Super-resolution QSM in little or no additional time for imaging (NATIve) using 2D EPI imaging in 3 orthogonal planes

Quantitative Susceptibility Mapping has the potential to provide additional insights into neurological diseases but is typically based on a quite long (5 – 10 min) 3D gradient-echo scan which is highly sensitive to motion. We propose an ultra-fast acquisition based on three orthogonal (sagittal, coronal and axial) 2D simultaneous multi-slice EPI scans with 1 mm in-plane resolution and 3 mm thick slices. Images in each orientation are corrected for susceptibility-related distortions and co-registered with an iterative non-linear Minimum Deformation Averaging (Volgenmodel) approach to generate a high SNR, super-resolution data set with an isotropic resolution of close to 1 mm. The net acquisition time is 3 times the volume acquisition time of EPI or about 12 s, but the three volumes could also replace “ dummy scans ” in fMRI, making it feasible to acquire QSM in little or No Additional Time for Imaging (NATIve). NATIve QSM values agreed well with reference 3D GRE QSM in the basal ganglia in healthy subjects. In patients with multiple sclerosis, there was also a good agreement between the susceptibility values within lesions and control ROIs and all lesions which could be seen on 3D GRE QSMs could also be visualized on NATIve QSMs. The approach is faster than conventional 3D GRE by a factor of 25 – 50 and faster than 3D EPI by a factor of 3 – 5. As a 2D technique, NATIve QSM was shown to be much more robust to motion than the 3D GRE and 3D EPI, opening up the possibility of studying neurological diseases involving iron accumulation and demyelination in patients who find it difficult to lie still for long enough to acquire QSM data with conventional methods.


Introduction
The prevalence of neurodegenerative diseases, such as Alzheimer's, Parkinson's and Huntington's disease, is rising and expected to reach 152 million by the year 2050 (Livingston et al., 2020).Protein misfolding and aggregation, impaired metabolism and related oxidative stress amongst other factors, have been suggested to play an important role in many of these pathologies (Gerlach et al., 1994;Li and Reichmann, 2016;Dexter et al., 1991).Quantitative Susceptibility Mapping (QSM) has been shown to reveal increased iron deposition (Langkammer et al., 2012), making it a valuable tool for the assessment and monitoring of neurodegenerative diseases (Ravanfar et al., 2021).QSM also provides excellent contrast between grey matter, white matter and myelin and thus allows delineation of deep grey matter structures and assessment of demyelination, for instance (Shmueli et al., 2009).Nevertheless, the use of susceptibility mapping in clinical practice is limited by the long acquisition times of the conventionally-used 3D gradient-echo (GRE) sequence, which makes it both problematic to acquire within clinical protocols and highly sensitive to motion.Patients with neurodegenerative diseases often suffer from uncontrollable motion and are not able to lie still during such long acquisitions.Motion artefacts decrease the reliability of the results and have been shown to obscure statistically significant differences in QSM between controls and patients, leading to false findings (Meineke et al., 2018).
Recent years have seen some use of EPI imaging for QSM; either with dedicated, high-resolution (Langkammer et al., 2015;Tourell et al., 2020;Sun and Wilman, 2015;Stäb et al., 2017) acquisitions or from fMRI data (Sun et al., 2017).Susceptibility mapping has been shown to require high-resolution, isotropic data for accurate results, however (Karsa et al., 2019).3D EPI, an alternative to 3D GRE for susceptibility mapping, can provide the required high-resolution, isotropic images in significantly reduced acquisition time.Nevertheless, 3D EPI acquisition still takes between 30 s and 3 mins because of the long echo train required to encode the whole brain volume.In patient cohorts, such as those suffering from neurodegenerative diseases, this may still result in significant motion artefacts, impairing the validity of the results.2D EPI, on the other hand, provides very short acquisition times (40-80 ms per slice, 1-5 s per volume), particularly when acquired using simultaneous multi-slice methods (Setsompop et al., 2012), making it much more robust to motion.At high slice resolution, though, 2D EPI suffers from low SNR, requiring anisotropic acquisitions with thick slices to achieve satisfactory image quality.Such thick-slice acquisitions are suboptimal for susceptibility mapping (Karsa et al., 2019), however.
Super-resolution (SR) imaging refers to a group of methods that generate a high-resolution image from a number of low-resolution (LR) acquisitions (Fiat, 2001;Greenspan et al., 2002;Ropele et al., 2010).In MRI, super-resolution techniques are mainly used to improve the through-slice resolution of 2D imaging and the trade-off between signal-to-noise ratio (SNR) and the acquisition time (TA) compared to direct high-resolution (HR) acquisition (Plenge et al., 2012).Super-resolution techniques have been widely applied to fetal MR imaging in combination with fast turbo spin-echo acquisition to reach motion artefact-free high-resolution, isotropic images (Rousseau et al., 2010;Rousseau et al., 2006;Sui et al., 2021;Askin Incebacak et al., 2022).Various acquisition schemes have been suggested; acquiring the LR images either shifted relative to each other by a subpixel distance in the through-plane (slice) direction (Greenspan et al., 2002) or rotated relative to each other in the frequency-and/or phase-encoding direction (Shilling et al., 2009), with the extreme case of orthogonal LR images (Van Reeth et al., 2012;Scherrer et al., 2012).The combination of super-resolution techniques with 2D EPI imaging with thick slices has the potential of achieving high SNR, high-resolution imaging that is fast enough to avoid motion artefacts.This idea was first demonstrated with 2D EPI for fMRI (Peeters et al., 2004), in which several LR volumes shifted along the slice-selection direction were used to reconstruct the HR, isotropic image.The redundancy between the shifted LR images was shown, however, to limit the gain which could be achieved with super-resolutionrotational increments provide more efficient k-space sampling (Plenge et al., 2012;Shilling et al., 2009).Super-resolution techniques frequently assume a signal acquisition model and try to solve the inverse problem of generating a high-resolution image from several low-resolution scans, which can be solved by iterative minimization using prior knowledge (e.g.smoothness) (Plenge et al., 2012;Van Reeth et al., 2012).
Regardless of acquisition or processing strategy, super-resolution techniques require precise registration of the LR images.Only when the geometric transformations between the LR images are correctly estimated with sub-pixel accuracy can the LR images be combined to generate a high-resolution image that contains additional frequency content (Van Reeth et al., 2012).EPI imaging, however, suffers from geometric distortions along the phase-encoding (PE) direction due to the long readout and thus low-frequency bandwidth in that dimension.In the case of shifted LR EPI images, these distortions arise along the same axis, so that a high-quality (albeit distorted) super-resolution image can be generated without the need for their correction.In the case of rotational increments, these distortions arise along different directions and thus must be corrected to avoid the introduction of blurring into the super-resolution image.Although distortion correction methods (Dymerska et al., 2016;Jezzard and Balaban, 1995;Andersson et al., 2001) can be used to mitigate them, as was shown by Scherrer et al. for super-resolution DWI from orthogonal EPI acquisitions (Livingston et al., 2020), none of these methods works reliably enough to ensure precise co-registration of the three orthogonal images, particularly not at high field strengths (> 3T) or in areas of severe distortions, such as the brainstem or orbito-frontal regions.Conventional super-resolution techniques assume a prior, precise co-registration of the low-resolution images and lead to an increased blurring if that is not achieved (He et al., 2007).
Iterative non-linear Minimum Deformation Averaging (Volgenmodel) co-registration has been shown to allow precise co-registration of brain images over cohorts of subjects and thus the generation of highresolution brain atlases (Grabner et al., 2006;Grabner et al., 2013;Fonov et al., 2011;Janke and Ullmann, 2015).It has also been applied to motion-correct fMRI time-series data, where the motion in combination with magnetic field inhomogeneities and physiological fluctuations leads to non-linear deformations between the fMRI volumes (Bollmann et al., 2017).In that work, Bollmann et al. showed that the sub-voxel shifts between the individual EPI volumes which are introduced by the distortions inherent to EPI allow sub-voxel information to be gathered and thus increase the spatial resolution of the results (Bollmann et al., InpressBollmann et al., 2017;Shaw et al., 2019).
In this study, we propose the use of orthogonal 2D EPI acquisitions with thick slices to generate a super-resolution, isotropic and high SNR image for Quantitative Susceptibility Mapping.An iterative non-linear co-registration (Volgenmodel) (Bollmann et al., 2017; https://github.com/CAIsr/volgenmodel-nipype) approach allows the orthogonal low-resolution EPIs to be precisely co-registered and sub-voxel information retrieved.Additionally, to remove gross distortions and thus generate not only sharp but also distortion-reduced (i.e.closer to anatomical shape) susceptibility maps, we propose applying fieldmap-based distortion correction to the acquired orthogonal LR images.With very short slice acquisition times, a net acquisition time of only three times the volume TA of EPI and the possibility to co-register the individual EPI volumes, the proposed approach drastically reduces the motion sensitivity of QSM.At the beginning of fMRI acquisition, circa 10 s of "dummy scans" (i.e.3-5 scans depending on the sequence TR) -executions of exactly the same pulse sequence but with the data acquisition disabledare generally used to establish steady-state magnetization and thus ensure signal consistency between the acquired EPI volumes (Soares et al., 2016, Bernstein et al., 2004).The three orthogonal EPI images acquired for the proposed method could replace the dummy scans, providing the possibility of high-resolution susceptibility mapping in No Additional Time for Imaging (NATIve).We propose NATIve as an approach for fast susceptibility mapping in patients with reduced ability to stay still for long acquisitions, such as patients with neurodegenerative diseases.

