Pi Day: Optimization for kidney paired donation

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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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Kidney paired donation (KPD)
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Graph recipient / donor pairs
NODE An incompatible donor / recipient pair
EDGE Connects two pairs if an exchange is
possible
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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
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Maximum cardinality matching Paths, Trees, and
Flowers, Edmonds (1965) 14 of 40 get transplants
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Simulated patients and social networks
Mother
Father
Relation-ship of Donor
Parent 19.7
Child 16.8
Sibling 42.4
Spouse 10.0
Friend 11.2
Sibling
Friend
Patient
Sibling
Spouse
Child
Child
Each Patient has between 1-4 available donors
Gentry, Segev, et al. 2005. Am J Transplant.
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Blood-type inheritance
Mother AA
Father BO
Friend BO
Recipient AO
Spouse OO
Sibling AB
Daughter OO
Son AO
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Decision tree model of family
Potential donors
Medical workup (pass 56 or 75), crossmatch
tests (11), bloodtyping
No willing, healthy donor
Incompatible donor/recipient pairs
Direct donation
Simulate until reach of real live donors (6468)
2406-4443 pairs annually
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Match and travel in KPD
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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)