Noise Effects in Various Quantitative Susceptibility Mapping Methods

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.

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.

[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.

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.

Deep grey matter quantitative susceptibility mapping from small spatial coverages using deep learning

INTRODUCTION

Quantitative Susceptibility Mapping (QSM) is generally acquired with full brain coverage, even though many QSM brain-iron studies focus on the deep grey matter (DGM) region only. Reducing the spatial coverage to the DGM vicinity can substantially shorten the scan time or enhance the spatial resolution without increasing scan time; however, this may lead to significant DGM susceptibility underestimation.

METHOD

A recently proposed deep learning-based QSM method, namely xQSM, is investigated to assess the accuracy of dipole inversion on reduced brain coverages. The xQSM method is compared with two conventional dipole inversion methods using simulated and in vivo experiments from 4 healthy subjects at 3T. Pre-processed magnetic field maps are extended symmetrically from the centre of globus pallidus in the coronal plane to simulate QSM acquisitions of difference spatial coverages, ranging from 100% (∼32mm) to 400% (∼128mm) of the actual DGM physical size.

RESULTS

The proposed xQSM network led to the lowest DGM contrast loss in both simulated and in vivo subjects, with the smallest susceptibility variation range across all spatial coverages. For the digital brain phantom simulation, xQSM improved the DGM susceptibility underestimation more than 20% in small spatial coverages, as compared to conventional methods. For the in vivo acquisition, less than 5% DGM susceptibility error was achieved in 48mm axial slabs using the xQSM network, while a minimum of 112mm coverage was required for conventional methods. It is also shown that the background field removal process performed worse in reduced brain coverages, which further deteriorated the subsequent dipole inversion.

CONCLUSION

The recently proposed deep learning-based xQSM method significantly improves the accuracy of DGM QSM from small spatial coverages as compared with conventional QSM algorithms, which can shorten DGM QSM acquisition time substantially.

Multiecho complex total field inversion method (mcTFI) for improved signal modeling in quantitative susceptibility mapping

PURPOSE

Typical quantitative susceptibility mapping (QSM) reconstruction steps consist of first estimating the magnetization field from the gradient-echo images, and then reconstructing the susceptibility map from the estimated field. The errors from the field-estimation steps may propagate into the final QSM map, and the noise in the estimated field map may no longer be zero-mean Gaussian noise, thus, causing streaking artifacts in the resulting QSM. A multiecho complex total field inversion (mcTFI) method was developed to compute the susceptibility map directly from the multiecho gradient echo images using an improved signal model that retains the Gaussian noise property in the complex domain. It showed improvements in QSM reconstruction over the conventional field-to-source inversion.

METHODS

The proposed mcTFI method was compared with the nonlinear total field inversion (nTFI) method in a numerical brain with hemorrhage and calcification, the numerical brains provided by the QSM Challenge 2.0, 18 brains with intracerebral hemorrhage scanned at 3T, and 6 healthy brains scanned at 7T.

RESULTS

Compared with nTFI, the proposed mcTFI showed more accurate QSM reconstruction around the lesions in the numerical simulations. The mcTFI reconstructed QSM also showed the best image quality with the least artifacts in the brains with intracerebral hemorrhage scanned at 3T and healthy brains scanned at 7T.

CONCLUSION

The proposed multiecho complex total field inversion improved QSM reconstruction over traditional field-to-source inversion through better signal modeling.

The 2016 QSM Challenge: Lessons learned and considerations for a future challenge design

PURPOSE

The 4th International Workshop on MRI Phase Contrast and QSM (2016, Graz, Austria) hosted the first QSM Challenge. A single-orientation gradient recalled echo acquisition was provided, along with COSMOS and the χ33 STI component as ground truths. The submitted solutions differed more than expected depending on the error metric used for optimization and were generally over-regularized. This raised (unanswered) questions about the ground truths and the metrics utilized.

METHODS

We investigated the influence of background field remnants by applying additional filters. We also estimated the anisotropic contributions from the STI tensor to the apparent susceptibility to amend the χ33 ground truth and to investigate the impact on the reconstructions. Lastly, we used forward simulations from the COSMOS reconstruction to investigate the impact noise had on the metric scores.

RESULTS

Reconstructions compared against the amended STI ground truth returned lower errors. We show that the background field remnants had a minor impact in the errors. In the absence of inconsistencies, all metrics converged to the same regularization weights, whereas structural similarity index metric was more insensitive to such inconsistencies.

CONCLUSION

There was a mismatch between the provided data and the ground truths due to the presence of unaccounted anisotropic susceptibility contributions and noise. Given the lack of reliable ground truths when using in vivo acquisitions, simulations are suggested for future QSM Challenges.

Data-Driven Quantitative Susceptibility Mapping Using Loss Adaptive Dipole Inversion (LADI)

BACKGROUND

Quantitative susceptibility mapping (QSM) uses prior information to reconstruct maps, but prior information may not show pathology and introduce inconsistencies with susceptibility maps, degrade image quality and inadvertently smoothing image features.

PURPOSE

To develop a local field data-driven QSM reconstruction that does not depend on spatial edge prior information.

STUDY TYPE

Retrospective.

SUBJECTS, ANIMAL MODELS

A dataset from 2016 ISMRM QSM Challenge, 11 patients with glioblastoma, a patient with microbleeds and porcine heart.