Subjects, phantoms, hardware
Six healthy volunteers (3 females; age 31.7 ± 3.9 years) were scanned using a 3T Siemens Prisma scanner and a 64-channel Siemens headneck coil.Volunteers 1-5 were measured for qualitative comparison of the methods with a protocol consisting of 3D GRE, 3D EPI, isotropic 2D EPI and three orthogonal low-resolution 2D EPIs for NATIve.Volunteer 6 (male, 18 years) was scanned for SNR comparison and Volunteer 3 (male, 45 years) was scanned a second time for a comparison of motion robustness.A group of 21 patients with Multiple Sclerosis (MS) -a chronic inflammatory autoimmune disease of the CNS, leading to focal demyelinated grey and white matter lesionswas also measured with a 20-channel Siemens head-neck coil to assess the capability of the proposed method to detect smaller structures, such as MS lesions, and to assess its motion robustness within a patient population.Written, informed consent was given by all volunteers and patients and the study was approved by the Ethics committees of the Medical University of Vienna (volunteers) and Medical University of Graz (patients).Two patient datasets were excluded because the phase combination was performed incorrectly, leaving 19 patient datasets (of 11 females; age 42.8 ± 10.6 years).A round homogeneous oil phantom was also measured to compare the sharpness of edge profiles as a measure of estimating spatial resolution and for the SNR assessment.
As a gold standard for QSM, a sagittal 3D GRE image was acquired with FLASH sequence (Haase et al., 1986) To compare the image quality of NATIve with direct high-resolution 2D SMS EPI imaging, for volunteers and for the oil phantom, an isotropic sagittal 2D EPI scan was acquired with PE posterior-anterior, slicethickness = 0.9 mm, 126 slices (the maximum possible) with an 11 % slice-gap, TE = 35 ms, single-shot, TR = 7.1 s (equal to net TA) and other parameters being the same as for the low-resolution EPIs, including the acceleration.As an alternative fast Quantitative Susceptibility Mapping Fig. 1.The processing pipeline of Quantitative Susceptibility Mapping with NATIve.In the first step, the three orthogonal 2D EPI phase images with thick slices are unwrapped and distortion-corrected (DC) based on a short field-mapping prescan.In the second step, these "total fields" are background field removed (BFR), generating "local fields".In the third step, the local fields are non-linearly co-registered, using the deformation fields estimated from magnitude data using Volgenmodel, and averaged.In the final step, the dipole inversion (DI) is applied to generate the NATIve QSM image.method, a 3D EPI sagittal scan was acquired in the volunteers, three MS patients and in the oil phantom, using a CAIPIRINHA-encoded (Breuer et al., 2005, Breuer et al., 2006) research application sequence (Jin et al., 2021), with PE posterior-anterior, TE = 34 ms, 4 shots, TR = 67 ms, resolution = 1.0 × 1.0 × 1.0 mm, matrix = 224 × 224 × 160, rBW/pixel = 1397 Hz, FA = 17 • , parallel imaging acceleration of R = 1 × 2 with 3D shift = 1 and using water-only excitation (with special card parameters bipolar WE enabled and improved water excitation set to weak), resulting in net TA = 23 s.The sagittal orientation was used for all reference methods as this requires the lowest number of slices for full brain coverage.
For the SNR assessment, the oil phantom was scanned in a second session with the given protocol but with each sequence changed to acquire 12 repetitions.To avoid the potential motion of oil inside, the phantom was put inside the scanner and left to stabilize for 15 min before starting the measurement.For in vivo SNR assessment, Volunteer 6 was scanned with two repetitions of each sequence.
For the assessment of motion robustness, Voluneer 3 was scanned a second time, but with the same protocol acquired twicethe first time without a motion and the second time with a motion, when the volunteer was instructed to roll his head about the z-axis to the left and right (yaw motion) approximately every 20 s of the acquisition and the motion taking circa 5 s.For isotropic 2D EPI and the low-resolution 2D EPI acquisitions, a series of 12 and 15 vol respectively were acquired instead of a single volume acquisition to ensure that some of these captured the periods of motion.

