This article is from the Organ Transplant FAQ, by firstname.lastname@example.org (Michael Holloway) with numerous contributions by others.
In the case of liver, heart and lung transplants no 'matching' is done
except for blood group (O,A,B,AB) and organ size. An O organ can be used in
an O, A, B, or AB patient, whereas, an O patient can only receive an O
organ. The reason it works this way is because cells have proteins for the
blood group on their surface such that:
* AB patients have both A and B proteins
* A patients have A but not B protein
* B patients have B but not A
* O patients have neither protein.
If a patient lacks particular proteins, they develop antibodies to the ones
they are lacking (the reason for this is unclear):
* AB patients develop no antibodies
* A patients develop antibodies against B
* B patients develop antibodies against A
* O patients develop antibodies against A and B proteins.
Now in practice, if a patient has a transplant with an organ that has
proteins on it (say an A organ that has A proteins on it) and that patient
already has antibodies against that protein (say a B patient that naturally
has antibodies against A proteins) the organ will fail very quickly (within
minutes). So if the B patient gets transplanted with an A kidney, it will
not function and be promptly rejected (by antibodies against B protein).
This makes O a universal donor and AB a universal recipient.
For reasons of fairness, organs are allocated primarily to their own blood
group. Otherwise, the O patients would only have access to a fraction of
the organs, while AB patients would have access to all organs.
Nevertheless, there are some inequities in the waiting times on particular
blood group lists.
Finally, what I have just explained does not seem to make much of a
difference in the case of liver transplants; the reason for this is
unclear. In other words it is known that one can use "blood group
incompatible" livers (an A liver in a B patient) with success rates almost
as good as blood group identical livers. We still use blood group identical
livers when at all possible because the success rate is higher overall. The
allocation schemes for organs takes these principles into account.
University of Michigan