By 4 p.m., six hours after the surgery began, Ms. Roy, the drapes removed from her face, was blinking in the glare of the operating room, and moving her arms and legs. An anesthesiologist told her the surgery was finished and had gone well. Ms. Roy managed a sleepy smile.

Three days later, in a robe and bright red socks, she was sitting up in bed, chatting with her husband over lunch. It was hard to believe she’d so recently had brain surgery.

“I just feel good,” she said.

She jokingly accused Dr. Langer of having told her “a story” about potential side effects and a difficult recovery. It was the week before Christmas, and she had decorated her tree and finished wrapping gifts before heading to the hospital, fearing that she would be unable to do so after the surgery.

But the operation, she said, “was, like, nothing.”

“They don’t all go so well,” Dr. Langer said. “These things are high risk, and they don’t always turn out perfectly.”

Without surgery, for patients like Ms. Roy, estimates for the risk of a stroke range from 20 percent to 50 percent or even higher within five years, he said. After successful surgery, the risk drops to a few percent a year or less.

Ms. Roy, to be released that day, was more than ready to leave the hospital.

“I need some air,” she said. She was looking forward to the walk across town with her husband to catch an express bus home to the Bronx.

“I am lucky,” she said.