To present a novel 3D trajectory and associated image reconstruction that enables k-space correction of severe motion at high temporal resolution, with application to functional MRI.3D EPI has a number of potential benefits for high-resolution fMRI, including high SNR¹, acceleration along multiple dimensions and the ability to resolve thin slices. However, whole brain acquisitions typically need multiple seconds to sample a full 3D k-space, which make them susceptible to temporal fluctuations such as motion and physiological noise. Retrospective corrections for motion² and physiological noise³ can mitigate these effects, but these methods cannot correct for intra-volume fluctuations. Our recently proposed acquisition scheme enables correction of these artefacts, using a hybrid radial-Cartesian readout^4-6 in which k_xy-k_z EPI “blades” are rotated in a golden ratio angle scheme⁷ about the k_z-axis (Fig. 1a). This scheme ensures near-uniform angular coverage of k-space for an arbitrary number of blades, which allows flexible post-acquisition definition of spatial and temporal resolution (Fig. 1b). To exploit this property for motion and physiological noise correction, we first reconstruct a low-spatial/high-temporal resolution timeseries to calculate motion estimates and respiration-induced B₀ drift. These estimates are fed into the second stage, in which motion and respiration fluctuations are corrected in k-space, and used to reconstruct the final timeseries at high-spatial/moderate-temporal resolution.

Acquisition: Data was acquired at 3T on 3 healthy volunteers. Two experiments with deliberate subject motion were performed: (1) Set motion: subjects visually queued to perform 6 different motions (x/y/z translations, x/y/z rotations) during a 130 second scan. (2) Natural motion: subjects asked to be fidgety (e.g. move their legs or cough) during a 300 second task fMRI experiment with visual stimulus (30s ON/OFF 8Hz checkerboard) and simultaneous bilateral finger tapping. All acquisitions used TR/TE=50/25ms, blade EPI matrix 100x76, 2mm isotropic, R=2 along blade PE.

General reconstruction information: Image reconstruction was performed in MATLAB. Parallel imaging was performed using the GRAPPA and SPIRiT⁸ algorithms.

Correction: The motion and 0-order phase offset are first estimated (stage 1) and subsequently corrected in k-space (stage 2) prior to the final reconstruction. Stage 1: Rigid body motion was estimated in image-space from 10-blade timeseries (TRvol = 0.5s), using MCFLIRT (FSL). Shifts in the z-direction (nominally blade PE direction) were estimated blade-by-blade (TR=0.05s) in the centre of k-space by fitting a linear and 0-order phase changes. Stage 2: To correct for rotations, k-space coordinates were rotated accordingly and shifts were removed by subtracting the corresponding phase ramps and the phase offset from k-space.

Final reconstruction and analysis: Final reconstructions were performed using 50 blades (TRvol = 2.5s) corresponding to a total under-sampling factor of ~6 (2x3.14). Before fMRI analysis, rigid body motion correction (MCFLIRT) was performed across all datasets (to assess the advantage of our method over standard retrospective rigid body motion correction). fMRI analysis was performed in FEAT (FSL) using no temporal filtering, spatial smoothing or pre-whitening.

Motion estimates and residual motion after correction are displayed for a representative subject in Figs. 2-3. Subject motion was removed very accurately for translations and rotations. Uncorrected datasets contain volumes with severe intra-volume inconsistency artifacts (Fig. 2, bottom), which are significantly reduced in the corrected timeseries. Voxel-wise mean temporal variance was reduced by 16/38/45% for subjects 1-3 for set motions and 42/25 % for subjects 2/3 for natural motion scans. The natural motion scan of subject 1 was excluded because of extreme motion (>20mm/>10deg). The number of voxels with activation (z≥2.3) in visual cortex ROIs increased by 21/25% for subjects 2/3 and by 41/42% in the motor cortex. Average z-stats increased by 9/3% for subjects 2/3 in the visual cortex and 9/1% in the motor cortex. Example variance and z-stat maps are shown in Fig. 4. In the presence of extreme and very rapid motion residual artifact is still observed (Fig. 5). We have demonstrated the motion correction capabilities of hybrid radial-Cartesian 3D EPI even in the presence of severe motion. The approach requires no designated hardware, and is self-navigated. This makes the approach suitable for fMRI, where the TR needs to be short and re-acquisition is not possible. The remaining artifacts in some volumes after correction likely come from estimating motion over 0.5s intervals, although residual error might also come from variation in distortion and coil sensitivity, which we cannot account for. In future work we aim to refine the temporal resolution of motion estimates using fewer blades at a time (e.g. 2-3 blades, enabling 0.1-0.15s resolution) to estimate more accurate x/y shifts and rotations.