First of two articles.

In 2004, Rick Segal, a father of four living in Rye, N.Y., found his stamina inexplicably failing him as he did his regular runs. He went to see his doctor, and learned he had a genetic disease that enlarges and weakens the heart. Segal was about to turn 50, but his heart was pumping at one-eighth of a normal heart’s effectiveness. He needed a transplant.

He got on a waiting list, and for the next five years, he was in and out of hospitals while his heart deteriorated further. He underwent multiple 12-hour operations. A defibrillator was installed in his chest. Then came mechanical pumps for both ventricles. “I got a belt from a police wholesale site to carry around these huge batteries,” he said. Because the heart pumps had an 18-month life span, an imminent transplant became his only option.

So he and his family played a risky card. “You are allowed to choose a 30-day period where you can be listed as ‘1A,’” he said, referring to the highest priority designation for transplant. During that month, Segal needed to be matched with a donor with blood type O who weighed at least 180 pounds. It didn’t help that he lived in New York, which ranked 49th of the 50 states in the percentage of people registered as organ donors.

On Monday, Feb. 9, 2009, the 29th day of his 1A status, he and his wife were driving on the Hutchinson River Parkway to NewYork-Presbyterian Hospital to seek end-of life-counseling — “We had pretty much given up hope,” he said — when the phone rang. “They said: Go home, pack your bags. A heart has been found.” A 26-year-old intravenous drug user from Boston had overdosed. The next day his heart was pumping in Segal’s body.