1 Excitation
Learning Objectives
The key concepts for today are organized around vocabulary terms we’ll use for the whole course:
- Magnetization (Huettel Ch. 3, “Magnetization of a spin system”).
- Excitation (Huettel Ch 2, “Radiofrequency coils” and Huettel Ch. 3 “Excitation of a Spin System and Signal Reception”).
- Flip Angle (Huettel Ch. 3 “Excitation of a Spin System and Signal Reception” and Fig. 3.17)
- Acquisition (Huettel Ch. 3 “Signal reception” and “Excitation of a Spin System and Signal Reception”)
- Linewidth (no direct analogy to Huettel early chapters).
We open with a short recap of resonance and an answer to the question: why are bigger magnets better?
The first part of the Excitation lecture is the concept of M, the bulk magnetization that is the observable property of an object.
Exercises
Topic 1. Vector sums
1.1 If I add up 3 vectors, all of length 1, and 2 are pointing to the left and 1 is pointing to the right … what direction is the ‘vector sum’ pointing in, and how long is it?
1.2 Now I’m adding up 6 vectors, each is a 45 degree angle away from vertical. Three are pointing up and to the left; three are pointing up and to the right. What direction is the sum of all those vectors pointing in?
Topic 2. Spin isochromat
2.1 What does ‘iso’ refer to in the term ‘spin isochromat’?
2.2 What does ‘chromat’ refer to in the term ‘spin isochromat’?
Next, we briefly consider the construction of RF (radiofrequency) coils and how they interact with your head during an fMRI experiment.
Exercises
Topic 3. Coils vs. antennae
3.1 How is a RF coil similar to a radio stations broadcast tower or your radio’s receive antenna?
3.2 The difference between a radio antennae and a RF coil we use in an experiment is where they’re trying to put the power. A radio station is trying to broadcast signal as far as possible. A RF coil in an MRI experiment is trying to do what?
Topic 4. RF safety
4.1 What happens to the temperature of a wire (a normal wire with resistance) when you run current through it?
4.2 When I do an MRI experiment, my goal is to use a uniform B field throughout your head to excite the spins (promote the protons on water molecules to a high energy state, and put them all in phase, so they will start generating a signal I can use to create an image). However, E fields always come with B fields. Since you are mostly made of salt water, that E field starts a current moving around in you. What happens if I create too much current?
Now we start talking about what happens to the protons in a sample when we put RF energy into a sample. Along the way, I mention the experiment that lead to the discovery of NMR, described in more detail here, and a PhET simulation that lets you explore the physics of excitation in an MRI experiment.
Exercises
Topic 5. Trigonometry
5.1. After M rotates 90 degrees, what is Mz (remaining projection to the longitudinal, or z, axis) and what is MT (projection to the transverse plane)?
5.2. After M rotates 30 degrees fr