SEQUENCE/FIELD STRENGTH

3D gradient echo sequence on 3T and 7T scanners.

ASSESSMENT

Accuracy was compared to Calculation of Susceptibility through Multiple Orientation Sampling (COSMOS), and several published techniques using region of interest (ROI) measurements, root-mean-squared error (RMSE), structural similarity index metric (SSIM), and high-frequency error norm (HFEN). Numerical ranking and semiquantitative image grading was performed by three expert observers to assess overall image quality (IQ) and image sharpness (IS).

STATISTICAL TESTS

Bland-Altman, Friedman test, and Conover multiple comparisons.

RESULTS

Loss adaptive dipole inversion (LADI) (β = 0.82, R² = 0.96), morphology-enabled dipole inversion (MEDI) (β = 0.91, R² = 0.97), and fast nonlinear susceptibility inversion (FANSI) (β = 0.81, R² = 0.98) had excellent correlation with COSMOS and no bias was detected (bias = 0.006 ± 0.014, P < 0.05). In glioblastoma patients, LADI showed consistently better performance (IQ_Grade = 2.6 ± 0.4, IS_Grade = 2.6 ± 0.3, IQ_Rank = 3.5 ± 0.4, IS_Rank = 3.9 ± 0.2) compared with MEDI (IQ_Grade = 2.1 ± 0.3, IS_Grade = 2 ± 0.5, IQ_Rank = 2.4 ± 0.5, IS_Rank = 2.8 ± 0.2) and FANSI (IQ_Grade = 2.2 ± 0.5, IS_Grade = 2 ± 0.4, IQ_Rank = 2.8 ± 0.3, IS_Rank = 2.1 ± 0.2). Dark artifact visible near the infarcted region in MEDI (Inf_MEDI = -0.27 ± 0.06 ppm) was better mitigated by FANSI (Inf_FANSI-TGV = -0.17 ± 0.05 ppm) and LADI (Inf_LADI = -0.18 ± 0.05 ppm).

CONCLUSION

For neuroimaging applications, LADI preserved image sharpness and fine features in glioblastoma and microbleed patients. LADI performed better at mitigating artifacts in cardiac QSM.

EVIDENCE LEVEL

4 TECHNICAL EFFICACY STAGE: 1 J. Magn. Reson. Imaging 2020;52:823-835.

Weak-harmonic regularization for quantitative susceptibility mapping

PURPOSE

Background-field removal is a crucial preprocessing step for quantitative susceptibility mapping (QSM). Remnants from this step often contaminate the estimated local field, which in turn leads to erroneous tissue-susceptibility reconstructions. The present work aimed to mitigate this undesirable behavior with the development of a new approach that simultaneously decouples background contributions and local susceptibility sources on QSM inversion.

METHODS

Input phase data for QSM can be seen as a composite scalar field of local effects and residual background components. We developed a new weak-harmonic regularizer to constrain the latter and to separate the 2 components. The resulting optimization problem was solved with the alternating directions of multipliers method framework to achieve fast convergence. In addition, for convenience, a new alternating directions of multipliers method-based preconditioned nonlinear projection onto dipole fields solver was developed to enable initializations with wrapped-phase distributions. Weak-harmonic QSM, with and without nonlinear projection onto dipole fields preconditioning, was compared with the original (alternating directions of multipliers method-based) total variation QSM algorithm in phantom and in vivo experiments.

RESULTS

Weak-harmonic QSM returned improved reconstructions regardless of the method used for background-field removal, although the proposed nonlinear projection onto dipole fields method often obtained better results. Streaking and shadowing artifacts were substantially suppressed, and residual background components were effectively removed.

CONCLUSION

Weak-harmonic QSM with field preconditioning is a robust dipole inversion technique and has the potential to be extended as a single-step formulation for initialization with uncombined multi-echo data.

Patents on Quantitative Susceptibility Mapping (QSM) of Tissue Magnetism

BACKGROUND

Quantitative susceptibility mapping (QSM) depicts biodistributions of tissue magnetic susceptibility sources, including endogenous iron and calcifications, as well as exogenous paramagnetic contrast agents and probes. When comparing QSM with simple susceptibility weighted MRI, QSM eliminates blooming artifacts and shows reproducible tissue susceptibility maps independent of field strength and scanner manufacturer over a broad range of image acquisition parameters. For patient care, QSM promises to inform diagnosis, guide surgery, gauge medication, and monitor drug delivery. The Bayesian framework using MRI phase data and structural prior knowledge has made QSM sufficiently robust and accurate for routine clinical practice.

OBJECTIVE

To address the lack of a summary of US patents that is valuable for QSM product development and dissemination into the MRI community.

METHOD

We searched the USPTO Full-Text and Image Database for patents relevant to QSM technology innovation. We analyzed the claims of each patent to characterize the main invented method and we investigated data on clinical utility.

RESULTS

We identified 17 QSM patents; 13 were implemented clinically, covering various aspects of QSM technology, including the Bayesian framework, background field removal, numerical optimization solver, zero filling, and zero-TE phase.