NATIve reconstruction
To reconstruct high-resolution, isotropic susceptibility map from the three orthogonal low-resolution 2D EPIs (Fig. 1), the LR magnitude images were distortion-corrected using a fieldmap-based approach, FSL FUGUE (FUGUE -FslWiki, n.d.), then non-linearly co-registered and upsampled to the high-resolution image using Volgenmodel (Janke and Ullmann, 2015; https://github.com/CAIsr/volgenmodel-nipype).Over a number of iterations, with increasing resolution in each, Volgenmodel estimates non-linear transformations between several images using the NlpFit function from MINC tools (https://github.com/BIC-MNI/minc-tools),with upsampling based on sinc interpolation.The Volgenmodel was set up to start with a grid of 32 mm and to finish with 1 mm, with the iterations reducing from 20 per stage for the biggest step sizes to 5 per stage for the lowest step sizes, and with the symmetric averaging and robust averaging (used for atlas composition) deactivated.A combination of phase images over coils was performed online, using Siemens' pre-scan normalize and Adaptive Combine approach (Jellus and Kannengiesser, 2014).The coil-combined phase data were unwrapped using ROMEO (Dymerska et al., 2021, https://github.com/korbinian90/ROMEO), distortion-corrected (Jezzard andBalaban, 1995, FUGUE -FslWiki, n.d., Robinson andJovicich, 2011) and background fields removed using RESHARP (Sun and Wilman, 2014).The resulting maps of local fields were sinc-interpolated to the high resolution and the deformation fields, estimated from the magnitude data, were applied.The co-registered local fields were averaged and a susceptibility map was generated using a dipole inversion with STAR (Li et al., 2015).For RESHARP and STAR, the implementations within the Sepia toolbox (Chan and Marques, 2020) were used.Lastly, the susceptibility maps were referenced using a whole-brain average.

Analysis
For all methods being compared (iso2D EPI, 3D EPI and 3D GRE), the same QSM processing pipeline as for NATIve was used, other than that for 3D GRE, ASPIRE coil-combination (Eckstein et al., 2018) was used.
To assess the effects of the proposed processing without the potential confound of discrepancies between orthogonal acquisitions (motion, distortions, slice profiles, etc.), the acquired 1 mm isotropic 3D GRE image was down-sampled to three orthogonal images with 3 mm thick slices, which were then processed with the NATIve processing pipeline described.The magnitude images and the susceptibility maps of the original high-resolution 3D GRE and of the NATIve GRE were compared.
To compare the spatial resolution of the acquired images with consideration of image sharpness (i.e.not the nominal, but the achieved resolution), signal profiles at the edge of the phantoma sharp borderwere examined.The steepness of profiles through the edge of the spherical phantom in NATIve EPI images was compared with those of the low-resolution 2D EPI images with thick slices, and with isotropic 2D EPI, 3D EPI and 3D GRE images, with a higher steepness indicative of a higher resolution (Greenspan et al., 2002).For each, a border profile of 16 voxels along each of the three planes (x, y and z), normal to the phantom circumference, was obtained.Some displacements were present between profiles in different image series due to residual distortions, different matrix sizes, etc.To align them, profiles were shifted by an integer number of voxels until the highest correlation (and thus best correspondence) was achieved.10 voxels spanning the phantom border were used in the assessment.For NATIve EPI, 2D EPI and 3D EPI, the three orthogonal profiles of each were averaged.For the three low-resolution 2D EPI images with thick slices, the six high-resolution profiles and the three low-resolution profiles were averaged, respectivelya) HR profiles: along i) posterior-anterior and ii) left-right of the transversal acquisition, along iii) posterior-anterior and iv) head-foot of the sagittal acquisition, and along v) head-foot and vi) left-right of the coronal acquisition and b) LR profiles: along i) head-foot of the transversal acquisition, ii) left-right of the sagittal acquisition and iii) posterior-anterior of the coronal acquisition.
The edge widths in NATIve EPI, isotropic 2D EPI and 3D EPI images, and also in the high-resolution plane of low-resolution 2D EPI images, were also compared quantitatively; 20 edge profiles of 10 voxels length were extracted and fit with a sigmoid function (Greenspan et al., 2002): where a is given by the slope of the function, c is the location of the centre and b and d give the y-axis range of the function.The edge width was then calculated as (Greenspan et al., 2002): and the mean values over the 20 edges were compared.
To assess the SNR and SNR efficiency (Sodickson et al., 1999), given as: of the compared methods -NATIve EPI, isotropic 2D EPI, 3D EPI and 3D GREtwo different approaches were used.The 7 echoes of the 3D GRE data were prior combined using the root-sum-of-squares approach to maximize the SNR (Jutras et al., 2017).In phantom assessment, the SNR was estimated from the magnitude images on a pixel-by-pixel basis (Reeder et al., 2005) (i.e.generating SNR maps) from the 12 identical acquisitions, given as: where S t is the average signal and σ t is the standard deviation over the multiple measurements.An ROI extending over the whole phantom was then defined by masking the magnitude images using FSL BET tool (Smith, 2002) and subsequent erosion by 3 voxels.Over this ROI, median SNR and SNR efficiency were calculated.For in vivo SNR assessment, an approach requiring only two identical acquisitions was used thanks to its higher motion robustness 157 .First, the magnitude images Bachrata et al. from all acquisitions were co-registered and 16 ROIs were manually defined -8 within the thalamus and 8 within the white matter, each of 25 voxels.The SNR was then calculated as: The super-resolution NATIve EPI susceptibility maps were compared with the QSMs generated from other scans; the isotropic 2D EPI, 3D EPI and the gold-standard 3D GRE data.The comparison included a qualitative visual assessment (including visible noise, smoothness, streaking artefacts, motion artefacts and correspondence to the known anatomy) and an assessment of image sharpness (Fonov and Collins, 2018).The sharpness was calculated using the mincblur function from MINC tools (https://github.com/BIC-MNI/minc-tools)as: where G is a Gaussian smoothing kernel with a full-width half-maximum of 1 mm and I is the image, with higher values indicating higher sharpness and vice versa.
For volunteers, a quantitative comparison of susceptibility values within deep grey matter structures was also performed.10 ROIs were defined using Slicer (Fedorov et al., 2012) in deep grey matter structures namely caudate nucleus (CN), globus pallidus (GP), thalamus (T), red nucleus (RN), dentate nucleus (DN); each left (l) and right (r) -and median susceptibility values over each ROI were calculated.As susceptibility values within the deep grey matter structures are expected to vary even between healthy volunteers, statistical tests between the imaging methods were performed across all 50 ROIs (5 volunteers x 10 ROIs), rather than per ROI.Acquisition methods were compared to the gold-standard 3D GRE over all ROIs using paired t-tests with a Bonferroni correction for multiple comparisons (hence at p = 0.05/3).
MS lesions may appear hypointense, isointense or hyperintense on QSM depending on the degree of demyelination, remyelination and iron accumulation (Rahmanzadeh et al., 2022).In the three MS patients for whom 3D EPI data were available, the 3D GRE, 3D EPI and NATIve susceptibility values were quantitatively compared within four QSM-hyperintense MS lesions which were previously defined on the FLAIR images by a multiple sclerosis expert with long-term experience in quantitative assessment of susceptibility imaging on ultra-high field MRI (ADB).For each lesion, a respective "control" ROI was defined in the neighbouring normal-appearing white matter and for one of the three patients (P10, the only patient with several QSM-isointense lesions) the susceptibility was also quantified in 4 QSM-isointense lesions.
As the susceptibility values are expected to vary between the MS lesions, statistical tests between the imaging methods were performed across all 28 ROIs (2 patients with 8 ROIs + 1 patient with 12 ROIs), rather than per ROI.Acquisition methods were compared to the gold-standard 3D GRE over all ROIs using paired t-test with a Bonferroni correction for multiple comparisons (hence at p = 0.05/2).
For the assessment of motion-robustness, single volumes acquired during the motion were chosen from the multiple volumes of isotropic 2D EPI and the low-resolution 2D EPI data acquired for NATIve (volume 6 for iso2D EPI and volumes 12, 11 and 8 for the sagittal, coronal and transversal LR 2D EPI acquisitions respectively -Supplementary Videos 1-4 depict the motion during the multi-volume acquisitions) and the images were visually compared to those ones acquired without motion.
To allow the same mask for QSM processing and the same ROIs to be used for all compared methods, the NATIve images, which were acquired with 224 slices, were cropped to 160 slices after averaging the three orthogonal images, to match the reference 3D GRE and 3D EPI.The isotropic 2D EPI images, which were acquired with only 126 slices, were zero-padded to 160 slices.Note that co-registration between the NATIve EPI, isotropic 2D EPI, 3D EPI and 3D GRE images was only applied for the ROI analysis in order to not introduce the effects of blurring in the other comparisons.Due to some motion between the individual acquisitions, a rather conservative mask was generated for each volunteer/patient using FSL Brain Extraction Tool (BET) (Smith, 2002) (with the default fractional intensity threshold of 0.5, followed by 2 voxel erosion and by further 4 voxel erosion due to the RESHARP radius) and used for susceptibility mapping of the methods under comparison.Note that some slight mismatch between the images might also be visible due to residual motion.images without excessive blurring.If only the distortion correction was applied, the residual distortions confounded the linear co-registration and led to excessive blurring in the super-resolution image.On the other hand, when the Volgenmodel was applied without prior distortion correction, a super-resolution image without excessive blurring was generated, but it suffered from gross distortions (average distortions of the three LR images).

