2.1 MRI measurements and image reconstruction

Healthy volunteers (N = 22, 29 ± 11 y; eight females) were scanned at 9.4T (Siemens Healthineers, Erlangen, Germany) with a 16 channel transmit/31 channel receive array³⁴ after providing written, informed consent, as approved by the Ethics Review Board of the Eberhard-Karl's University, Tübingen.

Actual flip angle³⁵ (FA = 60°; TR1/TR2 = 20/100 ms; TE = 7 ms, voxel size = 3 x 3 x 5 mm³) and MP2RAGE³⁶ (TI1/TI2 = 900/3500 ms; FA = 4/6°; TR = 6 ms; volume TR = 8894 ms, 0.8 mm isotropic voxels) images were processed to yield tissue segmentations and regions of interest³⁷ (ROI) as described previously³⁸. Monopolar, multi-echo 3D gradient-echo (GRE) images (5 echoes, TE = 6-30 ms in steps of 6 ms; TR = 35 ms; FA = 11°; matrix: 512x464; FoV = 192x174mm; 96 partitions; 0.8 or 1 mm thick slices, GRAPPA = 2; partial Fourier acquisition (PFA) = 6/8; read-out bandwidth = 240 Hz/pixel) were acquired for QSM, with offline reconstruction of single echo images: k-space zero-filling to twice the acquired 3D matrix, Projection Onto Convex Sets reconstruction³⁹, ASPIRE¹³ phase offset correction but without spatial smoothing of the phase offset maps, and adaptive channel combination based on the ASPIRE-corrected first echo image with a block size of one.⁴⁰ Combination of three or five echoes was made with Fit_ppm_complex_TE^41-43.

A field map (FM) was measured at 3T (PrismaFit, Siemens Healthineers, Erlangen, Germany) using the UTE sequence (TE = 0.1; 1.11; 2.22 ms; voxel size = [1.5 mm]³, Siemens WIP992D) to minimize phase wraps, albeit neglecting differences in eddy currents and shim with respect to 9.4T (N = 1). After reconstruction using scanner software and voxel-wise phase unwrapping in the TE domain, the FM was generated from the first two echoes, interpolated to match the 9.4T data and smoothed (Gaussian, full width half maximum, FWHM = 8 mm, Supporting Information Figure S1, which is available online) before simulating phase evolutions with echo time and field (Supporting Information Figure S2). The phase image with TE = 18 ms at 9.4T was used to identify a mask, P_Itoh by thresholding $$$ {Test}_{Itoh}=\sqrt{{G_x}^2+{G_y}^2+{G_z}^2} $$$ (where $$$ {G}_x $$$, $$$ {G}_y $$$, and $$$ {G}_z $$$ indicate the phase gradient along the x, y, and z direction, respectively) at a value of π.

2.2 Generation of tissue masks

Magnitude masking MM was obtained with FSL's brain extraction tool⁴⁴ (BET) with the -R option (and -B at 3T) and different values for the fractional intensity threshold FIT (−f 0.1–0.8 in steps of 0.1) followed by Gaussian smoothing (FWHM = 4 voxels) to include voxels close to the brain surface.

Phase-based masks from the first (PG) and second (PB) derivative of the sign, S, of the wrapped phase wP were generated in Matlab (Natick, MA, USA) in five steps:

step1: calculate S of wP;

step2: generate a) PG: norm of the gradient images of S; b) PB: absolute value of the Laplacian of S;

step3: smooth to obtain test functions in 3D, $$$ {Test}^{PG} $$$ and $$$ {Test}^{PB} $$$;

step4: threshold and multiply with MM;

step5: close and open image (to fill holes within the mask, maintaining voxels at the brain surface).

Maximum values, $$$ {Test^{PG}}_{\mathrm{max}} $$$, $$$ {Test^{PB}}_{\mathrm{max}} $$$ were identified by simulations of phase noise in 3D for a matrix of 100x100x100 voxels. Steps 1–3 were applied, maximum values in the central 90x90x90 voxels extracted and explored using the ‘cftool’ in Matlab. The effects of smoothing with a sphere (radius, $$$ 1\le r\le 8 $$$ voxels) and a Gaussian kernel ($$$ 1\le FWHM\le 8 $$$ voxels) on $$$ {Test}_{max} $$$ were explored.

