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
NODE:
An incompatible
donor / recipient
pair
Pair 1
Donor: B
Recipient: A
Pair 2
Donor: A
Recipient: B
Pair 3
Donor: O
Recipient: A
XM+
Pair 4
Donor: A
Recipient: O
EDGE:
Connects two
pairs if an
exchange is
possible
12
11
10
9
8
13
7
14
6
15
5
16
4
17
3
18
2
19
1
20
0
21
39
22
38
23
37
24
36
25
35
26
34
27
33
28
29
30
31
32
12
11
10
9
8
13
7
14
6
15
5
16
4
17
3
18
2
19
1
20
0
21
39
22
38
23
37
24
36
25
35
26
34
27
33
28
29
30
31
32
12
11
10
9
8
13
7
14
6
15
5
16
4
17
3
18
2
19
1
20
0
21
39
23
37
24
36
25
35
26
34
27
33
28
29
30
31
32
12
11
10
9
8
13
7
14
15
16
17
Arrival-order
matching:
6
When a pair arrives,
5
match
with one of
4
the compatible pairs
3
enrolled to date.
18
2
Only 10 1of 40
patients get
a
0
transplant
39
19
20
21
22
38
23
37
24
36
25
35
26
34
27
33
28
29
30
31
32
12
11
10
9
8
13
7
14
6
15
5
16
4
17
3
18
2
19
1
20
0
21
39
22
38
Maximum cardinality
23
matching:
24
37
36
Paths, Trees, and Flowers,
25
Edmonds (1965)
35
26
14 of 40 get
transplants
34
27
33
28
29
30
31
32
3
4
2
5
1
6
0
7
11
8
10
9
3
4
2
5
1
6
0
7
11
8
10
9
Simulated patients and
social networks
Mother Father
Sibling
Sibling
Friend
Patient
Child
Spouse
Relationship of
Donor
%
Parent
19.7
Child
16.8
Sibling
42.4
Spouse
10.0
Friend
11.2
Child
Each Patient has between 1-4 available donors
Gentry, Segev, et al. 2005. Am J Transplant.
Blood-type inheritance
Mother
AA
Father
BO
Friend
BO
Sibling
AB
Recipient
AO
Spouse
OO
Daughter
OO
Son
AO
Decision tree model of family
Potential donors
Medical workup
(pass 56% or 75%),
crossmatch tests (11%),
bloodtyping
Incompatible
donor/recipient
pairs
2406-4443 pairs annually
No willing,
healthy donor
Direct donation
Simulate until reach
# of real live donors (6468)
Match % and travel in KPD
60
50
40
%Must Travel
%No Travel
%Must Travel
%No Travel
30
20
10
0
First-A
Optimized
None
First-A
Optimized
All 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)