Fig
Using three orthogonal low-resolution 2D EPI acquisitions, NATIve allowed the generation of super-resolution EPI images with nominal isotropic resolution of 1 mm and only 12 s net acquisition time (Fig. 3).These were generally high quality, high SNR, with few streaking artefacts and no residual sign of the anisotropic low-resolution acquisitions, showing brain structures with good delineation.Compared to the lowresolution 2D EPI acquisitions with thick slices (1 × 1 × 3 mm), NATIve showed slightly increased blurring in what were, in the contributing three images, the high-resolution planes (i.e. the achieved resolution was slightly lower than the nominal resolution).Nevertheless, it greatly improved delineation of structures and increased resolution in the low-resolution planes.Compared to simple sinc-upsampling of the low-resolution images, which despite increasing resolution introduced artefacts and artificial signal alternations, NATIve allowed the extraction and combination of the sub-voxel information from the three orthogonal images and thus increased the image resolution and improved the anatomical delineation.Volgenmodel, a central part of NATIve processing, is quite computationally demanding; the processing of a single dataset of our study, took circa 11 h on a PC with Intel Xeon® CPU ES-1620 v2 @ 3.70 GHz x 8, Graphics NVD9 and 64 GB RAM.The processing time of all the other processing steps was negligible in comparison.
Fig. 4 compares the achieved spatial resolution, indicated by the slope of signal profiles at the sharp border of the periphery of the phantom.NATIve EPI showed a steeper profile than the 2D EPI in the low-resolution through-slice direction and a slightly flatter profile compared to the 2D EPI in the high-resolution plane, suggesting that the resolution of NATIve EPI is slightly reduced compared to the in-plane resolution (Fig. 4a).This is in accord with the visual impression in the volunteer assessment in Fig. 3.In the second comparison (Fig. 4b), 3D GRE showed the steepest profile, with the 3D EPI profile being just slightly less steep.The profiles of the isotropic 2D EPI and NATIve EPI were visibly flatter, with the NATIve EPI profile being just slightly less steep than the isotropic 2D EPI profile.This was also confirmed by the quantitative assessment of edge width in Table 1, where 3D EPI had by far the lowest edge width among the compared EPIs.NATIve EPI had the highest, but it was only slightly higher than that of the high-resolution plane of low-resolution 2D EPI and of the isotropic 2D EPI.Together, these findings indicate that the resolution achieved with NATIve with three contributions with nominal 1 × 1 × 3 mm voxels is close to that with 2D EPI with nominal 1 × 1 × 1 mm voxels.Sigmoid fitting to the 3D GRE profiles wasn't possible, as the very sharp profiles resulted in too few sampling points along the ramp.
The simulation on GRE data also showed that the NATIve reconstruction does not fully recover the sharpness of the original data, with increased blurring being evident (Fig. 5).On the other hand, the noise was decreased in NATIve images, visible in the magnitude images and also demonstrated by the decreased sharpness values in the homogenous tissue areas.Simulated NATIve and reference susceptibility maps showed generally good correspondence, with some differences mainly around vessels, where the abrupt changes in susceptibility values were blurred in NATIve.Nevertheless, the grey matter structures were well defined in the NATIve QSMs, as well as the white matter -grey matter boundary.The decreased sharpness at the tissue boundaries in NATIve varies within the image, with some boundaries having almost the same sharpness as the reference 3D GRE (e.g.ventricle boundaries) and with some showing a more pronounced decrease (e.g.small veins and the brain boundary).
In the phantom and in vivo assessments of SNR and SNR efficiency of the compared methods (Table 2), the 3D GRE showed high SNR, but the lowest SNR efficiency (due to the acquisition time of 5 min).With a net acquisition time of 23 s, 3D EPI showed intermediate SNR and relatively high SNR efficiency, while the isotropic 2D EPI, with a net acquisition time of 7.1 s, showed the lowest SNR and medium SNR efficiency.NATIve EPI with a net acquisition time of 3 × 4.1 s, showed both the highest SNR and far the highest SNR efficiency from all compared methods.Supplementary Fig. 1 shows an additional comparison of SNR and perceived resolution between a number of isotropic 2D EPIs with resolution ranging from 1 mm to 1.9 mm isotropic and NATIve EPI with an isotropic resolution of close to 1 mm.The phantom SNR maps showed high spatial variability related to parallel imaging reconstruction and the coil sensitivity profiles (Fig. 6).
The susceptibility maps of 3D EPI showed close correspondence to the reference 3D GRE QSMs, with some disparities and increased streaking artefacts around the vessels (Fig. 7 and Supplementary Fig. 2).The isotropic 2D EPIs yielded susceptibility maps with high noise levels and low tissue contrast.The NATIve QSMs showed good correspondence to the reference 3D GRE QSMs and little noise, particularly close to vessels, but increased blurring.Motion artefacts were not visible with any of the methods.
All the EPI methods -3D EPI, isotropic 2D EPI and NATIve EPIshowed, in some deep grey matter ROIs, good correspondence in susceptibility estimates relative to the reference 3D GRE (Fig. 8 and Supplementary Fig. 3).The standard deviations were generally highest with isotropic 2D EPI, suggesting higher noise levels, and lowest with NATIve EPI, suggesting lower noise levels.Nevertheless, all the methods were consistent for brain structures on the left and the right hemisphere (i.e. if the values were higher for an ROI on the left hemisphere, they were also higher for the same ROI on the right hemisphere).The comparison of the susceptibility differences to the gold-standard 3D GRE showed a statistically significant difference for isotropic 2D EPI acquisition, with a median absolute difference of 0.0058 pm.Although 3D EPI also showed a statistically significant difference from the 3D GRE, it showed the lowest median absolute difference of 0.0037 ppm.NATIve, as the only method didn't show a statistically significant difference from the 3D GRE due to the largest variance, but it showed a median absolute difference of 0.0043 ppm.
Fig. 9 and Supplementary Figs.4-7 depict the performance of NATIve in susceptibility mapping of multiple sclerosis, with respect to the reference 3D GRE.Despite some increased blurring of the NATIve susceptibility maps, all MS lesions which were visible on the 3D GRE QSMs were also visible on the NATIve QSMs.The net acquisition time with NATIve was greatly reducedfrom 5 min to 12 s.
The susceptibility values within the MS lesions which were previously classified as QSM-hyperintense by a multiple sclerosis expert (ADB) had higher susceptibilities than the control ROIs in all but one lesion (Fig. 10 and Supplementary Fig. 8) with all the compared methods -3D GRE, 3D EPI and NATIve EPI.The isointense lesions in Patient 10 showed similar susceptibilities to the control ROIs.Despite some Fig. 3. Comparison of low-resolution coronal (left), sinc-upsampled (middle) and NATIve (right) magnitude (top rows) and QSM (bottom rows) images, shown for one exemplary volunteer in all three planes.Pixelation of the low-resolution images in the slice direction is evident in the transversal view (top, where the voxel size is 3 mm in AP) and in the sagittal view (middle, where the voxel size is 3 mm in LR).The upsampled images show increased blurring and signal variation stemming from the sinc interpolation.The NATIve images show improved resolution and good tissue contrast in those planes (top and middle rows).In the coronal view (bottom), the low-resolution and the upsampled images show high-resolution (with 1 mm in-plane resolution) and sharp structure delineation.NATIve achieves a high-resolution image with good tissue contrast but with slight blurring compared to the original low-resolution image.statistically significant differences between the methods when comparing the susceptibility values within individual ROIs, the comparison of differences over the 28 ROIs did not show any significant difference from the gold-standard 3D GRE for either 3D EPI (with a median absolute difference of 0.0022 ppm) or for NATIve EPI (with a median absolute difference of 0.0035 ppm).
The comparison of motion robustness between the individual methods showed greatly improved robustness of 2D compared to the 3D acquisitions (Fig. 11 and Supplementary Fig. 9).The 3D GRE data were corrupted by severe motion artefacts throughout the whole volume, leading to artefacts and reduced tissue contrast in QSMs.Despite the greatly reduced acquisition time, the same was true for 3D EPI data, even when the acceleration was increased to achieve the same net TA as with NATIve (Supplementary Fig. 10).The iso2D EPI didn't contain any visible motion-related blurring or aliasing, but suffered from spinhistory artefacts leading to a very low signal from some slices.NATIve achieved very high motion robustness with no visible motion artefacts, despite the motion of up to several degrees visible between 2 subsequent EPI volumessee Supplementary Videos 1-4).

