HOW A KIDNEY TRANSPLANT SWAP WORKS. Maria Wallon described the magnitude of the calculations underlying a kidney transplant chain. For a 72 person exchange (and she describes in her article a 70 person exchange that is in process}, there would be 105,716 possible configurations. The exchange process will permit a person to receive a kidney that is a “better match” than would be the kidney that his own friend or relative might donate. But how do you determine which of the possible matches would work best?
This article by Katie M Palmer on the Wired site (March 9, 2015) describes a twelve person kidney transplant chain that had just been completed. In addition to issues of blood type, which can rule out some matches entirely, the software used in the chain in Palmer’s article takes into consideration 14 human lykocyte antigens which can affect the success of a transplant (there are half a dozen software programs which are available for use.) The software also takes into consideration thousands of antibodies which can affect transplant success. You can see that the mathematical optimization problem is enormous.