At least four million Americans under age 65 are exposed to high doses of radiation each year from medical imaging tests, according to a new study in The New England Journal of Medicine. About 400,000 of those patients receive very high doses, more than the maximum annual exposure allowed for nuclear power plant employees or anyone else who works with radioactive material. The paper, being published on Thursday, was based on a survey from 2005 to 2007 covering almost one million patients insured by UnitedHealthcare. It did not estimate the number of cancer cases that the radiation might cause over the next several decades. But Dr. Rita Redberg, a cardiologist and researcher at the University of California, San Francisco, who has extensively studied the use of medical imaging, said it would probably result in tens of thousands of additional cancers. Each individual patient is at relatively minor additional risk from the tests, Dr. Redberg said, but because they are given to so many people, the cumulative risk is significant.