Calculation of susceptibility through multiple orientation sampling (COSMOS): a method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in MRI

χ-sepnet: Deep Neural Network for Magnetic Susceptibility Source Separation

Magnetic susceptibility source separation (χ-separation), an advanced quantitative susceptibility mapping (QSM) method, enables the separate estimation of paramagnetic and diamagnetic susceptibility source distributions in the brain. Similar to QSM, it requires solving the ill-conditioned problem of dipole inversion, suffering from so-called streaking artifacts. Additionally, the method utilizes reversible transverse relaxation (R 2 ' = R 2 * - R 2 $$ {R}_2^{\prime }={R}_2^{\ast }-{R}_2 $$ ) to complement frequency shift information for estimating susceptibility source concentrations, requiring time-consuming data acquisition forR 2 $$ {R}_2 $$ (e.g., multi-echo spin-echo) in addition to multi-echo GRE data forR 2 * $$ {R}_2^{\ast } $$ . To address these challenges, we develop a new deep learning network, χ-sepnet, and propose two deep learning-based susceptibility source separation pipelines, χ-sepnet-R 2 ' $$ {R}_2^{\prime } $$ for inputs with multi-echo GRE and multi-echo spin-echo (or turbo spin-echo) and χ-sepnet-R 2 * $$ {R}_2^{\ast } $$ for input with multi-echo GRE only. The neural network is trained using multiple head orientation data that provide streaking artifact-free labels, generating high-quality χ-separation maps. The evaluation of the pipelines encompasses both qualitative and quantitative assessments in healthy subjects, and visual inspection of lesion characteristics in multiple sclerosis patients. The susceptibility source-separated maps of the proposed pipelines delineate detailed brain structures with substantially reduced artifacts compared to those from the conventional regularization-based reconstruction methods. In quantitative analysis, χ-sepnet-R 2 ' $$ {R}_2^{\prime } $$ achieves the best outcomes followed by χ-sepnet-R 2 * $$ {R}_2^{\ast } $$ , outperforming the conventional methods. When the lesions of multiple sclerosis patients are classified into subtypes, most lesions are identified as the same subtype in the maps from χ-sepnet-R 2 ' $$ {R}_2^{\prime } $$ and χ-sepnet-R 2 * $$ {R}_2^{\ast } $$ (paramagnetic susceptibility: 99.6% and diamagnetic susceptibility: 98.4%; both out of 250 lesions). The χ-sepnet-R 2 * $$ {R}_2^{\ast } $$ pipeline, which only requires multi-echo GRE data, has demonstrated its potential to offer broad clinical and scientific applications, although further evaluations for various diseases and pathological conditions are necessary.

XSIM: A structural similarity index measure optimized for MRI QSM

PURPOSE

The structural similarity index measure (SSIM) has become a popular quality metric to evaluate QSM in a way that is closer to human perception than RMS error (RMSE). However, SSIM may overpenalize errors in diamagnetic tissues and underpenalize them in paramagnetic tissues, resulting in biasing. In addition, extreme artifacts may compress the dynamic range, resulting in unrealistically high SSIM scores (hacking). To overcome biasing and hacking, we propose XSIM: SSIM implemented in the native QSM range, and with internal parameters optimized for QSM.

METHODS

We used forward simulations from a COSMOS ground-truth brain susceptibility map included in the 2016 QSM Reconstruction Challenge to investigate the effect of QSM reconstruction errors on the SSIM, XSIM, and RMSE metrics. We also used these metrics to optimize QSM reconstructions of the in vivo challenge data set. We repeated this experiment with the QSM abdominal phantom. To validate the use of XSIM instead of SSIM for QSM quality assessment across a range of different reconstruction techniques/algorithms, we analyzed the reconstructions submitted to the 2019 QSM Reconstruction Challenge 2.0.

RESULTS

Our experiments confirmed the biasing and hacking effects on the SSIM metric applied to QSM. The XSIM metric was robust to those effects, penalizing the presence of streaking artifacts and reconstruction errors. Using XSIM to optimize QSM reconstruction regularization weights returned less overregularization than SSIM and RMSE.

CONCLUSION

XSIM is recommended over traditional SSIM to evaluate QSM reconstructions against a known ground truth, as it avoids biasing and hacking effects and provides a larger dynamic range of scores.

ProxiMO: Proximal Multi-operator Networks for Quantitative Susceptibility Mapping

Quantitative Susceptibility Mapping (QSM) is a technique that derives tissue magnetic susceptibility distributions from phase measurements obtained through Magnetic Resonance (MR) imaging. This involves solving an ill-posed dipole inversion problem, however, and thus time-consuming and cumbersome data acquisition from several distinct head orientations becomes necessary to obtain an accurate solution. Most recent (supervised) deep learning methods for single-phase QSM require training data obtained via multiple orientations. In this work, we present an alternative unsupervised learning approach that can efficiently train on single-orientation measurement data alone, named ProxiMO (Proximal Multi-Operator), combining Learned Proximal Convolutional Neural Networks (LP-CNN) with multi-operator imaging (MOI). This integration enables LP-CNN training for QSM on single-phase data without ground truth reconstructions. We further introduce a semi-supervised variant, which further boosts the reconstruction performance, compared to the traditional supervised fashions. Extensive experiments on multicenter datasets illustrate the advantage of unsupervised training and the superiority of the proposed approach for QSM reconstruction. Code is available at https://github.com/shmuelor/ProxiMO.

DF-QSM: Data Fidelity based Hybrid Approach for Improved Quantitative Susceptibility Mapping of the Brain

Quantitative Susceptibility Mapping (QSM) is an advanced magnetic resonance imaging (MRI) technique to quantify the magnetic susceptibility of the tissue under investigation. Deep learning methods have shown promising results in deconvolving the susceptibility distribution from the measured local field obtained from the MR phase. Although existing deep learning based QSM methods can produce high-quality reconstruction, they are highly biased toward training data distribution with less scope for generalizability. This work proposes a hybrid two-step reconstruction approach to improve deep learning based QSM reconstruction. The susceptibility map prediction obtained from the deep learning methods has been refined in the framework developed in this work to ensure consistency with the measured local field. The developed method was validated on existing deep learning and model-based deep learning methods for susceptibility mapping of the brain. The developed method resulted in improved reconstruction for MRI volumes obtained with different acquisition settings, including deep learning models trained on constrained (limited) data settings.

SIPAS: A comprehensive susceptibility imaging process and analysis studio

Quantitative susceptibility mapping (QSM) is a rising MRI-based technology and quite a few QSM-related algorithms have been proposed to reconstruct maps of tissue susceptibility distribution from phase images. In this paper, we develop a comprehensive susceptibility imaging process and analysis studio (SIPAS) that can accomplish reliable QSM processing and offer a standardized evaluation system. Specifically, SIPAS integrates multiple methods for each step, enabling users to select algorithm combinations according to data conditions, and QSM maps could be evaluated by two aspects, including image quality indicators within all voxels and region-of-interest (ROI) analysis. Through a sophisticated design of user-friendly interfaces, the results of each procedure are able to be exhibited in axial, coronal, and sagittal views in real-time, meanwhile ROIs can be displayed in 3D rendering visualization. The accuracy and compatibility of SIPAS are demonstrated by experiments on multiple in vivo human brain datasets acquired from 3T, 5T, and 7T MRI scanners of different manufacturers. We also validate the QSM maps obtained by various algorithm combinations in SIPAS, among which the combination of iRSHARP and SFCR achieves the best results on its evaluation system. SIPAS is a comprehensive, sophisticated, and reliable toolkit that may prompt the QSM application in scientific research and clinical practice.

Quantitative susceptibility mapping for susceptibility source separation with adaptive relaxometric constant estimation (QSM-ARCS) from solely gradient-echo data

To separate the contributions of paramagnetic and diamagnetic sources within a voxel, a magnetic susceptibility source separation method based solely on gradient-echo data has been developed. To measure the opposing susceptibility sources more accurately, we propose a novel single-orientation quantitative susceptibility mapping method with adaptive relaxometric constant estimation (QSM-ARCS) for susceptibility source separation. Moreover, opposing susceptibilities and their anisotropic effects were determined in healthy volunteers in the white matter. Multiple spoiled gradient echo and diffusion tensor imaging of ten healthy volunteers was obtained using a 3 T magnetic resonance scanner. After the opposing susceptibility and fractional anisotropy (FA) maps had been reconstructed, the parametric maps were spatially normalized. To evaluate the agreements of QSM-ARCS against the susceptibility source separation method using R2 and R2* maps (χ-separation) by Bland-Altman plots, the opposing susceptibility values were measured using white and deep gray matter atlases. We then evaluated the relationships between the opposing susceptibilities and FAs in the white matter and used a field-to-fiber angle to assess the fiber orientation dependencies of the opposing susceptibilities. The susceptibility maps in QSM-ARCS were successfully reconstructed without large artifacts. In the Bland-Altman analyses, the opposing QSM-ARCS susceptibility values excellently agreed with the χ-separation maps. Significant inverse and proportional correlations were observed between FA and the negative and positive susceptibilities estimated by QSM-ARCS. The fiber orientation dependencies of the negative susceptibility represented a nonmonotonic feature. Conversely, the positive susceptibility increased linearly with the fiber angle with respect to the B0 field. The QSM-ARCS could accurately estimate the opposing susceptibilities, which were identical values of χ-separation, even using gradient echo alone. The opposing susceptibilities might offer direct biomarkers for assessment of the myelin and iron content in glial cells and, through the underlying magnetic sources, provide biologic insights toward clinical transition.

