He gave a kidney to a stranger and 30 transplants followed

On 15 August 2011, Rick Ruzzamenti walked into Riverside Community Hospital, in California, and let them take out his left kidney to give it to a person he did not know and was never going to meet. He was forty-four.

The idea was not his. A few months earlier, the receptionist at the yoga studio he went to had told him, the way anything gets told across a counter, that she had given a kidney to an ailing friend she had run into by chance in a department store. Ruzzamenti asked how that was done. Then he asked whether it could be done without knowing the patient. And then he did it.

A kidney like that, one not directed at anybody in particular, poses a problem of arithmetic before it poses one of surgery. The easy answer would be to give it to whoever is first on the waiting list, and then the story would end here, with one healthy person and one cured. It did not end here. That kidney started a chain that took four months to close, passed through seventeen hospitals in eleven different states and finished in December, in an operating theatre on the outskirts of Chicago, with thirty kidneys transplanted and sixty people operated on.

Most people who need a kidney have somebody willing to give them one. A brother, a wife, a son, a lifelong friend. The trouble is that willingness is not enough: you have to be compatible. The blood group has to fit and, above all, the recipient cannot be carrying antibodies against the donor's tissue, because then the kidney is rejected within hours. A very large share of volunteer living donors falls at exactly that hurdle, in the tests, once they have already made up their minds. The two of them are left in the same position they were in, with the difference that now they know precisely what they came within one step of having.

Out of that frustration comes the idea of the swap. It was proposed by the surgeon Felix Rapaport, of Stony Brook University, in an article in 1986: if pair A does not match and pair B does not either, it may happen that A's donor is compatible with B's patient and B's donor is compatible with A's patient. They cross over and both are saved. The first exchanges were carried out by Korean surgeons in 1991; in the United States it took almost another decade before anyone dared.

With three pairs you can make a triangle, and with four a square. And there it jams, and the reason is one of calendars. A closed swap has to be done all at once. Picture a circle of four pairs in which the operations are spread over a fortnight: the moment the patient in the first pair receives their kidney, their donor has nothing left to gain and an operating theatre to walk into. If they change their mind —and they have every right to change their mind up to the last minute— those behind them are left with nothing, plus the added insult of having kept their word. To stop that happening, the whole circle is operated on the same morning: eight people and eight theatres running at once, with their teams and their anaesthetics. A big hospital can arrange that with three or four pairs. With twelve, nobody can.

The unjamming came in 2007. Michael Rees, a transplant surgeon at the university hospital in Toledo, Ohio, realised the problem disappears if the chain begins with a gift instead of a trade. If the first kidney is put in by somebody who asks for nothing in return —an altruistic donor, somebody like Ruzzamenti— then at every moment the chain has given one kidney more than it has received. It is always running ahead. And when you are running ahead you do not need simultaneity: you can operate on the first pair's patient on Monday and leave their donor waiting, knowing that donor owes the chain a kidney and will hand it over when the right recipient turns up, three weeks or three months later.

That person waiting with a live debt has a name of their own in the jargon: bridge donor. It is the figure the whole thing rests on, and also the only point at which the chain can break. If a bridge donor pulls out, the chain stops. But the patient in their family already has a kidney, and those behind are exactly where they were, waiting as they were waiting before. The chain stops and takes nobody down with it. Rees published the first of these chains in the New England Journal of Medicine in 2009: ten transplants out of a single man who walked in to give a kidney without knowing anybody.

What was still missing was the plumbing. A long chain cannot be run by one hospital: it takes a national census of incompatible pairs, a program that searches all of them for possible fits, and hospitals prepared to operate under a protocol that is not their own. That is the National Kidney Registry, which Garet Hil set up in late 2007 for the usual reason. His ten-year-old daughter had been found to have a kidney disease in the February of that year; he shared her blood group and offered himself, and two days before the operation the doctors cancelled it because the girl had developed antibodies against him. Hil, who came from the business world, put the problem into a computer and started crossing lists.

It sounds like a market and it is not one: in the United States selling an organ has been a crime since the transplant act of 1984, and in a chain not a single dollar changes hands. It looked so much like a trade that in 2007 Congress had to clarify in writing that paired exchanges do not break that law. What moves is your place in the queue. You give a kidney today and somebody in your family jumps straight to the front of a list they had been standing in for four years.

The registry called that chain 124. Ruzzamenti's kidney left California that same night of 15 August, on a red-eye flight from Los Angeles to Newark, in a box packed with ice that travelled with an escort. The patient who received it had a relative willing to donate who was no use to him, and that relative handed theirs over a few days later to a stranger in another state. That person's relative did the same. And so on thirty times, hopping from hospital to hospital over four months, with several bridge donors holding out for weeks with their debt live and no guarantee beyond an email and an approximate date.

The last operation was carried out on 20 December 2011 at Loyola University Medical Center, on the outskirts of Chicago. The kidney went to Don Terry Jr., of Joliet, Illinois, who had spent nearly a year on dialysis: three sessions a week, close to four hours each, some six hundred hours a year hooked up to a machine doing by hand the work of two organs the size of a fist.

And the chain ended there because somebody decided it should: the registry picks the moment to close and deliberately places the last kidney in a patient who brings no donor along behind them. Chain 124 was closed at Loyola because Loyola had earlier supplied an altruistic donor, so the circle came out even there. Thirty kidneys went in and thirty patients came out operated on.

Ruzzamenti went back to Riverside with one kidney fewer and carried on going to his yoga class. Of the twenty-nine who came after him he did not learn the names until a newspaper printed them, four years later, and the chain he started that 15 August was the longest that had been completed up to then.