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The Effect of Oblique Image Slices on the Accuracy of Quantitative Susceptibility Mapping and a Robust Tilt Correction Method
Oliver C. Kiersnowski1, Anita Karsa1, John S. Thornton2, and Karin Shmueli1
1Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom, 2UCL Queens Square Institute of Neurology, London, United Kingdom

### Synopsis

Quantitative susceptibility mapping (QSM) using the MRI phase to calculate tissue magnetic susceptibility is finding increasing clinical applications. Oblique image slices are often acquired to facilitate radiological viewing and reduce artifacts. Here, we show that artifacts and errors arise in susceptibility maps if oblique acquisition is not properly taken into account in QSM. We performed a comprehensive analysis of the effects of oblique acquisition on brain susceptibility maps and compared tilt correction schemes for three susceptibility calculation methods, using a numerical phantom and human in-vivo images. We demonstrate a robust tilt correction method for accurate QSM with oblique acquisition.

### Introduction

Quantitative susceptibility mapping (QSM) is finding increasing clinical applications. Acquisition of oblique image slices is common clinical practice to facilitate radiological viewing but pilot studies suggest this gives incorrect susceptibility ($\chi$) estimates when unaccounted for1. Using a numerical brain phantom2, we performed a comprehensive analysis of the effects of oblique acquisition and compared proposed tilt correction methods for the final $\chi$ calculation step in the QSM pipeline. We confirmed these results in vivo, and demonstrate a robust tilt correction method for accurate $\chi$ calculation.

### Methods

Numerical Phantom:
Local field maps were obtained from a non-linear fit3 over echo times of complex data, created from magnitude and phase images of a numerical brain phantom2, with no background fields. These background-field-free maps were used to independently analyse the $\chi$ calculation step in the QSM pipeline without confounds from phase unwrapping or background field removal. To simulate oblique slice acquisition, the untilted reference local field map (at 0°) was tilted by -45° to +45° in 5° steps. All rotations were carried out about the x-axis (u-axis, Figure 1) using FSL FLIRT4 with trilinear interpolation.

We tested four proposed tilt correction schemes (Figure 1):

• RotPrior: image rotated into scanner frame prior to $\chi$ calculation (with a k-space dipole defined in the scanner frame)
• DipK: image left unaligned (k-space dipole defined in the tilted image frame)
• DipIm: image left unaligned (image-space dipole defined in the tilted image frame)
• NoRot: image left unaligned (simulating mistaken definition of the k-space dipole in the scanner frame misaligned to the tilted image)
To facilitate comparisons, all susceptibility maps left in the image-frame after correction (DipK, DipIm and NoRot) were rotated back into alignment with the scanner axes. These schemes were compared for three $\chi$ calculation methods: thresholded k-space division (TKD)5 (threshold = 2/3), iterative fitting with Tikhonov regularisation6,7 (α = 0.003), both corrected for $\chi$ underestimation8, and weighted linear total variation (wlTV) regularisation (FANSI toolbox9,10, α =2x10-4 ). Mean $\chi$ values were calculated in five deep grey matter regions of interest (ROIs) provided with the phantom. Susceptibility maps were compared using the root mean squared error (RMSE) relative to the ground truth susceptibility map and the QSM-tuned structural similarity index (XSIM)11.

In Vivo:
3D gradient-echo brain images of a healthy volunteer were acquired on a 3T Siemens Prisma MR system (National Hospital for Neurology and Neurosurgery, London, UK) using a 64-channel head coil. The image volume was tilted about the x-axis from -20° to +20° in 5° increments and acquired in 3 min 23 s (per volume) with TE1/ΔTE/TE5 = 4.92/4.92/24.60ms; TR=30ms; 1.23 mm isotropic voxels; 6/8 partial Fourier; and GRAPPAPE acceleration = 3.

For all angles/volumes, a total field map and noise map were obtained using a non-linear fit of the complex data3. A brain mask was created using BET12,13, eroded by 6 voxels, and multiplied with a mask created by thresholding the inverse noise map at its mean to remove noisy voxels. Residual phase wraps were removed using Laplacian unwrapping13,14 and background fields were removed using the Laplacian boundary value (LBV)13,15 technique as it is independent of tilt angle. The four tilt correction schemes were compared using the same three $\chi$ calculation methods as for the numerical phantom.