CONCLUSION

Our patent search identified patents that enable QSM technology for imaging the brain and other tissues. QSM can be applied to study a wide range of diseases including neurological diseases, liver iron disorders, tissue ischemia, and osteoporosis. MRI manufacturers can develop QSM products for more seamless integration into existing MRI scanners to improve medical care.

Quantitative susceptibility mapping (QSM) with an extended physical model for MRI frequency contrast in the brain: a proof-of-concept of quantitative susceptibility and residual (QUASAR) mapping

Quantitative susceptibility mapping (QSM) aims to calculate the tissue's magnetic susceptibility distribution from its perturbing effect on the MRI static main magnetic field. The method is increasingly being applied to study iron and myelin in clinical and preclinical settings. However, recent experimental and theoretical findings have challenged the fundamental theoretical assumptions that form the basis of current numerical implementations of QSM algorithms. The present work introduces a new class of susceptibility mapping algorithms, termed quantitative susceptibility and residual mapping (QUASAR), which takes into account frequency contributions not related to the spatial variation of bulk magnetic susceptibility in the Lorentz sphere model. We present a simple proof-of-concept QUASAR algorithm that, unlike most of the QSM algorithms currently used widely, results in an improved anatomical accuracy of the susceptibility distribution without any a priori assumptions about the susceptibility distribution during the field-to-source inversion. The algorithm was evaluated both in silico and in vivo in the preclinical setting. Our preliminary application of QUASAR in rodents provides the first in vivo evidence that the susceptibility-field model traditionally used in the QSM field cannot fully explain the frequency contrast in brain tissues. Only when an additional local frequency contribution is added to the physical model can the frequency contrast in the brain be related properly to the underlying anatomy.

Pros and cons of ultra-high-field MRI/MRS for human application

Magnetic resonance imaging and spectroscopic techniques are widely used in humans both for clinical diagnostic applications and in basic research areas such as cognitive neuroimaging. In recent years, new human MR systems have become available operating at static magnetic fields of 7 T or higher (≥300 MHz proton frequency). Imaging human-sized objects at such high frequencies presents several challenges including non-uniform radiofrequency fields, enhanced susceptibility artifacts, and higher radiofrequency energy deposition in the tissue. On the other side of the scale are gains in signal-to-noise or contrast-to-noise ratio that allow finer structures to be visualized and smaller physiological effects to be detected. This review presents an overview of some of the latest methodological developments in human ultra-high field MRI/MRS as well as associated clinical and scientific applications. Emphasis is given to techniques that particularly benefit from the changing physical characteristics at high magnetic fields, including susceptibility-weighted imaging and phase-contrast techniques, imaging with X-nuclei, MR spectroscopy, CEST imaging, as well as functional MRI. In addition, more general methodological developments such as parallel transmission and motion correction will be discussed that are required to leverage the full potential of higher magnetic fields, and an overview of relevant physiological considerations of human high magnetic field exposure is provided.

A robust multi-scale approach to quantitative susceptibility mapping

Quantitative Susceptibility Mapping (QSM), best known as a surrogate for tissue iron content, is becoming a highly relevant MRI contrast for monitoring cellular and vascular status in aging, addiction, traumatic brain injury and, in general, a wide range of neurological disorders. In this study we present a new Bayesian QSM algorithm, named Multi-Scale Dipole Inversion (MSDI), which builds on the nonlinear Morphology-Enabled Dipole Inversion (nMEDI) framework, incorporating three additional features: (i) improved implementation of Laplace's equation to reduce the influence of background fields through variable harmonic filtering and subsequent deconvolution, (ii) improved error control through dynamic phase-reliability compensation across spatial scales, and (iii) scalewise use of the morphological prior. More generally, this new pre-conditioned QSM formalism aims to reduce the impact of dipole-incompatible fields and measurement errors such as flow effects, poor signal-to-noise ratio or other data inconsistencies that can lead to streaking and shadowing artefacts. In terms of performance, MSDI is the first algorithm to rank in the top-10 for all metrics evaluated in the 2016 QSM Reconstruction Challenge. It also demonstrated lower variance than nMEDI and more stable behaviour in scan-rescan reproducibility experiments for different MRI acquisitions at 3 and 7 Tesla. In the present work, we also explored new forms of susceptibility MRI contrast making explicit use of the differential information across spatial scales. Specifically, we show MSDI-derived examples of: (i) enhanced anatomical detail with susceptibility inversions from short-range dipole fields (hereby referred to as High-Pass Susceptibility Mapping or HPSM), (ii) high specificity to venous-blood susceptibilities for highly regularised HPSM (making a case for MSDI-based Venography or VenoMSDI), (iii) improved tissue specificity (and possibly statistical conditioning) for Macroscopic-Vessel Suppressed Susceptibility Mapping (MVSSM), and (iv) high spatial specificity and definition for HPSM-based Susceptibility-Weighted Imaging (HPSM-SWI) and related intensity projections.

Prospective motion correction improves high-resolution quantitative susceptibility mapping at 7T

PURPOSE

Recent literature has shown the potential of high-resolution quantitative susceptibility mapping (QSM) with ultra-high field MRI for imaging the anatomy, the vasculature, and investigating their magnetostatic properties. Higher spatial resolutions, however, translate to longer scans resulting, therefore, in higher vulnerability to, and likelihood of, subject movement. We propose a gradient-recalled echo sequence with prospective motion correction (PMC) to address such limitation.

