One surgeon on a transplant center team at Johns Hopkins, Dorry Segev, happens to be married to a mathematician. His wife, Sommer Gentry, an assistant professor of mathematics at the U.S. Naval Academy, specializes in a procedure called optimization. On their drive home one evening, he asked whether she might be able to figure out how to make the best matches among a pool of incompatible pairs of kidney transplant donors and patients.

Chronicle of Higher Education
Susan Brown
March 23, 2007


A patient can wait years for an organ from someone who has died. Some who have a willing friend or relative can get a transplant right away, but only if their immune system would accept the offered organ.

So transplant centers have started organizing organ swaps for patients who have willing but incompatible donors. The husband of one patient might donate his kidney to another, more compatible patient, whose sister simultaneously donates her kidney to the original patient, for example. By matching such pairs, surgeons can increase the number of people they help.

Last year a team at the Johns Hopkins University extended that idea to transplant five kidneys in a domino chain of donations. Hopkins had been arranging paired donations for some time, but doctors there were concerned that they were not always choosing pairs in a way that would maximize the number of exchanges they could make.

One surgeon on the team, Dorry Segev, happens to be married to a mathematician. His wife, Sommer Gentry, an assistant professor of mathematics at the U.S. Naval Academy, specializes in a procedure called optimization. On their drive home one evening, he asked whether she might be able to figure out how to make the best matches among a pool of incompatible pairs.

Ms. Gentry's solution relies on a branch of mathematics called graph theory. Her strategy is to create a diagram with incompatible pairs plotted as a circle of points with lines between them linking mismatched pairs who could successfully swap kidneys.

What quickly becomes apparent is that making one match can preclude others within the pool, leaving out some potential recipients. Ms. Gentry's solutions find the set of matches that helps the most patients. Several transplant centers have already used her scheme to sort through potential matches within their own groups of patients.

If exchanges like this were considered on a national scale, more people might be helped, but there is a potential snag. As the director of Hopkins's transplant team, Robert A. Montgomery, noted at the time of the domino transplants, the legality of the exchange was unclear. The 1984 National Organ Transplant Act prohibits the exchange of an organ for "valuable consideration," which might be interpreted to include the expectation that one's intended recipient would receive a kidney from another donor.

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