What you’ll be able to do after this lesson
- Explain why a 90° pulse is the wrong choice in a fast gradient echo sequence
- Use the Ernst angle relationship to reason about flip angle, TR and T1 together
- Predict how raising or lowering flip angle changes contrast on a spoiled GRE
- Recognise flip angle as the T1 contrast lever when TR is fixed and short
Why 90° stops being optimal
In spin echo, the excitation is 90° and there is little to discuss: TR is long enough that magnetisation largely recovers between excitations, so tipping everything into the transverse plane is simply the best use of it.
Gradient echo changes the arithmetic completely. Its whole point is a very short TR — a few milliseconds to a few tens of milliseconds. There is no time for recovery. So consider what a 90° pulse does under those conditions: it dumps all the longitudinal magnetisation into the transverse plane, and with TR far shorter than T1, almost none of it comes back before the next pulse arrives. The second excitation finds nothing to tip, the third less still. The signal saturates — collapses after the first few excitations and stays collapsed.
A small flip angle avoids this. Tip by 15° and you convert only a small fraction (sin 15° ≈ 0.26) into transverse signal, but you leave cos 15° ≈ 0.97 of the longitudinal magnetisation standing. Almost nothing needs to recover, so the next pulse finds nearly as much as the last one did. A steady state is established in which every excitation yields a modest but sustainable signal.
Small and sustainable beats large and extinct. That is the trade, and the optimum has a name.
The Ernst angle
The flip angle giving maximum steady-state signal for a spoiled gradient echo is:
α_E = arccos( e^(−TR/T1) )
Three worked examples make the behaviour concrete (angles as given in Elster’s treatment):
- T1 = 800 ms, TR = 3000 ms → α_E ≈ 89°. With TR much longer than T1, the optimum is essentially 90° — the spin echo case.
- T1 = 800 ms, TR = 100 ms → α_E ≈ 28°.
- T1 = 800 ms, TR = 30 ms → α_E ≈ 16°.
Put numbers on that last one using the spoiled gradient echo steady-state expression, S ∝ sin α (1 − E₁) / (1 − E₁ cos α) with E₁ = e^(−TR/T1). At the Ernst angle the signal is about 0.137 M0; at 90° it is (1 − E₁) = about 0.037 M0. The small angle is worth roughly three and a half to four times the signal of the large one.
That is why fast gradient echo imaging is possible at all. Run the same sequence at 90° and you throw away three-quarters of the available signal for nothing.
A note on a widely reproduced figure: some references quote about 0.009 M0 for the 90° case here and a fifteen-fold advantage. That does not follow from the steady-state equation above, which gives 0.037 M0 at 90° for TR/T1 = 30/800. The direction of the argument is unaffected — small angles win, and win decisively — but the multiplier is closer to four than to fifteen.
Three things follow that are worth carrying:
- The Ernst angle rises with TR and falls with T1. Shorter TR or longer T1 means less recovery, so a gentler tip.
- The optimum is tissue-specific, because T1 is. There is no single Ernst angle for an image containing fat, muscle and fluid — the scanner’s suggested angle is optimised for a representative T1, not for everything.
- The peak is broad. The signal-versus-angle curve is flat-ish near its maximum, so being a few degrees off costs little. Being far off — 90° at short TR — costs enormously.
Flip angle as a contrast lever
Ernst tells you where signal is maximised. It does not tell you where contrast is best, and those are different questions.
Because the optimum angle depends on T1, the flip angle you choose determines which tissues are favoured:
- Large flip angle (say 60–90° at short TR) drives longer-T1 tissues into saturation while short-T1 tissue, which recovers fastest, is comparatively spared. The result is increased T1 weighting — and lower overall signal.
- Small flip angle (say 5–15°) saturates nothing much. T1 differences barely express themselves, and the image drifts towards proton density or, at long TE, T2* character.
So in a spoiled gradient echo with TR pinned short by a breath-hold, flip angle is your T1 contrast control. This is the fourth member of the Excite–Wait family and the one most specific to the gradient echo world: in spin echo you reach for TR, in gradient echo you reach for α.