METHODS

Data from 4 subjects were acquired at 7T. The effect of small and large motion on QSM with and without PMC was assessed qualitatively and quantitatively. Full brain QSM and QSM-based venograms with up to 0.33 mm isotropic voxel size were reconstructed.

RESULTS

With PMC, motion artifacts in QSM and QSM-based venograms were largely eliminated, enabling-in both large- and small-amplitude motion regimes-accurate depiction of the cortex, vasculature, and other small anatomical structures that are often blurred as a result of head movement or indiscernible at lower image resolutions. Quantitative analyses demonstrated that uncorrected motion could bias regional susceptibility distributions, a trend that was greatly reduced with PMC.

CONCLUSION

Qualitatively, PMC prevented image degradation because of motion artifacts, providing highly detailed QSM images and venograms. Quantitatively, PMC increased the reproducibility of susceptibility measures.

Morphology-adaptive total variation for the reconstruction of quantitative susceptibility map from the magnetic resonance imaging phase

Quantitative susceptibility mapping (QSM) is a magnetic resonance imaging technique that quantifies the magnetic susceptibility distribution within biological tissues. QSM calculates the underlying magnetic susceptibility by deconvolving the tissue magnetic field map with a unit dipole kernel. However, this deconvolution problem is ill-posed. The morphology enabled dipole inversion (MEDI) introduces total variation (TV) to regularize the susceptibility reconstruction. However, MEDI results still contain artifacts near tissue boundaries because MEDI only imposes TV constraint on voxels inside smooth regions. We introduce a Morphology-Adaptive TV (MATV) for improving TV-regularized QSM. The MATV method first classifies imaging target into smooth and nonsmooth regions by thresholding magnitude gradients. In the dipole inversion for QSM, the TV regularization weights are a monotonically decreasing function of magnitude gradients. Thus, voxels inside smooth regions are assigned with larger weights than those in nonsmooth regions. Using phantom and in vivo datasets, we compared the performance of MATV with that of MEDI. MATV results had better visual quality than MEDI results, especially near tissue boundaries. Preliminary brain imaging results illustrated that MATV has potential to improve the reconstruction of regions near tissue boundaries.

Susceptibility difference weighted imaging in vertical-field MRI

To realize susceptibility-weighted imaging in vertical-field magnetic resonance imaging (MRI), we developed an image-processing method called "susceptibility difference weighted imaging" (SDWI). In SDWI, contrasts are enhanced using a susceptibility map calculated by using a weighted least-square algorithm with a small iteration number. Experiments were performed on human volunteers to compare image contrast obtained from the conventional method (SWI) and SDWI. In horizontal-field MRI, SDWI results show that veins and deep-gray-matter nuclei were visualized as well as those with SWI. In vertical-field MRI, SDWI visualized veins and deep-gray-matter nuclei without severe streaking artifacts, while SWI did not. In our experiments, the time taken to calculate the susceptibility map in SDWI was less than 10 s. The results indicate that susceptibility-weighted imaging is feasible in vertical-field MRI using SDWI.

A new discrete dipole kernel for quantitative susceptibility mapping

PURPOSE

Most approaches for quantitative susceptibility mapping (QSM) are based on a forward model approximation that employs a continuous Fourier transform operator to solve a differential equation system. Such formulation, however, is prone to high-frequency aliasing. The aim of this study was to reduce such errors using an alternative dipole kernel formulation based on the discrete Fourier transform and discrete operators.

METHODS

The impact of such an approach on forward model calculation and susceptibility inversion was evaluated in contrast to the continuous formulation both with synthetic phantoms and in vivo MRI data.

RESULTS

The discrete kernel demonstrated systematically better fits to analytic field solutions, and showed less over-oscillations and aliasing artifacts while preserving low- and medium-frequency responses relative to those obtained with the continuous kernel. In the context of QSM estimation, the use of the proposed discrete kernel resulted in error reduction and increased sharpness.

CONCLUSION

This proof-of-concept study demonstrated that discretizing the dipole kernel is advantageous for QSM. The impact on small or narrow structures such as the venous vasculature might by particularly relevant to high-resolution QSM applications with ultra-high field MRI - a topic for future investigations. The proposed dipole kernel has a straightforward implementation to existing QSM routines.

Quantitative Susceptibility Mapping (QSM) Algorithms: Mathematical Rationale and Computational Implementations

