Nonlinear formulation of the magnetic field to source relationship for robust quantitative susceptibility mapping.
TL;DR: This nonlinear QSM method reduced salt and pepper noise or checkerboard pattern in high susceptibility regions in healthy subjects and markedly reduced artifacts in patients with intracerebral hemorrhages.
Abstract: Quantitative susceptibility mapping (QSM) opens the door for measuring tissue magnetic susceptibility properties that may be important biomarkers, and QSM is becoming an increasingly active area of scientific and clinical investigations. In practical applications, there are sources of errors for QSM including noise, phase unwrapping failures, and signal model inaccuracy. To improve the robustness of QSM quality, we propose a nonlinear data fidelity term for frequency map estimation and dipole inversion to reduce noise and effects of phase unwrapping failures, and a method for model error reduction through iterative tuning. Compared with the previous phase based linear QSM method, this nonlinear QSM method reduced salt and pepper noise or checkerboard pattern in high susceptibility regions in healthy subjects and markedly reduced artifacts in patients with intracerebral hemorrhages.
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TL;DR: 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 inQSM.
Abstract: 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. Magn Reson Med 73:82–101, 2015. © 2014 The Authors. Magnetic Resonance in Medicine Published by Wiley Periodicals, Inc. on behalf of International Society of Medicine in Resonance. This is an open access article under the terms of the Creative commons Attribution License, which permits use, distribution, and reproduction in any medium, provided the original work is properly cited.
666 citations
TL;DR: The basic principles of SWI, its clinical and research applications, the mechanisms governing brain susceptibility properties, and its practical implementation are reviewed, with a focus on brain imaging.
Abstract: Susceptibility-weighted imaging (SWI) is a magnetic resonance imaging (MRI) technique that enhances image contrast by using the susceptibility differences between tissues. It is created by combining both magnitude and phase in the gradient echo data. SWI is sensitive to both paramagnetic and diamagnetic substances which generate different phase shift in MRI data. SWI images can be displayed as a minimum intensity projection that provides high resolution delineation of the cerebral venous architecture, a feature that is not available in other MRI techniques. As such, SWI has been widely applied to diagnose various venous abnormalities. SWI is especially sensitive to deoxygenated blood and intracranial mineral deposition and, for that reason, has been applied to image various pathologies including intracranial hemorrhage, traumatic brain injury, stroke, neoplasm, and multiple sclerosis. SWI, however, does not provide quantitative measures of magnetic susceptibility. This limitation is currently being addressed with the development of quantitative susceptibility mapping (QSM) and susceptibility tensor imaging (STI). While QSM treats susceptibility as isotropic, STI treats susceptibility as generally anisotropic characterized by a tensor quantity. This article reviews the basic principles of SWI, its clinical and research applications, the mechanisms governing brain susceptibility properties, and its practical implementation, with a focus on brain imaging.
402 citations
TL;DR: HARPERELLA preserves the tissue phase signal in gray matter, white matter and cerebrospinal fluid with excellent robustness, providing a convenient and accurate solution for QSM.
Abstract: Quantitative susceptibility mapping (QSM) is a recently developed MRI technique that provides a quantitative measure of tissue magnetic susceptibility. To compute tissue magnetic susceptibilities based on gradient echoes, QSM requires reliable unwrapping of the measured phase images and removal of contributions caused by background susceptibilities. Typically, the two steps are performed separately. Here, we present a method that simultaneously performs phase unwrapping and HARmonic (background) PhasE REmovaL using the LAplacian operator (HARPERELLA). Both numerical simulations and in vivo human brain images show that HARPERELLA effectively removes both phase wraps and background phase, whilst preserving all low spatial frequency components originating from brain tissues. When compared with other QSM phase preprocessing techniques, such as path-based phase unwrapping followed by background phase removal, HARPERELLA preserves the tissue phase signal in gray matter, white matter and cerebrospinal fluid with excellent robustness, providing a convenient and accurate solution for QSM. The proposed algorithm is provided, together with QSM and susceptibility tensor imaging (STI) tools, in a shared software package named 'STI Suite'.
244 citations
TL;DR: 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.
Abstract: 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.
238 citations
Additional excerpts
...With the advent of faster [69] and more advanced regularisation strategies [43,122], and combining multi-contrast information [118,123–125], the applicability of magnetic susceptibility mapping to study the human brain is only bound to grow....
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TL;DR: This review briefly recapitulate the fundamental theoretical foundation of QSM and STI, as well as computational strategies for the characterization of magnetic susceptibility with MRI phase data.
