Introduction

Simultaneous multi-slice arterial spin labelling (SMS-ASL) acquisitions enable higher resolutions to be achieved for ASL images, such as those acquired by the Human Connectome Project (HCP) Aging and Development studies.¹ However, the acquisitions can lead to sharp discontinuities in intensity between slices in different bands, particularly when physically adjacent slices are acquired serially in time. Motion estimates are then degraded as the algorithm aligns the bands in preference to brain structures, preventing effective motion correction.² Gaussian processes have been used to improve motion estimation in diffusion MRI with severe distortion artefacts.^3,4 We introduce a Gaussian Process (GP) model, used as part of the process to correct the artefacts in SMS-ASL multiple post-labelling delay (multi-PLD) data. We demonstrate its effectiveness on 10 subjects from the HCP Aging (HCP-A) study where two effects interact to produce discontinuities.

Methods

We introduce an algorithm which models how SMS-ASL multi-PLD non-background suppressed signal varies with partial volume estimates (PVEs), slice number and PLD. We obtain 2 predictions: the model’s prediction of the original image with banding and its prediction of the corrected image. We then use the ratio between these 2 predictions to correct the original image.
Instead of using a fully deterministic model, we use a GP where our mean function is the product of a constant, $$$c$$$ , and a saturation recovery term:
$$m\left(\mathbf{x}\right)=c\times\left[ p_{gm}M_{0_{gm}}\left(1-e^{-\frac{t}{T_{1_{gm}}}}\right)+p_{wm}M_{0_{wm}}\left(1-e^{-\frac{t}{T_{1_{wm}}}}\right)+p_{csf}M_{0_{csf}}\left(1-e^{-\frac{t}{T_{1_{csf}}}}\right)\right]$$
$$$\mathbf{x}$$$ is the voxel's $$$5\times1$$$ feature vector and $$$p_{tissue}$$$ are the PVEs at the voxel. $$$c$$$, $$$M_{0_{tissue}}$$$ and $$$T_{1_{tissue}}$$$ are hyperparameters to be estimated. Our covariance function is:
$$K\left(\mathbf{x},\mathbf{x'};\mathbf{\Omega},v,l\right)=k_{pve}\left(\mathbf{p},\mathbf{p'};\mathbf{\Omega}\right)\times\left(k_{slice}\left(s,s';v\right)+k_t\left(t,t';l\right)\right)$$
$$K\left(\mathbf{x},\mathbf{x'};\mathbf{\Omega},v,l\right)=exp\left(-\frac{1}{2}\left(\mathbf{p}-\mathbf{p'}\right)^T\mathbf{\Omega}^{-1}\left(\mathbf{p}-\mathbf{p'}\right)\right)\times\left(\left(v\times s\times s'\right)+exp\left(-\frac{\left(t-t'\right)^2}{l^2}\right)\right)$$
$$$\mathbf{p}$$$ is a $$$3\times1$$$ vector of PVEs, $$$s$$$ is the position of the voxel in a band, $$$t$$$ is the PLD and the hyperparameters $$$\mathbf{\Omega}$$$, $$$v$$$ and $$$l$$$ are lengthscales which determine how the predictions vary in feature space.

The HCP-A ASL data consists of 43 label-control pairs at 5 PLDs (0.2s, 0.7s, 1.2s, 1.7s, 2.2s), labelling duration of 1.5s, varying numbers of repeats (6, 6, 6, 10, 15 respectively), 2.5mm isotropic resolution, 60 slices acquired with 6-fold acceleration (slice readout time of 0.059s). Two M0 images (TR>8s) were acquired at the same spatial resolution. Two reversed phase-encoded spin-echo images were processed using TOPUP for susceptibility distortion correction.⁵ Correction for gradient nonlinearity was also performed. T1 and T2-weighted structural images (0.8mm isotropic resolution) were processed using FreeSurfer.^1,6 PVEs were obtained in ASL native space using Toblerone.⁷ Motion estimation was performed using FSL mcflirt (first M0 image as reference image).⁸ Registration to structural space was performed using FreeSurfer’s bbregister.⁹ Receive-coil bias correction was applied using sensitivity maps estimated from a grey matter mask in the first M0 image.
The GP’s hyperparameters are optimised on a subject-specific basis. 200 voxels are sampled from the first (control) image at each PLD and M0 image, totalling 1200 training points, with 10% of the voxels within the ventricular CSF mask. During model prediction, at each voxel, the data from the 43 control volumes and the 2 M0 images are used alongside the training data.

Results

We observe 2 effects in the HCP-A data which interact to produce the banding visible in Figure 1. The first, believed to be a magnetisation transfer (MT) effect, is visible in Figures 1a and 1b and causes signal intensity to decrease as slice number increases. Figure 2 shows this effect is approximately linear within the data and stronger in white matter than in grey matter. The second, the saturation recovery effect, causes signal intensity to increase with PLD. This is most pronounced at PLD=0.2s because the slice readout time is largest relative to the nominal PLD. The two effects largely cancel out at this PLD, resulting in less obvious discontinuities in Figure 1c.
Figures 3a-c show predictions from the GP which has learned the data’s signal variation with PLD. Figure 3d shows the model learns that signal varies linearly with slice number and that the effect is stronger in white matter than in grey matter, as seen in Figure 2.
Figure 4 shows the discontinuities in mean slicewise signal are reduced after correction compared to Figure 2, indicating the approximately linear trend with slice number is alleviated.
Figure 5 shows the ratio of the GP’s predictions visibly removes the banding pattern, particularly at later PLDs.

Discussion

This work introduced a GP which models SMS-ASL multi-PLD signal as a function of PVEs, slice number and PLD. Predictions from the GP corrected the banding in HCP-A data and we expect this will result in improved motion correction and a reduction in artefacts. We anticipate this will generalise to other SMS-ASL datasets, including SMS acquisitions with background suppression. The correction was less effective at early PLDs where banding is less substantial, even before correction. Figure 5d shows the GP produces low predictions of CSF signal at earlier PLDs, resulting in suppressed CSF signal in the corrected images.

Conclusion

The GP successfully corrects artefacts in non-background suppressed, SMS-ASL multi-PLD data on a subject-specific basis, particularly at later PLDs. It is expected to generalise to other ASL datasets. Further work is required to improve the correction at earlier PLDs and in CSF.

Acknowledgements

JT and MAC have received support from the Engineering and Physical Sciences Research Council UK (EP/P012361/1). FKM is supported by the Beacon of Excellence in Precision Imaging, University of Nottingham. YS is supported by the Royal Academy of Engineering under the Research Fellowship scheme (RF/201920/19/236) and core funding from the Wellcome Trust (203139/Z/16/Z). MPH is supported by grants: U01MH109589 and U01AG052564. MFG is supported by grants: R24MH108315 and R24MH122820.