Quantitative susceptibility mapping (QSM) solves the magnetic field-to-magnetization (tissue susceptibility) inverse problem under conditions of noisy and incomplete field data acquired using magnetic resonance imaging. Therefore, sophisticated algorithms are necessary to treat the ill-posed nature of the problem and are reviewed here. The forward problem is typically presented as an integral form, where the field is the convolution of the dipole kernel and tissue susceptibility distribution. This integral form can be equivalently written as a partial differential equation (PDE). Algorithmic challenges are to reduce streaking and shadow artifacts characterized by the fundamental solution of the PDE. Bayesian maximum a posteriori estimation can be employed to solve the inverse problem, where morphological and relevant biomedical knowledge (specific to the imaging situation) are used as priors. As the cost functions in Bayesian QSM framework are typically convex, solutions can be robustly computed using a gradient-based optimization algorithm. Moreover, one can not only accelerate Bayesian QSM, but also increase its effectiveness at reducing shadows using prior knowledge based preconditioners. Improving the efficiency of QSM is under active development, and a rigorous analysis of preconditioning needs to be carried out for further investigation.Quantitative susceptibility mapping (QSM) solves the magnetic field-to-magnetization (tissue susceptibility) inverse problem under conditions of noisy and incomplete field data acquired using magnetic resonance imaging. Therefore, sophisticated algorithms are necessary to treat the ill-posed nature of the problem and are reviewed here. The forward problem is typically presented as an integral form, where the field is the convolution of the dipole kernel and tissue susceptibility distribution. This integral form can be equivalently written as a partial differential equation (PDE). Algorithmic challenges are to reduce streaking and shadow artifacts characterized by the fundamental solution of the PDE. Bayesian maximum a posteriori estimation can be employed to solve the inverse problem, where morphological and relevant biomedical knowledge (specific to the imaging situation) are used as priors. As the cost functions in Bayesian QSM framework are typically convex, solutions can be robustly computed using a gradient-based optimization algorithm. Moreover, one can not only accelerate Bayesian QSM, but also increase its effectiveness at reducing shadows using prior knowledge based preconditioners. Improving the efficiency of QSM is under active development, and a rigorous analysis of preconditioning needs to be carried out for further investigation.

Quantitative susceptibility mapping: Report from the 2016 reconstruction challenge

PURPOSE

The aim of the 2016 quantitative susceptibility mapping (QSM) reconstruction challenge was to test the ability of various QSM algorithms to recover the underlying susceptibility from phase data faithfully.

METHODS

Gradient-echo images of a healthy volunteer acquired at 3T in a single orientation with 1.06 mm isotropic resolution. A reference susceptibility map was provided, which was computed using the susceptibility tensor imaging algorithm on data acquired at 12 head orientations. Susceptibility maps calculated from the single orientation data were compared against the reference susceptibility map. Deviations were quantified using the following metrics: root mean squared error (RMSE), structure similarity index (SSIM), high-frequency error norm (HFEN), and the error in selected white and gray matter regions.

RESULTS

Twenty-seven submissions were evaluated. Most of the best scoring approaches estimated the spatial frequency content in the ill-conditioned domain of the dipole kernel using compressed sensing strategies. The top 10 maps in each category had similar error metrics but substantially different visual appearance.

CONCLUSION

Because QSM algorithms were optimized to minimize error metrics, the resulting susceptibility maps suffered from over-smoothing and conspicuity loss in fine features such as vessels. As such, the challenge highlighted the need for better numerical image quality criteria. Magn Reson Med 79:1661-1673, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Cyclic Continuous Max-Flow: A Third Paradigm in Generating Local Phase Shift Maps in MRI

Sensitivity to phase deviations in MRI forms the basis of a variety of techniques, including magnetic susceptibility weighted imaging and chemical shift imaging. Current phase processing techniques fall into two families: those which process the complex image data with magnitude and phase coupled, and phase unwrapping-based techniques that first linearize the phase topology across the image. However, issues, such as low signal and the existence of phase poles, can lead both methods to experience error. Cyclic continuous max-flow (CCMF) phase processing uses primal-dual-variational optimization over a cylindrical manifold, which represent the inherent topology of phase images, increasing its robustness to these issues. CCMF represents a third distinct paradigm in phase processing, being the only technique equipped with the inherent topology of phase. CCMF is robust and efficient with at least comparable accuracy as the prior paradigms.

Fast nonlinear susceptibility inversion with variational regularization

PURPOSE

Quantitative susceptibility mapping can be performed through the minimization of a function consisting of data fidelity and regularization terms. For data consistency, a Gaussian-phase noise distribution is often assumed, which breaks down when the signal-to-noise ratio is low. A previously proposed alternative is to use a nonlinear data fidelity term, which reduces streaking artifacts, mitigates noise amplification, and results in more accurate susceptibility estimates. We hereby present a novel algorithm that solves the nonlinear functional while achieving computation speeds comparable to those for a linear formulation.

METHODS

We developed a nonlinear quantitative susceptibility mapping algorithm (fast nonlinear susceptibility inversion) based on the variable splitting and alternating direction method of multipliers, in which the problem is split into simpler subproblems with closed-form solutions and a decoupled nonlinear inversion hereby solved with a Newton-Raphson iterative procedure. Fast nonlinear susceptibility inversion performance was assessed using numerical phantom and in vivo experiments, and was compared against the nonlinear morphology-enabled dipole inversion method.

RESULTS

Fast nonlinear susceptibility inversion achieves similar accuracy to nonlinear morphology-enabled dipole inversion but with significantly improved computational efficiency.

CONCLUSION

The proposed method enables accurate reconstructions in a fraction of the time required by state-of-the-art quantitative susceptibility mapping methods. Magn Reson Med 80:814-821, 2018. © 2018 International Society for Magnetic Resonance in Medicine.

