The magnetic susceptibility of tissue can be determined in gradient echo MRI by deconvolving the local magnetic field with the magnetic field generated by a unit dipole. This Quantitative Susceptibility Mapping (QSM) problem is unfortunately ill-posed. By transforming the problem to the Fourier domain, the susceptibility appears to be undersampled only at points where the dipole kernel is zero, suggesting that a modest amount of additional information may be sufficient for uniquely resolving susceptibility. A Morphology Enabled Dipole Inversion (MEDI) approach is developed that exploits the structural consistency between the susceptibility map and the magnitude image reconstructed from the same gradient echo MRI. Specifically, voxels that are part of edges in the susceptibility map but not in the edges of the magnitude image are considered to be sparse. In this approach an L1 norm minimization is used to express this sparsity property. Numerical simulations and phantom experiments are performed to demonstrate the superiority of this L1 minimization approach over the previous L2 minimization method. Preliminary brain imaging results in healthy subjects and in patients with intracerebral hemorrhages illustrate that QSM is feasible in practice.

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.

Purpose Within multiple sclerosis (MS) lesions iron is present in chronically activated microglia. Thus, iron detection with MRI might provide a biomarker for chronic inflammation within lesions. Here, we examine contributions of iron and myelin to magnetic susceptibility of lesions on quantitative susceptibility mapping (QSM). Methods Fixed MS brain tissue was assessed with MRI including gradient echo data, which was processed to generate field (phase), R2* and QSM. Five lesions were sectioned and evaluated by immunohistochemistry for presence of myelin, iron and microglia/macrophages. Two of the lesions had an elemental analysis for iron concentration mapping, and their phospholipid content was estimated from the difference in the iron and QSM data. Results Three of the five lesions had substantial iron deposition that was associated with microglia and positive susceptibility values. For the two lesions with elemental analysis, the QSM derived phospholipid content maps were consistent with myelin labeled histology. Conclusion Positive susceptibility values with respect to water indicate the presence of iron in MS lesions, though both demyelination and iron deposition contribute to QSM.

This study demonstrates the dependence of non-local susceptibility effects on object orientation in gradient echo MRI and the reduction of non-local effects by deconvolution using quantitative susceptibility mapping (QSM). Imaging experiments were performed on a 3T MRI system using a spoiled 3D multi-echo GRE sequence on phantoms of known susceptibilities, and on human brains of healthy subjects and patients with intracerebral hemorrhages. Magnetic field measurements were determined from multiple echo phase data. To determine the QSM, these field measurements were deconvolved through a dipole inversion kernel under a constraint of consistency with the magnitude images. Phantom and human data demonstrated that the hypointense region in GRE magnitude image corresponding to a susceptibility source increased in volume with TE and varied with the source orientation. The induced magnetic field extended beyond the susceptibility source and varied with its orientation. In QSM, these blooming artifacts, including their dependence on object orientation, were reduced and material susceptibilities were quantified.

White matter is an essential component of the central nervous system and is of major concern in neurodegenerative diseases such as multiple sclerosis (MS). Recent MRI studies have explored the unique anisotropic magnetic properties of white matter using susceptibility tensor imaging. However, these measurements are inhibited in practice by the large number of different head orientations needed to accurately reconstruct the susceptibility tensor. Adding reasonable constraints reduces the number of model parameters and can help condition the tensor reconstruction from a small number of orientations. The macroscopic magnetic susceptibility is decomposed as a sum of molecular magnetic polarizabilities, demonstrating that macroscopic order in molecular arrangement is essential to the existence of and symmetry in susceptibility anisotropy and cylindrical symmetry is a natural outcome of an ordered molecular arrangement. Noise propagation in the susceptibility tensor reconstruction is analyzed through its condition number, showing that the tensor reconstruction is highly susceptible to the distribution of acquired subject orientations and to the tensor symmetry properties, with a substantial over- or under-estimation of susceptibility anisotropy in fiber directions not favorably oriented with respect to the acquired orientations. It was found that a careful acquisition of three non-coplanar orientations and the use of cylindrical symmetry guided by diffusion tensor imaging allowed reasonable estimation of magnetic susceptibility anisotropy in certain major white matter tracts in the human brain.

