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Optimal Graph Crossmath Model for Kidney Paired Donation (KPD) Program [Software Demo]

Problem Definition

• Kidney transplantation has emerged as the treatment for the most serious forms of kidney disease. However, there is a considerable shortage of donor kidneys in the U.S.: more than 80;000 patients are on the waiting list for transplants by the end of 2010. In the real world clinical application, deceased donation and living donation are the two resources of organs for kidney transplantation, and living-donor transplant has a higher chance of success. Unfortunately, about one-third of patients with willing live donors will be excluded from kidney transplantation because of ABO blood type mismatch or HLA incompatibility. Therefore, KPD program is established as a promising clinical solution to overcome the shortage of donors. The essential idea of such program is to exchange living kidney donors between two willing but incompatible donor-recipient pairs. The fundamental question in the KPD program is how to make an optimal decision of kidney exchanges that benefit patients the best.

Algorithms

• A kidney exchange problem can be represented as a directed graph G =(V, E). Let |V| be the number of vertices (nodes) and |E| be the number of edges in a KPD graph, where || denotes cardinality. Each vertex in graph G represents an incompatible donorrecipient pair (e.g., vertex 1) or an altruistic donor (e.g., vertex 7). Each edge from vertex i to vertex j indicates that the donor kidney in vertex i is compatible with the recipient in vertex j (e.g., 7 ->1). In this directed graph, each edge is assigned a weight representing edge utility ui j of the kidney transplant from the donor in vertex i to the recipient in vertex j (e.g., u_{71} = 9). In addition, an edge probability pi j is considered for each edge to reflect the possibility of an actual successful kidney transplant from i to j (e.g., p_{71} = 0.6). All the directed edges are established for compatibility of ABO blood types and HLA sensitizations (see above Figure).
• The goal of optimization for kidney exchange program is to find a collection of mutually disjoint cycles or chains that attain the maximum overall expected utility of graph G. This task of optimizing matches on graph G by the following setup of integer programming:

Results

• We compared two allocation strategies in terms of accumulated number of transplants, in the settings where the KPD only involved donor-recipient pairs (namely no ADs). The two strategies to be compared are (1) Cycle-Without-AD-Base: a traditional method that does not consider the expected utility in the optimization; (2) Cycle- Without-AD: a new method that uses the expected utility and accounts for the chance of failure in the optimization. The accumulated number of transplants obtained by the two approaches with different arrival rates shown in the following figures. It implies that the more pairs participate in the kidney exchanges program, the higher likelihood of achieving matches in the KPD pool. Moreover, the accumulated number of transplants gained by the new approach (i.e., Cycle-Without-AD) is significantly higher than the traditional method (i.e., Cycle-Without-ADBase) in the magnitude of 2-4 folds.
• We integrated the ADs into the new allocation strategy and investigated the role of ADs in the kidney exchanges. In the following figures (a)-(c) display the accumulated number of transplants obtained by two strategies: (1) Cycle- Without-AD and (2) Cycle-With-AD, where the edge utility is generated from a uniform distribution on interval from [10,10] to [10,30] and the arrival rate is 10. In these panels, based on the accumulated number of transplants over 12 match runs, method Cycle-With-AD gives at least 10% more matches than the method without using ADs. Moreover, we plotted the results for the case of arrival rate equal to 20 in the following figures (d)-(f). Again, when more people enters, method with ADs clearly performed better than the one without ADs. As a result, using ADs in the kidney exchanges would help clinicians to achieve more transplants.
• We also compared accumulated utility of these two methods (1) Cycle-Without-AD and (2) Cycle-With-AD. From the following figures (a)-(c), we noticed that the accumulated utility of the Cycle-With- AD method enjoys a gain between 15% to 30% over the Cycle-Without-AD method when the edge utility distribution changes from [10,10] to [10,30] with arrival rate equal to 10. Likewise, in the following figures (d)-(f) report the accumulated utility of method using ADs is about at least 10% higher than that of the method not using ADs with arrival rate equal to 20. Therefore, it is obvious that on average the method without using ADs is consistently outperformed by the method using ADs over all match runs in terms of accumulated utilities.
• We developed a general KPD computerized platform and graphic user interface (GUI) that allow to model, visualize, and monitor the real world kidney exchange program. The following is a flowchart of computerized platform for kidney exchanges.

Related Publications

• Yanhua Chen, Jack Kalbfleisch, Yijiang Li, Peter X.-K. Song, and Yan Zhou, "Computerized Platform for Optimal Organ Allocations in Kidney Exchanges," Proceedings of the 2011 International Conference of Bioinformatics and Computational Biology (BIOCOMP), Las Vegas, NV, USA, 2011 (acceptance rate = 21%).
• Yanhua Chen and Peter X.-K. Song, "Computerized Decision Support System for Kidney Paired Donation Program ", Proceedings of 33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society(EMBC), Boston, MA, USA, 2011.
• Yanhua Chen, Yijiang Li, Jack D. Kalbfleisch, Yan Zhou, Alan Leichtman and Peter X.-K. Song, "Graph-based Optimization Algorithm and Software on Kidney Exchanges", IEEE Transactions on Biomedical Engineering (TBME), Vol. 59, No. 7, pp. 1985-1991, July 2012