Background field removal using a region adaptive kernel for quantitative susceptibility mapping of human brain

Background field removal is an important MR phase preprocessing step for quantitative susceptibility mapping (QSM). It separates the local field induced by tissue magnetic susceptibility sources from the background field generated by sources outside a region of interest, e.g. brain, such as air-tissue interface. In the vicinity of air-tissue boundary, e.g. skull and paranasal sinuses, where large susceptibility variations exist, present background field removal methods are usually insufficient and these regions often need to be excluded by brain mask erosion at the expense of losing information of local field and thus susceptibility measures in these regions. In this paper, we propose an extension to the variable-kernel sophisticated harmonic artifact reduction for phase data (V-SHARP) background field removal method using a region adaptive kernel (R-SHARP), in which a scalable spherical Gaussian kernel (SGK) is employed with its kernel radius and weights adjustable according to an energy "functional" reflecting the magnitude of field variation. Such an energy functional is defined in terms of a contour and two fitting functions incorporating regularization terms, from which a curve evolution model in level set formation is derived for energy minimization. We utilize it to detect regions of with a large field gradient caused by strong susceptibility variation. In such regions, the SGK will have a small radius and high weight at the sphere center in a manner adaptive to the voxel energy of the field perturbation. Using the proposed method, the background field generated from external sources can be effectively removed to get a more accurate estimation of the local field and thus of the QSM dipole inversion to map local tissue susceptibility sources. Numerical simulation, phantom and in vivo human brain data demonstrate improved performance of R-SHARP compared to V-SHARP and RESHARP (regularization enabled SHARP) methods, even when the whole paranasal sinus regions are preserved in the brain mask. Shadow artifacts due to strong susceptibility variations in the derived QSM maps could also be largely eliminated using the R-SHARP method, leading to more accurate QSM reconstruction.

Joint 2D and 3D phase processing for quantitative susceptibility mapping: application to 2D echo-planar imaging

Quantitative susceptibility mapping (QSM) measures tissue magnetic susceptibility and typically relies on time-consuming three-dimensional (3D) gradient-echo (GRE) MRI. Recent studies have shown that two-dimensional (2D) multi-slice gradient-echo echo-planar imaging (GRE-EPI), which is commonly used in functional MRI (fMRI) and other dynamic imaging techniques, can also be used to produce data suitable for QSM with much shorter scan times. However, the production of high-quality QSM maps is difficult because data obtained by 2D multi-slice scans often have phase inconsistencies across adjacent slices and strong susceptibility field gradients near air-tissue interfaces. To address these challenges in 2D EPI-based QSM studies, we present a new data processing procedure that integrates 2D and 3D phase processing. First, 2D Laplacian-based phase unwrapping and 2D background phase removal are performed to reduce phase inconsistencies between slices and remove in-plane harmonic components of the background phase. This is followed by 3D background phase removal for the through-plane harmonic components. The proposed phase processing was evaluated with 2D EPI data obtained from healthy volunteers, and compared against conventional 3D phase processing using the same 2D EPI datasets. Our QSM results were also compared with QSM values from time-consuming 3D GRE data, which were taken as ground truth. The experimental results show that this new 2D EPI-based QSM technique can produce quantitative susceptibility measures that are comparable with those of 3D GRE-based QSM across different brain regions (e.g. subcortical iron-rich gray matter, cortical gray and white matter). This new 2D EPI QSM reconstruction method is implemented within STI Suite, which is a comprehensive shareware for susceptibility imaging and quantification. Copyright © 2016 John Wiley & Sons, Ltd.

The clinical utility of QSM: disease diagnosis, medical management, and surgical planning

Quantitative susceptibility mapping (QSM) is an MR technique that depicts and quantifies magnetic susceptibility sources. Mapping iron, the dominant susceptibility source in the brain, has many important clinical applications. Herein, we review QSM applications in the diagnosis, medical management, and surgical treatment of disease. To assist in early disease diagnosis, QSM can identify elevated iron levels in the motor cortex of amyotrophic lateral sclerosis patients, in the substantia nigra of Parkinson's disease (PD) patients, in the globus pallidus, putamen, and caudate of Huntington's disease patients, and in the basal ganglia of Wilson's disease patients. Additionally, QSM can distinguish between hemorrhage and calcification, which could prove useful in tumor subclassification, and can measure microbleeds in traumatic brain injury patients. In guiding medical management, QSM can be used to monitor iron chelation therapy in PD patients, to monitor smoldering inflammation of multiple sclerosis (MS) lesions after the blood-brain barrier (BBB) seals, to monitor active inflammation of MS lesions before the BBB seals without using gadolinium, and to monitor hematoma volume in intracerebral hemorrhage. QSM can also guide neurosurgical treatment. Neurosurgeons require accurate depiction of the subthalamic nucleus, a tiny deep gray matter nucleus, prior to inserting deep brain stimulation electrodes into the brains of PD patients. QSM is arguably the best imaging tool for depiction of the subthalamic nucleus. Finally, we discuss future directions, including bone QSM, cardiac QSM, and using QSM to map cerebral metabolic rate of oxygen. Copyright © 2016 John Wiley & Sons, Ltd.

An illustrated comparison of processing methods for phase MRI and QSM: removal of background field contributions from sources outside the region of interest

The elimination of so-called background fields is an essential step in phase MRI and quantitative susceptibility mapping (QSM). Background fields, which are caused by sources outside the region of interest (ROI), are often one to two orders of magnitude stronger than tissue-related field variations from within the ROI, hampering quantitative interpretation of field maps. This paper reviews the current literature on background elimination algorithms for QSM and provides insights into similarities and differences between the many algorithms proposed. We discuss the basic theoretical foundations and derive fundamental limitations of background field elimination. Copyright © 2016 John Wiley & Sons, Ltd.

