07 MRI
Inversion-recovery signal
M_z(TI) = M₀ (1 − 2 e^{−TI/T1} + e^{−TR/T1}). Null when TI = T1 ln 2 (long TR).
Listen
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Simulation
Inversion-recovery signal — Change the numbers; the scene follows.
Where it works
MRI scanner
RF coil
At the RF coil — flip angle, SAR, SNR, receive bandwidth, and the pulse sequence.
Open this machineFormula
Variables
Results
M_z/M_0
Longitudinal magnetisation
-0.0542
TI_null
Null TI (long TR)
173.2868ms
Curve
Explanation
What it means
A 180° pulse inverts M_z; it recovers through zero at TI ≈ T1 ln 2 (0.69 T1) if TR ≫ T1. STIR nulls fat (T1 ~ 250 ms at 1.5 T → TI ~ 150–170 ms). FLAIR nulls CSF (T1 ~ 4000 ms → TI ~ 2000–2500 ms). Magnitude images fold the negative lobe, so the null is a dark band rather than a sign change (unless phase-sensitive IR is used). This is a working relation in MRI physics.
Where it is used
Clinically it sits on the MRI scanner — RF coil. At the RF coil — flip angle, SAR, SNR, receive bandwidth, and the pulse sequence. MRI physics lives in the magnet, the gradient, and the voxel: Larmor, Ernst, diffusion, and SAR. These relations decide whether a sequence is possible, safe, and worth the time.
MRI scanner · Open this machineHow to use it
Enter T1, TI, TR (ms). Read Mz/M0 and the null TI for this T1 (long-TR formula T1 ln 2, plus the finite-TR correction). Fat at 1.5 T: T1=250, TI=160, TR=2000. Change one input and watch the curve and the simulation follow.
Symbols
- T1Longitudinal relaxation250 ms
- TIInversion time160 ms
- TRRepetition time2,000 ms
Worked example
A typical case from the default values: T1 = 250 ms (Longitudinal relaxation); TI = 160 ms (Inversion time); TR = 2,000 ms (Repetition time). Substituting into the relation gives M_z/M_0 = -0.0542; TI_null = 173.2868 ms. These are teaching numbers — align them with your machine.
Typical values give
- M_z/M_0 = -0.0542
- TI_null = 173.2868ms
Where it comes from
The displayed formula is the working relation. M_z(TI) = M₀ (1 − 2 e^{−TI/T1} + e^{−TR/T1}). Null when TI = T1 ln 2 (long TR). Usual reference: McRobbie / Bernstein. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: McRobbie / Bernstein
Assumptions & limits
Perfect 180°, no residual xy, spoiled. Magnitude vs signed is not selected — the calculator reports signed Mz. STIR also has a J-coupling / T2 effect on fat that this 1-D model ignores.
Pitfalls
γ for ¹H is not γ for ¹³C. Ernst angle needs the true T1 at that field, not a 1.5 T table used at 3 T. SAR scales with B₀² and flip² — a 3 T copy of a 1.5 T protocol is not automatically legal. Perfect 180°, no residual xy, spoiled. Magnitude vs signed is not selected — the calculator reports signed Mz. STIR also has a J-coupling / T2 effect on fat that this 1-D model ignores.
Keep this
Name the nucleus and the field before you quote a Larmor frequency. Perfect 180°, no residual xy, spoiled. Magnitude vs signed is not selected — the calculator reports signed Mz. STIR also has a J-coupling / T2 effect on fat that this 1-D model ignores.
In this specialty