Quantitative susceptibility mapping: Report from the 2016 reconstruction challenge

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.

Value of Quantitative Susceptibility Mapping in Clinical Neuroradiology

Quantitative susceptibility mapping (QSM) is a unique technique for providing quantitative information on tissue magnetic susceptibility using phase image data. QSM can provide valuable information regarding physiological and pathological processes such as iron deposition, hemorrhage, calcification, and myelin. QSM has been considered for use as an imaging biomarker to investigate physiological status and pathological changes. Although various studies have investigated the clinical applications of QSM, particularly regarding the use of QSM in clinical practice, have not been examined well. This review provides on an overview of the basics of QSM and its clinical applications in neuroradiology. LEVEL OF EVIDENCE: 2 TECHNICAL EFFICACY: Stage 2.

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.

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.

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.

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.

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.

Quantitative susceptibility mapping in multiple sclerosis: A systematic review and meta-analysis

BACKGROUND

Quantitative susceptibility mapping (QSM) is a quantitative measure based on magnetic resonance imaging sensitive to iron and myelin content. This makes QSM a promising non-invasive tool for multiple sclerosis (MS) in research and clinical practice.

OBJECTIVE

We performed a systematic review and meta-analysis on the use of QSM in MS.

METHODS

Our review was prospectively registered on PROSPERO (CRD42022309563). We searched five databases for studies published between inception and 30th April 2023. We identified 83 English peer-reviewed studies that applied QSM images on MS cohorts. Fifty-five included studies had at least one of the following outcome measures: deep grey matter QSM values in MS, either compared to healthy controls (HC) (k = 13) or correlated with the score on the Expanded Disability Status Scale (EDSS) (k = 7), QSM lesion characteristics (k = 22) and their clinical correlates (k = 17), longitudinal correlates (k = 11), histological correlates (k = 7), or correlates with other imaging techniques (k = 12). Two meta-analyses on deep grey matter (DGM) susceptibility data were performed, while the remaining findings could only be analyzed descriptively.

RESULTS

After outlier removal, meta-analyses demonstrated a significant increase in the basal ganglia susceptibility (QSM values) in MS compared to HC, caudate (k = 9, standardized mean difference (SDM) = 0.54, 95 % CI = 0.39-0.70, I2 = 46 %), putamen (k = 9, SDM = 0.38, 95 % CI = 0.19-0.57, I2 = 59 %), and globus pallidus (k = 9, SDM = 0.48, 95 % CI = 0.28-0.67, I2 = 60 %), whereas thalamic QSM values exhibited a significant reduction (k = 12, SDM = -0.39, 95 % CI = -0.66--0.12, I2 = 84 %); these susceptibility differences in MS were independent of age. Further, putamen QSM values positively correlated with EDSS (k = 4, r = 0.36, 95 % CI = 0.16-0.53, I2 = 0 %). Regarding rim lesions, four out of seven studies, representing 73 % of all patients, reported rim lesions to be associated with more severe disability. Moreover, lesion development from initial detection to the inactive stage is paralleled by increasing, plateauing (after about two years), and gradually decreasing QSM values, respectively. Only one longitudinal study provided clinical outcome measures and found no association. Histological data suggest iron content to be the primary source of QSM values in DGM and at the edges of rim lesions; further, when also considering data from myelin water imaging, the decrease of myelin is likely to drive the increase of QSM values within WM lesions.

CONCLUSIONS

We could provide meta-analytic evidence for DGM susceptibility changes in MS compared to HC; basal ganglia susceptibility is increased and, in the putamen, associated with disability, while thalamic susceptibility is decreased. Beyond these findings, further investigations are necessary to establish the role of QSM in MS for research or even clinical routine.

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.

Deep-learning-based reconstruction of undersampled MRI to reduce scan times: a multicentre, retrospective, cohort study

BACKGROUND

The extended acquisition times required for MRI limit its availability in resource-constrained settings. Consequently, accelerating MRI by undersampling k-space data, which is necessary to reconstruct an image, has been a long-standing but important challenge. We aimed to develop a deep convolutional neural network (dCNN) optimisation method for MRI reconstruction and to reduce scan times and evaluate its effect on image quality and accuracy of oncological imaging biomarkers.

METHODS

In this multicentre, retrospective, cohort study, MRI data from patients with glioblastoma treated at Heidelberg University Hospital (775 patients and 775 examinations) and from the phase 2 CORE trial (260 patients, 1083 examinations, and 58 institutions) and the phase 3 CENTRIC trial (505 patients, 3147 examinations, and 139 institutions) were used to develop, train, and test dCNN for reconstructing MRI from highly undersampled single-coil k-space data with various acceleration rates (R=2, 4, 6, 8, 10, and 15). Independent testing was performed with MRIs from the phase 2/3 EORTC-26101 trial (528 patients with glioblastoma, 1974 examinations, and 32 institutions). The similarity between undersampled dCNN-reconstructed and original MRIs was quantified with various image quality metrics, including structural similarity index measure (SSIM) and the accuracy of undersampled dCNN-reconstructed MRI on downstream radiological assessment of imaging biomarkers in oncology (automated artificial intelligence-based quantification of tumour burden and treatment response) was performed in the EORTC-26101 test dataset. The public NYU Langone Health fastMRI brain test dataset (558 patients and 558 examinations) was used to validate the generalisability and robustness of the dCNN for reconstructing MRIs from available multi-coil (parallel imaging) k-space data.

