Repeatability of Susceptibility Source Separation Methods in Human Brain: A Single‐Site Study at 3 T

ABSTRACT

Susceptibility source separation offers new subvoxel insights into iron and myelin distribution in the human brain, overcoming a known limitation of conventional quantitative susceptibility mapping (QSM), which is sensitive only to the net effect of the iron and myelin mixture. Several algorithms have been developed to perform susceptibility separation; however, their repeatability has not been thoroughly evaluated. The repeatability of three R₂′‐based algorithms (χ‐Separation, χ‐SepNet, and APART) was investigated using 3‐T scan–rescan data from 21 healthy subjects. Repeatability was assessed using intraclass correlation coefficient (ICC) and repeatability coefficient (RC). Additionally, the average value of the generated maps was used to evaluate the contrast produced by different algorithms. Results showed that repeatability varied between methods and across regions, with better performance achieved by APART and χ‐SepNet. The obtained paramagnetic (χ ⁺) and diamagnetic (χ ⁻) maps had an overall moderate to good reliability, lower than that of conventional QSM primarily because of the lower reliability of the R₂′ input. Region‐wise, repeatability was lower in the frontal lobe and near air–tissue interfaces. The average RC for APART was 4 ppb, except for iron‐rich regions on χ ⁺ maps, where it was 7 ppb. For χ‐SepNet, the average RC was 5 ppb and 10 ppb for χ ⁺ in iron‐rich regions. APART maps had the lowest average susceptibility values, but this was highly dependent on the method used to calculate the initial QSM input. In conclusion, susceptibility source separation showed moderate to good repeatability in most brain regions; however, results were greatly influenced by the algorithm used.

Repeatability of three susceptibility source separation algorithms (χ‐Separation, χ‐SepNet, and APART) was investigated using 3‐T scan–rescan data from 21 healthy subjects. The separation methods showed moderate to good repeatability in most brain regions; however, results were greatly influenced by the algorithm used, with better performance achieved by APART and χ‐SepNet. The average RC for APART was 4 ppb, except for iron‐rich regions on χ ⁺ maps (7 ppb). For χ‐SepNet, the average RC was 5 and 10 ppb, respectively.

Abbreviations

ant

anterior

ANTs

advanced normalization tools

APART

iterative magnetic susceptibility sources separation

AV

average value

CC

corpus callosum

CP

cerebellar peduncle

CR

corona radiata

CRP

cerebral peduncle

CST

corticospinal tract

EC

external capsule

FNIRT

FMRIB's nonlinear image registration tool

FSL

FMRIB Software Library

GRAPPA

generalized autocalibrating partial parallel acquisition

GRE

gradient recalled echo

IC

internal capsule

ICC

intraclass correlation coefficient

JHU

Johns Hopkins University

LOA

limits of agreement

MEDI

morphology‐enabled dipole inversion

MEGE

multiecho gradient echo

ML

medial lemniscus

MNI152

Montreal Neurological Institute 152‐subject average brain template

PCT

pontine crossing tract

post

posterior

ppb

part per billion

ppm

part per million

QSM

quantitative susceptibility mapping

R₂

irreversible transverse relaxation rate

R₂*

effective transverse relaxation rate

R₂′

reversible transverse relaxation rate

RC

repeatability coefficient

retro

retrolenticular

ROMEO

rapid opensource minimum spanning tree algorithm

SD

standard deviation

SD_d

standard deviation of differences

SLF

superior longitudinal fasciculus

SNR

signal‐to‐noise ratio

SOF

superior fronto‐occipital fasciculus

SS

sagittal stratum

STAR

streaking artifact reduction

THR

thalamic radiation

UF

uncinate fasciculus

V‐SHARP

variable‐radius sophisticated harmonic artifact reduction for phase

1. Introduction

Iron and myelin are key players in brain function and measuring their abnormalities and evolution over time is of particular interest in studying neurodegenerative diseases, such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease [1, 2, 3, 4, 5, 6]. Iron and myelin are the dominant sources of magnetic susceptibility in the brain [7] and can be measured using a noninvasive MR technique known as quantitative susceptibility mapping (QSM) produced from phase images obtained using gradient‐echo (GRE) sequences [8, 9]. QSM has been used in a wide range of pathological [10, 11, 12] and lifespan studies [13, 14, 15]. However, it is only sensitive to the net voxel susceptibility and cannot measure individual iron and myelin contributions to a voxel of mixed susceptibility sources.

