Here's some of what the NY Times article has to say:
"A law-abiding American in need of a kidney has two options. The first is to wait on the national list for an organ donor to die in (or near) a hospital. The second is to find a person willing to donate a kidney to you. More than half the time, such donor-and-recipient pairs are incompatible, because of differences in blood type or the presence, in the donor’s blood, of proteins that might trigger the recipient’s immune system to reject the new kidney. The genius of the computer algorithms driving the kidney chains is that they find the best medical matches — thus increasing the odds of a successful transplant — by decoupling donors from their intended recipients. In the United States, half a dozen of these software programs allow for a kind of barter market for kidneys. This summer, doctors will most likely complete the last two operations in a record-breaking 70-person chain that involved flying donated kidneys on commercial airlines to several hospitals across the country.
"Economists call an arrangement like this a matching market. “It is not fundamental to economic theory to assume people are selfish,” Alvin E. Roth, an economist who teaches at Stanford University, told me. Roth won the Nobel Prize in economics in 2012 for his work using game theory to design matching markets, which pair unmatched things in mutually beneficial ways — students with public schools and doctors with hospitals. In such markets, money does not decide who gets what. Instead, these transactions are more akin to elaborate courtships.
"The classic example of a matching market is the college-admissions process. Every year, tens of thousands of students apply to Harvard University. But just because a student wants a spot in the freshman class and can afford tuition does not mean he gets in. Harvard must also want him to attend. In the case of kidney exchange, this matchmaking happens at a microcellular level. White blood cells contain genetic markers, proteins that help our immune systems distinguish between our bodies and foreign invaders. The more closely a transplant recipient’s genetic markers match a donor’s, the more likely the body is to adopt that foreign kidney as its own rather than attacking it."
The average chain length for nondirected donor chains in the U.S. has lately been around 5, The latest longest chain accomplished 34 transplants (so it involved 68 people, donors and recipients).It's possible that that the number of transplants in the chain in this story was limited by the particular, proprietary commercial software that was used. One of the interesting things about kidney exchange is that most of the software is provided for free by the researchers who develop it, and is described in the open scientific literature. The software used by the UNOS kidney paired donation pilot program is designed by Tuomas Sandholm and his colleagues at CMU, and Itai Ashlagi (at MIT until next year, when he comes to Stanford) and his colleagues have software that is very widely used by kidney exchange networks and large transplant centers, and the latest version of this software was described in January in the Proceedings of the National Academy of Science.
You can download kidney exchange software from Itai's web page: here I've copied his instructions:
- Kidney exchange source code. Instructions for how to compile can be found here. An older version in c# can be found here (for both cycles and chains), which also generates patient-donor pairs as well as compatibility matrices. The software finds an allocation that maximizes the number of transplants using cycles and chains each of a different bounded length. CPLEX is needed to use.