Discussion
We have shown that high resolution, high SNR susceptibility maps with good correspondence to gold-standard 3D GRE QSMs can be generated from three orthogonal 2D EPI acquisitions with thick slices.The proposed method, with a net acquisition time of only three times the volume acquisition time of EPI (i.e. 3 × 4.1 s) allowed a reduction of the net acquisition time by a factor of 25 compared to the gold-standard 3D GRE and by a factor of two compared to CAIPIRINHA-enabled 3D EPI.The three orthogonal EPI acquisitions could replace the dummy scans used in fMRI acquisitions so that high-resolution susceptibility maps could be acquired in No Additional Time for Imaging (NATIve).Fast acquisition and the possibility to motion correct the individual EPI volumes drastically reduce the motion sensitivity of QSM and give the proposed method the potential to allow QSM in motion-prone patients and improve clinical workflow.
In this project, the three orthogonal EPI acquisitions used in the NATIve reconstruction were performed separately.As a result, dummy scans, "autocalibration data (ACS)" for parallel imaging and simultaneous multi-slice reconstructions, and the prescan for intensity normalization were acquired three times, rather than once.These repeated acquisitions prolonged the overall acquisition time of the lowresolution 2D EPI scans from a net TA of 4 s to a total TA of 29 s and for the isotropic 2D EPI, from a net TA of 7 s to a total TA of 49 s.Although this also prolonged the overall acquisition timewith NATIve from 3 × 4 s to 3 × 29 sit didn't increase its motion sensitivity.The research 3D EPI sequence allowed the dummy scans to be omitted, which was not possible with the Siemens' product multi-band sequence, resulting in a smaller difference between the net TA and total TA (23 s vs 28 s).Looking beyond our compound, proof-of-principle implementation, a genuine integrated triplanar NATIve sequence could avoid the repetition of the dummy scans and the reacquisition of reference data required for parallel imaging reconstruction.This would allow extremely short acquisition times to be realized and, additionally, single planning for all