Recently, new susceptibility mapping techniques enabled independent measurement of paramagnetic (${\chi }^{+}$) and diamagnetic (${\chi }^{-}$) contributions by utilizing both phase and magnitude information of GRE images [16, 17, 18, 19, 20]. The foundation of these advanced methods is that the magnitude of the GRE signal is sensitive to the sum of paramagnetic and diamagnetic sources in a voxel, while the phase is sensitive to the net difference between these sources. Ideally, the R₂ effect should be removed first from the GRE signal decay before applying source separation techniques [16, 19] by utilizing additional images from a spin echo–based sequence. However, some techniques have employed approximations to reduce acquisition time by only requiring GRE images [17, 18, 20].

Susceptibility source separation has shown promising results in phantoms [16, 17, 19], ex vivo [16, 17, 19] and in vivo [16, 17, 18, 19, 20], and has been used to track iron and myelin changes in multiple sclerosis lesions [21, 22, 23] and lifespan trajectories [19, 24, 25]. However, further testing is required to understand how reliable these paramagnetic/diamagnetic measurements are against variability encountered in MRI. QSM, for instance, has shown to be highly repeatable and reproducible across different sites [26, 27, 28, 29, 30], field strengths [31, 32, 33], and variations in imaging parameters [30]. However, there are currently no comprehensive studies on repeatability of source separation methods. Thus, we evaluated the repeatability of three common susceptibility source separation methods in brain using scan–rescan data of healthy subjects collected at a single site at 3 T.

2. Methods

2.1. Data Acquisition

Twenty‐four healthy adults (11 males and 13 females, aged 20–49 years) were imaged at 3 T using a Siemens MAGNETOM Prisma (Siemens Healthineers, Erlangen, Germany) with a 64‐channel head coil after providing written informed consent and under the approval of the local ethics committee. Each participant was scanned twice in two different sessions with a median interval between scans of 5 h (17 subjects completed the two sessions within 22 h, with seven subjects experiencing longer delays between 16 days and 3.6 months, see Table S1). Subjects were part of the Alberta 300 study [34], and scan–rescan variability in QSM and R₂* has been previously reported [30]. Of the 24 subjects who completed the two scans, three subjects were excluded due to poor image quality in one of the acquisitions; thus, 21 subjects were analyzed.

The imaging protocol included a 3D multiecho gradient echo (MEGE) for susceptibility and R₂* mapping with 240 × 203 mm² FOV, 256 × 177 matrix size, 0.9 × 0.9 mm² reconstructed resolution, 88 slices of 1.7‐mm thickness, 13° flip angle, TE1/TR of 3.8/37 ms, six echoes spaced by 5.5 ms using monopolar readouts, GRAPPA factor of 2, and 5.5‐min acquisition time. R₂ mapping used a 2D dual‐echo fast spin echo with 240 × 180 mm² FOV, 256 × 192 matrix size, 0.9 × 0.9 mm² reconstructed resolution, 41 slices of 3.5‐mm thickness, TE1/TE2/TR of 10/93/4000 ms, GRAPPA factor of 2, and 2‐min acquisition time. To accurately measure the flip angle for R₂ modeling, a 2D Bloch–Siegert B1⁺ mapping sequence was also performed with 240 × 240 mm² FOV, 96 × 96 matrix size, 1.3 × 1.3 mm² reconstructed resolution, 40 slices with 3‐mm thickness, 5° flip angle, TE/TR of 2.2/4.6 ms, and 39‐s acquisition time. In addition, a 3D T1‐weighted acquisition from the first scan was used for nonlinear registration to the MNI152 space (250 × 250 mm² FOV, 288 × 288 matrix size, 0.9 × 0.9 mm² reconstructed resolution, 208 sagittal slices of 0.9‐mm thickness, 8° flip angle, and TI/TE/TR of 900/2.4/1800 ms acquired in 3.65 min).

2.2. Relaxation and Field Mapping

Images from individual coil elements for all sequences were combined using the scanner built‐in “adaptive combine” method (software version: VE11C), and no singularities were observed in produced MEGE phase images. R₂ mapping was done by fitting the two points of the dual‐echo fast spin‐echo magnitude signal to a dictionary of simulated signals using Bloch equations over R₂ range of 0.5–100 s⁻¹ [35, 36]. R₂* maps were obtained by solving the monoexponential decay model of MEGE magnitude images as a nonlinear minimization (github.com/MRItech/Quantitative‐Mapping‐Tools).