Spinet-QSM: model-based deep learning with schatten p-norm regularization for improved quantitative susceptibility mapping

OBJECTIVE

Quantitative susceptibility mapping (QSM) provides an estimate of the magnetic susceptibility of tissue using magnetic resonance (MR) phase measurements. The tissue magnetic susceptibility (source) from the measured magnetic field distribution/local tissue field (effect) inherent in the MR phase images is estimated by numerically solving the inverse source-effect problem. This study aims to develop an effective model-based deep-learning framework to solve the inverse problem of QSM.

MATERIALS AND METHODS

This work proposes a Schatten p -norm-driven model-based deep learning framework for QSM with a learnable norm parameter p to adapt to the data. In contrast to other model-based architectures that enforce the l2 -norm or l1 -norm for the denoiser, the proposed approach can enforce any p -norm ( 0 < p ≤ 2 ) on a trainable regulariser.

RESULTS

The proposed method was compared with deep learning-based approaches, such as QSMnet, and model-based deep learning approaches, such as learned proximal convolutional neural network (LPCNN). Reconstructions performed using 77 imaging volumes with different acquisition protocols and clinical conditions, such as hemorrhage and multiple sclerosis, showed that the proposed approach outperformed existing state-of-the-art methods by a significant margin in terms of quantitative merits.

CONCLUSION

The proposed SpiNet-QSM showed a consistent improvement of at least 5% in terms of the high-frequency error norm (HFEN) and normalized root mean squared error (NRMSE) over other QSM reconstruction methods with limited training data.

A subject-specific unsupervised deep learning method for quantitative susceptibility mapping using implicit neural representation

Quantitative susceptibility mapping (QSM) is an MRI-based technique that estimates the underlying tissue magnetic susceptibility based on phase signal. Deep learning (DL)-based methods have shown promise in handling the challenging ill-posed inverse problem for QSM reconstruction. However, they require extensive paired training data that are typically unavailable and suffer from generalization problems. Recent model-incorporated DL approaches also overlook the non-local effect of the tissue phase in applying the source-to-field forward model due to patch-based training constraint, resulting in a discrepancy between the prediction and measurement and subsequently suboptimal QSM reconstruction. This study proposes an unsupervised and subject-specific DL method for QSM reconstruction based on implicit neural representation (INR), referred to as INR-QSM. INR has emerged as a powerful framework for learning a high-quality continuous representation of the signal (image) by exploiting its internal information without training labels. In INR-QSM, the desired susceptibility map is represented as a continuous function of the spatial coordinates, parameterized by a fully-connected neural network. The weights are learned by minimizing a loss function that includes a data fidelity term incorporated by the physical model and regularization terms. Additionally, a novel phase compensation strategy is proposed for the first time to account for the non-local effect of tissue phase in data consistency calculation to make the physical model more accurate. Our experiments show that INR-QSM outperforms traditional established QSM reconstruction methods and the compared unsupervised DL method both qualitatively and quantitatively, and is competitive against supervised DL methods under data perturbations.

Chaos and COSMOS-Considerations on QSM methods with multiple and single orientations and effects from local anisotropy

PURPOSE

Field-to-susceptibility inversion in quantitative susceptibility mapping (QSM) is ill-posed and needs numerical stabilization through either regularization or oversampling by acquiring data at three or more object orientations. Calculation Of Susceptibility through Multiple Orientations Sampling (COSMOS) is an established oversampling approach and regarded as QSM gold standard. It achieves a well-conditioned inverse problem, requiring rotations by 0°, 60° and 120° in the yz-plane. However, this is impractical in vivo, where head rotations are typically restricted to a range of ±25°. Non-ideal sampling degrades the conditioning with residual streaking artifacts whose mitigation needs further regularization. Moreover, susceptibility anisotropy in white matter is not considered in the COSMOS model, which may introduce additional bias. The current work presents a thorough investigation of these effects in primate brain.

METHODS

Gradient-recalled echo (GRE) data of an entire fixed chimpanzee brain were acquired at 7 T (350 μm resolution, 10 orientations) including ideal COSMOS sampling and realistic rotations in vivo. Comparisons of the results included ideal COSMOS, in-vivo feasible acquisitions with 3-8 orientations and single-orientation iLSQR QSM.

RESULTS

In-vivo feasible and optimal COSMOS yielded high-quality susceptibility maps with increased SNR resulting from averaging multiple acquisitions. COSMOS reconstructions from non-ideal rotations about a single axis required additional L2-regularization to mitigate residual streaking artifacts.

CONCLUSION

In view of unconsidered anisotropy effects, added complexity of the reconstruction, and the general challenge of multi-orientation acquisitions, advantages of sub-optimal COSMOS schemes over regularized single-orientation QSM appear limited in in-vivo settings.

So You Want to Image Myelin Using MRI: Magnetic Susceptibility Source Separation for Myelin Imaging

In MRI, researchers have long endeavored to effectively visualize myelin distribution in the brain, a pursuit with significant implications for both scientific research and clinical applications. Over time, various methods such as myelin water imaging, magnetization transfer imaging, and relaxometric imaging have been developed, each carrying distinct advantages and limitations. Recently, an innovative technique named as magnetic susceptibility source separation has emerged, introducing a novel surrogate biomarker for myelin in the form of a diamagnetic susceptibility map. This paper comprehensively reviews this cutting-edge method, providing the fundamental concepts of magnetic susceptibility, susceptibility imaging, and the validation of the diamagnetic susceptibility map as a myelin biomarker that indirectly measures myelin content. Additionally, the paper explores essential aspects of data acquisition and processing, offering practical insights for readers. A comparison with established myelin imaging methods is also presented, and both current and prospective clinical and scientific applications are discussed to provide a holistic understanding of the technique. This work aims to serve as a foundational resource for newcomers entering this dynamic and rapidly expanding field.

Quantitative susceptibility mapping in the brain reflects spatial expression of genes involved in iron homeostasis and myelination

Quantitative susceptibility mapping (QSM) is an MRI modality used to non-invasively measure iron content in the brain. Iron exhibits a specific anatomically varying pattern of accumulation in the brain across individuals. The highest regions of accumulation are the deep grey nuclei, where iron is stored in paramagnetic molecule ferritin. This form of iron is considered to be what largely contributes to the signal measured by QSM in the deep grey nuclei. It is also known that QSM is affected by diamagnetic myelin contents. Here, we investigate spatial gene expression of iron and myelin related genes, as measured by the Allen Human Brain Atlas, in relation to QSM images of age-matched subjects. We performed multiple linear regressions between gene expression and the average QSM signal within 34 distinct deep grey nuclei regions. Our results show a positive correlation (p < .05, corrected) between expression of ferritin and the QSM signal in deep grey nuclei regions. We repeated the analysis for other genes that encode proteins thought to be involved in the transport and storage of iron in the brain, as well as myelination. In addition to ferritin, our findings demonstrate a positive correlation (p < .05, corrected) between the expression of ferroportin, transferrin, divalent metal transporter 1, several gene markers of myelinating oligodendrocytes, and the QSM signal in deep grey nuclei regions. Our results suggest that the QSM signal reflects both the storage and active transport of iron in the deep grey nuclei regions of the brain.