Table 1
Edge widths estimated from the slope of sigmoid fits to the signal profiles of the phantom edge.Note that average values over edge 20 profiles are shown.three orientations, greatly improving the clinical workflow.Alternatively, as already mentioned, the orthogonal NATIve EPI acquisition could replace the dummy scans used in fMRI acquisitions.In cases when fMRI is performed to assess cognitive and structural decline related to neurodegenerative disorders such as multiple sclerosis (Enzinger and DeLuca, 2012, Rocca et al., 2014, Filippi et al., 2019) and Parkinson's disease (Wolters et al., 2019, Tahmasian et al., 2015), NATIve dummy scans could provide additional information about iron accumulation and demyelination, improving the estimation of disease progression without extra acquisition time.We note that achieving equilibrium longitudinal magnetization with triplanar dummy scans is more complex than with conventional EPI acquisition as the interval between excitations is dependent on the position within the object.As a result, the most favourable implementation for fMRI would involve the last NATIve acquisition having the same orientation as the fMRI acquisition itself.Nevertheless, the acquisition of additional 1-2 dummy scans might still Fig. 6.Comparison of SNR (upper row) and SNR efficiency (bottom row) maps between the reference 3D GRE, 3D EPI, isotropic 2D EPI and NATIve EPI magnitude images of an oil phantom, calculated from 12 identical acquisitions.Parallel imaging reconstruction SNR dropouts and the higher SNR at the edges closer to the headcoil are visible.The 3D GRE shows SNR dropouts due to some motion of the oil within the phantom (despite no motion artefacts in the magnitude images).data, demonstrated for one exemplary volunteer.The 3D EPI QSM shows high tissue contrast and close correspondence to the 3D GRE QSM, but the sharpness image indicates increased streaking artefacts around vessels (red arrows).The isotropic 2D EPI QSM shows high noise levels and low tissue contrast, indicated also by the high sharpness within homogeneous tissues and low sharpness at the tissue boundaries.The NATIve QSM shows generally good tissue contrast and good correspondence to the 3D GRE QSM but increased blurring.The sharpness is decreased at the tissue borders, but also within homogeneous tissues, indicating decreased noise.(Note that the lateral slices of the iso2D EPI are missing due to the limit on the maximum number of slices.).be required for improved stabilization of the magnetization and could be used to acquire the ACS data for parallel imaging and SMS imaging.
To generate a super-resolution image from the three orthogonal EPIs with thick slices, the distortions spanning along the respective phaseencoding directions have to be corrected.We have shown that using distortion correction only, some residual distortions remain and degrade the quality of the reconstructed super-resolution image.Several factors compromise the quality of the conventional, fieldmap-based distortion correction-i) noise in the fieldmap, ii) masking of the fieldmap, iii) dynamic (temporal) changes of the field inhomogeneities.Dynamic distortion correction methods (Dymerska et al., 2016, Dymerska et al., 2018, Lamberton et al., 2007, Marques and Bowtell, 2005, Robinson et al., 2022) have been shown to reduce residual distortions and could be integrated into NATIve, but these do not remove the other sources of error and therefore some residual distortions are still expected to occur.To achieve accurate co-registration of the orthogonal EPIs, non-linear co-registration of sub-voxel precision, such as Volgenmodel, is thus additionally required.On the other hand, if only the Volgenmodel co-registration was to be used, a high-quality image could be reconstructed, but it would be subject to a distortion which is the average of those affecting the three orthogonal EPI acquisitions.Therefore, to remove the gross distortions and to generate a high-quality high-resolution image, we have applied both the fieldmap-based distortion correction (FUGUE -FslWiki, n.d.) and the iterative non-linear Minimum Deformation Averaging (Volgenmodel) co-registration approach (Bollmann et al., 2017; https://github.com/CAIsr/volgenmodel-nipype).
Instead of solving the super-resolution inverse problem (Plenge et al., 2012, Van Reeth et al., 2012), we have performed non-linear co-registration in combination with iterative up-sampling using Volgenmodel, followed by averaging to reconstruct the high-resolution image.Conventional super-resolution methods require the low-resolution images to be co-registered with sub-voxel precision, which is difficult to achieve for EPI with standard co-registration methods due to distortions.Although Volgenmodel achieved sub-voxel precise co-registration of the three orthogonal EPIs with residual distortions, which is the most crucial premise of achieving high-quality super-resolution, the reconstructed images contained some increased blurring.The assessment of achieved spatial resolution, including the effects of blurring, also showed that NATIve greatly improves the resolution in the low-resolution (slice) direction but introduces some blurring in each of the two high-resolution (in-plane) directions.This was also visible in the simulation performed on 3D GRE data, where no motion and no non-linear deformations were present, suggesting that this originates solely from the up-sampling and simple averaging rather than from shortcomings in the co-registration.To reduce this blurring and achieve robust The boxplots depict the distribution of absolute susceptibility differences over the 50 ROIs (5 volunteers x 10 ROIs).Asterisks mark the statistically significant differences from the reference 3D GRE (using paired t-test corrected for multiple comparisons using Bonferroni correction (p = 0.05/3)).super-resolution from three orthogonal EPIs, the non-linear co-registration could be combined with a true super-resolution reconstruction, which considers the effects of non-ideal slice profiles and the information content of the individual acquisitions (i.e.high vs low frequency).
Several other EPI-based methods have been proposed for rapid susceptibility mapping.3D EPI (Langkammer et al., 2015;Tourell et al., 2020;Stäb et al., 2017) has been shown to generate high-quality susceptibility maps with good correspondence to the reference 3D GRE QSMs, but with some increased streaking artefacts around the veins.Those findings were confirmed in this study.3D EPI, however, requires several times longer acquisition than 2D EPI (generally at least 30 s compared to 3 s) and therefore is still quite susceptible to motion.Also, while in 2D EPI, only the motion within the acquisition of a certain slice (i.e.within the slice TR) leads to a degradation of the given slice, with 3D EPI any motion during the acquisition degrades the quality of the whole volume.Finally, the rapid, repeated excitations in the 3D acquisition lead to low GM/WM/CSF contrast, reducing the information content in the magnitude and making them problematic to segment and co-registera consideration which has led to the use of multiple 3D EPIs with different contrasts (such as PD-weighted, T 1 -weighted and magnetisation transfer-weighted) for QSM (Ferreira et al., 2022).Susceptibility mapping with 2D EPI has previously been proposed (Sun andWilman, 2015, Sun et al., 2017), but this approach has, to date, used thick slices to achieve sufficient SNR, which is suboptimal for QSM and also for the assessment of smaller structures, such as calcification, haemorrhages, MS lesions, etc. NATIve combines the benefits of rapid, motion-insensitive 