For MEGE phase images, wraps were resolved using the ROMEO method [37] with phase offset removal option, and phase contribution from sources outside brain was eliminated using a variable‐radius sophisticated harmonic artifact reduction for phase (V‐SHARP) data algorithm with a maximum kernel radius of 12 mm [38]. The tissue field map(s) was then obtained by normalizing the resultant phase images by the imaging frequency and echo time and then averaging along the time dimension if the used algorithm required a single field map input.

2.3. Susceptibility Source Separation

Susceptibility source separation algorithms take R₂′ (i.e., R₂* − R₂) and tissue field map ($\mathrm{\Delta }f$) as input and generate paramagnetic (${\chi }^{+}$) and diamagnetic (${\chi }^{-}$) maps as output. The relation between the inputs and outputs are governed by

$${\mathrm{R}}_2^{\prime }=D_r\left({\chi }^{+}+{\chi }^{-}\right)$$ (1)

$$\mathrm{\Delta }f=d*\left({\chi }^{+}-{\chi }^{-}\right)$$ (2)

where $D_r$ is a relaxometric coefficient relating R₂′ to the susceptibility components and ${\chi }^{+}$ and ${\chi }^{-}$ are the absolute quantities. The tissue field map ($\mathrm{\Delta }f$) captures the net susceptibility effect after convolution ($*$) with a magnetic dipole response ($d$). Because of the convolution in Equation (2), Equations (1) and (2) are solved as a minimization problem with regularization terms [16, 17, 18, 19].

Here, susceptibility source separation was performed using three commonly used algorithms. The first algorithm, χ‐Separation, uses morphology‐enabled dipole inversion (MEDI) with a constant relaxometric coefficient $D_r$ of 137 Hz/ppm obtained via linear regression between R₂′ and standard susceptibility maps in a few iron‐rich regions of interest (ROIs) [16]. This algorithm can optionally take an initial estimate for total susceptibility (${\chi }_0$) as input or otherwise computes it internally using thresholded k‐space division [39]. Thus, the algorithm was tested without and with providing an initial susceptibility map calculated by MEDI dipole inversion [40] or STAR dipole inversion [41]. The second method, 𝜒‐SepNet, is a deep learning model trained on multiorientation dataset, and it was run with a $D_r$ of 114 Hz/ppm [20]. This method calculates ${\chi }_0$ internally. The third method, APART, uses a dipole inversion algorithm with a relaxometric coefficient determined iteratively for each voxel starting from an initial theoretical value of 323.5 Hz/ppm at 3 T [19]. The initial guess is mandatory for APART, and it was computed using STAR (as suggested by authors) and also using MEDI. QSM processing steps adhere to the QSM consensus guidelines [42].

2.4. Registration and ROI Segmentation

R₂ maps were transformed into MEGE space by first rigidly registering the T2w images to the sum‐of‐squares (of all echoes) MEGE magnitude using ANTs software [43] and then applying the obtained registration matrices to the R₂ maps. A total of 31 ROIs were defined on the MNI152 template and used for performance analysis: 24 in white matter (WM) and 7 iron‐rich regions in deep gray matter (DGM). WM ROIs were based on JHU segmentations [44], namely, corticospinal tract (CST); cerebral peduncle (CRP); pontine crossing tract (PCT); genu, body, and splenium of corpus callosum (CC); medial lemniscus (ML); anterior (ant), posterior (post), and retrolenticular (retro) limbs of internal capsule (IC); anterior, superior, and posterior corona radiata (CR); inferior, middle, and superior cerebellar peduncle (CP); posterior thalamic radiation (THR); sagittal stratum (SS); external capsule (EC); cingulum; fornix; superior longitudinal fasciculus (SLF); superior fronto‐occipital fasciculus (SFO); and uncinate fasciculus (UF). Additionally, seven DGM regions were manually segmented on the MNI152 template: caudate, putamen, thalamus, globus pallidus, red nucleus, substantia nigra, and dentate nucleus.

All 31 ROIs were then transformed into MEGE space after nonlinearly registering the MEGE magnitude images to the MNI152 template using FNIRT tool in the FSL package [45]. The nonlinear transformation between MEGE and MNI152 spaces comprised two stages: an initial linear stage from MEGE to T1w space, then a nonlinear stage from T1w to MNI152 space. Segmentations in MEGE space were eroded by one voxel to avoid contamination from surrounding tissue. Mean value in each ROI was recorded and averaged across both hemispheres. Outliers were identified as values above three times the standard deviation of the differences (SD_d) between the two scans, computed over all measurements in DGM or WM. Depending on the separation method, 5–6 outliers out of 147 DGM measurements (i.e., 21 subjects × 7 ROIs) and 13–18 outliers out of 504 WM measurements were excluded from the analysis.