Plug-and-Play latent feature editing for orientation-adaptive quantitative susceptibility mapping neural networks

Quantitative susceptibility mapping (QSM) is a post-processing technique for deriving tissue magnetic susceptibility distribution from MRI phase measurements. Deep learning (DL) algorithms hold great potential for solving the ill-posed QSM reconstruction problem. However, a significant challenge facing current DL-QSM approaches is their limited adaptability to magnetic dipole field orientation variations during training and testing. In this work, we propose a novel Orientation-Adaptive Latent Feature Editing (OA-LFE) module to learn the encoding of acquisition orientation vectors and seamlessly integrate them into the latent features of deep networks. Importantly, it can be directly Plug-and-Play (PnP) into various existing DL-QSM architectures, enabling reconstructions of QSM from arbitrary magnetic dipole orientations. Its effectiveness is demonstrated by combining the OA-LFE module into our previously proposed phase-to-susceptibility single-step instant QSM (iQSM) network, which was initially tailored for pure-axial acquisitions. The proposed OA-LFE-empowered iQSM, which we refer to as iQSM+, is trained in a simulated-supervised manner on a specially-designed simulation brain dataset. Comprehensive experiments are conducted on simulated and in vivo human brain datasets, encompassing subjects ranging from healthy individuals to those with pathological conditions. These experiments involve various MRI platforms (3T and 7T) and aim to compare our proposed iQSM+ against several established QSM reconstruction frameworks, including the original iQSM. The iQSM+ yields QSM images with significantly improved accuracies and mitigates artifacts, surpassing other state-of-the-art DL-QSM algorithms. The PnP OA-LFE module's versatility was further demonstrated by its successful application to xQSM, a distinct DL-QSM network for dipole inversion. In conclusion, this work introduces a new DL paradigm, allowing researchers to develop innovative QSM methods without requiring a complete overhaul of their existing architectures.

Quantitative susceptibility mapping through model-based deep image prior (MoDIP)

The data-driven approach of supervised learning methods has limited applicability in solving dipole inversion in Quantitative Susceptibility Mapping (QSM) with varying scan parameters across different objects. To address this generalization issue in supervised QSM methods, we propose a novel training-free model-based unsupervised method called MoDIP (Model-based Deep Image Prior). MoDIP comprises a small, untrained network and a Data Fidelity Optimization (DFO) module. The network converges to an interim state, acting as an implicit prior for image regularization, while the optimization process enforces the physical model of QSM dipole inversion. Experimental results demonstrate MoDIP's excellent generalizability in solving QSM dipole inversion across different scan parameters. It exhibits robustness against pathological brain QSM, achieving over 32 % accuracy improvement than supervised deep learning methods. It is also 33 % more computationally efficient and runs 4 times faster than conventional DIP-based approaches, enabling 3D high-resolution image reconstruction in under 4.5 min.

Recommended implementation of quantitative susceptibility mapping for clinical research in the brain: A consensus of the ISMRM electro-magnetic tissue properties study group

This article provides recommendations for implementing QSM for clinical brain research. It is a consensus of the International Society of Magnetic Resonance in Medicine, Electro-Magnetic Tissue Properties Study Group. While QSM technical development continues to advance rapidly, the current QSM methods have been demonstrated to be repeatable and reproducible for generating quantitative tissue magnetic susceptibility maps in the brain. However, the many QSM approaches available have generated a need in the neuroimaging community for guidelines on implementation. This article outlines considerations and implementation recommendations for QSM data acquisition, processing, analysis, and publication. We recommend that data be acquired using a monopolar 3D multi-echo gradient echo (GRE) sequence and that phase images be saved and exported in Digital Imaging and Communications in Medicine (DICOM) format and unwrapped using an exact unwrapping approach. Multi-echo images should be combined before background field removal, and a brain mask created using a brain extraction tool with the incorporation of phase-quality-based masking. Background fields within the brain mask should be removed using a technique based on SHARP or PDF, and the optimization approach to dipole inversion should be employed with a sparsity-based regularization. Susceptibility values should be measured relative to a specified reference, including the common reference region of the whole brain as a region of interest in the analysis. The minimum acquisition and processing details required when reporting QSM results are also provided. These recommendations should facilitate clinical QSM research and promote harmonized data acquisition, analysis, and reporting.

Neuroimaging of Parkinson's disease by quantitative susceptibility mapping

Parkinson's disease (PD) is a common neurodegenerative disease, and apart from a few rare genetic causes, its pathogenesis remains largely unclear. Recent scientific interest has been captured by the involvement of iron biochemistry and the disruption of iron homeostasis, particularly within the brain regions specifically affected in PD. The advent of Quantitative Susceptibility Mapping (QSM) has enabled non-invasive quantification of brain iron in vivo by MRI, which has contributed to the understanding of iron-associated pathogenesis and has the potential for the development of iron-based biomarkers in PD. This review elucidates the biochemical underpinnings of brain iron accumulation, details advancements in iron-sensitive MRI technologies, and discusses the role of QSM as a biomarker of iron deposition in PD. Despite considerable progress, several challenges impede its clinical application after a decade of QSM studies. The initiation of multi-site research is warranted for developing robust, interpretable, and disease-specific biomarkers for monitoring PD disease progression.

Incorporating a-priori information in deep learning models for quantitative susceptibility mapping via adaptive convolution

Quantitative susceptibility mapping (QSM) has attracted considerable interest for tissue characterization (e.g., iron and calcium accumulation, myelination, venous vasculature) in the human brain and relies on extensive data processing of gradient-echo MRI phase images. While deep learning-based field-to-susceptibility inversion has shown great potential, the acquisition parameters applied in clinical settings such as image resolution or image orientation with respect to the magnetic field have not been fully accounted for. Furthermore, the lack of comprehensive training data covering a wide range of acquisition parameters further limits the current QSM deep learning approaches. Here, we propose the integration of a priori information of imaging parameters into convolutional neural networks with our approach, adaptive convolution, that learns the mapping between the additional presented information (acquisition parameters) and the changes in the phase images associated with these varying acquisition parameters. By associating a-priori information with the network parameters itself, the optimal set of convolution weights is selected based on data-specific attributes, leading to generalizability towards changes in acquisition parameters. Moreover, we demonstrate the feasibility of pre-training on synthetic data and transfer learning to clinical brain data to achieve substantial improvements in the computation of susceptibility maps. The adaptive convolution 3D U-Net demonstrated generalizability in acquisition parameters on synthetic and in-vivo data and outperformed models lacking adaptive convolution or transfer learning. Further experiments demonstrate the impact of the side information on the adaptive model and assessed susceptibility map computation on simulated pathologic data sets and measured phase data.

A spatially adaptive regularization based three-dimensional reconstruction network for quantitative susceptibility mapping

Objective.Quantitative susceptibility mapping (QSM) is a new imaging technique for non-invasive characterization of the composition and microstructure ofin vivotissues, and it can be reconstructed from local field measurements by solving an ill-posed inverse problem. Even for deep learning networks, it is not an easy task to establish an accurate quantitative mapping between two physical quantities of different units, i.e. field shift in Hz and susceptibility value in ppm for QSM.Approach. In this paper, we propose a spatially adaptive regularization based three-dimensional reconstruction network SAQSM. A spatially adaptive module is specially designed and a set of them at different resolutions are inserted into the network decoder, playing a role of cross-modality based regularization constraint. Therefore, the exact information of both field and magnitude data is exploited to adjust the scale and shift of feature maps, and thus any information loss or deviation occurred in previous layers could be effectively corrected. The network encoding has a dynamic perceptual initialization, which enables the network to overcome receptive field intervals and also strengthens its ability to detect features of various sizes.Main results. Experimental results on the brain data of healthy volunteers, clinical hemorrhage and simulated phantom with calcification demonstrate that SAQSM can achieve more accurate reconstruction with less susceptibility artifacts, while perform well on the stability and generalization even for severe lesion areas.Significance. This proposed framework may provide a valuable paradigm to quantitative mapping or multimodal reconstruction.

Incorporating the effect of white matter microstructure in the estimation of magnetic susceptibility in ex vivo mouse brain

PURPOSE

To extend quantitative susceptibility mapping to account for microstructure of white matter (WM) and demonstrate its effect on ex vivo mouse brain at 16.4T.

THEORY AND METHODS

Previous studies have shown that the MRI measured Larmor frequency also depends on local magnetic microstructure at the mesoscopic scale. Here, we include effects from WM microstructure using our previous results for the mesoscopic Larmor frequencyΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ of cylinders with arbitrary orientations. We scrutinize the validity of our model and QSM in a digital brain phantom includingΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ from a WM susceptibility tensor and biologically stored iron with scalar susceptibility. We also apply susceptibility tensor imaging to the phantom and investigate how the fitted tensors are biased fromΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ . Last, we demonstrate how to combine multi-gradient echo and diffusion MRI images of ex vivo mouse brains acquired at 16.4T to estimate an apparent scalar susceptibility without sample rotations.

