This study will investigate the causes of acute and chronic rejection of transplanted hearts. To find better ways to detect, treat and possibly prevent heart transplant rejection, more information about the cause is needed. Acute and chronic heart transplant rejection may be caused by certain substances the body produces in response to the new heart. This study will try to find a blood or urine test that detects genes and proteins that can serve as markers of rejection. Such a test may lead to earlier detection and improved treatment.