FINDINGS

In the EORTC-26101 test dataset, the median SSIM of undersampled dCNN-reconstructed MRI ranged from 0·88 to 0·99 across different acceleration rates, with 0·92 (95% CI 0·92-0·93) for 10-times acceleration (R=10). The 10-times undersampled dCNN-reconstructed MRI yielded excellent agreement with original MRI when assessing volumes of contrast-enhancing tumour (median DICE for spatial agreement of 0·89 [95% CI 0·88 to 0·89]; median volume difference of 0·01 cm3 [95% CI 0·00 to 0·03] equalling 0·21%; p=0·0036 for equivalence) or non-enhancing tumour or oedema (median DICE of 0·94 [95% CI 0·94 to 0·95]; median volume difference of -0·79 cm3 [95% CI -0·87 to -0·72] equalling -1·77%; p=0·023 for equivalence) in the EORTC-26101 test dataset. Automated volumetric tumour response assessment in the EORTC-26101 test dataset yielded an identical median time to progression of 4·27 months (95% CI 4·14 to 4·57) when using 10-times-undersampled dCNN-reconstructed or original MRI (log-rank p=0·80) and agreement in the time to progression in 374 (95·2%) of 393 patients with data. The dCNN generalised well to the fastMRI brain dataset, with significant improvements in the median SSIM when using multi-coil compared with single-coil k-space data (p<0·0001).

INTERPRETATION

Deep-learning-based reconstruction of undersampled MRI allows for a substantial reduction of scan times, with a 10-times acceleration demonstrating excellent image quality while preserving the accuracy of derived imaging biomarkers for the assessment of oncological treatment response. Our developments are available as open source software and hold considerable promise for increasing the accessibility to MRI, pending further prospective validation.

FUNDING

Deutsche Forschungsgemeinschaft (German Research Foundation) and an Else Kröner Clinician Scientist Endowed Professorship by the Else Kröner Fresenius Foundation.

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.

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.

Coil sketching for computationally efficient MR iterative reconstruction

PURPOSE

Parallel imaging and compressed sensing reconstructions of large MRI datasets often have a prohibitive computational cost that bottlenecks clinical deployment, especially for three-dimensional (3D) non-Cartesian acquisitions. One common approach is to reduce the number of coil channels actively used during reconstruction as in coil compression. While effective for Cartesian imaging, coil compression inherently loses signal energy, producing shading artifacts that compromise image quality for 3D non-Cartesian imaging. We propose coil sketching, a general and versatile method for computationally-efficient iterative MR image reconstruction.

THEORY AND METHODS

We based our method on randomized sketching algorithms, a type of large-scale optimization algorithms well established in the fields of machine learning and big data analysis. We adapt the sketching theory to the MRI reconstruction problem via a structured sketching matrix that, similar to coil compression, considers high-energy virtual coils obtained from principal component analysis. But, unlike coil compression, it also considers random linear combinations of the remaining low-energy coils, effectively leveraging information from all coils.

RESULTS

First, we performed ablation experiments to validate the sketching matrix design on both Cartesian and non-Cartesian datasets. The resulting design yielded both improved computatioanal efficiency and preserved signal-to-noise ratio (SNR) as measured by the inverse g-factor. Then, we verified the efficacy of our approach on high-dimensional non-Cartesian 3D cones datasets, where coil sketching yielded up to three-fold faster reconstructions with equivalent image quality.

CONCLUSION

Coil sketching is a general and versatile reconstruction framework for computationally fast and memory-efficient reconstruction.

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.

Thin slab quantitative susceptibility mapping

PURPOSE

Susceptibility maps reconstructed from thin slabs may suffer underestimation due to background-field removal imperfections near slab boundaries and the increased difficulty of solving a 3D-inversion problem with reduced support, particularly in the direction of the main magnetic field. Reliable QSM reconstruction from thin slabs would enable focal acquisitions in a much-reduced scan time.

METHODS

This work proposes using additional rapid low-resolution data of extended spatial coverage to improve background-field estimation and regularize the inversion-to-susceptibility process for high resolution, thin slab data. The new method was tested using simulated and in-vivo brain data of high resolution (0.33 × 0.33 × 0.33 mm3 and 0.54 × 0.54 × 0.65 mm3 , respectively) at 3T, and compared to the standard large volume approach.

RESULTS

Using the proposed method, in-vivo high-resolution QSM at 3T was obtained from slabs of width as small as 10.4 mm, aided by a lower-resolution dataset of 24 times coarser voxels. Simulations showed that the proposed method produced more consistent measurements from slabs of at least eight slices. Reducing the mean ROI error to 5% required the low-resolution data to cover ˜60 mm in the direction of the main field, have at least 2-mm isotropic resolution that is not coarser than the high-resolution data by more than four-fold in any direction.

CONCLUSION

Applying the proposed method enabled focal QSM acquisitions at sub-millimeter resolution within reasonable acquisition time.

Deep Learning k-Space-to-Image Reconstruction Facilitates High Spatial Resolution and Scan Time Reduction in Diffusion-Weighted Imaging Breast MRI

BACKGROUND

For time-consuming diffusion-weighted imaging (DWI) of the breast, deep learning-based imaging acceleration appears particularly promising.

PURPOSE

To investigate a combined k-space-to-image reconstruction approach for scan time reduction and improved spatial resolution in breast DWI.

STUDY TYPE

Retrospective.

POPULATION

133 women (age 49.7 ± 12.1 years) underwent multiparametric breast MRI.

FIELD STRENGTH/SEQUENCE

3.0T/T2 turbo spin echo, T1 3D gradient echo, DWI (800 and 1600 sec/mm2 ).

ASSESSMENT

DWI data were retrospectively processed using deep learning-based k-space-to-image reconstruction (DL-DWI) and an additional super-resolution algorithm (SRDL-DWI). In addition to signal-to-noise ratio and apparent diffusion coefficient (ADC) comparisons among standard, DL- and SRDL-DWI, a range of quantitative similarity (e.g., structural similarity index [SSIM]) and error metrics (e.g., normalized root mean square error [NRMSE], symmetric mean absolute percent error [SMAPE], log accuracy error [LOGAC]) was calculated to analyze structural variations. Subjective image evaluation was performed independently by three radiologists on a seven-point rating scale.

STATISTICAL TESTS

Friedman's rank-based analysis of variance with Bonferroni-corrected pairwise post-hoc tests. P < 0.05 was considered significant.