PG and PB masks were generated from the simulated phase with TE = 18 ms at 9.4T. The Dice coefficients between the ground truth P_Itoh mask and PG or PB masks obtained by thresholding at different levels of $$$ {Test^{\mathrm{max}}}_{PG} $$$ and $$$ {Test^{\mathrm{max}}}_{PB} $$$ (25, 50, 75, and 100%) were calculated and the percentage of voxels included in PG or PB but outside P_Itoh were determined. The same parameters were also evaluated for MM.

2.3 Generation of Quantitative Susceptibility Maps

Phase images were unwrapped using the Laplacian approach¹⁰ and ROMEO¹⁴.

Whole brain referencing consisted of subtraction of the median value of the unwrapped phase inside the tissue mask. The background field was removed using ‘sophisticated harmonic artifact reduction for phase data’ (SHARP⁹) algorithms, either RESHARP¹⁷ with kernel sizes between 0.8 and 4 mm and Tikhonov regularization parameters ranging from 10⁻³(Tk-3) to 10⁻¹²(Tk-12) or V-SHARP²⁰ with a maximum value for the spherical mean value (SMV) between 4-20 mm. Alternatively, the Laplacian boundary value (LBV) method²¹ with a tolerance of 0.005 and other parameters set to default values in the MEDI toolbox⁴⁵ was used.

Dipole inversion to obtain QSM maps was performed using iLSQR^{20, 46, 47} and MEDI⁴³ with a lambda factor of 100.

2.4 Quantification of iron-dependent QSM contrast

QSM values were extracted from six cortical ROIs (with gray matter tissue probability>0.98) and three subcortical ROIs (eroded with a sphere of radius 2 voxels). The median QSM value was calculated for each ROI within the final MM or PB mask obtained after erosion during background removal.

2.5 QSM bench test using QSM2016 challenge 3T data

The performance of the QSM processing was tested on the fully corrected and on the wrapped phase from the QSM2016 challenge data set,²⁶ compared with the ground truth susceptibility maps, chi_33. The wrapped phase was unwrapped (Laplacian or ROMEO), and tissue masking was performed using the original mask provided in the challenge and with MM and PB generated from the challenge data. Background removal was performed with V-SHARP (SMV 20 mm) or RESHARP (Tk-12). In addition to iLSQR and MEDI, the closed-form L2-regularized dipole inversion was also used to generate QSM. To obtain $$$ {k}_{Fe} $$$ tissue segmentation and ROI identification was obtained by processing the provided MPRAGE.

3.1 Evaluation of tissue masks

MM with FIT between 0.4 and 0.6 covered brain tissue voxels at 3T (Figure 1A) while FIT = 0.1 was chosen at 9.4T to include voxels at the brain surface, also in presence of slab selection inhomogeneities (Figure 1E).

Some relevant features of the acquired phase at 9.4T were reproduced by the simulated phase evolution (Supporting Information Figure S2), with dense wraps above the nasal air cavity, especially at late echo times. No large differences between masks were present at 3T or the first two TEs at 9.4T; therefore, the phase at 9.4T, TE = 18 ms was chosen for further analysis.

The shape and size of the smoothing kernel influenced the maximum values of the test function, found in simulations of pure phase noise (Supporting Information Figure S3). For a spherical kernel $$$ {Test^{PG}}_{max}=6.35\cdot {r}^{2.87} $$$ (p < 0.001; $$$ {R}^2 $$$ = 0.9997) and $$$ {Test^{PB}}_{max}=6.06\cdot {r}^{2.84} $$$ (p < 0.001; $$$ {R}^2 $$$ = 0.9997). With a Gaussian smoothing kernel, we obtained $$$ {Test^{PG}}_{max}=1.16+0.75\cdot {e}^{-0.51\cdot FWHM} $$$(p < 0.001; $$$ {R}^2 $$$ = 0.9998) and $$$ {Test^{PB}}_{max}=1.04+1.30\cdot {e}^{-0.56\cdot FWHM} $$$(p < 0.001; $$$ {R}^2 $$$ = 0.9986).

Both PG (Figure 1B,F) and PB (Figure 1C,G) showed greater values in brain areas with dense phase wraps. Compared with the ground truth P_Itoh mask (Figure 1D), MM with FIT = 0.6 yielded the highest Dice coefficient (0.91), but also included 6% of voxels outside P_Itoh. For phase-based masking, the Dice coefficient for PB was more similar across thresholds than PG (Supporting Information Figure S3). A spherical kernel ($$$ r $$$ = 6), with 75%(50%) threshold yielded Dice coefficients of 0.92(0.87) for PG and 0.93(0.93) for PB, with 1.4%(0.1%) and 2.0%(0.4%) of voxels violating Itoh's condition, respectively.

