Matching Theory in Kidney Transplants
Matching Theory: Kidney Allocation https://ojs.lib.uwo.ca/index.php/uwomj/article/download/4632/3825/8049
Since 1954, kidney transplants have saved millions of people. The problem is, not every donor matches the blood and tissue of the patient they are trying to donate their kidney to. This incompatibility has led to many patients having to wait in extremely long transplant lists and can lead to months or even years of pain and suffering. In recent years, the National Resident Matching Program has redesigned its matching program to become the Kidney Paired Exchange (KPE). This allows incompatible donors to have the opportunity to be matched to a recipient in another pair of people, creating a mutually beneficial exchange where both patients would receive a compatible donor. As the system of exchanges has become more complicated, KPE has been adapted to better utilize the rising number of altruistic or non-directed donors. By using a domino-paired donation, altruistic donors are able to donate a kidney to a recipient of an incompatible pair, then the donor of that pair will donate their kidney to a compatible recipient on the waitlist. The longest domino chain has contained 30 kidneys and 60 individuals. This method has expanded from county-wide to state-wide to national to global, having effectively constructed programs in countries such as the Netherlands and Canada. If this program is used optimally, researchers suggest there could be as many as 1000-2000 additional transplants per year. This increasing number means patients experience a lessened burden of dialysis, better mortality, and an overall higher quality of life. In the future, non-simultaneous extended altruistic donor (NEAD) chains can be created so that the last donor does not donate to a waiting list recipient, but becomes a bridge donor to await more pairs. This prevents the need for simultaneous transplant to prevent donor reneging.
Programs like the Kidney Paired Exchange (KPE) program and Non-Simultaneous Extended Altruistic Donor (NEAD) Chains use matching theory to find each pair of donors and recipients a link to another pair of donors and recipients that are compatible. In networks, a Perfect Match is an assignment of each item to a different person so that each person is linked to an item they want or are willing to take. Similarly, if every pair of donors/recipients are linked to a compatible match, then it is a perfect matching. In networks, The Matching Theorem is when a bipartite graph (with equal numbers of left and right nodes) has no perfect matching then it has a constricted set. This can also be applied in this example, if there are not the same number of pairs of donors and recipients, it would be a constricted set and would not be a perfect match. These course topics can help researchers come up with ideal ways to connect incompatible pairs donors and recipients with other incompatible pairs. This helps decrease the amount of patients on waiting lists and allows more patients a higher quality of life.