RESULTS

Both DL- and SRDL-DWI allowed for a 39% reduction in simulated scan time over standard DWI (5 vs. 3 minutes). The highest image quality ratings were assigned to SRDL-DWI with good interreader agreement (ICC 0.834; 95% confidence interval 0.818-0.848). Irrespective of b-value, both standard and DL-DWI produced superior SNR compared to SRDL-DWI. ADC values were slightly higher in SRDL-DWI (+0.5%) and DL-DWI (+3.4%) than in standard DWI. Structural similarity was excellent between DL-/SRDL-DWI and standard DWI for either b value (SSIM ≥ 0.86). Calculation of error metrics (NRMSE ≤ 0.05, SMAPE ≤ 0.02, and LOGAC ≤ 0.04) supported the assumption of low voxel-wise error.

DATA CONCLUSION

Deep learning-based k-space-to-image reconstruction reduces simulated scan time of breast DWI by 39% without influencing structural similarity. Additionally, super-resolution interpolation allows for substantial improvement of subjective image quality.

EVIDENCE LEVEL

4 TECHNICAL EFFICACY: Stage 1.

A new 3D phase unwrapping method by region partitioning and local polynomial modeling in abdominal quantitative susceptibility mapping

Background

Accurate phase unwrapping is a critical prerequisite for successful applications in phase-related MRI, including quantitative susceptibility mapping (QSM) and susceptibility weighted imaging. However, many existing 3D phase unwrapping algorithms face challenges in the presence of severe noise, rapidly changing phase, and open-end cutline.

Methods

In this study, we introduce a novel 3D phase unwrapping approach utilizing region partitioning and a local polynomial model. Initially, the method leverages phase partitioning to create initial regions. Noisy voxels connecting areas within these regions are excluded and grouped into residual voxels. The connected regions within the region of interest are then reidentified and categorized into blocks and residual voxels based on voxel count thresholds. Subsequently, the method sequentially performs inter-block and residual voxel phase unwrapping using the local polynomial model. The proposed method was evaluated on simulation and in vivo abdominal QSM data, and was compared with the classical Region-growing, Laplacian_based, Graph-cut, and PRELUDE methods.

Results

Simulation experiments, conducted under different signal-to-noise ratios and phase change levels, consistently demonstrate that the proposed method achieves accurate unwrapping results, with mean error ratios not exceeding 0.01%. In contrast, the error ratios of Region-growing (N/A, 84.47%), Laplacian_based (20.65%, N/A), Graph-cut (2.26%, 20.71%), and PRELUDE (4.28%, 10.33%) methods are all substantially higher than those of the proposed method. In vivo abdominal QSM experiments further confirm the effectiveness of the proposed method in unwrapping phase data and successfully reconstructing susceptibility maps, even in scenarios with significant noise, rapidly changing phase, and open-end cutline in a large field of view.

Conclusion

The proposed method demonstrates robust and accurate phase unwrapping capabilities, positioning it as a promising option for abdominal QSM applications.

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.

Quantitative susceptibility mapping identifies hippocampal and other subcortical grey matter tissue composition changes in temporal lobe epilepsy

Temporal lobe epilepsy (TLE) is associated with widespread brain alterations. Using quantitative susceptibility mapping (QSM) alongside transverse relaxation rate (R 2 * ), we investigated regional brain susceptibility changes in 36 patients with left-sided (LTLE) or right-sided TLE (RTLE) secondary to hippocampal sclerosis, and 27 healthy controls (HC). We compared three susceptibility calculation methods to ensure image quality. Correlations of susceptibility andR 2 * with age of epilepsy onset, frequency of focal-to-bilateral tonic-clonic seizures (FBTCS), and neuropsychological test scores were examined. Weak-harmonic QSM (WH-QSM) successfully reduced noise and removed residual background field artefacts. Significant susceptibility increases were identified in the left putamen in the RTLE group compared to the LTLE group, the right putamen and right thalamus in the RTLE group compared to HC, and a significant susceptibility decrease in the left hippocampus in LTLE versus HC. LTLE patients who underwent epilepsy surgery showed significantly lower left-versus-right hippocampal susceptibility. SignificantR 2 * changes were found between TLE and HC groups in the amygdala, putamen, thalamus, and in the hippocampus. Specifically, decreased R2 * was found in the left and right hippocampus in LTLE and RTLE, respectively, compared to HC. Susceptibility andR 2 * were significantly correlated with cognitive test scores in the hippocampus, globus pallidus, and thalamus. FBTCS frequency correlated positively with ipsilateral thalamic and contralateral putamen susceptibility and withR 2 * in bilateral globi pallidi. Age of onset was correlated with susceptibility in the hippocampus and putamen, and withR 2 * in the caudate. Susceptibility andR 2 * changes observed in TLE groups suggest selective loss of low-myelinated neurons alongside iron redistribution in the hippocampi, predominantly ipsilaterally, indicating QSM's sensitivity to local pathology. Increased susceptibility andR 2 * in the thalamus and putamen suggest increased iron content and reflect disease severity.

Subregional analysis of striatum iron in Parkinson's disease and rapid eye movement sleep behaviour disorder

The loss of dopamine in the striatum underlies motor symptoms of Parkinson's disease (PD). Rapid eye movement sleep behaviour disorder (RBD) is considered prodromal PD and has shown similar neural changes in the striatum. Alterations in brain iron suggest neurodegeneration; however, the literature on striatal iron has been inconsistent in PD and scant in RBD. Toward clarifying pathophysiological changes in PD and RBD, and uncovering possible biomarkers, we imaged 26 early-stage PD patients, 16 RBD patients, and 39 age-matched healthy controls with 3 T MRI. We compared mean susceptibility using quantitative susceptibility mapping (QSM) in the standard striatum (caudate, putamen, and nucleus accumbens) and tractography-parcellated striatum. Diffusion MRI permitted parcellation of the striatum into seven subregions based on the cortical areas of maximal connectivity from the Tziortzi atlas. No significant differences in mean susceptibility were found in the standard striatum anatomy. For the parcellated striatum, the caudal motor subregion, the most affected region in PD, showed lower iron levels compared to healthy controls. Receiver operating characteristic curves using mean susceptibility in the caudal motor striatum showed a good diagnostic accuracy of 0.80 when classifying early-stage PD from healthy controls. This study highlights that tractography-based parcellation of the striatum could enhance sensitivity to changes in iron levels, which have not been consistent in the PD literature. The decreased caudal motor striatum iron was sufficiently sensitive to PD, but not RBD. QSM in the striatum could contribute to development of a multivariate or multimodal biomarker of early-stage PD, but further work in larger datasets is needed to confirm its utility in prodromal groups.