2.5. Repeatability and Quality Measures

Two measures were used for evaluating the repeatability of total susceptibility, paramagnetic and diamagnetic maps obtained using the studied methods. First, the intraclass correlation coefficient (ICC) assesses the reliability of measurements by quantifying the percentage of variation explained by intersubject differences. Second, the repeatability coefficient (RC), computed as 1.96·√2·SD_d, defines the lower bound for repeatable measurements. RC normalized by the mean value in DGM regions (i.e., the average of the seven ROIs) was also computed to remove bias towards methods that produce lower values in general. In addition, the average value (AV) of each output (total, paramagnetic, and diamagnetic maps) was used to determine if all algorithms produce comparable values, and it was calculated as the AV of the ROIs (or voxels) over all subjects and scans. All processing (except registration and segmentation), analyses, and plots were performed using MATLAB (Version R2021a; MathWorks, MA, USA).

3. Results

3.1. Repeatability of Different Algorithms

Example scan–rescan susceptibility maps of one subject and the differences between the output of the studied three source separation methods are illustrated in Figure 1A. Qualitatively, similar maps were obtained from the repeated scans using each method, but contrast varied across different methods. Diamagnetic maps from all methods had artifacts around air–tissue interfaces and vessels, although APART better managed those from small vessels (orange rectangles). While maps from χ‐Separation and 𝜒‐SepNet had higher values than those from APART, they also showed more scan–rescan differences, with 𝜒‐SepNet maps exhibiting fewer differences than χ‐Separation (Figure 1B–D). The influence of the initial QSM on the output of χ‐Separation is minimal, unlike APART that produced total maps that closely resemble the initial inputs (Figures S1 and S2).

FIGURE 1.

(A) Example scan–rescan images from one subject (49‐year‐old male) illustrating output differences between the three studied susceptibility separation methods: $\chi$‐Separation with MEDI‐QSM input, $\chi$‐SepNet, and APART with STAR‐QSM input. Maps obtained using APART generally have smaller values except in few regions (blue arrows) and less artifacts around vessels (orange rectangles) on diamagnetic maps. $\chi$‐SepNet showed fewer artifacts (green rectangles), compared with χ‐Separation. Scan–rescan measurements of four DGM ROIs from the same subject on (B) paramagnetic (${\chi }^{+}$) and (C) diamagnetic (${\chi }^{-}$) maps. The pulvinar segmentation was manually drawn within the thalamic ROI. (D) Diamagnetic profiles along the length of the splenium CC show more consistency with APART and $\chi$‐SepNet methods (scan solid and rescan dashed lines). The profiles were manually drawn curved lines along the center of the splenium CC ROI and averaged over four slices. (E) Illustration of ROIs used in B–D: caudate (blue), putamen (yellow), pulvinar (green), and splenium (brown).

The lower values in APART are in part dictated by the initial QSM input, as well as the generally higher relaxometric coefficients utilized by this method. The relaxometric coefficient determined by APART with the default initial QSM input (i.e., from STAR) varied remarkably within regions and across the brain, but the mean (±SD) was 209 (±99) Hz/ppm in iron‐rich ROIs and 299 (±62) Hz/ppm in WM ROIs. With initial QSM from MEDI, the mean (±SD) relaxometric coefficient decreased to 165 (±98) Hz/ppm in iron‐rich ROIs and 293 (±67) Hz/ppm in WM ROIs. In both cases, the APART relaxometric coefficient was much higher than the fixed 137 or 114 Hz/ppm used by the other two methods. However, APART showed moderately higher diamagnetic content in some iron‐rich regions, such as globus pallidus and pulvinar (blue arrows in Figure 1A, also Figure 1C).

The voxel‐based metric maps shown in Figure 2A–C indicate that separated susceptibility components using APART had overall lower AVs. For all methods, paramagnetic and diamagnetic maps had lower ICC than total or initial susceptibility maps (Figure S2). Although separation maps from 𝜒‐SepNet had slightly higher AVs than those from χ‐Separation, they showed higher ICC and lower RC values. In general, regions near air–tissue interfaces and WM tracts in the frontal lobe and central regions showed the lowest ICC. For the relaxation part (Figure 2D), R₂ had the highest overall ICC, and R₂′ had the lowest. Variability in R₂* stemmed mainly from field inhomogeneity caused by susceptibility (i.e., R₂′).