RESULTS

Our new model improves susceptibility estimation compared to QSM for the brain phantom. Applying susceptibility tensor imaging to the phantom withΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ from WM axons with scalar susceptibility produces a highly anisotropic susceptibility tensor that mimics results from previous susceptibility tensor imaging studies. For the ex vivo mouse brain we find theΩ ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ due to WM microstructure to be substantial, changing susceptibility in WM up to 25% root-mean-squared-difference.

CONCLUSION

Ω ‾ Meso $$ {\overline{\Omega}}^{\mathrm{Meso}} $$ impacts susceptibility estimates and biases susceptibility tensor imaging fitting substantially. Hence, it should not be neglected when imaging structurally anisotropic tissue such as brain WM.

Model resolution-based deconvolution for improved quantitative susceptibility mapping

Quantitative susceptibility mapping (QSM) utilizes the relationship between the measured local field and the unknown susceptibility map to perform dipole deconvolution. The aim of this work is to introduce and systematically evaluate the model resolution-based deconvolution for improved estimation of the susceptibility map obtained using the thresholded k-space division (TKD). A two-step approach has been proposed, wherein the first step involves the TKD susceptibility map computation and the second step involves the correction of this susceptibility map using the model-resolution matrix. The TKD-estimated susceptibility map can be expressed as the weighted average of the true susceptibility map, where the weights are determined by the rows of the model-resolution matrix, and hence a deconvolution of the TKD susceptibility map using the model-resolution matrix yields a better approximation to the true susceptibility map. The model resolution-based deconvolution is realized using closed-form, iterative, and sparsity-regularized implementations. The proposed approach was compared with L2 regularization, TKD, rescaled TKD in superfast dipole inversion, the modulated closed-form method, and iterative dipole inversion, as well as sparsity-regularized dipole inversion. It was observed that the proposed approach showed a substantial reduction in the streaking artifacts across 94 test volumes considered in this study. The proposed approach also showed better error reduction and edge preservation compared with other approaches. The proposed model resolution-based deconvolution compensates for the truncation of zero coefficients in the dipole kernel at the magic angle and hence provides a closer approximation to the true susceptibility map compared with other direct methods.

mcTFI QSM MRI ABC/2 intracranial hemorrhage to noncontrast head CT volume measurement equivalence

BACKGROUND/OBJECTIVES

Intracranial hemorrhage (ICH) volume assessment is an important part of patient management and is routinely obtained by non-contrast head CT (NCHCT) using the validated ABC/2 measurement method. Because conventional MRI imaging sequences demonstrate variability in ICH appearance, volumetric analyses for MRI bleed volume in a standardized manner using ABC/2 is not possible. The recently introduced multiecho-complex total field inversion quantitative susceptibility mapping (mcTFI QSM) MRI technique, which maps brain tissue susceptibility to both depict brain tissue structures and quantify tissue susceptibility, may provide a viable alternative. In this study we evaluated mcTFI QSM ABC/2 ICH volume assessment relative to NCHCT.

METHODS

Patients with ICH who had undergone NCHCT and MRI brain scans within 48 h were recruited for this retrospective study. The ABC/2 method was applied to estimate the bleed volume for both NCHCT and MRI by a CAQ-certified neuroradiologist with 10 years of experience and a trained laboratory assistant. Results were analyzed via Bland-Altman (B-A) and linear regression.

RESULTS

54 patients (27 females) who had undergone NCHCT and MRI within 48 h (<24 h., n = 31, 24-48 h, n = 10) were enrolled. mcTFI QSM ICH volume measurement method showed a positive correlation (99.5%) compared to NCHCT. B-A plot comparing ABC/2 ICH volume on NCHCT and mcTFI MRI done for patients within 24 h demonstrates a bias of -0.09%.

CONCLUSIONS

ICH volume calculation using ABC/2 on mcTFI QSM showed a high correlation with NCHCT measurement. These results suggest mcTFI QSM is a promising MRI method for ABC/2 for bleed volume measurement.

A latent code based multi-variable modulation network for susceptibility mapping

Quantitative susceptibility mapping (QSM) is a technique for obtaining quantitative information on tissue susceptibility and has shown promising potential for clinical applications, in which the magnetic susceptibility is calculated by solving an ill-posed inverse problem. Recently, deep learning-based methods are proposed to address this issue, but the diversity of data distribution was not well considered, and thus the model generalization is limited in clinical applications. In this paper, we propose a Latent Code based Multi-Variable modulation network for QSM reconstruction (LCMnet). Particularly, a specific modulation module is exploited to incorporate three variables, i.e., field map, magnitude image, and initial susceptibility. The latent code in the modulated convolution is learned from feature maps of the field data using the encoder-decoder framework. The susceptibility map pre-estimated from simple thresholding is the constant input of the module, thereby enhancing the network stability and accelerating training convergence. As another input, multi-level features generated by a cross-fusion block integrate the information of field and magnitude data effectively. Experimental results on in vivo human brain data, challenge data, clinical data and synthetic data demonstrate that the proposed method LCMnet can achieve outstanding performance on accurate susceptibility measurement and also excellent generalization.

BFRnet: A deep learning-based MR background field removal method for QSM of the brain containing significant pathological susceptibility sources

INTRODUCTION

Background field removal (BFR) is a critical step required for successful quantitative susceptibility mapping (QSM). However, eliminating the background field in brains containing significant susceptibility sources, such as intracranial hemorrhages, is challenging due to the relatively large scale of the field induced by these pathological susceptibility sources.

METHOD

This study proposes a new deep learning-based method, BFRnet, to remove the background field in healthy and hemorrhagic subjects. The network is built with the dual-frequency octave convolutions on the U-net architecture, trained with synthetic field maps containing significant susceptibility sources. The BFRnet method is compared with three conventional BFR methods and one previous deep learning method using simulated and in vivo brains from 4 healthy and 2 hemorrhagic subjects. Robustness against acquisition field-of-view (FOV) orientation and brain masking are also investigated.

RESULTS

For both simulation and in vivo experiments, BFRnet led to the best visually appealing results in the local field and QSM results with the minimum contrast loss and the most accurate hemorrhage susceptibility measurements among all five methods. In addition, BFRnet produced the most consistent local field and susceptibility maps between different sizes of brain masks, while conventional methods depend drastically on precise brain extraction and further brain edge erosions. It is also observed that BFRnet performed the best among all BFR methods for acquisition FOVs oblique to the main magnetic field.

CONCLUSION

The proposed BFRnet improved the accuracy of local field reconstruction in the hemorrhagic subjects compared with conventional BFR algorithms. The BFRnet method was effective for acquisitions of tilted orientations and retained whole brains without edge erosion as often required by traditional BFR methods.

Region Expansion of Background Field Removal with Local Spherical Harmonics Approximation for Whole-brain Quantitative Susceptibility Mapping

PURPOSE

Quantitative susceptibility mapping (QSM) is useful for obtaining biological information. To calculate susceptibility distribution, it is necessary to calculate the local field caused by the differences of susceptibility between the tissues. The local field can be obtained by removing a background field from a total field acquired by MR phase image. Conventional approaches based on spherical mean value (SMV) filtering, which are widely used for background field calculations, fail to calculate the background field of the brain surface region corresponding to the radius of the SMV kernel, and consequently cannot calculate the QSM of the brain surface region. Accordingly, a new method calculating the local field by expansively removing the background field is proposed for whole brain QSM.

METHODS

The proposed method consists of two steps. First, the background field of the brain surface is calculated from the total field using a locally polynomial approximation of spherical harmonics. Second, the whole brain local field is calculated by SMV filtering with a constraint term of the background field of the brain surface. The parameters of the approximation were optimized to reduce calculation errors through simulations using both a numerical phantom and a measured human brain. Performance of the proposed method with the optimized parameters was quantitatively and visually compared with conventional methods in an experiment of five healthy volunteers.

RESULTS

The proposed method showed the accurate local field over the expanded brain region in the simulation studies. It also showed consistent QSM with conventional methods inside of the brain surface and showed clear vein structures on the brain surface.

CONCLUSION

The proposed method enables accurate calculation of whole brain QSM without eroding the brain surface region while maintaining same values inside of the brain surface as the conventional methods.

