KPD was first suggested in the literature by Rapaport in 1986 [3], but some observers argued that this modality would help only a small number of people [4]. The earliest functioning exchange programs may have been those in Korea that accomplished more than 100 transplants by 1997 [5]. In the US, single-center programs were performing KPD at a low rate until 2005, when a national consensus conference was held to discuss the possibility of larger registries that would combine incompatible pairs from many transplant centers to find more matches. Because the National Organ Transplantation Act of 1984 forbade acquiring or transferring a kidney for valuable consideration, members of the transplant community pressed the US Congress to pass the Charlie W. Norwood Living Organ Donation Act of 2007 clarifying that kidney exchange was legal. The current landscape for KPD in the US includes several single-center programs [6], multicenter consortia [7–9], and a registry operated by the organization that administers deceased donation in the US, the United Network for Organ Sharing. Recently, a second consensus conference produced detailed recommendations for developing KPD in the US [10].

Once a paired donation program exceeds about 10 or 20 pairs, it requires a nontrivial mathematical optimization to find the combination of matches that achieves the greatest number and the most optimal transplants. Two possible combinations of matches for the same ten pairs are shown in Figs. 2.2a and b. Each small numbered circle represents two people: a kidney transplant candidate and his incompatible donor. The lines that connect some of the circles show cases in which a paired exchange is possible; that is, if a line connects two circles, then the donor of each pair is compatible with the recipient of the other pair. Sophisticated mathematical algorithms are required, in general, to find the optimal matching in Fig. 2.2a, in which the dark lines show how four exchanges could result in transplantation for eight of these ten participants. All of the decisions in any paired exchange registry affect the opportunities for other pairs in the group. For instance, after performing the three exchanges shown in Fig. 2.2b, only six people out of these same ten have been transplanted, and there is no way to find compatible transplants for the remaining four.

Many considerations besides the absolute number of transplants are important in choosing which incompatible pairs should be matched with more optimal donors and candidates. Matches that involve pediatric candidates, highly sensitized candidates, or matches in the same transplant center are preferred, as are matches for the pairs that have been waiting the longest. KPD registries generally use optimization methods like integer programming to maximize the benefit afforded to all pairs in the registry.

These static optimization methods require all donors and recipients to wait for some period of time before any matches are made, or else the entire advantage will be lost. KPD registries that do not wait for 25–100 registrants to accumulate between matches are predicted to achieve about 10–20 % fewer transplants than would otherwise be possible [11]. Competition among multiple registries might predictably lead to just this outcome, in which the drive to make matches earlier means fewer matches overall. A more advanced mathematical technology called dynamic optimization could alleviate this trade-off, but these methods for KPD matching are still being developed [12, 13].

An expanded definition of KPD would include exchanges among three or more pairs. The donor of one pair gives the recipient of the next pair, whose donor gives to the recipient of the next pair, and so on, until the last pair’s donor gives to the recipient of the first pair in the cycle. Moving to three-way or larger exchanges significantly increases the likelihood that any pair will find a match.

Desensitization protocols using high-dose intravenous immunoglobulin (IVIg) or plasmapheresis and low-dose IVIg have enabled successful transplants against either human leukocyte antigen (HLA) or blood type incompatibilities. Thus, desensitization might be viewed as an alternative to KPD. However, some incompatible pairs can only be transplanted through a combination of desensitization and KPD. This situation arises when a transplant candidate has very high donor-specific antibody levels against the intended donor, but the candidate has a lower level of donor-specific antibody for some other donor in the exchange pool. To offer one example, more than half of all KPD recipients in the Johns Hopkins Hospital Incompatible Kidney Transplant program have required desensitization.

One complicating factor in all paired donation registries is imperfect prior information about exactly which donors are compatible with which candidates. Even with proper histocompatibility testing , which includes donor and recipient HLA typing and recipient antibody testing to identify unacceptable antigens, unexpected positive crossmatches will occur. An unexpected positive crossmatch will cancel all of the transplants in a planned kidney exchange. These unexpected positive crossmatches are very disruptive to the operations of a KPD registry , causing delays and disappointment for enrolled incompatible pairs. Strict standards for histocompatibility laboratories might mitigate this difficulty. Histocompatibility experts play a vital role in managing KPD , especially for centers that combine KPD with desensitization.

