Real-world kidney exchange

Real-world kidney exchange programmes often have many more pairs than in our examples, and medical compatibility involves many more factors than just blood groups. The UK Living Kidney Share Scheme (UKLKSS) is the national kidney exchange programme in the UK, and often has over 200 donor-recipient pairs in their exchange pools for a matching run. In addition, these pools allow both two-way and three-way exchanges, as well as structures called chains. Chain arise when altruistic donors choose to donate a kidney. These people do not have a paired recipient, but are simply willing to donate a kidney out of the goodness of their heart. These chains terminate with a donation to the deceased donor waiting list (DDWL).

A graphic titled Pairwise exchange, depicting four people in two pairs of two. Each pair consists of a donor and recipient, and the pairs are indexed as 1 and 2. There is an arrow from d1 to r2, and an arrow from d2 to r1.

A graphic titled Short chain, depicting four people, two of which are near each other in a pair. One of the single people is labelled A1, and the other is labelled DDWL. The pair consists of a donor d2 and and a recipient r2. There is an arrow from A1 to r2, another arrow from d2 to DDWL.

A graphic titled Long chain, depicting six people, two people on their own, and the other four in two pairs of two. One of the single people is labelled A1, and the other is labelled DDWL. Each pair consists of a donor and recipient, and the two pairs are indexed by either 2 or 3. There is an arrow from A1 to r2, another arrow from d2 to r3, and an arrow from d3 to DDWL.

Optimal sets of exchanges in these real-world programmes are not found by dragging around items on a screen. Instead, we at the University of Glasgow develop sophisticated computer algorithms to find a best set of transplants according to some prescribed criteria. Dr Hannah Fry discusses this in the following video clip from the Royal Institution Christmas Lectures 2019.

Can you think of a clever way of finding the best possible set of transplants to choose? If this interests you, then you might have a future in algorithmics. See the School of Computing Science at the University of Glasgow to find out more.