Primal-dual and forward gradient implementation for quantitative susceptibility mapping

PURPOSE

To investigate the computational aspects of the prior term in quantitative susceptibility mapping (QSM) by (i) comparing the Gauss-Newton conjugate gradient (GNCG) algorithm that uses numerical conditioning (ie, modifies the prior term) with a primal-dual (PD) formulation that avoids this, and (ii) carrying out a comparison between a central and forward difference scheme for the discretization of the prior term.

THEORY AND METHODS

A spatially continuous formulation of the regularized QSM inversion problem and its PD formulation were derived. The Chambolle-Pock algorithm for PD was implemented and its convergence behavior was compared with that of GNCG for the original QSM. Forward and central difference schemes were compared in terms of the presence of checkerboard artifacts. All methods were tested and validated on a gadolinium phantom, ex vivo brain blocks, and in vivo brain MRI data with respect to COSMOS.

RESULTS

The PD approach provided a faster convergence rate than GNCG. The GNCG convergence rate slowed considerably with smaller (more accurate) values of the conditioning parameter. Using a forward difference suppressed the checkerboard artifacts in QSM, as compared with the central difference. The accuracy of PD and GNCG were validated based on excellent correlation with COSMOS.

CONCLUSIONS

The PD approach with forward difference for the gradient showed improved convergence and accuracy over the GNCG method using central difference. Magn Reson Med 78:2416-2427, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

Structure Prior Effects in Bayesian Approaches of Quantitative Susceptibility Mapping

Quantitative susceptibility mapping (QSM) has shown its potential for anatomical and functional MRI, as it can quantify, for in vivo tissues, magnetic biomarkers and contrast agents which have differential susceptibilities to the surroundings substances. For reconstructing the QSM with a single orientation, various methods have been proposed to identify a unique solution for the susceptibility map. Bayesian QSM approach is the major type which uses various regularization terms, such as a piece-wise constant, a smooth, a sparse, or a morphological prior. Six QSM algorithms with or without structure prior are systematically discussed to address the structure prior effects. The methods are evaluated using simulations, phantom experiments with the given susceptibility, and human brain data. The accuracy and image quality of QSM were increased when using structure prior in the simulation and phantom compared to same regularization term without it, respectively. The image quality of QSM method using the structure prior is better comparing, respectively, to the method without it by either sharpening the image or reducing streaking artifacts in vivo. The structure priors improve the performance of the various QSMs using regularized minimization including L1, L2, and TV norm.

Rapid reconstruction of quantitative susceptibility mapping via improved ℓ0 norm approximation

Quantitative susceptibility mapping (QSM) reconstruction is a well-known ill-posed problem. Various regularization techniques have been proposed for solving this problem. In this paper, a rapid method is proposed that uses ℓ₀ norm minimization in a gradient domain. Because ℓ₀ minimization is an NP-hard problem, a special alternating optimization strategy is employed to simplify the reconstruction algorithm. The proposed algorithm uses only simple point-wise multiplications and thresholding operations, and significantly speeds up the calculation. Both numerical simulations and in vivo experiments demonstrate that the proposed method can reconstruct susceptibility fast and accurately. Because morphology information weighted methods have achieved considerable success in QSM, we performed a quantitative comparison with some typical weighted methods, such as MEDI (morphology enabled dipole inversion), iLSQR (improved least squares algorithm), and wℓ₁ (weighted ℓ₁ norm minimization). The reconstructed results show that the proposed method can provide accurate results with a satisfactory speed.

Susceptibility underestimation in a high-susceptibility phantom: Dependence on imaging resolution, magnitude contrast, and other parameters

PURPOSE

We assessed the accuracy of quantitative susceptibility mapping in a gadolinium balloon phantom with a large range of susceptibility values and imaging resolutions at 1.5 and 3 Tesla (T).

THEORY AND METHODS

The phantom contained sources with susceptibility values of 0.4, 0.8, 1.6, and 3.2 ppm and was imaged at isotropic resolutions of 0.7, 0.8, 1.2, and 1.8 mm. Numerical simulations were performed to match the experimental findings. Voxel sensitivity effects were used to explain the susceptibility underestimations.

RESULTS

Both phantom data and simulation demonstrated that systematic underestimation of the susceptibility values increased with voxel size, field strength, and object susceptibility.

CONCLUSION

The underestimation originates from the signal formation in a voxel, which can be described by the voxel sensitivity function. The amount of underestimation is thus affected by imaging resolution, magnitude contrast, image filtering, and details of the susceptibility inclusions such as the susceptibility value and geometry. High-resolution imaging is therefore needed for accurate reconstruction of QSM values, especially at higher susceptibilities. Magn Reson Med 78:1080-1086, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Foundations of MRI phase imaging and processing for Quantitative Susceptibility Mapping (QSM)

Quantitative Susceptibility Mapping (QSM) is a novel MRI based technique that relies on estimates of the magnetic field distribution in the tissue under examination. Several sophisticated data processing steps are required to extract the magnetic field distribution from raw MRI phase measurements. The objective of this review article is to provide a general overview and to discuss several underlying assumptions and limitations of the pre-processing steps that need to be applied to MRI phase data before the final field-to-source inversion can be performed. Beginning with the fundamental relation between MRI signal and tissue magnetic susceptibility this review covers the reconstruction of magnetic field maps from multi-channel phase images, background field correction, and provides an overview of state of the art QSM solution strategies.

