Exercise 3 · T1 Mapping

Quantitative MRI mOOC

T₁ Mapping · Exercise 3

Inversion recovery at 1.5 T with a fixed TR of 3 s

a. The IR signal curves for WM/GM/CSF in Figure 2.2^* were simulated for 3T T₁ tissue values. Using Binder and the notebook that was used to generate that figure^*, regenerate that figure for T₁ values at 1.5 T (WM ~ 650 ms and GM ~ 1200 ms as reported by (Wright et al. 2008)). Assume the CSF value does not change.
b. An IR T₁ mapping pulse sequence that a previous student developed and is available at the MRI scanner has a fixed TR of 3 seconds. Could you use a data analysis pipeline that only has the long-TR IR T₁ fitting option available to map T₁ in WM, at 1.5T and/or 3T? Show this visually via simulations.
c. Are there any inversion times you should avoid using when designing an IR T₁ mapping protocol at 1.5T when using this TR? If so, demonstrate why and which one(s) using modified code from one of these notebook figures.

^* The book cites Figure 2.3 and “that blog post”; the WM/GM/CSF curves are Figure 2.2. The simulations on the next slides run live in this page with qmrust, the Rust/WebAssembly port of qMRLab.

a. Regenerate Figure 2.2 at 1.5 T (WM ~650 ms, GM ~1200 ms)

From the IR blog notebook (Octave + qMRLab) that generated Figure 2.2’s data. Edit it, then ▶ Run (Ctrl/⌘+Enter): qmrust recomputes it here.

% All times are in seconds
params.TR = 5.0;
params.TI = linspace(0.001, params.TR, 1000);
params.TE = 0.004;
params.T2 = 0.040;
params.EXC_FA = 90;  % Excitation flip angle
params.INV_FA = 180; % Inversion flip angle
params.signalConstant = 1;

% Option 4: long TR approximation (Eq. 2.3)

% White matter
params.T1 = 0.900; % in seconds
signal_WM = inversion_recovery.analytical_solution(params, 'GRE-IR', 4);

% Grey matter
params.T1 = 1.500;  % in seconds
signal_GM = inversion_recovery.analytical_solution(params, 'GRE-IR', 4);

% CSF
params.T1 = 4.000;  % in seconds
signal_CSF = inversion_recovery.analytical_solution(params, 'GRE-IR', 4);

b. Long-TR fitting with TR = 3 s

b. Could you use a data analysis pipeline that only has the long-TR IR T₁ fitting option available to map T₁ in WM, at 1.5T and/or 3T?

WM T₁ (ms)
TR (ms)

c. TIs to avoid: Figure 2.6

c. Are there any inversion times you should avoid using when designing an IR T₁ mapping protocol at 1.5T when using this TR?

Avoid TIs at the null of the tissue you want to measure: magnitude images there are dominated by Rician noise, which can negatively impact the fit under low SNR. For WM at 1.5 T with TR = 3 s, that is TI ≈ 444 ms.

The slide opens on Figure 2.6 as the book publishes it: Monte Carlo simulations for T1 = 900 ms with six TIs linearly spaced up to TR; the insets give the mean and STD of the fitted T1 against TR. Click 1: the slider moves to TR = 2900 ms, where the second TI (TR/5 = 580 ms) lands on the null (589 ms). Both are circled: that TI on the signal curve, and the STD of the fitted T1 in the inset, which blips up there (about 90 ms, against about 70–75 ms for nearby TRs). The simulations are noisy, so other TRs wobble too; drag the slider around 2600–3000 ms to show it. Click 2: the answer, from the book's text: avoid TIs where the signal of the tissue of interest is nulled. For WM at 1.5 T (650 ms) with TR = 3 s, the null is at 444 ms (Eq. 2.2; 451 ms with the long-TR approximation, as in part a).

Exercise 3: answers

Part	Answer
a	At 1.5 T the WM and GM nulls move earlier: ≈ 451 ms (WM) and 832 ms (GM); CSF is unchanged (2773 ms)
b	With TR = 3 s the long-TR fit underestimates WM T₁ by ≈ 1.7% at 1.5 T and ≈ 5.8% at 3 T: fine at 1.5 T, biased at 3 T
c	Avoid TIs at the WM null, ≈ 444 ms at TR = 3 s: Figure 2.6 shows the STD of the fitted T₁ blips up when a TI lands on the null

Simulations and fits in parts a and b: qmrust (Rust/WebAssembly port of qMRLab), running in the browser.

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