An examination by The New York Times has found that radiation overdoses were larger and more widespread than previously known, that patients have reported symptoms considerably more serious than losing their hair, and that experts say they may face long-term risks of cancer and brain damage. The review also offers insight into the way many of the overdoses occurred. While in some cases technicians did not know how to properly administer the test, interviews with hospital officials and a review of public records raise new questions about the role of manufacturers, including how well they design their software and equipment and train those who use them. The Times found the biggest overdoses at Huntsville Hospital — up to 13 times the amount of radiation generally used in the test. Officials there said they intentionally used high levels of radiation to get clearer images, according to an inquiry by the company that supplied the scanners, GE Healthcare.