5 Relaxation
Discussion of “relaxation” considers the different mechanisms by which protons give their energy back to the environment after excitation. Different relaxation constants in different voxels leads to different signal intensities in different voxels, which is where we get our image contrast from.
First, a brief reminder of exponential decay, in case it’s been a while since you’ve seen the math.
[Things I want to fix: brief description of what e is!]
Exercises
1. Plot the following 2 equations on the same graph: M = 3e-t/50 and M = 3e-t/100.
Now, we’ll move on to talking about three relaxation time constants, T1, T2, and T2*. Our first topic is T2 and T2*, which describe signal decay on the transverse plane.
[Things I want to fix: marks to indicate which axis is which before/after rotation; arrows actually shrink over time.]
Next up is T1, the spin-lattice time constant that describes how quickly our signal returns to equilibrium after excitation (longitudinal relaxation). T1 is generally much longer than T2. I spent a really long time confused about how T1 and T2 could be different, because I was picturing the vector M in my head: when it rotates away from z, the projection to the transverse plane is MT and the projection to the z-axis is Mz. As it rotates back up, MT shrinks and Mz grows, right? At the same rate, right? And the answer is nope: MT decays much faster than Mz recovers. This is because Mz recovers as spins flip back to the low energy state, but MT decays because spins are getting out of phase with each other, regardless of which energy state they’re in. So the classical flip angle picture lets us down, and we need to consider T2 separately from T1.
Exercises
2. Plot the following 2 equations on the same graph: M = 3e-t/50 and M = 3 – 6e-t/100. Note that this is almost identical to the previous exercise, except this time we’re mimicking the behavior of an inversion recovery experiment.
3. For now, this is just a conceptual question about how a person might go about fitting data to discover time constants. If you ran a basic gradient echo EPI experiment, with a really long TR (so you knew that the magnetization was fully relaxed before each excitation, so you knew that your image intensity values reflected only T2 or T2* decay properties, how would you take these numbers and determine the value of T2*?
| TE | 5 | 10 | 15 | 20 | 25 | 30 |
| Intensity, Voxel 1 | 78 | 61 | 47 | 37 | 29 | 22 |
| Intensity, Voxel 2 | 61 | 37 | 22 | 14 | 8 | 4 |
4. How would you determine whether or not the 2 voxels in the table above had the same proton density?
Exercises