Date of Submission

Spring 2014

Academic Programs and Concentrations

Mathematics

Project Advisor 1

Csilla Szabo

Abstract/Artist's Statement

Kidney transplantation is the treatment of choice for patients with end-stage renal disease (ESRD). There are three possible organ sources for these transplants; cadaver, living, and good samaritan donors. The living donors are usually friends or relatives of the patient. The benefits of living donors in kidney exchanges are to increase the patients’ chance of receiving an organ sooner than patients waiting for cadaver donors, as well as providing them with a higher graft survival rate. In cases where a living donor is incompatible with their loved-one in need of a transplant, kidney paired exchanges are possible. Kidney paired exchanges involve two donor-recipient pairs where each donor cannot give a kidney to the intended recipient because of immunological incompatibility, but each recipient can receive a kidney from the other donor. This type of exchange offers a lifesaving alternative to waiting for a kidney from a deceased-donor waiting list. We explore how three-way exchanges can expand the opportunity for incompatible pairs to find compatible donors for their recipients and also how it can ease the burden for reciprocal compatibility. In this project, we generate a simulated population of incompatible donor-recipient pairs using data from the U.S. general population and the Organ Procurement and Transplantation Network. We assign each individual in a pair a blood type. From these assignments, we create a directed graph, where nodes represent incompatible pairs and directed edges represent possible exchanges determined by blood type. In addition to blood type, the model includes other kidney allocation considerations, such as the age of the recipient, immunologic sensitization and the hospital or treatment location of incompatible pairs. We assign these factors as priorities or weights to the nodes and to the directed edges of the graph. We find all possible three-way exchanges in the graph and present an algorithm to identify maximum weighted kidney three-way exchanges from the simulated population of incompatible pairs.

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Open Access

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This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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