A conversation in the car with her husband, which took all of a few minutes, is what Dr. Sommer Gentry said got her started on a problem she has now been working on for 6 years.

The problem is easy enough to explain: basically, it can be really tough to get a kidney if you need one. Kidneys are the most common organ transplant, and although kidney donations are growing, so is the demand for kidneys. Most patients who need a kidney can find someone to donate one to them; after all, we all have an extra.

But about a third of the time, the person who wants to give you a kidney just can’t. The main reason is that some blood types are very accepting of organs of a different blood type and others are not. Sometimes and some places, this means the doctor will just send you home.

In to this problem comes Dr. Sommer Gentry, who’s mathematician with a focus in optimization who’s affiliated with Johns Hopkins School of Medicine. Dr. Gentry’s system of matching kidney donors to patients in need of a kidney can show how much of a missed opportunity sending home potential kidney donors really is.

In many cases, having a family member donate a kidney is the preferred way to replace a kidney. However, it’s not always that simple: sometimes even family members are incompatible. “But we have another family somewhere else in the world,” said Gentry. “So what I should do is get the two families together” and exchange kidneys.

This is called Kidney Pair Donation, where two donors give kidneys simultaneously and then trade them for their patients.

However, it’s illegal to give a kidney for compensation, and some worried that an exchange of kidneys violated this law. “In fact, there were hospitals refusing to do this because no one had told them it was legal,” said Gentry. The first step in the process was getting the practice of exchanging one kidney for the other out of a legal grey area.

Finally, several years ago, Congress passed a law allowing the practice. Gentry was in business.
Kidney Pair Donation is complicated enough with all the different blood types to consider, but sometimes a simple match between two donor/patient pairs is not enough, and triangles of three pairs are necessary. Gentry’s forte came in when optimizing giant graphs so that these more complicated kidney donations could happen.

This is where one kidney is not directly exchanged for another, but instead traded along a chain so that each patient gets the kidney that he or she needs.

Johns Hopkins first had a board of magnets, then a program that printed all possible combinations of patient/donor which then needed to be combed through – by hand – to find the ones which would actually work. The problem was that the standard operating procedure at the time, called Arrival Order Matching, wasn’t working for many patients.

Arrival Order Matching was a first-come, first-served approach which ended up with the patients who were easy to match getting matched soon after they checked into the hospital, with those hard to match often left out in the cold.

“Literally no one had recognized that there was an optimization problem to solve,” she said.

But if all the donors and patients were added into Gentry’s data set before matching pairs were chosen, then more patients would get correctly matched. “We won’t be able to see all these connections if we use Arrival Order Matching.”

Instead, she used Maximum Cardinality Matching, which waits for people to show up, and “the faster we can sign people up for it, the faster we’ll find matches.” The more, the merrier.
Gentry is now working with United Network for Organ Sharing (UNOS) to make a national kidney sharing list.

As of Oct. 2010, there are over 100 thousand people on waiting lists for organs. Gentry’s work will certainly not go to waste.

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