Introduction

When EPI fMRI is performed at 7T rapid signal decay in grey matter necessitates short TE for optimum BOLD sensitivity. This can be achieved by minimising the echo-spacing of the EPI readout. However, this is demanding on gradient performance and can lead to significant deviation from the expected k-space trajectory, eddy current formation, mechanical vibration, and consequently stronger Nyquist ghosting. B0 shim is also challenging at 7T with off-resonance effects further amplifying Nyquist ghost levels¹. Ghosts reduce functional sensitivity and specificity by displacing signal from its true position. Where ghosts overlap with the main image, functional sensitivity can be severely reduced if participant motion perturbs the overlapping interference pattern over time.

Methods

In the present work we have combined and developed several existing calibration and reference techniques for Nyquist ghost reduction.

Firstly, on a periodic basis, we perform a robust trajectory measurement² to measure the EPI readout gradient waveform using a gel phantom³. We found stable results (Fig. 1) across different scanning sessions and days. From these data we compute a generalised readout direction Fourier reconstruction matrix⁴ which is applied to ongoing EPI.

Secondly, three conventional alternating-polarity navigator echoes⁵ are acquired at short TE, prior to the main EPI readout. Although alone, at 7T, these provide only partial Nyquist ghost reduction, they can compensate for time-dependent variation occurring with respect to the initial calibration scan, e.g. temperature⁶ or participant motion (such as breathing). For our proposed correction, navigator measurements from an early volume serve as the baseline.

Thirdly, at the start of each functional run we acquire a single volume calibration scan with opposite readout gradient polarity to what is being used to acquire the time series. We follow the approach of Chen and Wyrwicz⁷. Appropriate lines are selected from the calibration volume, and from the first normal polarity volume to reconstruct two volumes formed under solely negative and solely positive gradients respectively, and the 3D phase difference map between the two (Fig. 2). Each on-going EPI image is then reconstructed analogously into pairs of images each with half the target field-of-view (since taking only half the readouts leaves the data two-fold under-sampled). A full-field-of-view image is computed by solving simultaneously, at each location in the half-field-of-view, for the pair of full-FOV voxel values that best fit the under-sampled images, given the phase difference map. This is described in ref. 7, equations 8 and 9, with a caveat that fitting is under-determined where only one of the voxel pair lies within the object. We recast the problem in a linear modelling framework, which can be augmented with Tikhonov regularisation for improved stability. Following their definitions of variables and with our regularisation term $$$\Lambda(x,y)$$$$$\left(\begin{array}{c}EPI_{odd}(x,y)\\ EPI_{even}(x,y)\\ 0\\0\end{array}\right)=\left(\begin{array}{c}\frac{1}{2} & \frac{1}{2}\\ \frac{1}{2}exp(i\theta(x,y)) & -\frac{1}{2}exp(i\theta(x,y-\frac{FOV}{2})) \\ \Lambda(x,y) & 0 \\ 0 & \Lambda(x,y-\frac{FOV}{2})\end{array}\right)\left(\begin{array}{c}\tilde{M}(x,y)\\ \tilde{M}(x,y-\frac{FOV}{2})\end{array}\right)+ \left(\begin{array}{c}\\ \epsilon \\\ \end{array}\right)$$where$$$\Lambda(x,y)=\frac{\lambda}{\sqrt{smooth(\sum_{coil}Regrouped_2Regrouped_2^*)}}$$$, $$$\epsilon$$$ represents an error term in the linear model and $$$smooth()$$$ represents 3D convolution.

In the case of minimal variation in the phase-encoded direction (here anterior-posterior, Fig.2b), the calibration can be collapsed by taking the mean. Without requiring a linear modelling approach, the mean phase (Fig.2a) can then be applied to one of the half-FOV images before recombination with the other giving a simpler reconstruction (referred to as "2D phase correction" below).

The method was implemented in Matlab⁸ using Gadgetron⁹ to enable real-time operation at the scanner.

In vivo data were acquired on a Siemens 7T Terra with the following key parameters: TE=35ms, TR=75ms, 108 x 96 voxels x 96 slices, 2mm isotropic resolution. The same in-house 2D-EPI sequence used to acquire task-free fMRI data was adapted to enable trajectory measurement and negative polarity calibration scan. To investigate the interaction of ghosting levels with gradient requirements¹⁰, two datasets were acquired with different echo-spacing of 530 or 550us respectively.

Results

Figures 3 and 4 demonstrate the inverted polarity pre-calibration measurement even with our simpler 2D phase correction dramatically reduces the ghosting, at both echo-spacings (Figs.3c, 4c).

Discussion

We have observed significantly reduced ghosting levels in 2D-EPI at 7T by measuring and accounting slice-wise for imperfections in gradient performance. Timing and waveform errors are measured via trajectory calibration², which is stable over time and imaging sessions. The session-specific calibration scan provides spatial information about the imperfections. In combination, correcting for both effects greatly reduces the ghosts that manifest in the time series.

The limited benefit of the conventional three navigator echoes may reflect sensitivity to short-term eddy current effects no longer present at the echo time of the EPI readout. However, this information can be beneficial when used to track changes with respect to the time at which the calibration data were acquired.

Our approach to average the 3D phase difference map in the phase encoded direction yields a simpler 2D phase correction that effectively suppresses ghosts. This simpler correction is intrinsically well conditioned and shares a consistent TE with the ongoing data acquisition and is robust against poor shim, unlike previously proposed "blip-off" pre-scans¹¹ which will inherently average across a range of phase dispersion that can lead to signal cancellation.

Conclusions

The presented method allows 2D EPI fMRI images to be reconstructed with very low ghost level at 7T in demanding gradient regimes.

Acknowledgements

The Wellcome Centre for Human Neuroimaging is supported by core funding from the Wellcome Trust [203147/Z/16/Z].