In one way, the cases are polar opposites: the parents of Jahi McMath in Oakland, Calif., have fought to keep their daughter connected to a ventilator, while the parents and husband of Marlise Muñoz in Fort Worth, Tex., want desperately to turn the machine off. In another way, the cases are identical: both families have been shocked to learn that a loved one was declared brain-dead — and that hospital officials defied the family’s wishes for treatment.

Their wrenching stories raise questions about how brain death is determined, and who has the right to decide how such patients are treated.

“These cases are quite different from those we’ve known in the past,” like Karen Ann Quinlan, Nancy Cruzan or Terri Schiavo, said Dr. Joseph J. Fins, director of the medical ethics division at NewYork-Presbyterian/Weill Cornell hospital. He explained: “Those patients could all breathe without a ventilator. They were in a vegetative state, not brain-dead, and that distinction makes all the difference.”

A person who has received a brain-death diagnosis cannot breathe on his or her own and is legally dead, in all 50 states. In two states, New York and New Jersey, hospitals must take into account the family’s religious or moral views in deciding how to proceed in such cases. In all others, including California and Texas, hospitals are not required to consult the family in how to terminate care.