[@KoL] hemodialysis is for kidney failure, not sure what that has to do with bone marrow.

I think think the medical term you could use is Allogeneic Bone Marrow transplant. From a donor(you victim), you receive blood that has the stem cells removed from the white blood cells. Stem cells help regenerate healthy bone marrow as well as give rise to all other blood cells. 

Instead of a machine to separate stem cells from white blood cells, you could use your alchemy. For the sake of the roleplay (and anime), you could just have some very abnormal kind of marrow because of the human transmutation that allows your genes to be compatible with some others.