Reproducibility of quantitative susceptibility mapping in the brain at two field strengths from two vendors

PURPOSE

To assess the reproducibility of brain quantitative susceptibility mapping (QSM) in healthy subjects and in patients with multiple sclerosis (MS) on 1.5 and 3T scanners from two vendors.

MATERIALS AND METHODS

Ten healthy volunteers and 10 patients were scanned twice on a 3T scanner from one vendor. The healthy volunteers were also scanned on a 1.5T scanner from the same vendor and on a 3T scanner from a second vendor. Similar imaging parameters were used for all scans. QSM images were reconstructed using a recently developed nonlinear morphology-enabled dipole inversion (MEDI) algorithm with L1 regularization. Region-of-interest (ROI) measurements were obtained for 20 major brain structures. Reproducibility was evaluated with voxel-wise and ROI-based Bland-Altman plots and linear correlation analysis.

RESULTS

ROI-based QSM measurements showed excellent correlation between all repeated scans (correlation coefficient R ≥ 0.97), with a mean difference of less than 1.24 ppb (healthy subjects) and 4.15 ppb (patients), and 95% limits of agreements of within -25.5 to 25.0 ppb (healthy subjects) and -35.8 to 27.6 ppb (patients). Voxel-based QSM measurements had a good correlation (0.64 ≤ R ≤ 0.88) and limits of agreements of -60 to 60 ppb or less.

CONCLUSION

Brain QSM measurements have good interscanner and same-scanner reproducibility for healthy and MS subjects, respectively, on the systems evaluated in this study.

Enhancing k-space quantitative susceptibility mapping by enforcing consistency on the cone data (CCD) with structural priors

PURPOSE

The inversion from the magnetic field to the magnetic susceptibility distribution is ill-posed because the dipole kernel, which relates the magnetic susceptibility to the magnetic field, has zeroes at a pair of cone surfaces in the k-space, leading to streaking artifacts on the reconstructed quantitative susceptibility maps (QSM). A method to impose consistency on the cone data (CCD) with structural priors is proposed to improve the solutions of k-space methods.

METHODS

The information in the cone region is recovered by enforcing structural consistency with structural prior, while information in the noncone trust region is enforced to be consistent with the magnetic field measurements in k-space. This CCD method was evaluated by comparing the initial results of existing QSM algorithms to the QSM results after CCD enhancement with respect to the COSMOS results in simulation, phantom, and in vivo human brain.

RESULTS

The proposed method demonstrated suppression of streaking artifacts and the resulting QSM showed better agreement with reference standard QSM compared with other k-space based methods.

CONCLUSION

By enforcing consistency with structural priors in the cone region, the missing data in the cone can be recovered and the streaking artifacts in QSM can be suppressed.

Quantitative susceptibility mapping (QSM): Decoding MRI data for a tissue magnetic biomarker

In MRI, the main magnetic field polarizes the electron cloud of a molecule, generating a chemical shift for observer protons within the molecule and a magnetic susceptibility inhomogeneity field for observer protons outside the molecule. The number of water protons surrounding a molecule for detecting its magnetic susceptibility is vastly greater than the number of protons within the molecule for detecting its chemical shift. However, the study of tissue magnetic susceptibility has been hindered by poor molecular specificities of hitherto used methods based on MRI signal phase and T2* contrast, which depend convolutedly on surrounding susceptibility sources. Deconvolution of the MRI signal phase can determine tissue susceptibility but is challenged by the lack of MRI signal in the background and by the zeroes in the dipole kernel. Recently, physically meaningful regularizations, including the Bayesian approach, have been developed to enable accurate quantitative susceptibility mapping (QSM) for studying iron distribution, metabolic oxygen consumption, blood degradation, calcification, demyelination, and other pathophysiological susceptibility changes, as well as contrast agent biodistribution in MRI. This paper attempts to summarize the basic physical concepts and essential algorithmic steps in QSM, to describe clinical and technical issues under active development, and to provide references, codes, and testing data for readers interested in QSM.

In vivo quantitative susceptibility mapping (QSM) in Alzheimer's disease

Background

This study explores the magnetostatic properties of the Alzheimer's disease brain using a recently proposed, magnetic resonance imaging, postprocessed contrast mechanism. Quantitative susceptibility mapping (QSM) has the potential to monitor in vivo iron levels by reconstructing magnetic susceptibility sources from field perturbations. However, with phase data acquired at a single head orientation, the technique relies on several theoretical approximations and requires fast-evolving regularisation strategies.

Methods

In this context, the present study describes a complete methodological framework for magnetic susceptibility measurements with a review of its theoretical foundations.

Findings and Significance

The regional and whole-brain cross-sectional comparisons between Alzheimer's disease subjects and matched controls indicate that there may be significant magnetic susceptibility differences for deep brain nuclei – particularly the putamen – as well as for posterior grey and white matter regions. The methodology and findings described suggest that the QSM method is ready for larger-scale clinical studies.