High angular resolution susceptibility imaging and estimation of fiber orientation distribution functions in primate brain

Uncovering brain-tissue microstructure including axonal characteristics is a major neuroimaging research focus. Within this scope, anisotropic properties of magnetic susceptibility in white matter have been successfully employed to estimate primary axonal trajectories using mono-tensorial models. However, anisotropic susceptibility has not yet been considered for modeling more complex fiber structures within a voxel, such as intersecting bundles, or an estimation of orientation distribution functions (ODFs). This information is routinely obtained by high angular resolution diffusion imaging (HARDI) techniques. In applications to fixed tissue, however, diffusion-weighted imaging suffers from an inherently low signal-to-noise ratio and limited spatial resolution, leading to high demands on the performance of the gradient system in order to mitigate these limitations. In the current work, high angular resolution susceptibility imaging (HARSI) is proposed as a novel, phase-based methodology to estimate ODFs. A multiple gradient-echo dataset was acquired in an entire fixed chimpanzee brain at 61 orientations by reorienting the specimen in the magnetic field. The constant solid angle method was adapted for estimating phase-based ODFs. HARDI data were also acquired for comparison. HARSI yielded information on whole-brain fiber architecture, including identification of peaks of multiple bundles that resembled features of the HARDI results. Distinct differences between both methods suggest that susceptibility properties may offer complementary microstructural information. These proof-of-concept results indicate a potential to study the axonal organization in post-mortem primate and human brain at high resolution.

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 quantitative susceptibility mapping (QSM) for clinical brain research. It is a consensus of the ISMRM 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 give rise to the need in the neuroimaging community for guidelines on implementation. This article describes relevant considerations and provides specific implementation recommendations for all steps in QSM data acquisition, processing, analysis, and presentation in scientific publications. We recommend that data be acquired using a monopolar 3D multi-echo GRE sequence, that phase images be saved and exported in DICOM format and unwrapped using an exact unwrapping approach. Multi-echo images should be combined before background removal, and a brain mask created using a brain extraction tool with the incorporation of phase-quality-based masking. Background fields should be removed within the brain mask 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 whole brain as a region of interest in the analysis, and QSM results should be reported with - as a minimum - the acquisition and processing specifications listed in the last section of the article. These recommendations should facilitate clinical QSM research and lead to increased harmonization in data acquisition, analysis, and reporting.

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.

Study protocol of IMAGINE-HD: Imaging iron accumulation and neuroinflammation with 7T-MRI + CSF in Huntington's disease

INTRODUCTION

Strong evidence suggests a significant role for iron accumulation in the brain in addition to the well-documented neurodegenerative aspects of Huntington's disease (HD). The putative mechanisms by which iron is linked to the HD pathogenesis are multiple, including oxidative stress, ferroptosis and neuroinflammation. However, no previous study in a neurodegenerative disease has linked the observed increase of brain iron accumulation as measured by MRI with well-established cerebrospinal fluid (CSF) and blood biomarkers for iron accumulation, or with associated processes such as neuroinflammation. This study is designed to link quantitative data from iron levels and neuroinflammation metabolites obtained from 7T MRI of HD patients, with specific and well-known clinical biofluid markers for iron accumulation, neurodegeneration and neuroinflammation. Biofluid markers will provide quantitative measures of overall iron accumulation, neurodegeneration and neuroinflammation, while MRI measurements on the other hand will provide quantitative spatial information on brain pathology, neuroinflammation and brain iron accumulation, which will be linked to clinical outcome measures.

METHODS

This is an observational cross-sectional study, IMAGINE-HD, in HD gene expansion carriers and healthy controls. We include premanifest HD gene expansion carriers and patients with manifest HD in an early or moderate stage. The study includes a 7T MRI scan of the brain, clinical evaluation, motor, functional, and neuropsychological assessments, and sampling of CSF and blood for the detection of iron, neurodegenerative and inflammatory markers. Quantitative Susceptibility Maps will be reconstructed using T2* weighted images to quantify brain iron levels and Magnetic Resonance Spectroscopy will be used to obtain information about neuroinflammation by measuring cell-specific intracellular metabolites' level and diffusion. Age and sex matched healthy subjects are included as a control group.

DISCUSSION

Results from this study will provide an important basis for the evaluation of brain iron levels and neuroinflammation metabolites as an imaging biomarker for disease stage in HD and their relationship with the salient pathomechanisms of the disease on the one hand, and with clinical outcome on the other.

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.

Simulated and experimental phantom data for multi-center quality assurance of quantitative susceptibility maps at 3 T, 7 T and 9.4 T

PURPOSE

To develop methods for quality assurance of quantitative susceptibility mapping (QSM) using MRI at different magnetic field strengths, and scanners, using different MR-sequence protocols, and post-processing pipelines.

METHODS

We built a custom phantom based on iron in two forms: homogeneous susceptibility ('free iron') and with fine-scaled variations in susceptibility ('clustered iron') at different iron concentrations. The phantom was measured at 3.0 T (two scanners), 7.0 T and 9.4 T using multi-echo, gradient echo acquisition sequences. A digital phantom analogue to the iron-phantom, tailored to obtain similar results as in experimentation was developed, with similar geometry and susceptibility values. Morphology enabled dipole inversion was applied to the phase images to obtain QSM for experimental and simulated data using the MEDI + 0 approach for background regularization.

