But beyond the medical advances, Dr. DeBakey’s story is emblematic of the difficulties that often accompany care at the end of life. It is a story of debates over how far to go in treating someone so old, late-night disputes among specialists about what the patient would want, and risky decisions that, while still being argued over, clearly saved Dr. DeBakey’s life.

But Dr. DeBakey’s rescue almost never happened.

He refused to be admitted to a hospital until late January. As his health deteriorated and he became unresponsive in the hospital in early February, his surgical partner of 40 years, Dr. George P. Noon, decided an operation was the only way to save his life. But the hospital’s anesthesiologists refused to put Dr. DeBakey to sleep because such an operation had never been performed on someone his age and in his condition. Also, they said Dr. DeBakey had signed a directive that forbade surgery.

As the hospital’s ethics committee debated in a late-night emergency meeting on the 12th floor of Methodist Hospital, Dr. DeBakey’s wife, Katrin, barged in to demand that the operation begin immediately.