Elutions and adsorptions are easily confused (and are used for completely different reasons):
Elutions are to remove antibodies attached to red cells;
Adsorptions are used to remove antibodies from serum.
Elutions
Elutions are used in the following situations:
A common situation might be where a patient has suffered a haemolytic transfusion reaction and is DAT positive - but the serum reveals no obvious antibody (a reason might be because the transfusion was several days/weeks ago and the antibodies in the serum have cleared); and the only antibody that remains is on the red cells.
To detect the antibody, an elution is required to dissociate the bound antibody from the red cell into the serum so it can be tested. Elutions can be used even if the DAT is negative if there is a strong suspicion of a haemolytic transfusion reaction (as elusions are more sensitive than DATs). Ensure you do a pre-transfusion DAT and eluate as a control for the post-transfusion samples that you need to perform!
Adsorptions
The key principle to recall here is Landsteiner's rule: individuals do not make antibodies to endogenous antigens under normal conditions. That is to say, for example that if you are group A RhD+, you will not make anti-A, or anti-D. However you can temporarily produce autoantibodies which may for example cause a warm autoimmune haemolytic anaemia, and this may make crossmatching blood difficult - hence the utility of adsorptions.
Adsorptions are used to help distinguish between alloantibodies and autoantibodies - these are extremely useful when you have a pan-reactive panel which might be suggestive of an autoantibody. However with a pan-reactive antibody panel one cannot rule out an underlying alloantibody. Here (unlike elutions) you remove the antibody from the serum onto the red cells - which are then in turn discarded after use. The serum is preserved for testing.
By removing autoantibodies from the serum you can retest it for alloantibodies, assuming the test has removed all autoantibodies. There are: