Quantitative MRI mOOCT1 Mapping · Exercise 2
Variable flip angle: the Ernst angle and contrast
- a. Using the Plotly figure in the VFA section that displays the signal curves for white matter, gray matter, and CSF, determine the Ernst angle for the following: white matter and a TR of 15 ms, gray matter for a TR of 50 ms, and CSF for a TR of 140 ms.
- b. Calculate the Ernst angle for these tissues and TRs with Eq. 2.6. Are they in agreement with the values you estimated with the interactive figure?
- c. It’s been shown (Deoni, Rutt, and Peters 2003) that the optimal flip angles for a two-measurement VFA T1 mapping imaging protocol are located at approximately 70% of the Ernst angle. Find the optimal flip angles to image each tissue above using their respective TRs.*
- d. For a TR of 30 ms, which flip angle would result in the best contrast between white matter and grey matter in an SPGR image?
* Deoni et al. place the two angles where the signal is about 71% of the Ernst signal, one on each side of the Ernst angle. Part c is solved that way.
a. Read the Ernst angles off Figure 2.8
a. Using the Plotly figure in the VFA section that displays the signal curves for white matter, gray matter, and CSF, determine the Ernst angle for the following: white matter and a TR of 15 ms, gray matter for a TR of 50 ms, and CSF for a TR of 140 ms.
Drag the slider to each TR, hover over the peak of the matching curve, and type your readings here. They carry over to the next slides.
| Tissue | TR (ms) | Ernst angle (°) |
|---|---|---|
| White matter | 15 | |
| Grey matter | 50 | |
| CSF | 140 |
b. Compare with Eq. 2.6
b. Calculate the Ernst angle for these tissues and TRs with Eq. 2.6. Are they in agreement with the values you estimated with the interactive figure?
| Tissue | TR (ms) | T1 (ms) | Read (°) | Eq. 2.6 | Diff. |
|---|---|---|---|---|---|
| WM | 15 | 900 | |||
| GM | 50 | 1500 | |||
| CSF | 140 | 4000 |
Yes, within the figure’s 1° sampling. GM and CSF share an angle because Eq. 2.6 depends only on TR/T1: 0.033 and 0.035.
c. Optimal flip angles for two-point VFA
c. It’s been shown (Deoni, Rutt, and Peters 2003) that the optimal flip angles for a two-measurement VFA T1 mapping imaging protocol are located at approximately 70% of the Ernst angle. Find the optimal flip angles to image each tissue above using their respective TRs.
Deoni et al.: two angles at 71% of the Ernst signal, one each side of θE.
d. Best WM/GM contrast at TR = 30 ms
d. For a TR of 30 ms, which flip angle would result in the best contrast between white matter and grey matter in an SPGR image?
Set the slider to 30 ms and compare the WM and GM curves.
d. The WM − GM signal difference
Signal difference from Eq. 2.5 for WM (T1 = 900 ms) and GM (1500 ms):
| TR (ms) |
Exercise 2: answers
| Part | Answer |
|---|---|
| a | Ernst angles read from Figure 2.8: ≈ 10° (WM, TR 15 ms), 15° (GM, TR 50 ms), 15° (CSF, TR 140 ms) |
| b | Eq. 2.6: 10.4°, 14.7°, 15.1°, in agreement within the figure’s 1° sampling |
| c | Angle pairs at 71% of the Ernst signal: WM 4° / 25°, GM 6° / 34°, CSF 6° / 35° |
| d | Best WM/GM contrast at TR 30 ms: ≈ 22° |