Human Leukocyte Antigen (HLA) and Islet Autoantibodies Are ...
Some mathematical aspects of kidney transplantation...Comparison of HLA (Human Leucocite Antigen)...
Transcript of Some mathematical aspects of kidney transplantation...Comparison of HLA (Human Leucocite Antigen)...
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Some mathematical aspects of kidneytransplantation
Roberto Lucchetti
October 22, 2020
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Introduction Some data
Here the waiting list in Italy
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Introduction Some data
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Introduction Some data
Transplants with living donors
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Introduction Some data
The situation in Europe (2017)
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Kidney disease I
Kidney transplant
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Kidney disease I
Early History
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Kidney disease I
Kidney transplant
total replacement of renalfunction
longer life expectancy withrespect to people ondialysis
good quality of life
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Kidney disease I
Kidney transplant
Sean Elliott was the first NBA player coming back to play professionally after akidney transplant.
Alonzo Mourning received a kidney from a living donor in 2003 and won the NBAfinals with Miami Heat in 2006.
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Kidney disease I
Compatibility
There are three tests to evaluate compatibility between recipient and donor(living or deceased):
ABO blood type test
Comparison of HLA (Human Leucocite Antigen)
Screen for antibodies
These factors can affect the possibility of donation, and/or making it moredangerous
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Kidney disease I
PRA
The PRA test is an index to show easiness to find a compatible donor. ThePRA measures the level of antibodies in the recipients blood:
LOW PRA: 80% (highly sensitized patients)
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Kidney exchange I
Crossover exchange
The idea of exchange of donors between patients was introduced byRapaport in 1986;
This can be done in several ways.
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Kidney exchange I
"Conventional" Kidney Exchange
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Kidney exchange I
List Exchange
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Kidney exchange I
Chain
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Kidney exchange I
History
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Kidney exchange I
Pairwise exchange
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Kidney exchange I
Characteristics of the model
The simplest method is the so called pairwise exchange. Features:Only two patients and their donors;
Patient preferences: indifference among all compatible donors which arestrictly better than the associated donor, strictly better of all otherincompatible donors
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Kidney exchange I
Compatibility matrix and graph
In the compatibility matrix 1 means that the two patient-donor pairs aremutually compatible
for example: the entry AE=1 means that a kidney exchange between coupleA e and couple E is possible
Edges in the graph have the same meaning
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Kidney exchange I
Efficient matching
1 A matching is efficient if it is not possible to add another edge to it to builda bigger matching
2 There can be more than one efficient matching;3 All efficient matchings have the same number of transplanted patients.
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Kidney exchange I
Example: priority mechanism
STEP 0 = {(1,5)(2,4); (1,5)(3,4);(2,5)(3,4); (2,4)(3,5)}
STEP 1 = {(1,5)(2,4); (1,5)(3,4)}STEP 2 = {(1,5)(2,4)}
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Kidney exchange I
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Identify those patients who would receive a transplant in any maximalmatching (overdemanded)
remove them from the graph
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Kidney exchange I
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The reduced graph hassome odd components (underdemanded)some even components (perfectly matched)
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Kidney exchange I
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perfectly matched patients are matched with each other
each overdemanded is matched to an underdemanded (priority ordering)
the remaining underdemanded are matched with each other (priority ordering)
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Kidney exchange I
Top trading cycles and chains
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Kidney exchange I
Preferences
p = patient(recipient); d = donor ;w = waitinglist
Preferences of patient 1:
1 donor of patient 92 donor of patient 43 her own donor (there are no other compatible donors)
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Kidney exchange I
Step 1
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Kidney exchange I
Step 2
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Kidney exchange I
Step 2
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Kidney exchange I
Step 3
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Kidney exchange I
Final matching
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Kidney exchange I
Good Samaritan donors
With Good Samaritan donation, a person donates a kidney to anunknown recipient, starting a chain of transplants
Chains starting with a samaritan can be very long, since transplant in thiscase, differently from the case of cycles, need not be contemporary
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Stories I
A chain in Italy in 2016
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Stories I
«60 lives, 30 kidneys, all linked »
One of the longest chain performed in the Usa starting with a samaritan donor(New York Times 2012)
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Stories I
Conclusions: towards the future
1 In November 2019 two chains originated by a deceased donor bothinvolved three patients and their donors, from three different regions: thisProgram is called Deck protocol and has been invented in Italy;
2 In October 2019 a second crossover exchange has been performedbetween Spain and Italy, under the Program SAT (South Alliance forTransplant)
3 Up to today in Italy, thanks to 20 crossover chains, 55 transplants havebeen performed, involving 41 pairs donors/recipients and 8 samaritans.
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IntroductionSome data
Kidney diseaseI
Kidney exchangeI
StoriesI