RESULTS

Across all scanners, QSM-values showed a linear increase with iron concentrations. The QSM-relaxivity was 0.231 ± 0.047 ppm/mM for free and 0.054 ± 0.013 ppm/mM for clustered iron, with adjusted determination coefficients (DoC) ≥ 0.87. Similarly, the simulations yielded linear increases (DoC ≥ 0.99). In both the experimental and digital phantoms, the estimated molar susceptibility was lower with clustered iron, because clustering led to highly localized field effects.

CONCLUSION

Our iron phantom can be used to evaluate the capability of QSM to detect local variations in susceptibility across different field strengths, when using different MR-sequence protocols. The devised simulation method captures the effect of iron clustering in QSM as seen experimentally and could be used in the future to optimize QSM processing pipelines and achieve higher accuracy for local field effects, as also seen in Alzheimer's beta-amyloid plaques.

New 3D phase-unwrapping method based on voxel clustering and local polynomial modeling: application to quantitative susceptibility mapping

Background

To develop an accurate and robust 3-dimensional (3D) phase-unwrapping method that works effectively in the presence of severe noise, disconnected regions, rapid phase changes, and open-ended lines for quantitative susceptibility mapping (QSM).

Methods

We developed a 3D phase-unwrapping method based on voxel clustering and local polynomial modeling named CLOSE3D, which firstly explores the 26-neighborhood to calculate local variation of the phasor and the phase, and then according to the local variation of the phasor, clusters the phase data into easy-to-unwrap blocks and difficult-to-unwrap residual voxels. Next, CLOSE3D sequentially performs intrablock, interblock, and residual-voxel unwrapping by using the region-growing local polynomial modeling method. CLOSED3D was evaluated in simulation and using in vivo brain QSM data, and was compared with classical region-growing and region-expanding labeling for unwrapping estimates methods.

Results

The simulation experiments showed that CLOSE3D achieved accurate phase-unwrapping results with a mean error ratio <0.39%, even in the presence of serious noise, disconnected regions, and rapid phase changes. The error ratios of region-growing (P=0.000 and P=0.000) and region-expanding labeling for unwrapping estimates (P=0.007, P=0.014) methods were both significantly higher than that of CLOSE3D, when the noise level was ≥60%. The results of the in vivo brain QSM experiments showed that CLOSE3D unwrapped the phase data and accurately reconstructed quantitative susceptibility data, even with serious noise, rapid-varying phase, or an open-ended cutline.

Conclusions

CLOSE3D achieves phase unwrapping with high accuracy and robustness, which will help phase-related 3D magnetic resonance imaging (MRI) applications such as QSM and susceptibility weighted imaging.

[A multi-channel input convolutional neural network for artifact reduction in quantitative susceptibility mapping]

OBJECTIVE

To develop a deep learning-based QSM reconstruction method for reducing artifacts to improve the accuracy of magnetic susceptibility results.

METHODS

To eliminate artifacts caused by susceptibility interfaces with gigantic differences, we propose a multi-channel input convolutional neural network for artifact reduction (MAR-CNN) for solving the dipole inversion problem in QSM. In this neural network, the original tissue field was first separated into two components, which were subsequently imported as additional channels into a multi-channel 3D U-Net. MAR-CNN was compared with 3 conventional model-based methods, namely truncated k-space deconvolution (TKD), morphology enabled dipole inversion (MEDI), and improved sparse linear equation and least squares method (iLSQR), and with a deep learning method (QSMnet). High-frequency error norm, peak signal-to-noise ratio, normalized root mean squared error, and structure similarity index were reported for quantitative comparisons.

RESULTS

Experiments on healthy volunteers demonstrated that the results obtained using MAR-CNN had superior peak signal-to-noise ratio (43.12±1.19) and normalized root mean squared error (51.98± 3.65) to those of TKD, MEDI, iLSQR and QSMnet. MAR-CNN outperformed QSMnet reconstruction on all the 4 quantitative metrics with significant differences (P < 0.05). Experiment on data of simulated hemorrhagic lesion demonstrated that MAR-CNN produced less shadow artifacts around the bleeding lesion than the other 4 methods.

CONCLUSION

The proposed MAR-CNN for artifact reduction is capable of improving the accuracy of deep learning- based QSM reconstruction to effectively reduce artifacts.

Quantitative susceptibility mapping using plug-and-play alternating direction method of multipliers

Quantitative susceptibility mapping employs regularization to reduce artifacts, yet many recent denoisers are unavailable for reconstruction. We developed a plug-and-play approach to QSM reconstruction (PnP QSM) and show its flexibility using several patch-based denoisers. We developed PnP QSM using alternating direction method of multiplier framework and applied collaborative filtering denoisers. We apply the technique to the 2016 QSM Challenge and in 10 glioblastoma multiforme datasets. We compared its performance with four published QSM techniques and a multi-orientation QSM method. We analyzed magnetic susceptibility accuracy using brain region-of-interest measurements, and image quality using global error metrics. Reconstructions on glioblastoma data were analyzed using ranked and semiquantitative image grading by three neuroradiologist observers to assess image quality (IQ) and sharpness (IS). PnP-BM4D QSM showed good correlation (β = 0.84, R² = 0.98, p < 0.05) with COSMOS and no significant bias (bias = 0.007 ± 0.012). PnP-BM4D QSM achieved excellent quality when assessed using structural similarity index metric (SSIM = 0.860), high frequency error norm (HFEN = 58.5), cross correlation (CC = 0.804), and mutual information (MI = 0.475) and also maintained good conspicuity of fine features. In glioblastoma datasets, PnP-BM4D QSM showed higher performance (IQ_Grade = 2.4 ± 0.4, IS_Grade = 2.7 ± 0.3, IQ_Rank = 3.7 ± 0.3, IS_Rank = 3.9 ± 0.3) compared to MEDI (IQ_Grade = 2.1 ± 0.5, IS_Grade = 2.1 ± 0.6, IQ_Rank = 2.4 ± 0.6, IS_Rank = 2.9 ± 0.2) and FANSI-TGV (IQ_Grade = 2.2 ± 0.6, IS_Grade = 2.1 ± 0.6, IQ_Rank = 2.7 ± 0.3, IS_Rank = 2.2 ± 0.2). We illustrated the modularity of PnP QSM by interchanging two additional patch-based denoisers. PnP QSM reconstruction was feasible, and its flexibility was shown using several patch-based denoisers. This technique may allow rapid prototyping and validation of new denoisers for QSM reconstruction for an array of useful clinical applications.