2D acquisition with the possibility of achieving isotropic, high-resolution and high SNR images required for QSM.In this study, we have shown that NATIve increased spatial resolution and achieved improved structural delineation compared to the original low-resolution 2D EPI and greatly increased SNR and SNR efficiency compared to the direct isotropic 2D EPI imaging and even to the 3D EPI imaging.Theoretically, NATIve should have a factor of 3√3 ≅ 5.2 higher SNR and a factor of 3.9 higher SNR efficiency than direct isotropic 2D EPI imaging, as it combines three images with 3x thicker slices.Additionally, the low-pass filtering effect of the interpolation, causing the increased blurring identified with NATIve, should theoretically also led to some SNR increase.In the phantom assessment, the SNR of NATIve was higher by a factor of 5.6 and the SNR efficiency by a factor of 4.3, being in close correspondence with the theoretically expected values.In the in vivo assessment, the SNR of NATIve was higher by a factor of 4.4 and the SNR efficiency by a factor of 3.4, where the difference to the theory could have been caused by several factors: i) a pre-smoothing of the images due to co-registration, ii) differences in TR, and iii) differences in the local g-factor penalties at the ROIs (Reeder et al., 2005, Dietrich et al., 2007, Goerner and Clarke, 2011).
Considering motion robustness, there were no artefacts visible in the datasets used in this study, which were acquired in healthy subjects and patients with multiple sclerosis in the early stages of the disease and who had already undergone numerous MRI examinations, so were familiar with the procedure and cooperative.More motion could be encountered in patients with neurodegenerative diseases such as Parkinson's and Alzheimer's diseases.Therefore, to assess the performance of the methods under motion, we have acquired an additional dataset in which we have instructed the volunteer to move.This confirmed the theoretical expectations of higher motion robustness on 2D acquisitions relative to the 3D ones, with both the 3D GRE and 3D EPI data being severely corrupted.On the other hand, NATIve EPI, with the rapid 2D acquisition (slice TR of 55 ms) didn't suffer from any visible artefacts due to the intra-scan motion nor due to the inter-scan motion.In cases where patients are expected to move significantly more than we have simulated (where it would cause motion artefacts even in 2D SMS EPI), with NATIve, a number of volumes in each orientation could be acquired and the motion-free volumes selected to generate high-resolution QSMs; an approach not be possible with 3D methods.As NATIve requires acquisition in three orthogonal planes, a larger field-of-view might be necessary to avoid wrap-around artefacts.However, this need not be the same in all 3 orientations (only the area of interest must be captured in Fig. 10.Upper row) Comparison of susceptibility values between the reference 3D GRE, 3D EPI and NATIve EPI in one exemplary patient with multiple sclerosis.The images show the positions of the ROIs within the QSM-hyperintense MS lesions ("hyper"), normal-appearing white matter ("control") and within the QSM-isointense lesions ("iso").The boxplots depict the distribution of susceptibility values within the given ROI.Bottom row) Comparison of absolute differences from the 3D GRE susceptibility values.The boxplots depict the distribution of absolute susceptibility differences over all 28 ROIs (2 patients x 8 ROIs + 1 patient x 12 ROIs).There are no statistically significant differences from the reference 3D GRE (using paired t-test corrected for multiple comparisons using Bonferroni correction (p = 0.05/2)).each orientation).The acquisition and processing we have outlined here could be applied to 2D EPI sequences with different contrasts (e.g.T 1 , T 2 ) and also in contexts in which motion is a recurrent problem, such as fetal imaging.
Using EPI acquisition instead of GRE has, however, some drawbacks for susceptibility mapping.Firstly, multi-echo acquisitions have been shown to provide optimal contrast-to-noise ratio over a range of tissues and result in fewer errors (Wu et al., 2012, Biondetti et al., 2020).Although multi-echo EPI sequences have been developed, they restrict the echo train length and hence the resolution and/or prolong the acquisition times.Secondly, the maximum achievable in-plane resolution of the 2D EPI is limited.As conventionally the whole k-space of the given slice is acquired after a single excitation pulse (single-shot EPI), the increased resolution leads to prolonged echo time and thus to more pronounced T 2 * decay.It was shown that TE equal to T 2 * of the tissue of interest should be used to achieve optimal susceptibility contrast (Wu et al., 2012).In this study, we have used echo times of 35 ms, which corresponds to the T 2 * values of deep grey matter structures at 3 T (Peters et al., 2007).If in-plane resolution higher than 1 mm would be desired, longer TEs would be required.Alternatively, a multi-shot acquisition could be used to acquire higher-resolution images at lower echo times, as was the case for the 3D EPI data measured in this study, but this prolongs the TA and hence leads to increased motion sensitivity.The long echo times of the EPI compared to GRE also lead to a wider point-spread function and hence to increased blurring (Frost et al., 2015), and possibly to unwrapping artefacts in structures with short T 2 *.This, together with the increased blurring observed in NATIve images, might limit the proposed method's capability of detecting sub-millimetre structures, such as iron rim or central vein sign of MS lesions.Lastly, due to long echo-times, EPI is prone to signal dropouts in regions with strong field gradients, e.g.close to ear cavities and around sinuses.As the dropouts scale with voxel size, the NATIve image reconstructed from the low-resolution EPIs showed more pronounced dropouts than the isotropic 2D EPI and 3D EPI images in those regions.If the areas of strong field inhomogeneities are of interest, direct high-resolution imaging might provide better results.The areas of focus in this study -deep gray matter structures and MS lesions -were not affected.
Despite the limitations of EPI-based susceptibility mapping, we have demonstrated that NATIve EPI provides susceptibility maps with good correspondence to the 3D GRE QSM in both healthy volunteers and patients with MS.NATIve EPI susceptibility maps showed increased blurring, mainly in and around veins, where abrupt changes in susceptibility were smoothed and reduced due to dipole averaging within the original low-resolution voxels.Nevertheless, they showed generally good contrast between grey matter and white matter and good delineation of grey matter structures.Notably, all the MS lesions which were visible on 3D GRE QSMs were also visible on NATIve EPI susceptibility maps.To assess if some of EPI-based methods, including NATIve, consistently underestimate or overestimate susceptibility or generally provide less reliable values, a much larger comparison study would have to be carried out on phantom or post-mortem data and include reproducibility measurements.Nevertheless, we have shown that the EPIbased methods achieved comparable susceptibility estimates to the gold-standard 3D GRE in both healthy volunteers and MS patients, but with greatly decreased acquisition times.In volunteers, susceptibility values showed the same trend of higher/lower values within the individual deep grey matter ROIs and in MS patients, there was a clear differentiation between the QSM-hyperintense ROIs and either control or QSM-isointense ROIs.