Optimal echo times for quantitative susceptibility mapping: A test-retest study on basal ganglia and subcortical brain nuclei

Quantitative Susceptibility Mapping (QSM) is a recent MRI-technique able to quantify the bulk magnetic susceptibility of myelin, iron, and calcium in the brain. Its variability across different acquisition parameters has prompted the need for standardisation across multiple centres and MRI vendors. However, a high level of agreement between repeated imaging acquisitions is equally important. With this study we aimed to assess the inter-scan repeatability of an optimised multi-echo GRE sequence in 28 healthy volunteers. We extracted and compared the susceptibility measures from the scan and rescan acquisitions across 7 bilateral brain regions (i.e., 14 regions of interest (ROIs)) relevant for neurodegeneration. Repeatability was first assessed while reconstructing QSM with a fixed number of echo times (i.e., 8). Excellent inter-scan repeatability was found for putamen, globus pallidus and caudate nucleus, while good performance characterised the remaining structures. An increased variability was instead noted for small ROIs like red nucleus and substantia nigra. Secondly, we assessed the impact exerted on repeatability by the number of echoes used to derive QSM maps. Results were impacted by this parameter, especially in smaller regions. Larger brain structures, on the other hand, showed more consistent performance. Nevertheless, with either 8 or 7 echoes we managed to obtain good inter-scan repeatability on almost all ROIs. These findings indicate that the designed acquisition/reconstruction protocol has wide applicability, particularly in clinical or research settings involving longitudinal acquisitions (e.g. rehabilitation studies).

DeepSTI: Towards tensor reconstruction using fewer orientations in susceptibility tensor imaging

Susceptibility tensor imaging (STI) is an emerging magnetic resonance imaging technique that characterizes the anisotropic tissue magnetic susceptibility with a second-order tensor model. STI has the potential to provide information for both the reconstruction of white matter fiber pathways and detection of myelin changes in the brain at mm resolution or less, which would be of great value for understanding brain structure and function in healthy and diseased brain. However, the application of STI in vivo has been hindered by its cumbersome and time-consuming acquisition requirement of measuring susceptibility induced MR phase changes at multiple head orientations. Usually, sampling at more than six orientations is required to obtain sufficient information for the ill-posed STI dipole inversion. This complexity is enhanced by the limitation in head rotation angles due to physical constraints of the head coil. As a result, STI has not yet been widely applied in human studies in vivo. In this work, we tackle these issues by proposing an image reconstruction algorithm for STI that leverages data-driven priors. Our method, called DeepSTI, learns the data prior implicitly via a deep neural network that approximates the proximal operator of a regularizer function for STI. The dipole inversion problem is then solved iteratively using the learned proximal network. Experimental results using both simulation and in vivo human data demonstrate great improvement over state-of-the-art algorithms in terms of the reconstructed tensor image, principal eigenvector maps and tractography results, while allowing for tensor reconstruction with MR phase measured at much less than six different orientations. Notably, promising reconstruction results are achieved by our method from only one orientation in human in vivo, and we demonstrate a potential application of this technique for estimating lesion susceptibility anisotropy in patients with multiple sclerosis.

Quantitative susceptibility mapping using multi-channel convolutional neural networks with dipole-adaptive multi-frequency inputs

Quantitative susceptibility mapping (QSM) quantifies the distribution of magnetic susceptibility and shows great potential in assessing tissue contents such as iron, myelin, and calcium in numerous brain diseases. The accuracy of QSM reconstruction was challenged by an ill-posed field-to-susceptibility inversion problem, which is related to the impaired information near the zero-frequency response of the dipole kernel. Recently, deep learning methods demonstrated great capability in improving the accuracy and efficiency of QSM reconstruction. However, the construction of neural networks in most deep learning-based QSM methods did not take the intrinsic nature of the dipole kernel into account. In this study, we propose a dipole kernel-adaptive multi-channel convolutional neural network (DIAM-CNN) method for the dipole inversion problem in QSM. DIAM-CNN first divided the original tissue field into high-fidelity and low-fidelity components by thresholding the dipole kernel in the frequency domain, and it then inputs the two components as additional channels into a multichannel 3D Unet. QSM maps from the calculation of susceptibility through multiple orientation sampling (COSMOS) were used as training labels and evaluation reference. DIAM-CNN was compared with two conventional model-based methods [morphology enabled dipole inversion (MEDI) and improved sparse linear equation and least squares (iLSQR) and one deep learning method (QSMnet)]. High-frequency error norm (HFEN), peak signal-to-noise-ratio (PSNR), normalized root mean squared error (NRMSE), and the structural similarity index (SSIM) were reported for quantitative comparisons. Experiments on healthy volunteers demonstrated that the DIAM-CNN results had superior image quality to those of the MEDI, iLSQR, or QSMnet results. Experiments on data with simulated hemorrhagic lesions demonstrated that DIAM-CNN produced fewer shadow artifacts around the bleeding lesion than the compared methods. This study demonstrates that the incorporation of dipole-related knowledge into the network construction has a potential to improve deep learning-based QSM reconstruction.

Toward a realistic in silico abdominal phantom for QSM

PURPOSE

QSM outside the brain has recently gained interest, particularly in the abdominal region. However, the absence of reliable ground truths makes difficult to assess reconstruction algorithms, whose quality is already compromised by additional signal contributions from fat, gases, and different kinds of motion. This work presents a realistic in silico phantom for the development, evaluation and comparison of abdominal QSM reconstruction algorithms.

METHODS

Synthetic susceptibility andR 2 * $$ {R}_2^{\ast } $$ maps were generated by segmenting and postprocessing the abdominal 3T MRI data from a healthy volunteer. Susceptibility andR 2 * $$ {R}_2^{\ast } $$ values in different tissues/organs were assigned according to literature and experimental values and were also provided with realistic textures. The signal was simulated using as input the synthetic QSM andR 2 * $$ {R}_2^{\ast } $$ maps and fat contributions. Three susceptibility scenarios and two acquisition protocols were simulated to compare different reconstruction algorithms.

RESULTS

QSM reconstructions show that the phantom allows to identify the main strengths and limitations of the acquisition approaches and reconstruction algorithms, such as in-phase acquisitions, water-fat separation methods, and QSM dipole inversion algorithms.

CONCLUSION

The phantom showed its potential as a ground truth to evaluate and compare reconstruction pipelines and algorithms. The publicly available source code, designed in a modular framework, allows users to easily modify the susceptibility,R 2 * $$ {R}_2^{\ast } $$ and TEs, and thus creates different abdominal scenarios.

msQSM: Morphology-based Self-supervised Deep Learning for Quantitative Susceptibility Mapping

Quantitative susceptibility mapping (QSM) has been applied to the measurement of iron deposition and the auxiliary diagnosis of neurodegenerative disease. There still exists a dipole inversion problem in QSM reconstruction. Recently, deep learning approaches have been proposed to resolve this problem. However, most of these approaches are supervised methods that need pairs of the input phase and ground-truth. It remains a challenge to train a model for all resolutions without using the ground-truth and only using one resolution data. To address this, we proposed a self-supervised QSM deep learning method based on morphology. It consists of a morphological QSM builder to decouple the dependency of the QSM on acquisition resolution, and a morphological loss to reduce artifacts effectively and save training time efficiently. The proposed method can reconstruct arbitrary resolution QSM on both human data and animal data, regardless of whether the resolution is higher or lower than that of the training set. Our method outperforms the previous best unsupervised method with a 3.6% higher peak signal-to-noise ratio, 16.2% lower normalized root mean square error, and 22.1% lower high-frequency error norm. The morphological loss reduces training time by 22.1% with respect to the cycle gradient loss used in the previous unsupervised methods. Experimental results show that the proposed method accurately measures QSM with arbitrary resolutions, and achieves state-of-the-art results among unsupervised deep learning methods. Research on applications in neurodegenerative diseases found that our method is robust enough to measure significant increase in striatal magnetic susceptibility in patients during Alzheimer's disease progression, as well as significant increase in substantia nigra susceptibility in Parkinson's disease patients, and can be used as an auxiliary differential diagnosis tool for Alzheimer's disease and Parkinson's disease.

APART-QSM: an improved sub-voxel quantitative susceptibility mapping for susceptibility source separation using an iterative data fitting method

The brain tissue phase contrast in MRI sequences reflects the spatial distributions of multiple substances, such as iron, myelin, calcium, and proteins. These substances with paramagnetic and diamagnetic susceptibilities often colocalize in one voxel in brain regions. Both opposing susceptibilities play vital roles in brain development and neurodegenerative diseases. Conventional QSM methods only provide voxel-averaged susceptibility value and cannot disentangle intravoxel susceptibilities with opposite signs. Advanced susceptibility imaging methods have been recently developed to distinguish the contributions of opposing susceptibility sources for QSM. The basic concept of separating paramagnetic and diamagnetic susceptibility proportions is to include the relaxation rate R₂^* with R₂^' in QSM. The magnitude decay kernel, describing the proportionality coefficient between R₂^' and susceptibility, is an essential reconstruction coefficient for QSM separation methods. In this study, we proposed a more comprehensive complex signal model that describes the relationship between 3D GRE signal and the contributions of paramagnetic and diamagnetic susceptibility to the frequency shift and R₂^* relaxation. The algorithm is implemented as a constrained minimization problem in which the voxel-wise magnitude decay kernel and sub-voxel susceptibilities are determined alternately in each iteration until convergence. The calculated voxel-wise magnitude decay kernel could realistically model the relationship between the R₂^' relaxation and the volume susceptibility. Thus, the proposed method effectively prevents the errors of the magnitude decay kernel from propagating to the final susceptibility separation reconstruction. Phantom studies, ex vivo macaque brain experiments, and in vivo human brain imaging studies were conducted to evaluate the ability of the proposed method to distinguish paramagnetic and diamagnetic susceptibility sources. The results demonstrate that the proposed method provides state-of-the-art performances for quantifying brain iron and myelin compared to previous QSM separation methods. Our results show that the proposed method has the potential to simultaneously quantify whole brain iron and myelin during brain development and aging. The proposed model was also deployed with multiple-orientation complex GRE data input measurements, resulting in high-quality QSM separation maps with more faithful tissue delineation between brain structures compared to those reconstructed by single-orientation QSM separation methods.

