Synopsis

Keywords: Data Acquisition, Pulse Sequence Design, SSFP, susceptibility

The behaviour of magnetisation under RF spoiling is typically considered to be pseudorandom from TR to TR. Here we describe a model for the coherent underlying phase behaviour which we exploit in a new acquisition strategy. We propose this as an SNR-efficient and motion-robust alternative to multi-echo spoiled gradient echo acquisitions.

Introduction

In this work, we use quadratic RF spoiling to give a short-TR alternative to a traditional multi-echo RF- and gradient-spoiled gradient echo (SPGR) sequence. We hypothesised that the inherent signal averaging in the proposed approach would make it robust to artifacts when imaging an area such as the brainstem, which usually suffers from transient phase artifacts from pulsatile motion.

Theory

Gradient spoiling and k-space aliasing
At short TRs and in the absence of gradient spoiling, balanced steady state free precession (bSSFP) sequences have a characteristic periodic off-resonance profile resulting in banding artifacts. By introducing a large unbalanced gradient within the TR, the frequency variation becomes compressed in space until the bands are no longer visible because they are confined to a single voxel (Figure 1). In k-space, these repeating banding patterns correspond to a series of evenly-spaced signals (S_F) that constitute the configuration states (F-states) in the extended phase graph formalism. By careful choice of the unbalanced gradient area, the signal components from higher order F-states can be pushed to a specific location in k-space (k-space aliasing¹, Figure 1).

Linear phase cycling
One common method for controlling banding artifacts (e.g., in bSSFP) is to shift them across an image with a linear phase cycling scheme. Here, the nth RF pulse has phase $$$\phi_n=n\phi_{lin}$$$. To obtain a band-free image, a series of images can be acquired with different $$$\phi_{lin}$$$ and combined via e.g. sum-of-squares². In k-space this is equivalent to rotating each F-state signal (S_F) by a constant term: $$$e^{iF\phi_{lin}}$$$.

Quadratic phase cycling (RF spoiling)
Rather than linear phase cycling, quadratic phase cycling (RF spoiling) can be employed, with the nth RF pulse having phase $$$\phi_n=0.5\phi_{quad}n^2$$$. This has the effect of shifting the off-resonance profile from one TR to the next. In k-space, this is equivalent to a phase term for S_F which increments with each RF pulse: $$$e^{inF\phi_{quad}}$$$.

An important feature of quadratic series is that they are N-periodic, where N=2π/$$$\phi_{quad}$$$ ^3,4. Provided N is an integer the off-resonance profile is consistent after every Nth RF pulse. Figure 2 demonstrates the magnetisation behaviour for different N-periodic experiments, where N=120, N=12 (used in this work), N=2 (FEMR⁵), and N=1 (bSSFP).

Phase dependency in RF-spoiled sequences
At low flip angles and short-TRs, the magnitude of each F-state signal in an RF-spoiled sequence can be described as follows³: $$M_F(TE)=e^{-(TE+F\cdot TR)/T_2^*}sin\alpha\frac{1-e^{-TR/T_1}}{1-(cos\alpha) e^{-TR/T_1}}\tag1$$ Incorporating local off-resonance ($$$\omega$$$), the signal from each F-state at TE is given by: $$S_F(TE)=M_F(TE)e^{i\omega(TE+F{\cdot}TR)}\tag2$$ The measured signal in the nth TR is then the sum across all F-states after incorporating RF phase cycling: $$S(TE,n)=\sum_{F} S_F(TE)e^{iF(n\phi_{quad}+\phi_{lin})}\tag3$$ $$=e^{i\omega TE}\sum_{F}M_F(TE)e^{iF(\phi_{lin}+\omega TR)}e^{inF\phi_{quad}}\tag4$$ The phase terms in Equation 4 can be grouped into: i) a global term, $$$e^{i{\omega}TE}$$$ ; ii) a constant linear term, $$$e^{iF(\phi_{lin}+{\omega}TR)}$$$, causing a constant spatial shift in the off-resonance profile; and iii) an n-dependent linear term in F, $$$e^{inF\phi_{quad}}$$$, which causes a per-TR spatial shift in the off-resonance profile. From here onwards, we assume $$$\phi_{lin}$$$=0° for simplicity.

Equation 4 allows us to isolate N separate F-state signals due to their relative phase evolution across N measurements. Meanwhile, we can set the exact amount of gradient spoiling needed to ensure that only N or fewer states remain within the acquired k-space. This can all be determined a priori. A schematic of the acquisition and reconstruction scheme is shown in Figure 3.

The signal magnitude from higher order F-states is more heavily T₂* weighted, and the phase is more susceptibility weighted (reflected in the F$$$\cdot$$$TR terms in Equations 1-2, Figure 3). For carefully chosen TR and TE, the S_F signals therefore have relative weightings equivalent to the echo signals obtained from a long-TR multi-echo SPGR sequence. However, there is inherent averaging across the N-periodic states which may increase its robustness to transient phase fluctuations.

Methods

We performed an experiment on a 7T Siemens MAGNETOM Terra (Erlangen, Germany) with a 1Tx/32Rx head coil (Nova Medical, Wilmington, MA, USA). The proposed k-space-aliased SPGR sequence (kaSPGR¹) was implemented with $$$\phi_{quad}$$$=30° to give a 12-periodic experiment with 7 directly measured F-states (S₀ to S₆), and compared to a matched multi-echo SPGR sequence with a longer TR and 7 TEs.

In a first healthy volunteer we conducted a single-slice 2D experiment, where the flip angle was varied for each sequence to measure SNR efficiency. In two more healthy volunteers, we conducted 3D experiments covering a 2cm axial section across the brainstem.

Results and Discussion

An SNR efficiency comparison is shown in Figure 4 for the 2D experiment with various flip angles. All images shown have an effective TE=28ms. kaSPGR appears to be more SNR efficient at the optimal flip angle (10-15°) compared to the equivalent long-TR SPGR (30-35°).

Figure 5 shows reconstructed 3D data, highlighting iron-rich brainstem structures which are more conspicuous on kaSPGR images. We hypothesise that the proposed approach reduces the sensitivity to transient phase fluctuation caused by cardiac pulsation, due to averaging across N-periodic states during reconstruction.

Conclusions

The inherent phase behaviour of magnetisation under RF spoiling can be exploited to give an SNR-efficient and motion-robust alternative to multi-echo SPGR experiments. This could enable higher resolution T₂*- or susceptibility-weighted imaging in areas such as the brainstem, where pulsatile motion can be otherwise problematic.

Acknowledgements

The authors thank Dr Iulius Dragonu (Siemens Healthineers) for providing support for sequence development, and the core team at the LoCUS 7T facility for their support with scanning. PJL acknowledges generous support from The Wellcome Trust (220473/Z/20/Z), The Edmond J Safra Foundation, UK Dementia Research Institute, NIHR Imperial Biomedical Research Centre, and National Institutes of Health (R01EB002524).