Multisite reproducibility of quantitative susceptibility mapping and effective transverse relaxation rate in deep gray matter at 3 T using locally optimized sequences in 24 traveling heads

Iron concentration in the human brain plays a crucial role in several neurodegenerative diseases and can be monitored noninvasively using quantitative susceptibility mapping (QSM) and effective transverse relaxation rate (R₂ *) mapping from multiecho T₂ *-weighted images. Large population studies enable better understanding of pathologies and can benefit from pooling multisite data. However, reproducibility may be compromised between sites and studies using different hardware and sequence protocols. This work investigates QSM and R₂ * reproducibility at 3 T using locally optimized sequences from three centers and two vendors, and investigates possible reduction of cross-site variability through postprocessing approaches. Twenty-four healthy subjects traveled between three sites and were scanned twice at each site. Scan-rescan measurements from seven deep gray matter regions were used for assessing within-site and cross-site reproducibility using intraclass correlation coefficient (ICC) and within-subject standard deviation (SDw) measures. In addition, multiple QSM and R₂ * postprocessing options were investigated with the aim to minimize cross-site sequence-related variations, including: mask generation approach, echo-timing selection, harmonizing spatial resolution, field map estimation, susceptibility inversion method, and linear field correction for magnitude images. The same-subject cross-site region of interest measurements for QSM and R₂ * were highly correlated (R²  ≥ 0.94) and reproducible (mean ICC of 0.89 and 0.82 for QSM and R₂ *, respectively). The mean cross-site SDw was 4.16 parts per billion (ppb) for QSM and 1.27 s^-1 for R₂ *. For within-site measurements of QSM and R₂ *, the mean ICC was 0.97 and 0.87 and mean SDw was 2.36 ppb and 0.97 s^-1 , respectively. The precision level is regionally dependent and is reduced in the frontal lobe, near brain edges, and in white matter regions. Cross-site QSM variability (mean SDw) was reduced up to 46% through postprocessing approaches, such as masking out less reliable regions, matching available echo timings and spatial resolution, avoiding the use of the nonconsistent magnitude contrast between scans in field estimation, and minimizing streaking artifacts.

Phase-based masking for quantitative susceptibility mapping of the human brain at 9.4T

PURPOSE

To develop improved tissue masks for QSM.

METHODS

Masks including voxels at the brain surface were automatically generated from the magnitude alone (MM) or combined with test functions from the first (PG) or second (PB) derivative of the sign of the wrapped phase. Phase images at 3T and 9.4T were simulated at different TEs and used to generate a mask, PItoh , with between-voxel phase differences less than π. MM, PG, and PB were compared with PItoh . QSM were generated from 3D multi-echo gradient-echo data acquired at 9.4T (21 subjects aged: 20-56y), and from the QSM2016 challenge 3T data using different masks, unwrapping, background removal, and dipole inversion algorithms. QSM contrast was quantified using age-based iron concentrations.

RESULTS

Close to air cavities, phase wraps became denser with increasing field and echo time, yielding increased values of the test functions. Compared with PItoh , PB had the highest Dice coefficient, while PG had the lowest and MM the highest percentage of voxels outside PItoh. Artifacts observed in QSM at 9.4T with MM were mitigated by stronger background filters but yielded a reduced QSM contrast. With PB, QSM contrast was greater and artifacts diminished. Similar results were obtained with challenge data, evidencing larger effects of mask close to air cavities.

CONCLUSION

Automatic, phase-based masking founded on the second derivative of the sign of the wrapped phase, including cortical voxels at the brain surface, was able to mitigate artifacts and restore QSM contrast across cortical and subcortical brain regions.

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/.

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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Regularized Asymmetric Susceptibility Tensor Imaging in the Human Brain in vivo

Susceptibility tensor imaging (STI) is a promising tool for studying orientation-dependent tissue magnetic susceptibility and for mapping white matter fiber orientations complementary to diffusion tensor imaging (DTI). However, the limited head rotation range within modern head coils for data acquisition makes in vivo STI reconstruction ill-conditioned. Conventional STI reconstruction method is usually vulnerable to noise and requires sufficiently large head rotations to solve this ill-conditioned inverse problem. In this study, based on the recently proposed asymmetric STI (aSTI) model, a new method termed aSTI+ was proposed to improve in vivo STI reconstruction by enforcing isotropic susceptibility tensor inside cerebrospinal fluid (CSF) and applying morphology constraint in white matter. Experimental results showed superior performance of the proposed method with reduced noise, improved tissue contrast and better fiber orientation estimation over previous methods. Thus aSTI+ may promote in vivo human brain STI studies on white matter and myelin-related brain diseases.

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

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.

