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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: BRecipient: A
Donor: ARecipient: B
Donor: ORecipient: A
XM+
Donor: ARecipient: O
Pair 2
Pair 1 Pair 4
Pair 3
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
PatientSibling
Sibling
Mother Father
Child Child
Spouse
Friend
Each Patient has between 1-4 available donors
Relation-ship of Donor %
Parent 19.7
Child 16.8
Sibling 42.4
Spouse 10.0
Friend 11.2
Gentry, Segev, et al. 2005. Am J Transplant.
Blood-type inheritance
MotherAA
FatherBO
RecipientAO
SpouseOO
SiblingAB
DaughterOO
SonAO
FriendBO
Decision tree model of family
Potential donors
Medical workup (pass 56% or 75%),
crossmatch tests (11%), bloodtyping
Incompatibledonor/recipient
pairsDirect donation
2406-4443 pairs annually
No willing, healthy donor
Simulate until reach# of real live donors (6468)
Match % and travel in KPD
0
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First-A Optimized First-A Optimized
None All Travel
%Must Travel
%No Travel
%Must Travel
%No Travel
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)