Cryopreserved allografts are morphologically nonviable; their collagen is flattened but largely preserved. They are unlikely to grow, remodel, or exhibit active metabolic functions, and their usual degeneration cannot be attributed to immunologic responses. In contrast, aortic valves of transplanted hearts maintain near-normal overall architecture and cellularity and do not show apparent immunologic injury, even in the setting of fatal myocardial parenchymal rejection or graft arteriosclerosis.