Two caveats keep this honest. First, all of the above assumes spoiled gradient echo — where residual transverse magnetisation is deliberately destroyed each TR (Siemens FLASH, GE SPGR, Philips T1-FFE). In balanced steady-state sequences (TrueFISP / FIESTA / balanced FFE) transverse magnetisation is preserved and recycled, the signal behaviour is different, contrast tracks the T2/T1 ratio, and Ernst-angle reasoning does not transfer.
Second, larger flip angles mean more transmitted RF energy. Where that becomes a limit, and how it is managed, is a safety matter governed by local policy and the site’s safety guides — not something to work around by editing a patient’s recorded weight.
At the console
A dynamic post-contrast liver study runs a 3D spoiled gradient echo in a breath-hold. The registrar, reasoning from spin echo, suggests raising the flip angle to 60° “to get more T1 weighting for the enhancement”.
The instinct is half right and the execution would be wrong. More T1 weighting is indeed what post-contrast imaging wants — gadolinium works by shortening T1, and you want that shortening to show. But at a TR of a few milliseconds, 60° is far past the Ernst angle for liver, and the sequence would saturate heavily. You would gain T1 weighting and lose so much signal that the net conspicuity of enhancement falls. Vendor protocols for this kind of sequence typically sit at modest angles for exactly this reason. If more T1 weighting is genuinely needed, the change belongs to the protocol as a whole — reviewed against phantom or volunteer images, not adjusted mid-list.
Second case, the diagnostic use of the same idea. A time-of-flight MRA of the circle of Willis relies on inflowing blood that has not been repeatedly excited being bright against stationary tissue that has been saturated by rapid, relatively large-angle excitation. Understanding that the background is dark because it is deliberately driven into saturation explains two things at once: why the slab must be thin enough that blood does not saturate as it traverses it, and why slow flow in the distal slab loses conspicuity. Flip angle here is not tuned for maximum signal — it is tuned to suppress the stationary background.
Check yourself
Your gradient echo runs at TR 5 ms and the tissue of interest has T1 around 1000 ms. Reason qualitatively: is the Ernst angle closer to 5°, 30°, or 60°? Then, without changing TR, describe what happens to (a) overall signal and (b) T1 contrast if you double whatever angle you are using. Finally, explain why none of this reasoning applies to a balanced SSFP cine.
This is a private prompt. Nothing you write is stored or assessed.
Key takeaways
- At short TR there is no time to recover, so a 90° pulse saturates the signal. Small angles preserve longitudinal magnetisation and sustain a steady state.
- The Ernst angle, α_E = arccos(e^(−TR/T1)), maximises steady-state signal. It rises with TR, falls with T1, and approaches 90° only when TR >> T1.
- The optimum is tissue-specific and the peak is broad — small errors are cheap, large ones are not.
- In spoiled gradient echo, flip angle is the T1 contrast lever: larger angle = more T1 weighting, less signal; smaller angle = more PD/T2* character.
- None of this transfers to balanced SSFP, where transverse magnetisation is preserved and contrast tracks T2/T1.
References
- Ernst RR, Anderson WA. Application of Fourier transform spectroscopy to magnetic resonance. Review of Scientific Instruments. 1966;37(1):93–102 https://doi.org/10.1063/1.1719961
- Elster AD. Questions and Answers in MRI — ‘Ernst angle’ / optimal flip angle https://mriquestions.com/optimal-flip-angle.html
- Bernstein MA, King KF, Zhou XJ. Handbook of MRI Pulse Sequences. Elsevier Academic Press, 2004 — §14.1, spoiled gradient echo steady state
- McRobbie DW, Moore EA, Graves MJ, Prince MR. MRI from Picture to Proton, 3rd ed. Cambridge University Press, 2017 — ch. 12, gradient echo steady states
- Radiopaedia. Ernst angle (physics article) https://radiopaedia.org/articles/ernst-angle