How does a paired kidney exchange program directly increase transplant opportunities for a recipient whose intended living donor is immunologically incompatible?

A paired kidney exchange program directly increases transplant opportunities for a recipient whose intended living donor is immunologically incompatible by facilitating a swap of donors among multiple incompatible donor-recipient pairs. Immunological incompatibility occurs when a recipient's immune system would reject their intended living donor's kidney, typically due to incompatible blood types (e.g., Recipient A is blood type O and Donor A is blood type B) or because the recipient has pre-formed antibodies against the donor's Human Leukocyte Antigens (HLA), which would result in a positive crossmatch test. These antibodies indicate a high risk of hyperacute rejection if the transplant proceeds directly. In a paired kidney exchange, such an incompatible pair (let's call them Pair A, consisting of Recipient A and Donor A) enters a program that pools other similarly incompatible pairs. Sophisticated....