Math saving lives: New models help address kidney organ donation shortages

On any given day in the United States, approximately 100,000 patients are waiting for a life-saving kidney transplant.  

The main problem is availability.  In 2012, only 14,209 transplants took place in the U.S., leaving many on the waiting list for an available kidney.  And the longer they wait, the lower their chances for survival.

So, what is there to be done?  While it’s very difficult to increase the amount of viable kidneys available for transplantation, researchers from Northwestern and Stanford Universities have proposed new, innovative ways of optimizing kidney distribution throughout the country – using simple mathematical models.

Their initiative, presented at the American Association for the Advancement of Science (AAAS) annual meeting in Chicago, helps to address two major issues within the organ donation process: decreasing geographic disparity and increasing available living donors.

Geographic disparity
According to the researchers, the U.S. population is continuing to live longer and longer, which ultimately leads to a growing incidence of kidney failure throughout the nation.  However, since most kidneys come from deceased donors, organ donation has remained fairly stagnant over the years, creating a wide gap between the number of donors and the number of recipients on the transplant waiting list.

And as the gap widens, the amount of time an individual waits for a kidney can be highly variable, depending on that person’s location. According to panelist Sanjay Mehrotra, organ allocation and wait times can vary drastically across certain regions of the country.

“From a geographic perspective, depending on where you live, the time that is spent while waiting on the waitlist can be quite different,” Mehrotra, professor in the department of industrial engineering and management sciences at Northwestern University, told “That difference can be within in a state and across states – and it can be significant. If you live in Illinois … you may be waiting four years, but just north in Wisconsin, it could be [two] years.”

Mehrotra explained that a patient’s expected wait time greatly depends on their state’s population, as well as the region’s number of organ procurement organizations (OPOs) – local facilities responsible for coordinating the donor process within a designated service area (DSA). For example, Illinois, a state with a larger population, only has one OPO, meaning a patient waiting for a kidney in that region is also waiting on a list with many other individuals – much more than in Wisconsin.

Nationwide, this kind of geographic disparity has gotten much worse, Mehrotra said.  So in an attempt to shorten wait times in the U.S., he has utilized both retrospective and prospective model-based analytics to devise new methods for organ allocation. Based on his research, he proposed a way of making supply and demand better balanced – by have OPOs that allocate the most organs send some of their kidneys to DSAs in need.  

He noted that oftentimes, these high-allocation centers discard their lower quality organs, which could be used in other regions that have longer wait times.

“What we’re finding is if you link up DSAs across regional states and DSAs within a state, you can actually make substantial progress to address this disparity issue,” Mehrotra said. “Our estimates are that 500 lives can be saved a year by essentially reducing this disparity.”

The panel also addressed the concept of better matching kidney life expectancy to recipient life expectancy, so that higher quality kidneys can be utilized for the longest periods of time.

“A kidney that may last someone 30 years may be given to someone with a 5-year life expectancy,” Dr. John Friedewald, an associate professor in medicine nephrology and surgery-organ transplantation at Northwestern University, told “A lot of kidneys are outliving their transplant recipients. And vice versa; there’s a mismatch in candidates to kidneys. One of the things we’re doing is doing longevity matching, where kidneys with the longest longevity will be matched with candidates with the longest estimated transplant survival.”

Friedewald estimated that longevity matching would add 8,000 additional life years for each year’s worth of donated kidneys.

Exchanges and chains
While these changes may help produce greater equity and boost life expectancy for some, they still don’t address one major issue surrounding organ donation: increasing the amount of kidneys available. Alvin Roth, the Craig and Susan McCaw professor of economics at Stanford University, spoke at the panel about the best way to utilize living donors – people who wish to donate one of their kidneys to help a loved one in need.

While these donors may be willing to donate a kidney, it’s not always possible for them help their intended recipient.

“If you wanted to donate a kidney to a loved one, you have to check to see if you’re a healthy donor,” Roth, who won the Nobel Memorial Prize in Economic Sciences in 2012 for his work on finding stable matches, told “…Sometimes you’re healthy enough to give a kidney, but can’t give it to a person you love because you’re incompatible. That’s where kidney exchange comes in.”

Kidney exchange involves matching one incompatible donor-recipient pair to another incompatible donor-recipient pair, so that they essentially “exchange” kidneys with one another. Then, through a total of four simultaneous surgeries, the donors give an organ to the opposite recipient, insuring that both donors donate and both patients receive a kidney.  

Roth is also known for his novel concept of kidney donor chains.  For chains to work, he explained that the process is initiated by a non-directed donor (NDD) – who wishes to donate a kidney to someone in need. That donor’s kidney is then given to a patient who is part of an incompatible donor-recipient pair. Once the patient in that pair receives the new, compatible kidney from the NDD, then the incompatible donor donates his or her kidney to another incompatible donor-recipient pair.

The process repeats again and again until there is a final recipient not involved in a donor-recipient pair.

“Each pair gets a kidney before they give one, so it’s not a tragedy if the chain breaks,” Roth explained. “The guys who are expecting a kidney, their donors haven’t given a kidney yet. And the chains can get very long. The first chain, the one reported in 2009, that one at the time of reporting had 10 transplants, and eventually had 16. The longest chain so far has 60 people in it.”

The researchers at the panel hope all of these models will ultimately inspire change and lead to policy alterations within the United Network for Organ Sharing. Dr. Michael Abecassis, a transplant surgeon at Northwestern Medical Hospital and organizer of the event, noted that there are definitely many ethical concerns behind what they are proposing, especially when it comes to distributing organs outside of their local areas, but he said their research is ultimately meant to help as many people as possible.

“The common thread is we don’t have enough organs, so we better make the best use of the ones we have,” Abecassis said. “We can’t do this with our brains, so we have to bring in these complicated mathematical models to make this happen.”