Tilted quantitative susceptibility mapping at oblique MRI (tiltQSM)

OBJECTIVE

If the phase image matrix was acquired from oblique MRI, it is needed to deal with the oblique effect for quantitative susceptibility mapping (QSM), as addressed in this paper.

METHODS

We proposed two methods for QSM reconstruction from slice-tilted MRI phase image (tiltQSM): 1) rotData per anti-tilting phase image rotation back into the B₀-upright system, and 2) rotKernel per pro-tilting dipole kernel rotation into the same oblique setting as defined by the tilted phase image. Both matrix methods were implemented in an additional preprocessing subroutine to ensure that the phase image and the dipole kernel were represented in the same coordinate system (either in B₀-upright system or in B₀-tilted system); thereafter tiltQSM could be completed through a regular QSM procedure. Besides the oblique effect, tiltQSM also suffers from MRI anisotropy. We provided numeric simulations, phantom tests and in vivo brain experiments on tiltQSM with oblique MRI (axial slice tilting at 3T).

RESULTS

The tiltQSM reconstruction could attain a performance corr > 0.90 (spatial correlation conformance) for small tilting angles <10°. The tiltQSM performance could be further degraded by voxel anisotropy due to image matrix rotation (digital geometry error).

CONCLUSIONS

To seek inverse solutions of MRI phase images acquired at oblique MRI (e.g. in axial slice tilting), we proposed tiltQSM to deal with the oblique effect per matrix rotation (either rotData or rotKernel) in a preprocessing subroutine prior to a regular QSM procedure. In practice, it is always recommended to acquire MRI phase images in isotropic matrix at zero obliqueness (or limited to small tilting angles <10°) for maximal (optimal) QSM reconstruction.

Larmor frequency shift from magnetized cylinders with arbitrary orientation distribution

The magnetic susceptibility of tissue can provide valuable information about its chemical composition and microstructural organization. However, the relation between the magnetic microstructure and the measurable Larmor frequency shift is understood only for a few idealized cases. Here we analyze the microstructure formed by magnetized, NMR-invisible infinite cylinders suspended in an NMR-reporting fluid. Through simulations, we scrutinize various geometries of mesoscopic Lorentz cavities and inclusions, and show that the cavity size should be approximately one order of magnitude larger than the width of the inclusions. We also analytically derive the Larmor frequency shift for a population of cylinders with arbitrary orientation dispersion and show that it is determined by the l = 2 Laplace expansion coefficients p 2 m of the cylinders' orientation distribution function. Our work underscores the need to account for microstructural organization when estimating magnetic tissue properties.

Affine transformation edited and refined deep neural network for quantitative susceptibility mapping

Deep neural networks have demonstrated great potential in solving dipole inversion for Quantitative Susceptibility Mapping (QSM). However, the performances of most existing deep learning methods drastically degrade with mismatched sequence parameters such as acquisition orientation and spatial resolution. We propose an end-to-end AFfine Transformation Edited and Refined (AFTER) deep neural network for QSM, which is robust against arbitrary acquisition orientation and spatial resolution up to 0.6 mm isotropic at the finest. The AFTER-QSM neural network starts with a forward affine transformation layer, followed by a Unet for dipole inversion, then an inverse affine transformation layer, followed by a Residual Dense Network (RDN) for QSM refinement. Simulation and in-vivo experiments demonstrated that the proposed AFTER-QSM network architecture had excellent generalizability. It can successfully reconstruct susceptibility maps from highly oblique and anisotropic scans, leading to the best image quality assessments in simulation tests and suppressed streaking artifacts and noise levels for in-vivo experiments compared with other methods. Furthermore, ablation studies showed that the RDN refinement network significantly reduced image blurring and susceptibility underestimation due to affine transformations. In addition, the AFTER-QSM network substantially shortened the reconstruction time from minutes using conventional methods to only a few seconds.

NeXtQSM-A complete deep learning pipeline for data-consistent Quantitative Susceptibility Mapping trained with hybrid data

Deep learning based Quantitative Susceptibility Mapping (QSM) has shown great potential in recent years, obtaining similar results to established non-learning approaches. Many current deep learning approaches are not data consistent, require in vivo training data or solve the QSM problem in consecutive steps resulting in the propagation of errors. Here we aim to overcome these limitations and developed a framework to solve the QSM processing steps jointly. We developed a new hybrid training data generation method that enables the end-to-end training for solving background field correction and dipole inversion in a data-consistent fashion using a variational network that combines the QSM model term and a learned regularizer. We demonstrate that NeXtQSM overcomes the limitations of previous deep learning methods. NeXtQSM offers a new deep learning based pipeline for computing quantitative susceptibility maps that integrates each processing step into the training and provides results that are robust and fast.

Multi-echo dipole inversion for magnetic susceptibility mapping

PURPOSE

Reconstructing tissue magnetic susceptibility (QSM) from MRI phase data involves solving multiple consecutive ill-posed inverse problems such as phase unwrapping, background field removal, and field-to-source inversion. Multi-echo acquisitions present an additional challenge, as the magnetization field is typically computed from the multiple phase data prior to reconstructing the susceptibility map. Processing the multiple phase data introduces errors during the field estimation, violating assumptions of the subsequent inverse problems, manifesting as streaking artifacts in the susceptibility map. To address this challenge, we propose a multi-echo field-to-source forward model that forgoes the field estimation step. Moreover, we propose a fully general underestimation correction step to recover susceptibility sources that were regularized away during the field-to-source inversion.

METHODS

The multi-echo forward model and correction step were validated on the QSM Challenge 2.0 datasets and compared to the standard single field-to-source model in in vivo human brains using different types of deconvolution algorithms.

RESULTS

On the QSM Challenge 2.0 datasets the multi-echo forward model and correction step attain state-of-the-art results on all metrics by a wide margin. Experiments in in vivo brains show that the multi-echo model is in agreement with the single field-to-source model and that the proposed forward model and correction step can be used with any available dipole inversion method.

CONCLUSION

A multi-echo field-to-source forward model forgoes the need to fit multi-echo phase data and achieves state-of-the-art results on the QSM Challenge 2.0 data. Underestimated low-frequency susceptibility distributions can be partially recovered using a correction step.

Comparison of quantitative susceptibility mapping methods for iron-sensitive susceptibility imaging at 7T: An evaluation in healthy subjects and patients with Huntington's disease

Quantitative susceptibility mapping (QSM) is a promising tool for investigating iron dysregulation in neurodegenerative diseases, including Huntington's disease (HD). Many diverse methods have been proposed to generate accurate and robust QSM images. In this study, we evaluated the performance of different dipole inversion algorithms for iron-sensitive susceptibility imaging at 7T on healthy subjects of a large age range and patients with HD. We compared an iterative least-squares-based method (iLSQR), iterative methods that use regularization, single-step approaches, and deep learning-based techniques. Their performance was evaluated by comparing: (1) deviations from a multiple-orientation QSM reference; (2) visual appearance of QSM maps and the presence of artifacts; (3) susceptibility in subcortical brain regions with age; (4) regional brain susceptibility with published postmortem brain iron quantification; and (5) susceptibility in HD-affected basal ganglia regions between HD subjects and healthy controls. We found that single-step QSM methods with either total variation or total generalized variation constraints (SSTV/SSTGV) and the single-step deep learning method iQSM generally provided the best performance in terms of correlation with iron deposition and were better at differentiating between healthy controls and premanifest HD individuals, while deep learning QSM methods trained with multiple-orientation susceptibility data created QSM maps that were most similar to the multiple orientation reference and with the best visual scores.

