In procuring organs from patients like Amanda, doctors have created a new class of potential organ donors who are not dead but dying. By arbitrarily drawing a line between death and life — five minutes after the heart stops — they have raised difficult ethical questions. Are they merely acknowledging death or hastening it in their zeal to save others’ lives?

With modern technology like respirators and tube feedings with synthetic formulas, Beaulieu might have kept her unconscious, brain-damaged child alive indefinitely. But as she sipped coffee in her apartment from a mug reading “#1 Mom,” Beaulieu told me that if Amanda had lived, she could “never bike, rollerblade or go out with friends, and she’d never want that.” If people with no hope for meaningful recovery can be kept alive artificially, shouldn’t they also be permitted to die artificially?

Since the inception of organ transplantation a half-century ago, defining death has taken on both medical and ethical urgency. Before Joseph Murray performed the world’s first successful kidney transplant in 1954 and showed that organs could be put to productive use outside their original host, doctors waited until the deceased was blue and stiff to declare death. Identifying a precise moment of death was a diversion for eccentric researchers like Duncan MacDougall, who, in the early 1900s, placed dying patients on a scale in order to determine when death occurred: the moment they lost three-quarters of an ounce, the presumed weight of the soul.

The paradox of needing a dead donor with a live body was first addressed in 1968. Henry Beecher, a Harvard anesthesiologist and medical ethicist, convened a 13-member committee to write a definition of “irreversible coma,” or brain death, for The Journal of the American Medical Association. Not everyone accepted the four-page report’s conclusions. After Norman Shumway, a Stanford University surgeon, performed the first American heart transplant from a brain-dead donor, he was threatened with prosecution by the Santa Clara County coroner. As a result of the widespread disagreement over the meaning of “brain death,” President Jimmy Carter asked a blue-ribbon commission to examine the issue. The commission culminated in the Uniform Determination of Death Act in 1981, which defined death as “irreversible cessation of all functions of the entire brain, including the brainstem.” The procedure to diagnose brain death, however, was never codified into law, and as a result, it varies from hospital to hospital. In 1987, the nation’s pediatrics authorities tried to standardize the diagnosis, listing 14 different criteria to confirm brain death, like the absence of reflexes, and requiring, under certain conditions, additional X-rays and tests for brain-wave activity. Last year, in the journal Pediatrics, researchers from Loma Linda University reported that of 277 brain-dead children in California who were referred to the regional organ bank over many years, only a single child received the full set of diagnostic tests.

In 2008, a young Oklahoman named Zack Dunlap was declared brain-dead after an all-terrain-vehicle accident and was considered for organ donation. Then, suddenly, he recovered. He later appeared on NBC’s “Today” show. The precise medical details of the case are not public, but it is possible that a diagnostic error was made because a checklist was not followed. Dr. Wiley Hall, the director of neurocritical care at the University of Massachusetts Medical School, where I am the chief of pediatric cardiology, told me about a similar case last year in Massachusetts; it turned out that a brain scan had been performed improperly.

Such sloppiness is potentially tragic, but it is also exceedingly rare. Whether or not a checklist is followed, by the time a neurologist is consulted to assess a critically ill patient for brain death, the odds of recovery are already minuscule. Doctors see that these patients have begun dying, and the uncertainty is not about whether it will happen but when. The families of dying patients often realize this, too, and ask to donate their relative’s organs. Dr. Robert Truog, a professor of medical ethics at Harvard Medical School, says he believes this is a situation where “all the ethical vectors are lined up,” since the patient’s family, the doctors and the recipient’s family all want to proceed with organ donation. The holdup is that the patient is not legally dead.

The current shortage of organs gives urgency to any new avenue for donation. The United Network for Organ Sharing, a nonprofit, coordinates the nation’s system of organ transplantation. Its Web site maintains a continuously updated count of people waiting for transplants. As of early this month, 105,172 men, women and children were in line. On an average day, the organization estimates, 18 people on the list die because they don’t receive an organ in time. Despite widespread campaigns to encourage donation, availability has changed only modestly over the past decade — last year there were fewer than 8,000 deceased donors — while waiting lists have doubled in size.