The worlds of regenerative medicine and industrial engineering meet at the University of Pittsburgh. Mark Roberts, MD, MPP, FACP, a McGowan Institute faculty member, a Pitt School of Medicine professor, and a UPMC physician, recently published a paper in the engineering journal Management Science explaining how engineering principles are being used to determine the best timing for a liver transplant. Pitt colleagues, Andrew Schaefer and Lisa Maillart, each an associate professor of industrial engineering, are also paper authors.
Currently, almost 17,000 people in the U.S. are waiting for a donated liver. The wait time on the list to receive an organ from a deceased donor averages about 2 years. Because many of those in need die waiting on this list, another option is to receive a liver from a live donor—a spouse, family member, close friend. The live donor gives a portion of his/her liver, which will regenerate to full-size in both the donor and the recipient. There is less than a 1% risk that the donor will die in this process.
"If you have a choice, what should you do? That's a real question," Dr. Roberts said. "How long should I wait before placing my loved one or significant other in some danger or some risk? That's a fascinating optimization problem."
For help in solving that problem, Dr. Roberts consulted Andrew Schaefer about how to decide when to remove a patient from the waiting list and accept a living donor’s liver. Schaefer recognized it as a Markov decision process—a framework named for a Russian mathematician that makes the best decision about problems and risks that change with time. Together, Schaefer and Lisa Maillart devised a formula that considers things such as: How sick is the person in need of a liver? What are the odds the patient will get a liver from a dead donor? What are the odds of survival for the patient and donor? One impediment of the program is it does not consider a patient’s quality of life before or after the transplant—suppose the program recommends the patient waits, will he/she be alive, but hooked to a ventilator, is something it cannot determine. Dr. Roberts would not estimate when the model would be available to doctors and patients. U.S. Food and Drug Administration approval of the model must be obtained.
Today, medical journals and engineering textbooks litter the offices of Roberts, Schaefer, and Maillart. Determining the best time for a liver transplant is but one medical issue being looked at from both an engineering and medicine viewpoint.
“When you read the engineering text, these mathematical algorithms are designed to optimize sequential decisions under uncertainty,” Dr. Roberts said. “Well, that's medicine—all we do is make sequential decisions under uncertainty.”
Illustration: McGowan Institute for Regenerative Medicine.
Pittsburgh Tribune-Review (10/15/07)
Abstract (MANAGEMENT SCIENCE, Published online in Articles in Advance, September 21, 2007, DOI: 10.1287/mnsc.1070.0726)