Pi Day: Optimization for kidney paired donation Sommer Gentry U.S. Naval Academy Dorry Segev Johns Hopkins University School of Medicine.

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Pi Day: Optimization for kidney paired donation Sommer Gentry U.S. Naval Academy Dorry Segev Johns Hopkins University School of Medicine

Kidney paired donation (KPD)

Graph: recipient / donor pairs Donor: B Recipient: A Donor: A Recipient: B Donor: O Recipient: A XM+ Donor: A Recipient: O Pair 2 Pair 1 Pair 4 Pair 3 NODE: An incompatible donor / recipient pair EDGE: Connects two pairs if an exchange is possible

Arrival-order matching: When a pair arrives, match with one of the compatible pairs enrolled to date. Only 10 of 40 patients get a transplant

Maximum cardinality matching: Paths, Trees, and Flowers, Edmonds (1965) 14 of 40 get transplants

Simulated patients and social networks Patient Sibling MotherFather Child Spouse Friend Each Patient has between 1-4 available donors Relation- ship of Donor% Parent19.7 Child16.8 Sibling42.4 Spouse10.0 Friend11.2 Gentry, Segev, et al Am J Transplant.

Blood-type inheritance Mother AA Father BO Recipient AO Spouse OO Sibling AB Daughter OO Son AO Friend BO

Decision tree model of family Potential donors Medical workup (pass 56% or 75%), crossmatch tests (11%), bloodtyping Incompatible donor/recipient pairs Direct donation pairs annually No willing, healthy donor Simulate until reach # of real live donors (6468)

Match % and travel in KPD

Numerical impact of KPD pairs predicted to present yearly About half of these pairs can match through live donor paired donation $340 million saved over dialysis using maximum edge weight matching for kidney paired donation 20% increase in living donor kidney transplantation (Segev, Gentry, et al., JAMA, 2005)