For QSM from the experimental 9.4T data, MM after echo summation with threshold = 0.1, and PB using smoothing with the spherical r = 6 kernel, a threshold value of 500 (51%), followed by image closure and opening using the same kernel were used (Figure 1E-H). The Dice coefficient between MM and PB was 0.96 ± 0.01. Without step 5 to fill holes within the mask and maintain voxels close to the brain surface, the Dice coefficient was 0.97 ± 0.01. A tighter MM was obtained from the single-echo magnitude image and yielded the same Dice coefficient with PB, and 0.97 ± 0.01 with MM.

3.2 Effect of masking and background removal on QSM at 9.4T

MM worked well in case of RESHARP with high regularization factors (Tk-3, Figure 2A), while less regularization caused strong variations in QSM values especially in the frontal part of the head (Tk-12, Figure 2B). These artifacts were less prominent with V-SHARP SMV (Figure 2C) than with LBV (Figure 2D). Conversely, with PB QSM maps were similar regardless of background removal (Figure 2F-H). The improvement observed varied from subject to subject, depending on brain coverage and head position (Supporting Information Figure S4).

3.3 Iron-dependent QSM contrast, $$$ {k}_{Fe} $$$, at 9.4T

The dependence of QSM values on the age-related estimates of non-heme tissue iron in cortical and subcortical ROIs (Figure 3A) was linear (p < 0.001) for all processing pipelines and for each subject, except for LBV using MM for which a significant (p < 0.05) linear fit was obtained in 13 out of the 21 subjects. Using MM, the residuals were generally greater in the putamen and caudate than with PB, but the tighter single-echo MM did not lead to a significant change in $$$ {k}_{Fe} $$$ (Student's paired t-test, T = 1.05, p = 0.34).

Significantly greater $$$ {k}_{Fe} $$$ were obtained with PB than with MM, regardless of background removal technique (two-way repeated-measures analysis of variance [ANOVA] F_{(1, 2, 20)}=5.99; p = 0.024; for RESHARP; F _{(1, 2, 20)} =5.29; p = 0.032 for V-SHARP). Pairwise differences were significant for LBV, all VSHARP kernel-sizes, and RESHARP Tk-8, Tk-12 (Figure 3B). Considering all echoes processed with RESHARP Tk-12, there was no significant overall effect, (F_{(2, 20)}≤1.9; p ≥ 0.16), but the pairwise MM-PB differences at TE = 18 ms or more were significant (Figure 3C). No difference between MM and PB was observed with multi-echo combination with an effective TE of 6 ms (Supporting Information Table S2, Supporting Information Figure S7). Combining the latest three echoes (18-30 ms) yielded a lower QSM contrast than 6-18 ms. LBV background removal yielded $$$ {k}_{Fe} $$$ = 0.58 ± 0.10 ppb/μg/g, and 0.60 ± 0.10 when step5 was excluded.

Using RESHARP Tk-12 combined with other phase-unwrapping and dipole-inversion algorithms did not influence the average $$$ {k}_{Fe} $$$, although locally higher QSM values could be observed with ROMEO and MEDI (Figure 4). Close to the nasal air-cavities, the unwrapped phase-values obtained with ROMEO were greater than with the Laplacian approach, while PB successfully identified voxels where discontinuities across the tissue border after unwrapping occurred (Figure S5).

In white matter tracts, PB mitigated the TE dependence of MM, with pronounced effects in the anterior thalamic radiation, the inferior fronto-occipital and the uncinate fasciculi (Supporting Information Figure S8).

3.4 Bench test results using QSM2016 challenge 3T data

QSM values obtained with MM, Laplacian unwrapping, RESHARP background removal and iLSQR dipole inversion were slightly lower than the ground truth chi_33 values with MM than with PB or with the original mask provided in the QSM2016 challenge (Figure 5A-C). Both MM and PB included more voxels at the cortical surface than the original mask (Figure 5D-E; Supporting Information Figure S6), but MM yielded increased standard deviations close to air cavities in the caudate and the temporal cortex, which were mitigated by PB. For all processing combinations, MM yielded higher root mean squared error and high frequency error norm values than PB, together with smaller structural similarity index metrics and larger white matter/gray matter errors (Supporting Information Table S3). ROMEO, RESHARP and MEDI dipole inversion using PB yielded a $$$ {k}_{Fe} $$$ which was 0.6% higher than for chi_33.