Ms. Sloan’s fruitless search for an explanation had taken her to the University of Alabama at Birmingham Hospital, Ochsner Health System in Louisiana and Vanderbilt University in Tennessee. “They had no clue,” she said. “I lost 15 pounds. I couldn’t sleep.”

Ms. Sloan had tried to cover her missing hair using bobby pins. But one day at school, a gust of wind blew and children saw her strip of missing hair. One got sick and vomited, she said. As word of her condition spread, former students flocked to her classroom, some crying. “We heard you were dying,” one said. “Is there something we can do?”

Another patient, an aerospace engineer who says she had a seizure after her scan, said her dermatologist wrote to Huntsville Hospital out of concern for her and another patient with similar symptoms.

“Even after the dermatologist put two and two together and asked Huntsville Hospital to contact me, they never did,” said the engineer, who provided a picture of her hair loss but asked that her name be withheld because of professional reasons.

She said she suffered from memory loss and confusion.

Huntsville Hospital officials said they did not routinely record radiation dose levels before 2009. Mr. Ingram, the spokesman, said the hospital did keep information needed to calculate the dose, but he declined to say whether officials had gone back to determine doses for all patients who had brain perfusion scans.

The form letter Huntsville sent to overdose patients appears to play down the damage that high doses can inflict. The hospital told patients that hair loss and skin redness might occur but would go away. “At this time, we have no recommendations for you to have any follow-up treatment,” the letter said.

Health experts elsewhere have warned of possible eye damage, in addition to the higher risk of cancer and brain damage.