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 from equilibrium (z), what is Mz and what is MT?
5.3. After a 60 degree rotation from z, what is Mz and what is MT?
What next? You’ve excited your sample; now you need to turn off the power and listen for the energy that comes back out of the sample. The details of the frequency and amplitude of that signal will eventually give us an image. Right now, however, we’re just conceptualizing what it means to “listen” for the “signal”.
Exercises
Topic 6. Transmit vs. receive in RF coils
6.1 Was the coil illustrated in the last video a “transceiver”, which is a RF coil that is used in both transmit mode and in receive mode, or was it a dedicated transmit coil, or was it a dedicated receive coil?
6.2 At this point, the lectures have not provided many hints for why you might choose to use a tranceiver vs. a pair of transmit and receive coils to run an experiment, but take a minute to offer an educated guess about one advantage of using a transceive coil and one advantage of using separate coils for transmit and receive.
Finally, we have the idea of linewidth. In our day-to-day existence, we talk about linewidth as a measure of how good our shim is (shimming is the process of trying to get the magnetic field in the magnet back to something reasonably uniform, after it gets messed up by the fact that we put a sample in there). A broad linewidth means a fast signal decay; a narrow linewidth means our signal lasts longer. Linewidth and signal deday are directly related to each other by the Fourier transform, which is something we will all know and love before too long. But first … linewidth:
Exercises
Topic 7: Destructive interference
7.1 If you add up 2 signals, each with an amplitude of 10 units, which are oscillating at exactly 127.304509 MHz and have exactly the same phase, what will be the amplitude and frequency of the resulting sum?
7.2 If you add up 2 signals, each with an amplitude of 10 units, which are oscillating at exactly 127.304509 MHz and have exactly the opposite phases, what will be the amplitude and frequency of the resulting sum (the current induced in my receive coil)?
7.3 If you add up 20 signals, all of which start out at the same phase, but each of which is oscillating at a slightly different frequency near 127.304500 MHz, but not exactly at 127.304500 MHz, how would you describe the resulting signal induced in my receive coil?
Exercises
Here is an answer key for the Excitation exercises.