The main problem is chronic rejection, which can occur despite the constant use of complication-prone immune-suppressive drugs.
Such chronic rejection presents itself as bronchiolitis obliterans, or less frequently, atherosclerosis.
Barnard said "eventually the chronic rejection had damaged the heart to such an extent that it failed."
Experts don't fully understand what causes chronic rejection.
The most likely explanation, the researchers write, is "that immunological factors, yet unidentified, might be contributing to chronic rejection.
The cause was chronic rejection of a lung transplant, complicated by infection, said her father, Jon.
It is a type of renal injury often associated with chronic antibody-mediated rejection.
There is no treatment for chronic rejection.
Perhaps the major cause of chronic rejection is arteriosclerosis.
It is also anticipated that chronic rejection will be more aggressive in xenotransplants as opposed to allotransplants.