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

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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)