Learn Less, Infer More: Learning in the Fourier Domain for Quantitative Susceptibility Mapping

Quantitative susceptibility mapping (QSM) aims to evaluate the distribution of magnetic susceptibility from magnetic resonance phase measurements by solving the ill-conditioned dipole inversion problem. Removing the artifacts and preserving the anisotropy of tissue susceptibility simultaneously is still a challenge in QSM. To deal with this issue, a novel k-QSM network is proposed to resolve dipole inversion issues in QSM reconstruction. The k-QSM network converts the results obtained by truncated k-space division (TKD) into the Fourier domain as inputs. After passing through several convolutional and residual blocks, the ill-posed signals of TKD are corrected by making the network output close to the calculation of susceptibility through multiple orientation sampling (COSMOS)-labeled QSM. To evaluate the superiority of k-QSM, comparisons with several state-of-the-art methods are performed in terms of QSM artifacts removing, anisotropy preserving, generalization ability, and clinical applications. Compared to existing methods, the k-QSM achieves a 22.31% lower normalized root mean square error, 10.30% higher peak signal-to-noise ratio (PSNR), 33.10% lower high-frequency error norm, and 1.06% higher structural similarity. In addition, the orientation-dependent susceptibility variation obtained by k-QSM is significant, verifying that k-QSM has the ability to preserve susceptibility anisotropy. When the trained models are tested on the dataset from different centers, our k-QSM shows a strong generalization ability with the highest PSNR. Moreover, by comparing the susceptibility maps between healthy controls and drug addicts with different methods, we found the proposed k-QSM is more sensitive to the susceptibility abnormality in the patients. The proposed k-QSM method learns less—only to fix the ill-posed signals of TKD, but infers more—both COSMOS-like and anisotropy-preserving QSM results. Its generalization ability and great sensitivity to susceptibility changes can make it a potential method for distinguishing some diseases.

MR susceptibility imaging for detection of tumor-associated macrophages in glioblastoma

PURPOSE

Tumor-associated macrophages (TAMs) are a key component of glioblastoma (GBM) microenvironment. Considering the differential role of different TAM phenotypes in iron metabolism with the M1 phenotype storing intracellular iron, and M2 phenotype releasing iron in the tumor microenvironment, we investigated MRI to quantify iron as an imaging biomarker for TAMs in GBM patients.

METHODS

21 adult patients with GBM underwent a 3D single echo gradient echo MRI sequence and quantitative susceptibility maps were generated. In 3 subjects, ex vivo imaging of surgical specimens was performed on a 9.4 Tesla MRI using 3D multi-echo GRE scans, and R2* (1/T2*) maps were generated. Each specimen was stained with hematoxylin and eosin, as well as CD68, CD86, CD206, and L-Ferritin.

RESULTS

Significant positive correlation was observed between mean susceptibility for the tumor enhancing zone and the L-ferritin positivity percent (r = 0.56, p = 0.018) and the combination of tumor's enhancing zone and necrotic core and the L-Ferritin positivity percent (r = 0.72; p = 0.001). The mean susceptibility significantly correlated with positivity percent for CD68 (ρ = 0.52, p = 0.034) and CD86 (r = 0.7 p = 0.001), but not for CD206 (ρ = 0.09; p = 0.7). There was a positive correlation between mean R2* values and CD68 positive cell counts (r = 0.6, p = 0.016). Similarly, mean R2* values significantly correlated with CD86 (r = 0.54, p = 0.03) but not with CD206 (r = 0.15, p = 0.5).

CONCLUSIONS

This study demonstrated the potential of MR quantitative susceptibility mapping as a non-invasive method for in vivo TAM quantification and phenotyping. Validation of these findings with large multicenter studies is needed.

Edge prior guided dictionary learning for quantitative susceptibility mapping reconstruction

BACKGROUND

Compared with conventional magnetic resonance imaging methods, the quantitative magnetic susceptibility mapping (QSM) technique can quantitatively measure the magnetic susceptibility distribution of tissues, which has an important clinical application value in the investigations of brain micro-bleeds, Parkinson's, and liver iron deposition, etc. However, the quantitative susceptibility mapping algorithm is an ill-posed inverse problem due to the near-zero value in the dipole kernel, and high-quality QSM reconstruction with effective streaking artifact suppression remains a challenge. In recent years, the performance of sparse representation has been well validated in improving magnetic resonance image (MRI) reconstruction.

METHODS

In this study, by incorporating feature learning into sparse representation, we propose an edge prior guided dictionary learning-based reconstruction method for the dipole inversion in quantitative susceptibility mapping reconstruction. The structure feature dictionary relies on magnitude images for susceptibility maps have similar structures with magnitude images, and this structure feature dictionary and edge prior information are used in the dipole inversion step.

RESULTS

The performance of the proposed algorithm is assessed through in vivo human brain clinical data, leading to high-quality susceptibility maps with improved streaking artifact suppression, structural recovery, and quantitative metrics.

CONCLUSIONS

The proposed edge prior guided dictionary learning method for dipole inversion in QSM achieves improved performance in streaking artifacts suppression, structural recovery and deep gray matter reconstruction.

Streaking artifact suppression of quantitative susceptibility mapping reconstructions via L1-norm data fidelity optimization (L1-QSM)

PURPOSE

The presence of dipole-inconsistent data due to substantial noise or artifacts causes streaking artifacts in quantitative susceptibility mapping (QSM) reconstructions. Often used Bayesian approaches rely on regularizers, which in turn yield reduced sharpness. To overcome this problem, we present a novel L1-norm data fidelity approach that is robust with respect to outliers, and therefore prevents streaking artifacts.

METHODS

QSM functionals are solved with linear and nonlinear L1-norm data fidelity terms using functional augmentation, and are compared with equivalent L2-norm methods. Algorithms were tested on synthetic data, with phase inconsistencies added to mimic lesions, QSM Challenge 2.0 data, and in vivo brain images with hemorrhages.

RESULTS

The nonlinear L1-norm-based approach achieved the best overall error metric scores and better streaking artifact suppression. Notably, L1-norm methods could reconstruct QSM images without using a brain mask, with similar regularization weights for different data fidelity weighting or masking setups.

CONCLUSION

The proposed L1-approach provides a robust method to prevent streaking artifacts generated by dipole-inconsistent data, renders brain mask calculation unessential, and opens novel challenging clinical applications such asassessing brain hemorrhages and cortical layers.