Because a selection bias skews blood types among incompatible pairs, the pairs who have overrepresented blood types will find it difficult to match to a complementary pair. For example, the population of incompatible pairs will be enriched for O blood type recipients because O recipients are blood type incompatible with all A, B, and AB donors. On the other hand, pairs with O blood type donors would only seek KPD in the comparatively rare circumstance that the donors were HLA incompatible with their intended recipients. The 28 % of incompatible pair donors who have O blood type will not be sufficient to match the 59 % of incompatible pair recipients who have O blood type [14]. Simulation studies suggest that O blood type recipients with non-O donors and all recipients with AB donors will wait longer and match at lower rates [15].

If donors who are compatible with their intended recipients also participated in KPD , the blood type imbalance could be corrected and twice as many incompatible pairs would find a match [16]. Compatible pairs might join a kidney exchange pool to find a donor who is a better size match, HLA match, or age match for the intended recipient; recent evidence supports this practice, particularly in the case of older living donors [17]. Compatible pairs also might offer to participate in kidney exchange out of an altruistic desire to help candidates with incompatible donors. The largest single-center KPD program in the US, at Methodist Specialty and Transplant Hospital in San Antonio, makes extensive use of compatible pairs and 35 % of its transplant volume is paired donation [6].

Nondirected donors, or altruistic donors , are people who volunteer to donate a kidney without naming any intended recipient. After appropriate screening and counseling, a nondirected donor might give to a candidate on the deceased donor waiting list. Alternatively, a nondirected donor might give to the recipient of an incompatible pair, and the incompatible donor’s kidney can go to another pair, and so on, thereby multiplying the gift of the nondirected donation. Figure 2.3 illustrates one such chain. A consensus conference recently urged that all nondirected donors be informed about KPD and their potential to trigger multiple transplants through these programs [10].

Nondirected donors are especially empowered to enable transplants for incompatible pairs. In many operating KPD programs , a majority of the transplants are accomplished in exchanges started by nondirected donors [18]. This is true both because of a favorable blood type distribution among nondirected donors , with 48 % of nondirected donors having O blood type, and because nondirected donors relax the reciprocality requirement that otherwise constrains the last donor to match the intended recipient of an initiating pair. Further, kidney exchanges that start with a nondirected donor can relax the restriction of simultaneity.

At the end of a chain of transplants initiated by a nondirected donor , the donor of the last pair might donate a kidney to a candidate on the deceased donor waiting list, or might be asked to wait a few months as a bridge donor. The bridge donor delays his donation so that he or she can serve as the starting donor for another chain of transplants after new incompatible pairs join the program. A chain that is always continued with a bridge donor after a delay is called a nonsimultaneous extended altruistic donor (NEAD) chain [19]. A chain of donations started by a nondirected donor that ends with a donation to a deceased donor waiting list candidate is called a domino paired donation [20]. A simultaneous domino paired donation ends immediately with a donation to the waiting list; a nonsimultaneous domino paired donation incorporates one or more bridge donors who extend the domino through time until it ultimately ends with a donation to the waiting list.

When the donations are performed in succession starting with a nondirected donor , there is less risk associated with nonsimultaneous operations. Because none of the donor operations in the chain occurs before the intended recipient of that donor has received a transplant, there is no way for a candidate to remain untransplanted after his bargaining chip, his intended donor, has already given a kidney. If a bridge donor decides not to donate, then the incompatible pairs farther down the chain can be matched into a different KPD arrangement , because every candidate still has his incompatible donor. This observation holds only for operations performed in the natural sequence. At least one group has reported performing a successful out-of-sequence nonsimultaneous chain [21].

In theory, each nondirected donor could begin a very long NEAD chain of donations extending over time. In practice, the bridge donors become increasingly difficult to match to the next recipient. In fact, the reason someone is designated as a bridge donor is usually that he or she does not match any of the recipients presently in the incompatible pairs registry. Transplant 9 in Fig. 2.3, for example, required desensitization across a blood type barrier to use an AB blood type donor, and the sequence of transplants halted again at an AB blood type donor after transplant 10. It might be the case that bridge donors who are difficult to match and who have to wait longer are more likely never to donate in the long run. Every KPD registry using bridge donors that we are aware of has had at least one bridge donor who ultimately did not donate.