A transplant is the only option for someone with end-stage liver disease, but patients face difficult questions when choosing the best time to receive a transplant. In a panel discussion at the 2005 American Association for the Advancement of Science (AAAS) Annual Meeting in Washington, D.C., a University of Pittsburgh researcher presented findings on how his mathematical models can help patients make the right decision.
Andrew Schaefer, an assistant professor and the Wellington C. Carl Faculty Fellow in Pitt's Department of Industrial Engineering, uses engineering techniques to examine the decision-making process facing potential recipients of livers from both living and cadaveric donors.
The liver is a unique organ in that it can regenerate itself: If a living person donates a part of his or her liver, the livers of both donor and recipient typically grow to normal size within two weeks of the surgery. Livers from cadaveric donors are difficult to come by, and, as a result, numerous patients die waiting for a life-saving organ. Nonetheless, many patients prefer to remain on the national waiting list, preferring not to put someone they know through a living-donor operation, which involves a small but real risk to the donor.
According to Schaefer, patients should use up the capacity of their current liver first--but waiting too long could be dangerous. So the questions become: In the case of a living donor, how long should the patient wait before accepting the transplant? And in the case of a cadaveric donor, what criteria should one follow in deciding to accept a potential offer? The answers to these questions are not at all obvious, and Schaefer and his colleagues-- Mark S. Roberts, associate professor of medicine in Pitt's Division of General Internal Medicine, and Oguzhan Alagoz and Lisa M. Maillart of Case Western Reserve University--have been able to show that mathematical models can provide insight. "We're actually able to model decisions that real patients face all the time," Schaefer said. "These mathematical models can give answers that make sense to doctors and can answer questions for which other standard techniques aren't as well suited."
For example, in a paper published in the October 2004 issue of the journal Management Science, the researchers noted, "[W]hen the liver quality is very low, it is optimal for the patient to choose never to have the transplant."
Schaefer and his colleagues are the first to study living donors, as well as the first to explicitly model patient physiology. "Our models are much more physiologically realistic than previous research," said Schaefer. "We are actually tracking the levels of various laboratory values in the patient's blood."
Their next step is to make the model better represent both the biology and the quality of life of organ recipients. In addition to their work on organ transplantation, Schaefer, Roberts, and several Pitt graduate students also are working on other decision-making scenarios, such as modeling the optimal time to switch HIV medications or to discharge a patient from intensive care.
Schaefer and his team plan to work with the clinical team at the University of Pittsburgh Medical Center's world-renowned Thomas E. Starzl Transplantation Institute to put their research to clinical use. "Pitt is the place to be doing this," said Schaefer. "I think this is going to be a very exciting area in the future."