FIGURE 2.

Voxel‐wise maps of (A) average voxel value over all subjects; (B) intraclass correlation coefficient (ICC); and (C) repeatability coefficient (RC) for total, paramagnetic, and diamagnetic maps reconstructed using the three studied algorithms. Overall, APART maps had lower susceptibility values. Regions of lowest ICC in paramagnetic and diamagnetic maps were near air–tissue interfaces and white matter tracts in the frontal lobe and the central region, as in R₂′. (D) Voxel‐wise maps for R₂*, R₂, and R₂′ relaxation rates showing superior and inferior metrics for R₂ and R₂′, respectively.

Table 1 complements Figure 2 by listing the mean of the ROIs in DGM and WM for the same three measures. All methods scored (on average) at least moderate reliability (ICC > 0.5) in both DGM and WM and on both paramagnetic and diamagnetic maps. However, both APART and 𝜒‐SepNet consistently showed better reliability and reached excellent level for paramagnetic measurements in DGM. When comparing the reliability of susceptibility separation to that of its inputs (i.e., R₂′ and QSM), the reliability of paramagnetic/diamagnetic values were overall intermediate, lying between the higher reliability of total susceptibility (i.e., QSM) and the lower reliability of R₂′ relaxation.

TABLE 1.

Mean (±standard deviation) of average value, ICC, and RC for relaxation and susceptibility maps, calculated based on ROI measurements. Susceptibility separation was performed using default settings for each method.

		R2*	R2	R2′	Total			${\chi }^{+}$			${\chi }^{-}$
					χ‐Separa.	χ‐SepNet	APART	χ‐ Separa.	χ‐SepNet	APART	χ‐Separa.	χ‐SepNet	APART
AV	DGM	28 ± 6	17 ± 2	11 ± 5	66 ± 41	72 ± 45	50 ± 28	75 ± 38	84 ± 42	58 ± 30	9 ± 4	12 ± 7	8 ± 2
	WM	22 ± 2	14 ± 1	7 ± 2	−14 ± 10	−19 ± 8	−11 ± 8	20 ± 6	19 ± 4	8 ± 2	34 ± 9	38 ± 8	19 ± 8
ICC	DGM	0.80 ± 0.19	0.92 ± 0.06	0.66 ± 0.29	0.95 ± 0.05	0.95 ± 0.03	0.96 ± 0.03	0.88 ± 0.18	0.91 ± 0.09	0.96 ± 0.04	0.52 ± 0.23	0.72 ± 0.14	0.78 ± 0.10
	WM	0.56 ± 0.20	0.85 ± 0.08	0.48 ± 0.20	0.82 ± 0.11	0.81 ± 0.11	0.83 ± 0.10	0.64 ± 0.12	0.65 ± 0.19	0.70 ± 0.13	0.61 ± 0.18	0.69 ± 0.13	0.73 ± 0.17
RC	DGM	3.2 ± 1.5	0.6 ± 0.4	3.4 ± 1.7	8.9 ± 4.9	10.8 ± 7	6.4 ± 3.4	12.1 ± 6	10.3 ± 6	7.1 ± 4.2	7.6 ± 4.0	4.8 ± 3.2	2.2 ± 1.0
	WM	2.2 ± 0.7	0.4 ± 0.2	2.1 ± 0.7	5.1 ± 2.1	3.5 ± 1.7	3.8 ± 1.8	6.9 ± 2.1	3.8 ± 1.8	2.6 ± 1.1	7.8 ± 2.4	4.1 ± 1.8	3.7 ± 1.5

Note: Bold font highlights the highest figure among separation methods in each category. Average values (AVs) are in units of Hz for relaxation rates and ppb for susceptibility.

The summary of all the performance measures assessing susceptibility separation methods is shown in Figure 3, where APART outperformed others in the repeatability measures and had the lowest AV measure. The advantage of the APART method is more remarkable in diamagnetic regions. Changing APART initial QSM to MEDI increased its AVs in DGM, but not in WM, to comparable levels with the other methods. On the other hand, the effect of the initial susceptibility map on the χ‐Separation output was minimal. Maps produced by 𝜒‐SepNet had higher or equal AV scores to those produced using χ‐Separation but better ICC and RC scores. When the RC measure was normalized by the mean value of DGM ROIs, the advantage of APART in RC measure became less pronounced versus 𝜒‐SepNet.