Abstract: Magnetic susceptibility describes the magnetizability of a material to an applied magnetic field and represents an important parameter in the field of MRI. With the recently introduced method of quantitative susceptibility mapping (QSM) and its conceptual extension to susceptibility tensor imaging (STI), the non-invasive assessment of this important physical quantity has become possible with MRI. Both methods solve the ill-posed inverse problem to determine the magnetic susceptibility from local magnetic fields. Whilst QSM allows the extraction of the spatial distribution of the bulk magnetic susceptibility from a single measurement, STI enables the quantification of magnetic susceptibility anisotropy, but requires multiple measurements with different orientations of the object relative to the main static magnetic field. In this review, we briefly recapitulate the fundamental theoretical foundation of QSM and STI, as well as computational strategies for the characterization of magnetic susceptibility with MRI phase data. In the second part, we provide an overview of current methodological and clinical applications of QSM with a focus on brain imaging. Copyright © 2016 John Wiley & Sons, Ltd.
224 citations
References
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TL;DR: An automated method for segmenting magnetic resonance head images into brain and non‐brain has been developed and described and examples of results and the results of extensive quantitative testing against “gold‐standard” hand segmentations, and two other popular automated methods.
Abstract: An automated method for segmenting magnetic resonance head images into brain and non-brain has been developed. It is very robust and accurate and has been tested on thousands of data sets from a wide variety of scanners and taken with a wide variety of MR sequences. The method, Brain Extraction Tool (BET), uses a deformable model that evolves to fit the brain's surface by the application of a set of locally adaptive model forces. The method is very fast and requires no preregistration or other pre-processing before being applied. We describe the new method and give examples of results and the results of extensive quantitative testing against "gold-standard" hand segmentations, and two other popular automated methods.
9,887 citations
Book•
01 Apr 1996
TL;DR: Theorems and statistical properties of least squares solutions are explained and basic numerical methods for solving least squares problems are described.
Abstract: Preface 1. Mathematical and statistical properties of least squares solutions 2. Basic numerical methods 3. Modified least squares problems 4. Generalized least squares problems 5. Constrained least squares problems 6. Direct methods for sparse problems 7. Iterative methods for least squares problems 8. Least squares problems with special bases 9. Nonlinear least squares problems Bibliography Index.
3,405 citations
TL;DR: The image intensity in magnetic resonance magnitude images in the presence of noise is shown to be governed by a Rician distribution and low signal intensities (SNR < 2) are therefore biased due to the noise.
Abstract: The image intensity in magnetic resonance magnitude images in the presence of noise is shown to be governed by a Rician distribution. Low signal intensities (SNR < 2) are therefore biased due to the noise. It is shown how the underlying noise can be estimated from the images and a simple correction scheme is provided to reduce the bias. The noise characteristics in phase images are also studied and shown to be very different from those of the magnitude images. Common to both, however, is that the noise distributions are nearly Gaussian for SNR larger than two.
2,425 citations
"Nonlinear formulation of the magnet..." refers background in this paper
...The distribution of the phase noise, Dh 1⁄4 h h, has a complicated expression as given in (21), which may be approximated as a zero-mean gaussian distribution with a variance (r/A)(2) when A > r, and as a uniformly distributed random variable in ( p, p) when A 1⁄4 0....
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TL;DR: In this paper, an approach to 'unwrapping' the 2 pi ambiguities in the two-dimensional data set is presented, where it is found that noise and geometrical radar layover corrupt measurements locally, and these local errors can propagate to form global phase errors that affect the entire image.
Abstract: Interferometric synthetic aperture radar observations provide a means for obtaining high-resolution digital topographic maps from measurements of amplitude and phase of two complex radar images. The phase of the radar echoes may only be measured modulo 2 pi; however, the whole phase at each point in the image is needed to obtain elevations. An approach to 'unwrapping' the 2 pi ambiguities in the two-dimensional data set is presented. It is found that noise and geometrical radar layover corrupt measurements locally, and these local errors can propagate to form global phase errors that affect the entire image. It is shown that the local errors, or residues, can be readily identified and avoided in the global phase estimation. A rectified digital topographic map derived from the unwrapped phase values is presented.
2,246 citations
"Nonlinear formulation of the magnet..." refers background in this paper
...However, noise may lead to an erroneous 2p multiple in unwrapping in one voxel, which may cascade to many downstream voxels in sequential phase unwrapping algorithms (22)....
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