Feasibility of ultrashort echo time quantitative susceptibility mapping with a 3D cones trajectory in the human brain

Purpose

Quantitative susceptibility mapping (QSM) has surfaced as a promising non-invasive quantitative biomarker that provides information about tissue composition and microenvironment. Recently, ultrashort echo time quantitative susceptibility mapping (UTE-QSM) has been investigated to achieve QSM of short T2 tissues. As the feasibility of UTE-QSM has not been demonstrated in the brain, the goal of this study was to develop a UTE-QSM with an efficient 3D cones trajectory and validate it in the human brain.

Materials and methods

An ultrashort echo time (UTE) cones sequence was implemented in a 3T clinical MRI scanner. Six images were acquired within a single acquisition, including UTE and gradient recalled echo (GRE) images. To achieve QSM, a morphology-enabled dipole inversion (MEDI) algorithm was incorporated, which utilizes both magnitude and phase images. Three fresh cadaveric human brains were scanned using the 3D cones trajectory with eight stretching factors (SFs) ranging from 1.0 to 1.7. In addition, five healthy volunteers were recruited and underwent UTE-QSM to demonstrate the feasibility in vivo. The acquired data were processed with the MEDI-QSM pipeline.

Results

The susceptibility maps estimated by UTE-QSM showed reliable tissue contrast. In the ex vivo experiment, high correlations were found between the baseline (SF of 1.0) and SFs from 1.1 to 1.7 with Pearson's correlations of 0.9983, 0.9968, 0.9959, 0.9960, 0.9954, 0.9943, and 0.9879, respectively (all p-values < 0.05). In the in vivo experiment, the measured QSM values in cortical gray matter, juxtacortical white matter, corpus callosum, caudate, and putamen were 25.4 ± 4.0, -21.8 ± 3.2, -22.6 ± 10.0, 77.5 ± 18.8, and 53.8 ± 7.1 ppb, consistent with the values reported in the literature.

Conclusion

Ultrashort echo time quantitative susceptibility mapping enables direct estimation of the magnetic susceptibility in the brain with a dramatically reduced total scan time by use of a stretched 3D cones trajectory. This technique provides a new biomarker for susceptibility mapping in the in vivo brain.

Quantitative susceptibility mapping of basal ganglia iron is associated with cognitive and motor functions that distinguish spinocerebellar ataxia type 6 and type 3

Background

In spinocerebellar ataxia type 3 (SCA3), volume loss has been reported in the basal ganglia, an iron-rich brain region, but iron content has not been examined. Recent studies have reported that patients with SCA6 have markedly decreased iron content in the cerebellar dentate, coupled with severe volume loss. Changing brain iron levels can disrupt cognitive and motor functions, yet this has not been examined in the SCAs, a disease in which iron-rich regions are affected.

Methods

In the present study, we used quantitative susceptibility mapping (QSM) to measure tissue magnetic susceptibility (indicating iron concentration), structural volume, and normalized susceptibility mass (indicating iron content) in the cerebellar dentate and basal ganglia in people with SCA3 (n = 10) and SCA6 (n = 6) and healthy controls (n = 9). Data were acquired using a 7T Philips MRI scanner. Supplemental measures assessed motor, cognitive, and mood domains.

Results

Putamen volume was lower in both SCA groups relative to controls, replicating prior findings. Dentate susceptibility mass and volume in SCA6 was lower than in SCA3 or controls, also replicating prior findings. The novel finding was that higher basal ganglia susceptibility mass in SCA6 correlated with lower cognitive performance and greater motor impairment, an association that was not observed in SCA3. Cerebellar dentate susceptibility mass, however, had the opposite relationship with cognition and motor function in SCA6, suggesting that, as dentate iron is depleted, it relocated to the basal ganglia, which contributed to cognitive and motor decline. By contrast, basal ganglia volume loss, rather than iron content, appeared to drive changes in motor function in SCA3.

Conclusion

The associations of higher basal ganglia iron with lower motor and cognitive function in SCA6 but not in SCA3 suggest the potential for using brain iron deposition profiles beyond the cerebellar dentate to assess disease states within the cerebellar ataxias. Moreover, the role of the basal ganglia deserves greater attention as a contributor to pathologic and phenotypic changes associated with SCA.

Quantitative susceptibility mapping (QSM) of the cardiovascular system: challenges and perspectives

Quantitative susceptibility mapping (QSM) is a powerful, non-invasive, magnetic resonance imaging (MRI) technique that relies on measurement of magnetic susceptibility. So far, QSM has been employed mostly to study neurological disorders characterized by iron accumulation, such as Parkinson's and Alzheimer's diseases. Nonetheless, QSM allows mapping key indicators of cardiac disease such as blood oxygenation and myocardial iron content. For this reason, the application of QSM offers an unprecedented opportunity to gain a better understanding of the pathophysiological changes associated with cardiovascular disease and to monitor their evolution and response to treatment. Recent studies on cardiovascular QSM have shown the feasibility of a non-invasive assessment of blood oxygenation, myocardial iron content and myocardial fibre orientation, as well as carotid plaque composition. Significant technical challenges remain, the most evident of which are related to cardiac and respiratory motion, blood flow, chemical shift effects and susceptibility artefacts. Significant work is ongoing to overcome these challenges and integrate the QSM technique into clinical practice in the cardiovascular field.

Quantitative susceptibility mapping as an imaging biomarker for Alzheimer’s disease: The expectations and limitations

Alzheimer’s disease (AD) is the most common type of dementia and a distressing diagnosis for individuals and caregivers. Researchers and clinical trials have mainly focused on β-amyloid plaques, which are hypothesized to be one of the most important factors for neurodegeneration in AD. Meanwhile, recent clinicopathological and radiological studies have shown closer associations of tau pathology rather than β-amyloid pathology with the onset and progression of Alzheimer’s symptoms. Toward a biological definition of biomarker-based research framework for AD, the 2018 National Institute on Aging–Alzheimer’s Association working group has updated the ATN classification system for stratifying disease status in accordance with relevant pathological biomarker profiles, such as cerebral β-amyloid deposition, hyperphosphorylated tau, and neurodegeneration. In addition, altered iron metabolism has been considered to interact with abnormal proteins related to AD pathology thorough generating oxidative stress, as some prior histochemical and histopathological studies supported this iron-mediated pathomechanism. Quantitative susceptibility mapping (QSM) has recently become more popular as a non-invasive magnetic resonance technique to quantify local tissue susceptibility with high spatial resolution, which is sensitive to the presence of iron. The association of cerebral susceptibility values with other pathological biomarkers for AD has been investigated using various QSM techniques; however, direct evidence of these associations remains elusive. In this review, we first briefly describe the principles of QSM. Second, we focus on a large variety of QSM applications, ranging from common applications, such as cerebral iron deposition, to more recent applications, such as the assessment of impaired myelination, quantification of venous oxygen saturation, and measurement of blood– brain barrier function in clinical settings for AD. Third, we mention the relationships among QSM, established biomarkers, and cognitive performance in AD. Finally, we discuss the role of QSM as an imaging biomarker as well as the expectations and limitations of clinically useful diagnostic and therapeutic implications for AD.

Influence of diffusion on transverse relaxation rates and phases of an ensemble of magnetic spheres

In quantitative susceptibility mapping, the tissue susceptibility is determined from the magnitude and phase of the gradient echo signal, which is influenced by the interplay of complex susceptibility and diffusion effect. Herein, we analytically analyze the influence of diffusion on magnitude and phase images generated by randomly arranged magnetic spheres as a model of intracerebral iron depositions. We demonstrate that both gradient and spin echo relaxation rate constants have a strong and nonlinear dependence on diffusion strength and give empirical formulas for magnitude and phase. This may be used in the future to improve QSM processing methods. In addition, we show that, in theory, combined acquisitions of gradient and spin echo can be used to determine the dimension of the magnetic spheres and the diffusion strength.

