CT/US are very basic technologies... MRI is probably the most technically intensive field in radiology.
Here is what you need to understand as far as physics goes in order to understand MRI at the functional level of a radiologist:
1) You need to know what nuclear spin is
2) You need to know how an MRI machine manipulates nuclear spin
3) You need to know what T1 and T2 relaxation is
4) You need to memorize the basic T1/T2 relaxation times are for different tissues (i.e. fat, white matter, gray matter, bone, blood, etc)
5) You need to understand how to choose TE (echo time) and TR (repetition time) in order to manipulate T1/T2 times to get the best contrast.
6) You need to understand how SNR (signal to noise ratio) and CNR (contrast to noise ratio) depends on slice thickness, # of phase encodes, # of readout gradients, # of averages, etc.
7) You need to understand the key differences between the pulse sequences roughly characterized as spin echo and gradient echo (there are many others, but most of the others rely on modified spin/grad echo profiles)
Once you understand those key concepts, which you can learn in one or 2 days, then you are ready to learn about how the specific MRI machine works. Usually the RT does all of this stuff, but you should know some basics like:
1) How to call up a new scan on the machine
2) The different parameters you need to choose with each different type of scan (i.e. diffusion imaging uses a diffusion coefficient parameter, b); Single shot EPI is critically dependent on the number of phase encodes per acquisition. In other words, different scans require different selective weighting of the same parameters.
3) How to manipulate the table with optical guiding to get to a specified body centered position in the magnet. In other words, if you are trying to image the lower right abdominal quadrant, you need to figure out how to get the patient precisely in the middle of the magnet bore (field homogeneity is critical).
4) How to shim the gradient coils and do other prep work
After you understand all that, the real work of the rads begins. 99% of rads has NOTHING to do with nuclear spin or pulse sequences. You need to understand the pros/cons of each different pulse sequence, but you definitely do NOT need to understand how each pulse sequence acquires an image (i.e. K space encoding, tagged spins for MRA, etc).
Like I said above, give me 3 days with you and I can teach you all the stuff listed above. Its not very hard; heck you dont even have to do any real math to understand it if you dont want (although math helps). Now, even if you know how to do all that stuff, you wont know how to interpret an MRI correctly.
Only rads that do heavy intense research into developing new MRI pulse sequences need to go into the heavy physics behind MRI. For the every day radiologist, the topics I showed above would be perfectly sufficient from a physics standpoint. After you understand that, you need to spend every waking moment looking at scans and getting used to how different tissues look in normal and diseased states. None of that work needs any kind of physics background really.
To work as a radiologist, you definitely dont need to know how to derive equations like Bloch's using diff equations or anythign like that. If you want greater understanding, it helps but certainly the vast majority of radiologists dont even know how to solve PDEs, much less derive the basic fundamental physical theories of MRI.
No calculus required for the work that radiologists do. Leave that stuff to the physics gurus who are the people who actually develop new MRI methods.