FIGURE 3.

Average performance metrics of the studied separation methods over all ROIs in deep gray matter and white matter regions. χ‐Separation was tested without QSM input and with QSM obtained using STAR and MEDI. APART was tested with QSM input produced using STAR and MEDI dipole inversion algorithms. APART method had higher scores in ICC and RC and lower AV. $\chi$‐SepNet scored in second place. Unlike χ‐Separation, changing the QSM input for APART affected its performance remarkably. RC is presented in negative form to indicated better performance by values far from the center.

3.2. Repeatability Across Regions

Figure 4 shows ICC scores across different ROIs for total, paramagnetic, and diamagnetic maps obtained using the different studied methods. In many ROIs, reliability varied across methods. Iron‐dominated ROIs in DGM showed good to excellent reliability (ICC > 0.75) on total and paramagnetic maps but only good ICC for the diamagnetic component with APART (moderate ICC otherwise). On the other hand, myelin‐dominated regions showed moderate to good reliability (0.5 < ICC < 0.9) on all maps with total susceptibility measurements being notably superior. Only few WM ROIs showed excellent ICC (only with APART) on separated components, such as anterior and post IC, middle CP, and UF on the diamagnetic part. Region of lowest diamagnetic reliability varied between methods, but most showed low reliability on R₂′ map as well. Common ROIs of poor diamagnetic reliability include superior CR and inferior CP. ROIs with lowest paramagnetic reliability were those with low R₂′ reliability or low iron content, such as SS, inferior CP, and body and splenium CC.

FIGURE 4.

(A) Illustration of ROI segmentations overlaid on the average diamagnetic map. (B) ICC of total, paramagnetic, and diamagnetic susceptibility and R₂′ measurements for different ROIs in deep gray matter and white matter regions. (C) Mean paramagnetic and diamagnetic susceptibility from the same ROIs. Susceptibility maps were obtained using the studied methods with default input. Most ROIs had moderate to good reliability on all maps, with only few ROIs scoring excellent (above blue dashed line) or poor (below red dashed line) reliability. Iron‐rich ROIs had good to excellent reliability on total and paramagnetic maps. The gray matter and white matter ROIs have been ordered based on best to worst ICC value of total susceptibility obtained using APART.

A Bland–Altman analysis for DGM and WM regions is shown in Figures 5 and 6 for ROI measurements from the three methods. The bias between the two scans was within 2 ppb, and only statistically significant (p < 0.05) in total susceptibility and main component (i.e., χ ⁺ in DGM) measurements of χ‐SepNet. The lowest limits of agreement were for APART maps, within ±3.7 ppb for the diamagnetic component across the brain, and within ±2.7 ppb in WM and ±8 ppb in iron‐rich regions for the paramagnetic part. Overall, measurements were symmetric around the bias line with the scan–rescan difference generally increasing for higher mean values. The highest scan–rescan difference in deep gray matter was observed in red nucleus and substantia nigra, both of which are small ROIs with high iron concentrations. For WM, the highest difference was found in small ROIs, those in proximity to veins, or in tracts that are parallel to the direction of B₀.

FIGURE 5.

Bland–Altman plots of susceptibility separation output from studied method with default settings for ROIs in deep gray matter. No significant bias was observed between the two scans except for the total and paramagnetic susceptibility obtained using $\chi$‐SepNet (bias was 2 and 1.8 ppb, respectively). Limits of agreement (LOA) are within 12, 10, and 8 ppb for χ‐Separation, $\chi$‐SepNet, and APART, respectively. Points are color‐coded according to the ROIs labels shown in Figure 4A.

FIGURE 6.

Bland–Altman plots of susceptibility separation output from studied method with default settings for ROIs in white matter. No significant bias was observed between the two scans except for the total and diamagnetic susceptibility obtained using $\chi$‐SepNet (less than 1 ppb). Limits of agreement (LOA) are within 7.6, 4.2, and 3.8 ppb for χ‐Separation, $\chi$‐SepNet, and APART, respectively. Points are color‐coded according to the ROIs labels shown in Figure 4A.

