Practical market design involves logistics, and here's a paper by five doctors at the Liver Transplantation Institute of Inonu University in Malatya, Turkey, explaining how they developed the logistics of their busy single-center liver exchange program.
They also explain the connection between liver exchange and the graph theory involved in kidney exchange. The relevant graphs are compatibility graphs indicating which donors are compatible with which recipients, which are different for kidneys (involving blood types and antibodies) and for livers (involving blood types and anatomy--chiefly size.) But in either case, when the graph is sparsely connected, two way cycles are likely to be rare, so longer cycles and chains become important.
Multiple Swaps Tested: Rehearsal for Triple and Five Liver Paired Exchanges, by Sezai Yilmaz, Ahmet Kizilay, Nuru Bayramov, Ahmet Tekin, and Sukru Emre, Transplantation Proceedings
Volume 56, Issue 9, November 2024, Pages 2003-2005
" many potential living liver donors cannot donate their organs to their relatives because of blood group incompatibility, unsuitable anatomy due to small graft to recipient weight ratio, small liver remnant size, and the donor's arterial, venous, or biliary anatomic variants. Liver paired exchange (LPE) can be used to overcome incompatibilities between living donor-recipient pairs and should be considered as a means to expand the donor pool and reduce deaths on the LT waiting list. A small number of liver pair exchanges have been performed [[4], [5], [6]]. In this study, we report the early and late results of three and five LDLTs performed simultaneously to initiate the more complex LPE program.
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"Inonu University Liver Transplantation Institute has 12 operating theatres, 3 intensive care units (each with a capacity of 12 patients), and 116 in-patient beds. In our institute, there are 25 LT surgeons, 8 anesthesiologists, 4 intensive care specialists, 3 radiologists, 3 hepatologists, 3 infectious disease specialists, and 1 pediatric hepatologist, and 3 infectious disease specialists who are specialized in both LT and LDLT in adults and pediatrics. As one of the leading LDLT centers in the world, our challenge has been always to deal with patients do not have matching donors. Therefore, our next challenge was to create the Liver Pair Exchange Program. Our experience, facilities, and need for an LPE program convinced us that we should initiate such a program. This was a major undertaking, and we would like to test what kind of problems we could face if we should start an LPE program. To test possible hurdles, we decided to perform five simultaneous LDLTs. In June 2019, we performed 5 simultaneous LDLTs, including 1 pediatric and 5 adult patients. All operations started at 8 am and ended between 4 and 6:30 pm.
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"Collaborations between medical and mathematical modeling professionals have resulted in widespread adoption of kidney pair exchange programs worldwide over the last 2 decades and resulted in a dramatic increase in the number of living donor kidney transplants obtained in this way using tools from fields of optimization and market design [10,11]. These techniques are recently extended to the LPE program as well [12]. One of the important contributions of mathematical modeling professionals had been showing the importance of larger than two-way donor exchanges for increasing the number of transplants that can be obtained through kidney pair exchange or LPE programs [13,14]. Therefore, by demonstrating that our center is capable of performing up to five LDLTs, we have taken an important step for establishing a complex LPE program that can conduct up to five-way donor exchange
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"[10] AE Roth, T Sönmez, MU Ünver, Kidney exchange
Quarterly J Econ, 119 (2004), pp. 151-188
[11]AE Roth, T Sönmez, M Utku Ünver, A kidney exchange clearinghouse in New England, Am Econ Rev, 95 (2005), pp. 376-380
[12]H. Ergin, T Sönmez, MU Ünver
Efficient and incentive-compatible liver exchange
Econometrica, 88 (2020), pp. 965-1005
[13] AE Roth, T Sönmez, MU Ünver, Efficient kidney exchange: coincidence of wants in markets with compatibility-based preferences, Am Econ Rev, 97 (2007), pp. 828-851
[14] SL Saidman, AE Roth, T Sönmez, MU Unver, FL Delmonico
Increasing the opportunity of live kidney donation by matching tor two-and three-way exchanges, Transplantation, 81 (2006), pp. 773-782 "
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