The pipeline for simulating DWIs.

<p>The pipeline for simulating DWIs.</p

Susceptibility-movement interaction.

<p>A. The x- and y- rotation parameters used for the simulation of the first 36 volumes (z-rotations not shown because they do not contribute to the dynamic susceptibility effect, translations were all 0). The coloured vertical lines highlight the motion of the volumes depicted in plot B. B. Top two rows show the errors in displacement field caused by the dynamic portion of the susceptibility artefact, for volumes 2-5 of the acquisition—the motion these volumes experienced is highlighted with colour in plot A. Bottom two rows show the error in intensity of these volumes after they are corrected for motion and the static portion of the susceptibility field, obtained by subtraction from ground truth images.</p

Simulated DWIs.

<p>Pairs of coloured arrows point to corresponding pairs of compression and expansion in the blip-up and blip-down images. The ‘streaking’ visible in the fieldmap is caused by the linear extrapolation to ensure a continuous field at the edge of the brain. The bounding box visible around the fieldmap is caused by its resampling into the space of POSSUM’s input object; this is not a problem for the simulation as the fieldmap is smooth and defined over all brain voxels in input object. Some Gibbs ringing is visible in the sagittal views of the distorted data—this is induced by sharp boundaries in regions of signal pile-up.</p

AP-LR comparison on real data.

<p>Figure shows corrected AP and LR b = 0 images, and the intensity difference between them.</p

Errors in FA metrics.

<p>FA maps estimated from corrected and ground truth images, along with error maps obtained by subtraction from the noise-free ground truth estimate. FA map shown for SNR infinite case. Red arrows show regions of high error caused by signal pileup that could not be corrected by the RB and MPB methods, despite estimation of the correct displacement field. The MPB/F method is able to reduce errors in these regions. Note the MPB/F method uses twice as much data as the other methods, increasing its effective SNR.</p

Error distribution.

<p>Histogram of the difference in absolute FA errors over the full brain, for datasets corrected for motion and static susceptibility: |ΔFA_static| − |ΔFA_dynamic|, so the heavy tail for negative values indicate higher errors for the dynamic case.</p

Errors introduced when failing to account for the susceptibility-movement interaction.

<p>Absolute errors in FA shown over one slice, for datasets corrected for motion and static susceptibility. Data in the static columns were simulated with only motion and static susceptibility artefacts, whilst the dynamic data contained motion and dynamic susceptibility. ‘One PE correction’ indicates only the AP data was used for correction, and ‘two PE correction’ indicates the AP and PA data were both use—note these are different from MPB and MPB/F, which are methods for both estimating and applying a displacement field, whilst in this case known ground-truth displacement fields have been applied.</p

Mean of absolute errors in displacement field across the brain.

<p>Values shown are the mean across the five noise realisations, and errors are the standard deviation of the mean value for each noise realisation. Note that the multiple phase-encode results cover both MPB and MPB/F methods.</p

Displacement field errors.

<p>Error in displacement fields estimated by the three methods, assessed by subtraction from the ground truth field. One axial slice shown.</p

Surrogate metrics for real data.

<p>Table shows whole-brain-mean intensity differences between AP and LR corrected datasets (units are arbitrary signal units). Errors are the standard deviation of the means over the ten subjects. Metrics show statistically significant differences between all methods at the p<0.001 level.</p