Quantitative assessment of myelination is important for characterizing tissue damage and evaluating response to therapy in white matter diseases such as multiple sclerosis. Conventional multicomponent T 2 relaxometry based on the twodimensional (2D) multiecho spin echo sequence is a promising method to measure myelin water fraction, but its clinical utility is impeded by the prohibitively long data acquisition and limited brain coverage. The objective of this study was to develop a signal-to-noise ratio efficient 3D T 2 prep spiral gradient echo (3D SPIRAL) sequence for full brain T 2 relaxometry and to validate this sequence using 3D multiecho spin echo as reference standard in healthy brains at 1.5 T. 3D SPIRAL was found to provide similar myelin water fraction in six selected white and gray matter areas using region-of-interest signal averaging analysis (N 5 7, P > 0.05). While 3D multiecho spin echo only provided partial brain coverage, 3D SPI-RAL enabled whole brain coverage with a fivefold higher acquisition speed per imaging slice and similar signal-tonoise ratio efficiency. Both 3D sequences provided superior signal-to-noise ratio efficiency when compared to the conventional 2D multiecho spin echo approach. Magn Reson Med 67:614-621, 2012. V C 2012 Wiley Periodicals, Inc. Key words: T 2 relaxometry; white matter; myelin water fraction; spiral sampling; 3D acquisition Quantitative assessment of myelin content is important for characterizing tissue damage and evaluating response to therapy of demyelinating diseases such as multiple sclerosis. Currently, multicomponent T 2 relaxometry (1,2) is considered one of the most promising noninvasive in vivo imaging biomarkers for myelin content. In this approach, multiple magnetic resonance images are acquired with different T 2 weightings, from which a T 2 distribution can be obtained for each voxel using a multiexponential analysis (3). The signal of the myelin water peak (typically corresponding to T 2 components of less than 50 ms at 1.5 T) relative to the total water signal is called the myelin water fraction (MWF) and has been proposed as an indirect measurement of the degree of myelination (4). MWF has been shown to correlate with histological myelin measurement in animal models (5,6) as well as in ex vivo human brains (7), and may be useful clinically (4,8).Accurate multicomponent T 2 relaxometry requires a large number of T 2 -weighted images with high signal-tonoise ratio (SNR; 9), resulting in lengthy acquisition. In the conventional method, image data are collected using a two-dimensional (2D) Carr-Purcell-Meiboom-Gill multiecho spin echo (MESE) sequence at various echo times (TEs; 2,8,10). The utility of 2D MESE for clinical practice is impeded by prohibitively long acquisition time of approximately 26 min for each 5 mm slice (10). 3D MESE acquisition with echo planar readout has been proposed to achieve whole brain coverage efficiently (11), but a direct comparison with the standard 2D MESE method is not available. MESE also uses a large number of 180...

Purpose To demonstrate the phase and QSM patterns created by solid and shell spatial distributions of magnetic susceptibility in MS lesions. Materials and Methods Numerical simulations and experimental phantoms of solid- and shell-shaped magnetic susceptibility sources were used to generate magnitude, phase, and QSM images. Imaging of 20 consecutive MS patients was also reviewed for this IRB-approved MRI study to identify appearance of solid and shell lesions on phase and QSM images. Results Solid and shell susceptibility sources were correctly reconstructed in QSM images, while the corresponding phase images depicted both geometries with shell-like patterns, making the underlying susceptibility distribution difficult to determine using phase alone. In MS patients, of the 60 largest lesions identified on T2, 30 lesions were detected on both QSM and phase, of which 83% were solid and 17% were shells on QSM, and of which 30% were solid and 70% were shell on phase. Of the 21 shell-like lesions on phase, 76% appeared solid on QSM, 24% appeared shell on QSM. Of the five shell-like lesions on QSM, all were shell-like on phase. Conclusion QSM accurately depicts both solid and shell patterns of magnetic susceptibility, while phase imaging fails to distinguish them.

Various regularization methods have been proposed for single-orientation quantitative susceptibility mapping (QSM), which is an ill-posed magnetic field to susceptibility source inverse problem. Noise amplification, a major issue in inverse problems, manifests as streaking artifacts and quantification errors in QSM and has not been comparatively evaluated in these algorithms. In this paper, various QSM methods were systematically categorized for noise analysis. Six representative QSM methods were selected from four categories: two non-Bayesian methods with alteration or approximation of the dipole kernel to overcome the ill conditioning; four Bayesian methods using a general mathematical prior or a specific physical structure prior to select a unique solution, and using a data fidelity term with or without noise weighting. The effects of noise in these QSM methods were evaluated by reconstruction errors in simulation and image quality in 50 consecutive human subjects. Bayesian QSM methods with noise weighting consistently reduced root mean squared errors in numerical simulations and increased image quality scores in the human brain images, when compared to non-Bayesian methods and to corresponding Bayesian methods without noise weighting (p ≤ 0.001). In summary, noise effects in QSM can be reduced using Bayesian methods with proper noise weighting.