Dr. Matthew Rhoa is still haunted by one of his lowest moments as a physician. Several years ago, on the first leg of an international flight, he was just settling in for a nap when a flight attendant came on the public address system to ask, “Is there a doctor on the plane?”

He fell asleep, only to be awakened an hour later by a second call for medical help. This time he answered, and at the back of the plane he found two anxious parents with their 18-month-old toddler, who had a cast on her broken leg and was crying inconsolably. The girl’s toes were blue. Limbs can often swell in flight, and it was clear that the cast was much too tight. Dr. Rhoa slit the cast and pried it open. The girl stopped crying at once. “I have been riddled by guilt to this day,” said Dr. Rhoa, who now promptly answers every call for medical help on a plane. “I never want that feeling again of a kid suffering like that when I could have done something sooner.” Since the earliest days of commercial aviation, airlines have coped with medical emergencies in flight by calling on physicians who happen to be passengers. And as more people travel by air, the number of emergencies has risen accordingly. “Passenger health is becoming more and more of an issue, because of increased life expectancy and more people flying with pre-existing conditions,” said Dr. Paulo Alves, a vice president at MedAire, a company that provides crew members with medical advice from physicians on the ground. MedAire, which advises more than 60 airlines around the world, managed about 19,000 in-flight medical cases for commercial airlines in 2010. Although few were life-threatening, 442 were serious enough to require diverting the plane — and 94 people died onboard. The numbers reflect a fraction of the actual number of in-flight emergencies. The Federal Aviation Administration does not track in-flight medical episodes, and airlines are not required to report them. Airborne calls for medical assistance pose a singular challenge for physicians, who find themselves suddenly caring for a stranger whose history they don’t know, often with a problem well outside their specialty, in a setting with limited equipment but no shortage of onlookers scrutinizing their every move. And they do this for no compensation. (The fact that Good Samaritan laws generally protect them from lawsuits is a small saving grace.) So it is little wonder that many physicians hesitate before responding to an emergency call. Three years ago, Dr. Peter Freed, a psychiatrist in Manhattan, answered a call for a physician during a cross-country flight. A passenger had just had a seizure. Dr. Freed told the flight attendant he had not practiced general medicine since his residency. Still, he was the only doctor to respond, and the flustered crew member told him she was grateful for any help at all. The passenger, a woman in her 30s traveling from Europe, told Dr. Freed she had a longstanding seizure disorder. He had her take her medication and remained with her, hoping she would be fine for the rest of the flight. But after another 20 minutes, she developed the uncontrollable shaking of a grand mal seizure and fell unconscious. He asked to speak to a neurologist on the ground, and within minutes the pilot was able to get one on the radio. But as Dr. Freed recalled, he was barred from the cockpit for security reasons and could not speak directly with the specialist. “I talked to the flight attendant, who talked to the captain in the cockpit, who talked to the doctor,” he said. Next came the question that many physicians who answer in-flight emergency calls face: Should the plane be diverted to a nearby airport? Ultimately, the decision rests with the pilot, but the pilot looks to the medical expert for guidance. And it is a decision that other passengers await most anxiously. After calculating that it would take as long to divert the plane as to reach their destination, Dr. Freed decided against it. Once the plane landed, an emergency medical team whisked the woman away. The pilot had Dr. Freed stand with him while passengers disembarked. As people filed past, they shook Dr. Freed’s hand and thanked him. But while that response was gratifying, the episode still felt unresolved. “Doctors typically like to hear how cases end,” Dr. Freed said. “But I didn’t hear a thing. I never even knew her name. I still think about her.” Physicians are not completely without backup in an airborne emergency. The F.A.A. requires that flight attendants undergo CPR training and that all United States airlines carry emergency medical kits and automated external defibrillators. But physicians who get a firsthand look at the kits say the contents vary. “With some planes, it’s a hospital in a box, and they have everything you could ever want,” said Dr. Paul Abramson, a primary care physician in San Francisco. “But often they look like they’ve been picked over.” Dr. Abramson said one kit he was given had implements for ventilating a patient unable to breathe, but no bag to push air into the patient — a situation akin to having a gasoline nozzle and tank, but no fuel. Another kit contained only enough intravenous saline solution to rehydrate a baby, not the 200-pound man he was tending. Dr. Paul Sullam, a faculty member at the University of California, San Francisco, said he was on a plane several years ago when a passenger seemed to be having a heart attack. The crew asked passengers if anyone had nitroglycerin tablets, small pills that are placed under the tongue to improve blood flow to the heart. No one responded. But when it asked for Valium, to calm the patient, “a forest of hands went up,” Dr. Sullam recalled. The lack of standardization was criticized in a recent article in The Journal of the American Medical Association. The paper argued not only that the medical kits should be standardized, down to the number of latex gloves, but also that a method for reporting incidents should be consistent among all airlines. “Aviation is held up as this paragon of safety, yet here’s this nasty thing that happens with no standard for reporting,” said one of the article’s authors, Dr. Melissa Mattison, associate director of hospital medicine at Beth Israel Deaconess Medical Center in Boston. “We know more about animals that die on airplanes than we do about people.” Dr. Abramson, the San Francisco physician, has answered so many emergency calls on planes that he now carries some basic medications in his toiletries bag whenever he flies, including antihistamines, prednisone, sedatives and painkillers, all “just in case they don’t have it.” He also books his flights with “Dr.” in front of his name. “That’s so that if I’m asleep, they might wake me,” he said. And he doesn’t take sleeping pills or drink alcohol in flight. “The last thing you want to do is be woken up and not be with it,” Dr. Abramson said. “I kind of like doing it,” he continued. “Because it’s what I do, and it seems helpful, and it’s interesting to make do with whatever minimal resources you have.” Dr. Abramson occasionally receives letters of thanks from the airline, and once received a free domestic ticket. “That was the best,” he said. Dr. Sullam, of U.C.S.F., said United Airlines once showed its gratitude by sending him an Arnold Palmer putter. “They must have figured all doctors play golf,” he said. (He does not, but he still has the putter.) Dr. Celine Gounder, an infectious disease specialist at Johns Hopkins who works in global public health, has answered numerous emergency calls on flights. After one such call, she was given a bottle of Champagne as she left the plane to rush for a connecting flight. “I thought, ‘What am I supposed to do with this?’ ” she recalled. She returned it to a flight attendant. Despite the pressures, the haphazard nature of the work, the lack of compensation and the risks, physicians continue to reach up and answer the call. In a world of insurance forms, rushed office visits and ubiquitous technology, many count such emergency calls among the purest expressions of their Hippocratic oath. “You feel good about trying to help someone, and that’s the most important thing,” said Dr. Ingrid Katz, an infectious disease specialist at Brigham and Women’s Hospital in Boston. “But don’t expect anything. It’s solely for the benefit of the person in need.”