Conclusion
We have presented a method for ultra-fast high-resolution high SNR Quantitative Susceptibility Mapping from three orthogonal 2D EPI acquisitions with thick slices.Using fieldmap-based distortion correction (FUGUE -FslWiki, n.d.) and an iterative non-linear Minimum Deformation Averaging (Volgenmodel) co-registration approach (Bollmann et al., 2017; https://github.com/CAIsr/volgenmodel-nipype),we have generated high-resolution susceptibility maps without excessive smoothing and gross distortions.Although the proposed method was shown to introduce some blurring, the resulting susceptibility maps and the susceptibility values within deep grey matter structures and MS lesions showed good correspondence to the gold-standard 3D GRE QSM.With a net acquisition time of only three times the TR of EPI (i.e.around 12 s), which could potentially replace the dummy scans used in fMRI acquisitions, the proposed method allows high-resolution susceptibility mapping in little or No Additional Time for Imaging (NATIve).Thanks to the rapid acquisition and the possibility to motion-correct the individual EPI volumes, NATIve drastically reduces the motion sensitivity of susceptibility mapping, making QSM viable in motion-prone patients, such as those with neurodegenerative diseases.

Fig. 2 .
Fig. 2 demonstrates that both distortion correction and Volgenmodel co-registration are required to generate distortion-free super-resolution

Fig. 4 .
Fig. 4. Comparison of achieved spatial resolution, given by the slope of signal profile at the sharp border of the round oil phantom, between the NATIve EPI images and a) the low-resolution 2D EPI images with thick slices and b) the isotropic 2D EPI, 3D EPI and 3D GRE.The upper rows show the placement of an example profile and the respective images zoomed at the given phantom border.The bottom rows show plots of average profiles.a) Three profiles contribute to the average lowresolution profile (along head-foot in the transversal acquisition, left-right in sagittal and posterior-anterior in coronal), six to the average high-resolution profile (along posterior-anterior and left-right in the transversal acquisition; posterior-anterior and head-foot in sagittal; and head-foot and left-right in coronal), and the three orthogonal profiles to the average NATIve EPI profile (along posterior-anterior, head-foot, and left-right).b) The three orthogonal profiles of each contribute to the average profiles.

Fig. 5 .
Fig. 5. Comparison of magnitude images (left), magnitude sharpness (middle left), susceptibility maps (middle right) and susceptibility map sharpness (right) between the reference 3D GRE (upper row) and the simulated NATIve GRE (bottom row) from the down-sampled reference 3D GRE data.The NATIve images show generally good tissue contrast and structural delineation, but also some blurring compared to the original HR images.The sharpness images of the NATIve GRE show decreased contrast at the tissue boundaries but also decreased sharpness in the homogeneous tissue areas, suggesting decreased noise levels.Note that the sharpness images of the reference 3D GRE and the simulated NATIve GRE are shown with the same scaling.

Fig. 7 .
Fig. 7. Comparison of susceptibility maps generated from the reference 3D GRE (left), 3D EPI (middle left), isotropic 2D EPI (middle right), and NATIve EPI (right)data, demonstrated for one exemplary volunteer.The 3D EPI QSM shows high tissue contrast and close correspondence to the 3D GRE QSM, but the sharpness image indicates increased streaking artefacts around vessels (red arrows).The isotropic 2D EPI QSM shows high noise levels and low tissue contrast, indicated also by the high sharpness within homogeneous tissues and low sharpness at the tissue boundaries.The NATIve QSM shows generally good tissue contrast and good correspondence to the 3D GRE QSM but increased blurring.The sharpness is decreased at the tissue borders, but also within homogeneous tissues, indicating decreased noise.(Note that the lateral slices of the iso2D EPI are missing due to the limit on the maximum number of slices.).

Fig. 8 .
Fig. 8. Upper row) Comparison of susceptibility values between the reference 3D GRE, 3D EPI, isotropic 2D EPI, and NATIve EPI in 10 deep grey matter ROIs (caudate nucleus (CN), globus pallidus (GP), thalamus (T), red nucleus (RN), caudate nucleus (CN), left (l) and right (r)), shown for one exemplary volunteer.The boxplots depict the distribution of susceptibility values within the given ROI.Bottom row) Comparison of absolute differences from the 3D GRE susceptibility values.The boxplots depict the distribution of absolute susceptibility differences over the 50 ROIs (5 volunteers x 10 ROIs).Asterisks mark the statistically significant differences from the reference 3D GRE (using paired t-test corrected for multiple comparisons using Bonferroni correction (p = 0.05/3)).

Fig. 9 .
Fig. 9. Comparison of reference 3D GRE (middle left), 3D EPI (middle right) and NATIve EPI (right) susceptibility maps of three exemplary patients with multiple sclerosis.The FLAIR images (left) depict the positions of the MS lesions.The 3D EPI QSM shows high tissue contrast and close correspondence to the reference 3D GRE QSM.The NATIve QSM shows generally good tissue contrast and correspondence to the reference 3D GRE QSM, but increased blurring.Note that the lesions visible on 3D GRE QSMs (indicated by red arrows on FLAIR images) are also visible on NATIve susceptibility maps.

Fig. 11 .
Fig. 11.Comparison of 3D GRE (left), 3D EPI (middle left), isotropic 2D EPI (middle right), and NATIve EPI (right) magnitude images (top) and susceptibility maps (bottom) from acquisition without (rows 1 and 3) and with (rows 2 and 4) motion.Note the severe motion artefacts in the 3D GRE and 3D EPI images.Isotropic 2D EPI suffers from spin-history signal dropouts, leading to severe artefacts in susceptibility maps.NATIve images don't suffer from any visible motion-related degradation.

Table 2
Comparison of SNR and SNR efficiency between the reference 3D GRE, 3D EPI, isotropic 2D EPI and NATIve EPI magnitude images.Note that the given values represent mean and standard deviations over a single large ROI in phantom and over 16 smaller ROIs in vivo.