The overall course is broken into 3 sections:
- basic physics of magnetic resonance imaging: excitation, relaxation, gradients, and contrast
- some applied details to think of when scanning people: safety, distortion, parallel imaging for speed
- finally, specific fMRI details: neurohemodynamic coupling, different kinds of contrast, signal-to-noise vs. contrast-to-noise ratio, and experiment design.
This introduction section isn’t part of any of those 3. The goal here is just reminders about physics you once saw, or maybe introductions to physics you haven’t seen yet. There are 2 intro lecture videos — one to remind us of what we know about nuclei, magnets, and resonance, and then a second video that introduces the concept of precession and helps us wrestle with conceptualizing what single nuclei are doing versus what a whole collection of nuclei is doing.
MRI stands for Magnetic Resonance Imaging. When the technology was first developed, it was sometimes called Nuclear Magnetic Resonance Imaging, because the things that are doing the resonating in the magnet, to produce the image, are the nuclei of atoms. NMR (nuclear magnetic resonance) was already an established technique for studying molecular structure, before folks figured out how to use it from imaging in the 1970s and it became a medical imaging technology in the 1980s. However, the word “nuclear” evokes thoughts of high-energy radiation and nuclear weapons, so to do a better job of communicating the fact that MRI is a relatively low-energy and safe technique (safer than Xray!), the N was dropped from the name.
Exercises
Topic 1: Periodic table
1.1. What is the atomic number of uranium?
1.2 What additional information do you need about an atom of uranium before you can tell me its atomic mass?
Topic 2: Gauss vs. Tesla
2.1. A refrigerator magnet has a field strength of 50 Gauss. What is this in Tesla?
2.2. A rare earth magnet you bought at the hardware store has a field strength of 2,500 Gauss. How many Tesla is it?
Topic 3: Electromagnetic radiation — energy, frequency and wavelength.
3.1. What is the frequency of electromagnetic radiation with a wavelength of 1 meter?
3.2. What is the frequency of EM radiation with a wavelength of 1 micron?
3.3. Which of the 2 photons (3.1 or 3.2) has higher energy?
Topic: 4 Summary
4. Doodle. Draw some kind of picture that combines these 3 ideas: nuclei, magnets, and resonance.
If you want 3 minutes of fun watching, here’s a review of force, torque, and angular momentum from Veritasium:
For the rest of the intro, here are 2 ways of thinking about the precession of magnetic moments in static magnetic fields. I call it “Reconciling the classical mechanical and quantum mechanical pictures of precession of protons in static magnetic fields”, and I think it’s really fun to see how you can get the same answer for resonant frequency from two completely different perspectives.
Here’s the classical picture, a spinning top that starts precessing when gravity tries to pull it down.
And here’s the quantum picture, a spin-1/2 particle making a transition from a high-energy state to a low-energy state
Exercises
Topic 5. Gyromagnetic ratio.
5.1 Describe in your own words the gyromagnetic ratio
5.2. What is the resonant frequency of a proton at 3.0 Tesla?
5.3. What is the resonant frequency of a proton at 7.0 Tesla?
5.4. What is the resonant frequency of a proton at 10.5 Tesla?
5.5. We have spent a lot of time and money solving the engineering (and subject comfort) problems associated with using bigger and bigger magnets. Suggest 1 or 2 things we might accomplish by using bigger magnets, and 1 or 2 problems we might encounter along the way.
Answer key
Here is the answer key for the exercises in this section.