4. Discussion

This study investigated the repeatability of susceptibility source separation at 3 T using single‐site data of healthy subjects. Paramagnetic and diamagnetic measures obtained using three commonly used and publicly available algorithms were assessed in 31 ROIs across deep gray matter and WM regions. Repeatability varied between methods and regions, with the APART method being overall superior for reliability, achieving ICC greater than 0.5 in most ROIs. $\chi$‐SepNet achieved ICC > 0.5 in 75% of the ROIs, remarkably better than χ‐Separation. With APART, the mean RC was within 3.7 ppb for the diamagnetic measure and 2.6 ppb/7.1 ppb for the paramagnetic measure in white/deep gray matter.

Performance variation across different methods stems from differences in their source separation models. The APART model, for instance, has several differences from the other two algorithms, which might aid in reliability performance. First, it solves the separation inverse model at each echo time, which increases the number of points used in solving the ill‐conditioned dipole inversion problem. Previous studies have shown that extending QSM model to multiple echoes improved robustness [46, 47, 48]. Second, it puts less weight on R₂′ information, compared with phase or regularization terms, which could minimize the propagation of additional variation from R₂′ data that was found to have much lower repeatability. While reducing R₂′ weighting could improve reliability, it may also lead to erroneous separation values. However, in the absence of ground truth data, it is difficult to draw definitive conclusions. In addition, APART calculates a voxel‐wise relaxometric coefficient, instead of using a global value for all voxels. The variable relaxometric coefficient allows for more flexible data fitting of R₂′ to QSM but is also more sensitive to noise and artifacts in R₂′ and thus may deviate from the biological meaning of the parameter. Furthermore, APART explicitly constrains total susceptibility and structural details to the QSM input, instead of relying on magnitude‐driven regularization. All these modifications seem to reduce variability in the APART outcome and lead to better repeatability. However, this method resulted in generally lower paramagnetic and diamagnetic values, which is in part influenced by the initial QSM inputted to the algorithm, and the dynamic assignment of relaxometric coefficients that forces smaller paramagnetic/diamagnetic values when $D_r$ increases (average D _r  > 165 Hz/ppm regardless of used initial QSM, compared with 137 or 114 Hz/ppm in the other two methods).

Compared with χ‐Separation, $\chi$‐SepNet had better performance, achieving higher repeatability and producing maps with fewer artifacts without dampening the values in the paramagnetic and diamagnetic maps. This deep learning method was trained on paramagnetic and diamagnetic maps obtained from multiorientation data of six directions [20]. This reduces streaking artifacts that are associated with single‐orientation susceptibility mapping and improves SNR due to the multiple phase images and R₂* maps used in the reconstruction. In addition, $\chi$‐SepNet assigns a lower weight to the R₂′ information compared with χ‐Separation, as the loss function used in the training of $\chi$‐SepNet minimized the error with respect to the initial QSM, the tissue field, and R₂′, while the cost function of χ‐Separation relied only on the tissue field and R₂′. This may have contributed to the improved repeatability of $\chi$‐SepNet. However, the generalizability of deep learning methods to unseen cases might be limited when trained on small or less diversified datasets. $\chi$‐SepNet was trained on just over 20,000 3D patches (cuboid with 64‐voxel side) produced from datasets of five healthy volunteers [20], and thus, further evaluation under more diverse conditions is needed. Note that the training data of $\chi$‐SepNet had an isotropic 1‐mm³ spatial resolution, which differs from the resolution used in this study (0.9 × 0.9 × 1.7 mm³). Although the network employs a resolution generalization technique [20], the resolution mismatch and voxel anisotropy might have negatively impacted the repeatability of $\chi$‐SepNet.

Repeatability was lower in paramagnetic and diamagnetic maps than in the total map likely because the separated maps inherit additional variability from the R₂′ map that has lower repeatability than the total susceptibility map. Within each of the two separated maps, repeatability also varied across regions: from poor to excellent in both maps. Potential factors contributing to this heterogeneity include variations in iron and myelin concentrations across the brain, with regions of low concentrations producing contrast closer to noise floor and thus less reliable measures. Also, lower repeatability is expected in regions close to sinuses, where signal can lose coherence rapidly from the strong susceptibility near the air–tissue interface, as well as regions likely to be corrupted by eye motion, such as near the frontal lobe. Another factor is the dependency of WM susceptibility and R₂′ measurements on the orientation of fiber tracts with respect to B₀. Several studies have shown a sinusoidal relationship between measured net susceptibility/R₂* and the angle between WM tracts and B₀ [49, 50, 51], making WM repeatability region/orientation dependent. Additionally, because the scan–rescan images were acquired in different sessions, it is expected that variation in head tilt can introduce variability between repeated measurements in regions of highly ordered anisotropic microstructure. In this study, the head tilt difference between the two scans ranged from −1.86° to 7.44° (mean ± SD of 2.24° ± 2.1°), potentially contributing to the observed variability.