Towards in vivo ground truth susceptibility for single-orientation deep learning QSM: a multi-orientation gradient-echo MRI dataset

Recently, deep neural networks have shown great potential for solving dipole inversion of quantitative susceptibility mapping (QSM) with improved results. However, these studies utilized their limited dataset for network training and inference, which may lead to untrustworthy conclusions. Thus, a common dataset is needed for a fair comparison between different QSM reconstruction networks. Additionally, finding an in vivo reference susceptibility map that matches acquired single-orientation phase data remains an open problem. Susceptibility tensor imaging (STI) χ₃₃ and Calculation of Susceptibility through Multiple Orientation Sampling (COSMOS) are considered reference susceptibility candidates. However, a large number of multi-orientation GRE data for both STI and COSMOS reconstruction are now unavailable for training supervised neural networks for QSM. In this study, we reported the largest multi-orientation dataset, to the best of our knowledge in the QSM research field, with a total of 144 scans from 8 healthy subjects collected using a 3D GRE sequence from the same MR scanner. In addition, the parcellation of deep gray matter is also provided for automatically extracting susceptibility values. Five recently developed deep neural networks, i.e., xQSM, QSMnet, autoQSM, LPCNN, and MoDL-QSM were performed on this dataset. This potential data source could provide a common framework and labels to test the accuracy and robustness of deep neural networks for QSM reconstruction. This dataset has the potential to provide a benchmark of reference susceptibility for the deep learning-based QSM methods. Additionally, the trained COSMOS-labeled and χ₃₃-labeled networks were tested on the pathological data to explore their potential applications. The data together with deep gray matter parcellation maps are now publicly available via an open repository at https://osf.io/yfms7/, and the raw multi-orientation GRE data were also available at https://osf.io/y6rc3/.

Quantitative Susceptibility Mapping: Basic Methods and Clinical Applications

Quantitative susceptibility mapping (QSM), one of the advanced MRI techniques for evaluating magnetic susceptibility, offers precise quantitative measurements of spatial distributions of magnetic susceptibility. Magnetic susceptibility describes the magnetizability of a material to an applied magnetic field and is a substance-specific value. Recently, QSM has been widely used to estimate various levels of substances in the brain, including iron, hemosiderin, and deoxyhemoglobin (paramagnetism), as well as calcification (diamagnetism). By visualizing iron distribution in the brain, it is possible to identify anatomic structures that are not evident on conventional images and to evaluate various neurodegenerative diseases. It has been challenging to apply QSM in areas outside the brain because of motion artifacts from respiration and heartbeats, as well as the presence of fat, which has a different frequency to the proton. In this review, the authors provide a brief overview of the theoretical background and analyze methods of converting MRI phase images to QSM. Moreover, we provide an overview of the current clinical applications of QSM. Online supplemental material is available for this article. ^©RSNA, 2022.

Multi-echo quantitative susceptibility mapping: how to combine echoes for accuracy and precision at 3 Tesla

Purpose

To compare different multi‐echo combination methods for MRI QSM. Given the current lack of consensus, we aimed to elucidate how to optimally combine multi‐echo gradient‐recalled echo signal phase information, either before or after applying Laplacian‐base methods (LBMs) for phase unwrapping or background field removal.

Methods

Multi‐echo gradient‐recalled echo data were simulated in a numerical head phantom, and multi‐echo gradient‐recalled echo images were acquired at 3 Tesla in 10 healthy volunteers. To enable image‐based estimation of gradient‐recalled echo signal noise, 5 volunteers were scanned twice in the same session without repositioning. Five QSM processing pipelines were designed: 1 applied nonlinear phase fitting over TEs before LBMs; 2 applied LBMs to the TE‐dependent phase and then combined multiple TEs via either TE‐weighted or SNR‐weighted averaging; and 2 calculated TE‐dependent susceptibility maps via either multi‐step or single‐step QSM and then combined multiple TEs via magnitude‐weighted averaging. Results from different pipelines were compared using visual inspection; summary statistics of susceptibility in deep gray matter, white matter, and venous regions; phase noise maps (error propagation theory); and, in the healthy volunteers, regional fixed bias analysis (Bland–Altman) and regional differences between the means (nonparametric tests).

Results

Nonlinearly fitting the multi‐echo phase over TEs before applying LBMs provided the highest regional accuracy of χ and the lowest phase noise propagation compared to averaging the LBM‐processed TE‐dependent phase. This result was especially pertinent in high‐susceptibility venous regions.

Conclusion

For multi‐echo QSM, we recommend combining the signal phase by nonlinear fitting before applying LBMs.

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Instant tissue field and magnetic susceptibility mapping from MRI raw phase using Laplacian enhanced deep neural networks

Quantitative susceptibility mapping (QSM) is an MRI post-processing technique that produces spatially resolved magnetic susceptibility maps from phase data. However, the traditional QSM reconstruction pipeline involves multiple non-trivial steps, including phase unwrapping, background field removal, and dipole inversion. These intermediate steps not only increase the reconstruction time but accumulates errors. This study aims to overcome existing limitations by developing a Laplacian-of-Trigonometric-functions (LoT) enhanced deep neural network for near-instant quantitative field and susceptibility mapping (i.e., iQFM and iQSM) from raw MRI phase data. The proposed iQFM and iQSM methods were compared with established reconstruction pipelines on simulated and in vivo datasets. In addition, experiments on patients with intracranial hemorrhage and multiple sclerosis were also performed to test the generalization of the proposed neural networks. The proposed iQFM and iQSM methods in healthy subjects yielded comparable results to those involving the intermediate steps while dramatically improving reconstruction accuracies on intracranial hemorrhages with large susceptibilities. High susceptibility contrast between multiple sclerosis lesions and healthy tissue was also achieved using the proposed methods. Comparative studies indicated that the most significant contributor to iQFM and iQSM over conventional multi-step methods was the elimination of traditional Laplacian unwrapping. The reconstruction time on the order of minutes for traditional approaches was shortened to around 0.1 seconds using the trained iQFM and iQSM neural networks.

Comparison of quantitative susceptibility mapping methods on evaluating radiation-induced cerebral microbleeds and basal ganglia at 3T and 7T

Quantitative susceptibility mapping (QSM) has the potential for being a biomarker for various diseases because of its ability to measure tissue susceptibility related to iron deposition, myelin, and hemorrhage from the phase signal of a T2 *-weighted MRI. Despite its promise as a quantitative marker, QSM is faced with many challenges, including its dependence on preprocessing of the raw phase data, the relatively weak tissue signal, and the inherently ill posed relationship between the magnetic dipole and measured phase. The goal of this study was to evaluate the effects of background field removal and dipole inversion algorithms on noise characteristics, image uniformity, and structural contrast for cerebral microbleed (CMB) quantification at both 3T and 7T. We selected four widely used background phase removal and five dipole field inversion algorithms for QSM and applied them to volunteers and patients with CMBs, who were scanned at two different field strengths, with ground truth QSM reference calculated using multiple orientation scans. 7T MRI provided QSM images with lower noise than did 3T MRI. QSIP and VSHARP + iLSQR achieved the highest white matter homogeneity and vein contrast, with QSIP also providing the highest CMB contrast. Compared with ground truth COSMOS QSM images, overall good correlations between susceptibility values of dipole inversion algorithms and the COSMOS reference were observed in basal ganglia regions, with VSHARP + iLSQR achieving the susceptibility values most similar to COSMOS across all regions. This study can provide guidance for selecting the most appropriate QSM processing pipeline based on the application of interest and scanner field strength.

Hybrid data fidelity term approach for quantitative susceptibility mapping

Purpose

Methods

Results

Conclusions

Brain pathological changes during neurodegenerative diseases and their identification methods: How does QSM perform in detecting this process?

The presence of iron is essential for many biological processes in the body. But sometimes, for various reasons, the amount of iron deposition in different areas of the brain increases, which leads to problems related to the nervous system. Quantitative susceptibility mapping (QSM) is one of the newest magnetic resonance imaging (MRI)-based methods for assessing iron accumulation in target areas. This Narrative Review article aims to evaluate the performance of QSM compared to other methods of assessing iron deposition in the clinical field. Based on the results, we introduced related basic definitions, some neurodegenerative diseases, methods of examining iron deposition in these diseases, and their advantages and disadvantages. This article states that the QSM method can be introduced as a new, reliable, and non-invasive technique for clinical evaluations.

Overview of quantitative susceptibility mapping using deep learning: Current status, challenges and opportunities

Quantitative susceptibility mapping (QSM) has gained broad interest in the field by extracting bulk tissue magnetic susceptibility, predominantly determined by myelin, iron and calcium from magnetic resonance imaging (MRI) phase measurements in vivo. Thereby, QSM can reveal pathological changes of these key components in a variety of diseases. QSM requires multiple processing steps such as phase unwrapping, background field removal and field-to-source inversion. Current state-of-the-art techniques utilize iterative optimization procedures to solve the inversion and background field correction, which are computationally expensive and require a careful choice of regularization parameters. With the recent success of deep learning using convolutional neural networks for solving ill-posed reconstruction problems, the QSM community also adapted these techniques and demonstrated that the QSM processing steps can be solved by efficient feed forward multiplications not requiring either iterative optimization or the choice of regularization parameters. Here, we review the current status of deep learning-based approaches for processing QSM, highlighting limitations and potential pitfalls, and discuss the future directions the field may take to exploit the latest advances in deep learning for QSM.