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T2 Mapping · Exercise 1

The best echo time for WM/GM contrast

  1. a. Using Figure 3.3, determine the approximate optimal echo time for T2 contrast between white matter and gray matter.
  2. b. Repeat for the T2* signal curves.
  3. c. Observe Figure 3.1, which shows the signal at different TE values and the corresponding T2 map. In practice, which TE out of these four images would you choose for a T2-weighted image and explain why that value coincides or doesn’t with the optimal TE you found above.

a. Optimal TE for T2 contrast

a. Using Figure 3.3, determine the approximate optimal echo time for T2 contrast between white matter and gray matter.

The best contrast is where the two curves are furthest apart.

The WM/GM contrast peaks at TE ≈ 103 ms.

Setting the derivative of the difference of the two curves (Eq. 3.1) to zero:

$$\begin{aligned} &\frac{d}{dTE}\left(e^{-\frac{TE}{T_{2,WM}}} - e^{-\frac{TE}{T_{2,GM}}}\right) = 0 \\ &\Rightarrow\; TE_{best} = \frac{T_{2,WM}\,T_{2,GM}}{T_{2,WM}-T_{2,GM}}\ln\frac{T_{2,WM}}{T_{2,GM}} \end{aligned}$$

b. Optimal TE for T2* contrast

b. Repeat for the T2* signal curves.

The WM/GM contrast peaks at TE ≈ 57 ms.

The same formula, with the T2* values. T2* decay is faster, so the best TE is shorter, and the two tissues’ values differ more (by 40% of GM’s, against 14% for T2), so the contrast is larger.

c. Which TE in practice?

c. Which TE out of these four images would you choose for a T2-weighted image? Does it coincide with the optimal TE?

TE = 128 ms: the closest of the four to the optimum (≈ 103 ms), with 97% of the best WM/GM contrast.

c. Close to the optimum, not on it

c. Explain why that value coincides or doesn’t with the optimal TE you found above.

  • Flat peak: 128 ms keeps 97% of the best contrast. Only 4 of the echoes are shown; 128 ms is the nearest.
  • 12.8 ms: little decay, mostly proton-density weighted. 256 and 384 ms: less contrast, and only 10% and 3% of the signal left.
  • The optimum depends on the tissues’ T2 (and the field strength): 103 ms is for Figure 3.3’s values.

Exercise 1: answers

PartAnswer
aBest T2 contrast at TE ≈ 103 ms
bBest T2* contrast at TE ≈ 57 ms (shorter, and a larger contrast)
cTE = 128 ms, the closest of the four to the optimum: 97% of the best contrast, as the peak is flat

Questions: github.com/qMRLab/mooc/discussions

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