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Exhaustive Comparison of QSM Background Field Removal and Masking using a Realistic Numerical Head Phantom
Carlos Milovic1,2, Patrick Fuchs3, Oriana Arsenov3, Oliver C Kiersnowski3, Russell Murdoch3, Laxmi Muralidharan3, Jannette Nassar3, and Karin Shmueli3
1School of Electrical Engineering, Pontificia Universidad Catolica de Valparaiso, Valparaiso, Chile, 2iHEALTH, Millennium Institute for Intelligent Healthcare Engineering, Santiago, Chile, 3University College London, London, United Kingdom

Synopsis

Keywords: Susceptibility, Susceptibility, QSM

Removing background fields is an important preprocessing step in QSM, enabling the reconstruction of fine tissue susceptibility variations in the region of interest (ROI) without being corrupted by susceptibility sources outside of this region. This requires a binary mask of the ROI and most background field removal methods are sensitive to the choice of mask. Here we compared 15 background field removal methods across 4 different masks. We found projection onto dipole fields (PDF) to perform best overall, although it is sensitive to the mask. V-SHARP and RESHARP were more robust to masking and showed good performance.

INTRODUCTION

Quantitative Susceptibility Mapping (QSM) is an ill-posed inverse problem, where tissue susceptibilities are inferred from local magnetic field estimations derived from gradient-echo phase data. The acquired phase is proportional to the macroscopic total field (Btot), which is composed of the local or tissue magnetization fields (Bint) and external or background fields arising from sources outside the region of interest (Bbg) with Btot = Bint + Bbg. Background fields usually are much larger than local fields, but it is possible to disentangle these by exploiting the harmonic property of background fields. Several Background Field Removal (BFR) algorithms have been proposed that utilize different properties of harmonic functions1. These algorithms require the definition of a region of interest (ROI) by means of a binary mask. It has been shown that this ROI definition impacts the quality of the results, but it is unclear how different BFR algorithms are affected by mask selection. Exhaustive comparisons between BFR methods have only been performed using simple simulations (or in vivo data without a ground truth) and a single predefined mask1. Here we present an updated comparison, including new deep learning-based BFR approaches, using a realistic simulated head phantom developed for the 2019 QSM Challenge2 and four different masks.

METHODS

The simulated 1mm isotropic multi-echo gradient-echo complex data from the QSM Challenge Phantom Toolbox2 was used, with and without background fields. Individual echoes were combined using the complex multi-echo nonlinear fitting3 function from the MEDI toolbox, and the result was unwrapped with SEGUE4. The total field map was provided to all BFR algorithms in radians, scaled to deltaTE = 8 ms. Four different ROI masks (see Figure 1) were defined as follows: M1) Brain mask generated by FSL BET5. M2) BET mask eroded using a spherical kernel of one voxel radius. M3) BET mask smoothed using 5-voxel opening and closing morphological operations and then eroded by 1 voxel. M4) BET mask dilated by 1 voxel and then multiplied by a thresholded phase quality map (complex multi-echo fit noise map3 <10-5). A “closing” operation (3-voxel) was used to fill holes inside the mask. The local field ground truth was extracted from the simulated complex data without background fields following the same pipeline.
We evaluated the root mean squared error (RMSE) of all local field results within two evaluation masks: E1) The intersection of all BFR masks. E2) The evaluation mask from the 2019 QSM Challenge (2-voxel erosion of M1). E1 is larger than E2. To analyze the mask-related variability of Bint from each BFR method, the normalized standard deviation of Bint across all masks was calculated for each BFR method.
For this comparison we included the following BFR algorithms: 1) Projection onto Dipole Fields, PDF6. 2) Sophisticated Harmonic Artifact Reduction for Phase data, SHARP7. 3) Extended SHARP, ESHARP8. 4) Regularized SHARP, RESHARP9. 5) Variable SHARP, V-SHARP10. 6) Iterative Spherical Mean Value, iSMV11. 7) Spatially Dependant Filtering, SDF12. 8) Multiscale SMV, MSMV13. 9) Multiscale SHARP, MSHARP13. 10) Laplacian Boundary Value, LBV14. 11) LBV adjusted by polynomial fit, pLBV15. 12) HARmonic (background) PhasE RemovaL, HARPERELLA16. We also included deep learning-based algorithms: 13) SHARQnet17. 14) BFRnet18. 15) LapInvNet19. Parameters were optimized to minimize RMSE for each mask, for all BFR methods.