In short, this study shows that diamagnetic and paramagnetic maps obtained using susceptibility source separation can achieve at least moderate reliability in many ROIs. Among the studied methods, APART had the best repeatability, followed by χ‐SepNet, with an average RC of 3.7 (7.1 ppb for χ ⁺ in DGM) and 4.8 ppb (10.3 ppb for χ ⁺ in DGM), respectively. The remarkable difference between average measurements obtained using different algorithms means that comparing or pooling diamagnetic/paramagnetic measurements produced using different methods might not be straightforward. Nevertheless, recent studies have reported paramagnetic or diamagnetic changes of similar or greater magnitude than the RCs cited above, whether in multiple sclerosis lesions [22] or in comparisons between healthy and clinical populations [52]. These findings suggest that utilizing susceptibility separation to track paramagnetic and diamagnetic changes is promising.

Limitations of this work include testing only one set of imaging parameters. However, the sequence parameters are reflective of typical whole brain studies that use 3D MEGE, although the R₂ sequence used a thicker 3.5‐mm slice. A further limitation is that only two scans were available per subject, because a simple scan–rescan design was used. In addition, the time between the two scans was variable, with three subjects having more than 20 days between scans; thus, results could also be affected by scanner fluctuation. However, scan–rescan differences for these subjects were below or around the group average in most ROIs. Another limitation is that only R₂′‐based source separation methods were investigated, as these use more accurate models compared with those utilizing approximations. Comparing the performance of R₂′ versus R₂*‐based source separation methods is out of scope of this work and has been partially evaluated in previous studies [18, 23, 53]. Finally, while repeatability can be exactly measured, the gold standard values for separated paramagnetic and diamagnetic components are not known; thus, accuracy of the separation methods remains uncertain.

5. Conclusion

The repeatability of susceptibility source separation is greatly influenced by the used algorithm. APART and χ‐SepNet outperformed χ‐Separation and achieved moderate to good reliability in most brain regions. Care should be taken when interpreting susceptibility changes on the order of the reported RCs.

Author Contributions

Nashwan Naji: methodology, software, formal analysis, investigation, writing – original draft, visualization. Peter Seres: data curation, software, writing – review and editing. Gerald Moran: supervision, writing – review and editing. Christian Beaulieu: conceptualization, investigation, project administration, writing – review and editing, funding acquisition. Alan H. Wilman: conceptualization, supervision, project administration, writing – review and editing, funding acquisition.

Funding

Funding from the Canadian Institutes of Health Research (A.H.W.), Mitacs Elevate and Siemens Healthcare Limited (N.N. and A.H.W.), and University Hospital Foundation and Canada Research Chairs (C.B.) is acknowledged.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Figure S1: (A) Scan–rescan R₂′ and initial Susceptibility maps used as input to χ‐Separation and APART for the same subject shown in Figure 1. (B) The influence of the supplied initial susceptibility map on the total map obtained using χ‐Separation and APART. With APART, the total susceptibility closely matches the input QSM, while χ‐Separation produces similar total map regardless of the initialization method.

Figure S2: Voxel‐wise maps of average voxel value over all subjects, intraclass correlation coefficient (ICC), and repeatability coefficient (RC) for (A) R₂′ and initial QSM used as input to susceptibility separation methods and (B) total susceptibility map obtained using χ‐Separation and APART. χ‐Separation‐produced total maps look similar to MEDI‐QSM and independent of initial QSM. However, they have slightly degraded ICC and higher RC (gray arrows) compared with MEDI‐QSM, likely because of the R₂′ influence. APART‐produced total maps (and their ICC and RC maps) closely match the input QSM.

Table S1: Distribution of interscan interval of all participants

Naji N., Seres P., Moran G., Beaulieu C., and Wilman A. H., “Repeatability of Susceptibility Source Separation Methods in Human Brain: A Single‐Site Study at 3 T,” NMR in Biomedicine 39, no. 2 (2026): e70225, 10.1002/nbm.70225.

Data Availability Statement

The measurements and analysis scripts of this study are available from the corresponding author upon request. Participant MRI images and maps are not publicly available due to ethical considerations.