For each angle, the magnitude image (RMS across echoes) was rigidly registered to the reference (0°) using NiftyReg16 and the transformation matrix was used to transform the $\chi$ maps into the reference space for comparison. ROIs were obtained by registering the EVE17 magnitude image with the same reference image and applying the resulting transformation to the EVE ROIs. Mean $\chi$ values were calculated in these ROIs for all angles. RMSE and XSIM were also used to compare tilt-corrected maps with the 0° reference susceptibility map.

### Results

Numerical Phantom:
All QSM methods are most accurate with RotPrior, and least accurate with NoRot when the dipole is misaligned to the main magnetic field (Figure 2). wlTV is relatively robust to oblique acquisition, with RotPrior and DipK performing similarly. However, DipK shows variability in $\chi$ across angles in different ROIs. $\chi$ maps (Figure 3) make clearly apparent the errors resulting from NoRot.

In Vivo:
Figure 4 confirms that NoRot results in large susceptibility errors and that RotPrior is comparable to DipK between $\pm$20°, both performing better than DipIm, in agreement with the phantom results. Difference images also confirm the phantom results (Figure 5). Subtle effects found in the phantom ROIs (Figure 2) were not apparent in vivo (not shown) due to noise, motion, rotation/registration interpolation effects and the expected variability in QSMs over repeated acquisitions18.

### Conclusions

We have shown that, for any susceptibility calculation method (TKD, iterative Tikhonov and wlTV) applied to an oblique acquisition, leaving the dipole kernel misaligned with the main magnetic field ($\mathbf{\hat{B}}_0$) direction, which is often the default mode of QSM toolboxes, leads to substantial $\chi$ errors. The most accurate susceptibilities can be obtained when local field maps are rotated into alignment with the scanner axes prior to $\chi$ calculation (RotPrior). For wlTV, accurate susceptibility calculation can be carried out in the tilted image frame without any rotations provided the correct ($\mathbf{\hat{B}}_0$) direction is used in defining the k-space dipole (DipK).

### Acknowledgements

Oliver Kiersnowski is supported by the EPSRC-funded UCL Centre for Doctoral Training in Intelligent, Integrated Imaging in Healthcare (i4health) (EP/S021930/1). Karin Shmueli is supported by ERC Consolidator Grant DiSCo MRI SFN 770939. We thank Dr Carlos Milovic for his assistance with FANSI.

### References

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13. http://pre.weill.cornell.edu/mri/pages/qsm.html
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### Figures

Figure 1: Schematic illustration of oblique acquisition and proposed tilt correction methods for QSM. The scanner frame (x,y,z) and the image frame (u,v,w) are shown with respect to the main magnetic field B0=B0z (left). Proposed tilt correction methods are shown with the k-space dipole (right). RotPrior involves rotation of the tilted image frame into alignment (u',v',w') with the scanner frame. NoRot represents incorrectly misaligning the dipole kernel with B0z simulating a common error.

Figure 2: Mean susceptibilities in the Caudate and Thalamus (top rows), and RMSE and XSIM (bottom rows) across all tilt angles for all tilt correction schemes and all three calculation methods in the numerical phantom. NoRot performs worst across all angles. RotPrior is the most accurate tilt correction scheme. For weighted linear TV, DipK and RotPrior have similar XSIM values but the mean thalamus varies more over angles with DipK. Note that DipIm is not shown for wlTV as this method fails.

Figure 3: $\chi$ maps and difference images illustrating the effects of all tilt correction schemes in the numerical phantom. An axial and a coronal slice are shown for a volume tilted at 25° and a reference 0° volume with all $\chi$ maps calculated using the iterative Tikhonov method. The ROIs analysed are also shown (bottom left). Qualitatively, RotPrior performs the best while NoRot results in substantial $\chi$ errors across the whole brain. The results from TKD and weighted linear TV (not shown) are very similar.

Figure 4: RMSE and XSIM plots over all angles for all tilt correction schemes and all three $\chi$ calculation methods in one subject in vivo. These results are similar to those in the numerical phantom (Figure 2) with RotPrior and DipK performing best and NoRot performing worst across all methods. At non-zero tilt angles, RMSE and XSIM have a respectively high/low baseline level arising from rotation and registration interpolations. DipIm fails for wlTV and is, therefore, omitted from the plots in the last column.

Figure 5: $\chi$ maps and difference images illustrating the effects of all tilt correction schemes in vivo. An axial and a coronal slice are shown for a volume tilted at -10° and a reference (0°) volume with all $\chi$ maps calculated using the iterative Tikhonov method (left) and weighted linear TV (right). NoRot leads to the largest differences and image artefacts throughout the brain. The EVE ROIs used are shown (bottom left). Results from TKD (not shown) are very similar.

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)
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