Our Projects

Optimization and Simulation of Kidney Paired Donation Programs


The above is an illustration of a KPD network, with pairs represented by red nodes and altruistic donors represented by purple nodes.  Edges connecting nodes represent donor-candidate matches based on a virtual (computer based) cross match.  A selection with five subsets is highlighted and the possible transplants are indicated by purple edges.  These subsets are locally relevant subsets of size four or less and are chosen to present fall back opportunities should some transplants not be viable.  We proceed by evaluating all transplants for viability indicated by the purple arrows, then choosing the best possible disjoint set of cycles and chains for transplant.  (See Bray et al., 2015)


Kidney paired donation (KPD) provides an approach to overcome the barriers faced by many patients with kidney failure who present with willing, but immunologically or blood type incompatible living donors. KPD programs use a computerized algorithm to match one incompatible donor/recipient pair to another pair with a complementary incompatibility, such that the donor of the first pair gives to the recipient of the second, and vice versa. More complex exchanges of organs involving three or more pairs are also considered as are altruistic or non-directed donors (NDD) who donate a kidney voluntarily and thereby have the potential to create a chain of kidney transplants.  Such donors and chains have become increasingly important in KPD programs. Checking the viability of all potential transplants in a pool is not logistically possible, and so a fundamental problem in a KPD program is selecting an optimal subset of matches to consider among the many possibilities that exist.  We are developing methods of selecting  potential matches that take account of the uncertainty in the process; namely that potential transplants that are identified on a computer algorithm often fail when an attempt is made to put them into practice. Our approaches select subsets of patients with many options or fallbacks that could be implemented depending upon which potential transplants are found to be viable, and have been shown to have the potential to greatly increase the number and/or utility of transplants performed. We are also developing user friendly and efficient software to implement these approaches. In this work, we utilize data from the University of Michigan Paired Donation Program and the Alliance for Paired Donation.    



KPD GUI: Software and Graphical Interface (download)

Our software platform can be used to manage and visualize exchanges suggested by optimization criteria in KPD, offering several advantages over other available software: 

  • Interactive visual display of the state of the KPD
  • Implementation of optimization methods from previous literature, accounting for probabilities of failure, as well as fallback options (uncertainties and contingencies)
  • Optimization extended to more general subsets of pairs and NDDs that facilitate fallback options. 


Related Publications:

Bray M, Wang W, Song PXK, and Kalbfleishch JD (2018).  Valuing Sets of Potential Transplants in a Kidney Paired Donation Network.  Statistics in Biosciences (Published Online March 2018). doi: 10.1007/s12561-018-9214-7
Wang W, Bray M, Song PXK, Kalbfleisch JD (2018).  An Efficient Algorithm to Enumerate Sets with Fallbacks in a Kidney Paired Donation Program.  Operations Research for Health Care.  (Submitted)

Bray M, Wang W, Song PXK, Kalbfleisch JD. Incorporating Transplant Candidates with Multiple Associated Incompatible Donors in Kidney Paired-Donation. ENAR Spring Meeting 2016. Austin, TX (March 6). Eastern North American Region of the International Biometrics Society.

Wang W, Bray M, Song PXK, Kalbfleisch JD. Locally Relevant Subgraph Enumeration in Transplant Patient Network. ENAR Spring Meeting 2016. Austin, TX (March 6). Eastern North American Region of the International Biometrics Society.

Bray M, Wang W, Rees MA, Song PXK, Leichtman AB, Ashby VB, Kalbfleisch JD. A Visualization Software Platform for Managing a Kidney Paired-Donation Program.  American Transplant Congress 2016. Boston, MA (June14). American Society of Transplant Surgeons & American Society of Transplantation

Ashby VB, Leichtman AB, Rees MA, Song PXK, Bray M, Wang W, Kalbfleisch JD. Mismatch in Age, Sex, and Body Size Inform a Calculator for Kidney Graft Survival. American Transplant Congress 2016. Boston, MA (June 11). American Society of Transplant Surgeons & American Society of Transplantation