Comparison of Phase Estimation Methods for Quantitative Susceptibility Mapping Using a Rotating-Tube Phantom

Quantitative Susceptibility Mapping (QSM) is an MRI tool with the potential to reveal pathological changes from magnetic susceptibility measurements. Before phase data can be used to recover susceptibility (Δχ), the QSM process begins with two steps: data acquisition and phase estimation. We assess the performance of these steps, when applied without user intervention, on several variations of a phantom imaging task. We used a rotating-tube phantom with five tubes ranging from Δχ=0.05 ppm to Δχ=0.336 ppm. MRI data was acquired at nine angles of rotation for four different pulse sequences. The images were processed by 10 phase estimation algorithms including Laplacian, region-growing, branch-cut, temporal unwrapping, and maximum-likelihood methods, resulting in approximately 90 different combinations of data acquisition and phase estimation methods. We analyzed errors between measured and expected phases using the probability mass function and Cumulative Distribution Function. Repeatable acquisition and estimation methods were identified based on the probability of relative phase errors. For single-echo GRE and segmented EPI sequences, a region-growing method was most reliable with Pr (relative error <0.1) = 0.95 and 0.90, respectively. For multiecho sequences, a maximum-likelihood method was most reliable with Pr (relative error <0.1) = 0.97. The most repeatable multiecho methods outperformed the most repeatable single-echo methods. We found a wide range of repeatability and reproducibility for off-the-shelf MRI acquisition and phase estimation approaches, and this variability may prevent the techniques from being widely integrated in clinical workflows. The error was dominated in many cases by spatially discontinuous phase unwrapping errors. Any postprocessing applied on erroneous phase estimates, such as QSM's background field removal and dipole inversion, would suffer from error propagation. Our paradigm identifies methods that yield consistent and accurate phase estimates that would ultimately yield consistent and accurate Δχ estimates.

Quantifying myelin in crossing fibers using diffusion-prepared phase imaging: Theory and simulations

PURPOSE

Myelin has long been the target of neuroimaging research. However, most available techniques can only provide a voxel-averaged estimate of myelin content. In the human brain, white matter fiber pathways connecting different brain areas and carrying different functions often cross each other in the same voxel. A measure that can differentiate the degree of myelination of crossing fibers would provide a more specific marker of myelination.

THEORY AND METHODS

One MRI signal property that is sensitive to myelin is the phase accumulation. This sensitivity is used by measuring the phase accumulation of the signal remaining after diffusion-weighting, which is called diffusion-prepared phase imaging (DIPPI). Including diffusion-weighting before estimating the phase accumulation has two distinct advantages for estimating the degree of myelination: (1) It increases the relative contribution of intra-axonal water, whose phase is related linearly to the thickness of the surrounding myelin (in particular the log g-ratio); and (2) it gives directional information, which can be used to distinguish between crossing fibers. Here the DIPPI sequence is described, an approach is proposed to estimate the log g-ratio, and simulations are used and DIPPI data acquired in an isotropic phantom to quantify other sources of phase accumulation.

RESULTS

The expected bias is estimated in the log g-ratio for reasonable in vivo acquisition parameters caused by eddy currents (~4%-10%), remaining extra-axonal signal (~15%), and gradients in the bulk off-resonance field (<10% for most of the brain).

CONCLUSION

This new sequence may provide a g-ratio estimate per fiber population crossing within a voxel.

QSM reconstruction challenge 2.0: Design and report of results

PURPOSE

The aim of the second quantitative susceptibility mapping (QSM) reconstruction challenge (Oct 2019, Seoul, Korea) was to test the accuracy of QSM dipole inversion algorithms in simulated brain data.

METHODS

A two-stage design was chosen for this challenge. The participants were provided with datasets of multi-echo gradient echo images synthesized from two realistic in silico head phantoms using an MR simulator. At the first stage, participants optimized QSM reconstructions without ground truth data available to mimic the clinical setting. At the second stage, ground truth data were provided for parameter optimization. Submissions were evaluated using eight numerical metrics and visual ratings.

RESULTS

A total of 98 reconstructions were submitted for stage 1 and 47 submissions for stage 2. Iterative methods had the best quantitative metric scores, followed by deep learning and direct inversion methods. Priors derived from magnitude data improved the metric scores. Algorithms based on iterative approaches and total variation (and its derivatives) produced the best overall results. The reported results and analysis pipelines have been made public to allow researchers to compare new methods to the current state of the art.

CONCLUSION

The synthetic data provide a consistent framework to test the accuracy and robustness of QSM algorithms in the presence of noise, calcifications and minor voxel dephasing effects. Total Variation-based algorithms produced the best results among all metrics. Future QSM challenges should assess whether this good performance with synthetic datasets translates to more realistic scenarios, where background fields and dipole-incompatible phase contributions are included.

A novel phantom with dia- and paramagnetic substructure for quantitative susceptibility mapping and relaxometry

PURPOSE

A phantom is presented in this study that allows for an experimental evaluation of QSM reconstruction algorithms. The phantom contains susceptibility producing particles with dia- and paramagnetic properties embedded in an MRI visible medium and is suitable to assess the performance of algorithms that attempt to separate isotropic dia- and paramagnetic susceptibility at the sub-voxel level.

METHODS

The phantom was built from calcium carbonate (diamagnetic) and tungsten carbide particles (paramagnetic) embedded in gelatin and surrounded by agarose gel. Different mass fractions and mixing ratios of both susceptibility sources were used. Gradient echo data were acquired at 1.5 T, 3 T and 7 T. Susceptibility maps were calculated using the MEDI toolbox and relaxation rates ΔR₂^∗ were determined using exponential fitting.

RESULTS

Relaxation rates as well as susceptibility values generally coincide with the theoretical values for particles fulfilling the assumptions of the the static dephasing regime with stronger deviations for relaxation rates at higher field strength and for high susceptibility values. MRI raw data are available for free academic use as supplementary material.

CONCLUSIONS

In this study, a susceptibility phantom is presented that might find its application in the development and quantitative validation of current and future QSM reconstruction algorithms which aim to separate the influence of isotropic dia- and paramagnetic substructure in quantitative susceptibility mapping.