RESULTS AND DISCUSSION

The lowest RMSE Bint for each BFR method is presented in Figure 2, highlighting the best ROI mask. M3 and M2 gave the worst RMSE scores. Error maps from most BFR algorithms do not show anatomical structure inside the brain (Figure 3). However, most SMV based methods (2-9) gave errors near the boundaries (likely due to over-filtering or the reduced output ROI). LBV gave smooth large-scale residuals that were removed by polynomial fitting (pLBV). Deep learning-based solutions gave the largest errors and did not perform well in this dataset.
Figure 4 shows the sensitivity of each BFR method to different masks. RESHARP, V-SHARP and BFRnet show low sensitivity inside the brain. MSMV and MSHARP show low sensitivity near the boundaries. LBV is very sensitive in low SNR regions, for example, near the supranasal region. PDF also shows considerable sensitivity near the boundaries, with some sensitivity extending into the brain. This mask-related variability is also shown in Figure 5, where the RMSE scores are compared across all masks.

CONCLUSION

Despite poor overall performance (Figure 3) BFRnet was notably robust against different masks (Figure 4). Current deep learning-based approaches need to improve their generalizability and robustness to be recommended for clinical studies. As suggested before15, this comparison shows that LBV benefits significantly by removing an additional 4th order polynomial as this substantially reduced errors and sensitivity to variable masking.
PDF scored best, although it is sensitive to masking. Most algorithms performed best using M4 suggesting the use of a large brain mask with unreliable voxels excluded using a phase quality map. This aligns well with findings in recent literature20.
Given their performance and lower sensitivity to masking, RESHARP and V-SHARP may be good BFR choices for large in-vivo datasets.
Future work will involve evaluation of QSMs estimated from the local fields calculated here to investigate interactions between BFR approaches and dipole inversion algorithms.

Acknowledgements

We thank Cancer Research UK Multidisciplinary Award C53545/A24348 and European Research Council Consolidator Grant DiSCo MRI SFN 770939 for their funding support. Oliver K Kiersnowski’s work was supported by the EPSRC-funded UCL Centre for Doctoral Training in Intelligent, Integrated Imaging in Healthcare (i4health)(EP/S021930/1).

References

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13. Milovic C, et al. Multiscale Spherical Mean Value based background field removal method for Quantitative Susceptibility Mapping. 27th International Conference of the ISMRM, Montreal, Canada, 2019;P4940.

14. Zhou D, Liu T, Spincemaille P, Wang Y. Background field removal by solving the Laplacian boundary value problem. NMR in Biomedicine. 2014 Mar;27(3):312-9.

15. Langkammer C, Schweser F, Shmueli K, Kames C, Li X, Guo L, Milovic C, Kim J, Wei H, Bredies K, Buch S, Guo Y, Liu Z, Meineke J, Rauscher A, Marques JP, Bilgic B; Quantitative Susceptibility Mapping: Report from the 2016 Reconstruction Challenge; Magnetic Resonance in Medicine, 2017 Jul 31. doi: 10.1002/mrm.26830.

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Figures

Figure 1: Overview of the four brain masks used as inputs for the background field removal methods. M1) BET brain mask. M2) BET masked eroded by one voxel. The white voxels in M1-M2 shows regions that were removed from the initial BET mask. M3) The result of applying morphological opening and closing operations to M1 and then eroding. Black voxels in M1-M3 are voxels included in M3 which were not included in M1. M4) The BET mask dilated by a single voxel and without unreliable phase voxels.

Figure 2: The solutions of each background field removal (BFR) algorithm with the lowest root mean square error (RMSE) relative to the ground truth. For each algorithm the mask which provided the lowest RMSE is shown below the solution. Mask 4 provided the lowest RMSE for 11/15 BFR algorithms included in this comparison.

Figure 3: Error maps showing the difference between the lowest RMSE solution for each algorithm and the ground truth local field. Error maps are shown with increased contrast relative to the local field maps in Figure 2 (6x). The RMSE scores calculated for the two evaluation masks is included for each method. The PDF solution had the lowest RMSE. Deep Learning-based solutions (SHARQnet, BFRnet and LapInvNet) and SDF show the largest structural errors

Figure 4: Standard deviations of the local field values calculated across all brain masks in the intercept of the masks. The overall standard deviation calculated for both the intercept and evaluations masks are included for each method.

Figure 5: Comparison of root mean square error (RMSE) values for each of the background field removal (BFR) algorithms, for all masks included in the comparison (M1-M4).

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)
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DOI: https://doi.org/10.58530/2023/4178