Exercise 2-2 · T2 Mapping

Quantitative MRI mOOC

T₂ Mapping · Exercise 2-2

Stimulated echoes

Three pulses, an imperfect 180°, and why every echo of a train mixes spin and stimulated echoes

Three pulses: where does the extra echo come from?
Imperfect 180°: what does a refocusing pulse below 180° add?
Even spacing: why do spin and stimulated echoes coincide in a train?

A stimulated echo

(a) Delay the third pulse. Which marker moves with it, and by how much?

Three 90° pulses: the first on its own at t = 0, then one per arrow press, whenever you like (spaced out, say near 20 and 50 ms, the echoes stand apart). Markers show every echo they will make: spin echoes SE, and the stimulated echo STE.

Pulse sequence

Signal

Spins Fan

Click and drag to reorient · V switches the view.

Three 90° pulses, the last two fired by the arrow keys whenever the class likes; pulses near 20 and 50 ms keep the echoes apart (the fan is a bit slower on this slide, ±200° by 10 ms, and the clock runs at 4 ms per second). After the second 90°, part of the fanned-out signal is tipped onto z, where it keeps a record of each spin’s phase (as a pattern of Mz) and only relaxes with T1. The third 90° brings it back, mirrored, and it refocuses τ after that pulse, where τ is the gap between the first two: the stimulated echo (STE). It is at most half of the signal. The spin echoes (SE) come at twice the spacings: 2·t2 (pulses 1 and 2), 2·t3 − 2·t2 (refocused again by the third pulse), 2·t3 (pulses 1 and 3). Try waiting longer before the third pulse: the STE moves with it, always τ later, and barely shrinks (T1 = 1000 ms), while the spin echoes fade with T2 = 80 ms.

What we saw · 1

Three pulses also make a stimulated echo

It comes τ after the third pulse: delay that pulse and the STE follows it, while the spin echoes move twice as far.
It waits along z, relaxing with T₁; with 90° pulses it carries up to half the signal.

An imperfect 180° is part 180°, part 90°

(b) Lower the angle from 180°. What appears, and from which pulse on?

Set the angle, press Play, then fire two refocusing pulses at that angle, whenever you like. At 180° only spin echoes come back; lower the angle and stimulated echoes appear.

Refocusing angle α °

like a 180° (refocused) · sin²(α/2)

like a 0° (left alone) · cos²(α/2)

like a 90° (tipped to z) · ½ sin α

Pulse sequence

Signal

Spins Fan

Click and drag to reorient · V switches the view.

What we saw · 2

An imperfect 180° is part 180°, part 90°

Its 90° part parks signal along z; the next pulse brings it back as a stimulated echo.
Only a perfect 180° gives pure spin echoes.

Evenly spaced: the echoes line up

Three 120° pulses. Press Pulses at 10, 30, 50 ms to space them evenly: the stimulated echoes land on the spin echoes (SE+STE). Or press Play and time them yourself. Exercise 2-3: measuring T₂ with an echo train →

Pulse sequence

Signal

Spins Fan

Click and drag to reorient · V switches the view.

What we saw · 3

Evenly spaced, the echoes coincide

In an echo train, each echo mixes spin and stimulated echoes.
Their parts can add or partly cancel.

Lessons

Stimulated echoes

Stimulated echo: waits along z (T₁), comes τ after the third pulse.
Imperfect 180° = part 180°, part 90°: stimulated echoes.
Evenly spaced pulses: every echo mixes spin and stimulated echoes.

Exercise 2-3: measuring T₂ with an echo train →