As a patient was being prepped on a recent day in New York, Rae Lynne Kinler told a fellow surgeon she was stepping out for an urgent matter. She logged onto a computer, clicked through a few screens and returned.

“Did you get it?” asked the patient, under local anesthesia before a hair-replacement procedure. Yes, Dr. Kinler said, she’d secured a spot in the Brooklyn Half marathon. The patient—a runner himself—said, “Yay! Congratulations,” before the knife descended.

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