I doubt nurses would replace anesthetists, but I'm not quite sure about the rads.
Currently, the images are taken by rad technicians on physicians' orders. Then, the only thing that is left out to the physician is to read these taken images and give them meanings and write a report (voice recognition software helps, so radiologist doesn't need to type on the keyboard, at all).
If not offshored (i.e., images being sent to India, China, etc.), these positions could be easily filled with physicians from other parts of the States, because you supposedly don't need to have the radiologist be physically living at the same location with the patients.
This is quite doable unless the government steps in to secure the patients' rights by not allowing any of these images to be sent to anywhere but be kept locally at that particular healthcare setting. HIPAA could be utilized for this purpose; official link is this:
HIPAA.
As everybody knows, all of your bank account information, citizenship or personal identification information including your social security number, driver licenses, etc. along with the secondary information gathered about your assets, employer, addresses, purchase information, purchase patterns, locations where you've been using your credit cards, etc. have been already taken offshore (to call center databases in India) by your bank. This shouldn't happen to patients' health related information, at all. But, what's the guarantee?