that eight of the 12 patients predicted by the equation died. The equation's specificity was 91% in light of predicting the survival of 39 patients of 43 that actually did survive. Furthermore, the equation's "negative predictive value" proved 100% correct in predicting the survival of 39 patients.
According to Sussman the eight deaths occurred because of multiple reasons, such as arriving too late to be treated even by transplant, whilst others failed to qualify for a transplant, which may have been due to serious drug or alcohol abuse and lack of family support.
The new approach of using calculus equations will enable doctors to determine rapidly whether a patient has a chance of survival with antidote treatment or whether he or she dies unless they get a transplant. To estimate when patients' took acetaminophen and what quantity, the new equations use the patients' measured levels of AST, ALT and INR including their creatinine levels, to accurately predict which Tylenol overdose patient will survive with treatment and who will need a liver transplant to survive.
Adler highlights that the new equation is based on a typical acute liver failure patient and may require adaptations for a better prediction the prognoses of certain special patients, for instance, in those taking other drugs, chronic alcoholics or those with anorexia.
The researchers call for another clinical trial to be conducted to ascertain the calculus' benefits, with Sussman planning to start a one-year prospective trial with 50 patients at the University of Utah and three hospitals in Houston. If this trial provides evidence that the method can accurately predict ahead of time how Tylenol-poisoning patients will get along, Sussman concludes: "we believe we could create a tool available and immediately useful to clinicians." According to Adler, the method could be developed as a smart phone application.
Written by Petra Rattue