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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.

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Presentation on theme: "Pi Day: Optimization for kidney paired donation Sommer Gentry U.S. Naval Academy Dorry Segev Johns Hopkins University School of Medicine."— Presentation transcript:

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

2 Kidney paired donation (KPD)

3 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

4

5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 39

7 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 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

8 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Maximum cardinality matching: Paths, Trees, and Flowers, Edmonds (1965) 14 of 40 get transplants

9 0 1 2 3 4 5 6 7 8 9 10 11

10 0 1 2 3 4 5 6 7 8 9 10 11

11

12 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. 2005. Am J Transplant.

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

14 Decision tree model of family Potential donors Medical workup (pass 56% or 75%), crossmatch tests (11%), bloodtyping Incompatible donor/recipient pairs Direct donation 2406-4443 pairs annually No willing, healthy donor Simulate until reach # of real live donors (6468)

15 Match % and travel in KPD

16 Numerical impact of KPD 2406-4443 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)

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