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Plus a tweak: The donor pig’s thymus gland, which trains the immune system, was attached to the donated kidney in hopes that it would help Pisano’s body tolerate the new organ.

In addition to the precursors of T cells, the thymus gland also contains other immune cells, the B cells.

To prevent these incidents of "friendly fire," T cells developing in the thymus gland need to first be educated to discriminate between the body's own proteins and those of foreign origin.

A pig thymus gland—a source of immune cells—was also transplanted to help reduce the risk of immune rejection.

The N.Y.U. procedure also calls for embedding the pig’s thymus gland, which is responsible for educating the immune system, underneath the outer layer of the new kidney to prevent an immune-system attack.