High-precision mapping of the magnetic field utilizing the harmonic function mean value property

Data adaptive regularization with reference tissue constraints for liver quantitative susceptibility mapping

PURPOSE

To improve repeatability and reproducibility across acquisition parameters and reduce bias in quantitative susceptibility mapping (QSM) of the liver, through development of an optimized regularized reconstruction algorithm for abdominal QSM.

METHODS

An optimized approach to estimation of magnetic susceptibility distribution is formulated as a constrained reconstruction problem that incorporates estimates of the input data reliability and anatomical priors available from chemical shift-encoded imaging. The proposed data-adaptive method was evaluated with respect to bias, repeatability, and reproducibility in a patient population with a wide range of liver iron concentration (LIC). The proposed method was compared to the previously proposed and validated approach in liver QSM for two multi-echo spoiled gradient-recalled echo protocols with different acquisition parameters at 3T. Linear regression was used for evaluation of QSM methods against a reference FDA-approvedR 2 $$ {R}_2 $$ -based LIC measure andR 2 ∗ $$ {R}_2^{\ast } $$ measurements; repeatability/reproducibility were assessed by Bland-Altman analysis.

RESULTS

The data-adaptive method produced susceptibility maps with higher subjective quality due to reduced shading artifacts. For both acquisition protocols, higher linear correlation with bothR 2 $$ {R}_2 $$ - andR 2 ∗ $$ {R}_2^{\ast } $$ -based measurements were observed for the data-adaptive method (r 2 = 0 . 74 / 0 . 69 $$ {r}^2=0.74/0.69 $$ forR 2 $$ {R}_2 $$ ,0 . 97 / 0 . 95 $$ 0.97/0.95 $$ forR 2 ∗ $$ {R}_2^{\ast } $$ ) than the standard method (r 2 = 0 . 60 / 0 . 66 $$ {r}^2=0.60/0.66 $$ and0 . 79 / 0 . 88 $$ 0.79/0.88 $$ ). For both protocols, the data-adaptive method enabled better test-retest repeatability (repeatability coefficients 0.19/0.30 ppm for the data-adaptive method, 0.38/0.47 ppm for the standard method) and reproducibility across protocols (reproducibility coefficient 0.28 vs. 0.53ppm) than the standard method.

CONCLUSIONS

The proposed data-adaptive QSM algorithm may enable quantification of LIC with improved repeatability/reproducibility across different acquisition parameters as 3T.

Introduction to Quantitative Susceptibility Mapping and Susceptibility Weighted Imaging

Quantitative Susceptibility Mapping (QSM) and Susceptibility Weighted Imaging (SWI) are MRI techniques that measure and display differences in the magnetization that is induced in tissues, i.e. their magnetic susceptibility, when placed in the strong external magnetic field of an MRI system. SWI produces images in which the contrast is heavily weighted by the intrinsic tissue magnetic susceptibility. It has been applied in a wide range of clinical applications. QSM is a further advancement of this technique that requires sophisticated post-processing in order to provide quantitative maps of tissue susceptibility. This review explains the steps involved in both SWI and QSM as well as describing some of their uses in both clinical and research applications.

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.

Background field removal for susceptibility mapping of human brain with large susceptibility variations

PURPOSE

In quantitative susceptibility mapping (QSM) of human brain, the background field induced by air-tissue interface varies significantly with respect to the rotation angle between the head and the static field, which may result in substantial error in the estimated magnetic susceptibility values. The goal of this study was to develop a strategy to better remove such orientation dependent background field.

METHODS

An improved background field removal method is proposed based on the sophisticated harmonic artifact reduction for phase data using a region adaptive kernel (R-SHARP), named iRSHARP. It uses a spatially weighted spherical Gaussian kernel exploiting the amplitude, gradient, and wrap count of the phase map. The method was validated using both numerical simulations and in vivo human brain data at multiple head orientations. Performance was compared with the variable kernel (V-SHARP) and R-SHARP methods.

RESULTS

The proposed iRSHARP method showed improved background removal over R-SHARP while cutting the computational time in half. As compared to V-SHARP and R-SHARP, the iRSHARP generated local field and susceptibility maps showed fewer artifacts in regions of large susceptibility variations, and for the in vivo human brain, the susceptibilities of the deep gray matter nuclei were consistent with the in vivo gold-standard "Calculation of Susceptibility through Multiple Orientation Sampling" (COSMOS) values.

CONCLUSION

iRSHARP can remove the orientation dependent background field effectively. Using iRSHARP, the paranasal sinus regions can be preserved in the brain mask and the brain integrity was conserved, which may facilitate further data analysis and clinical application.

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.

A comprehensive numerical analysis of background phase correction with V-SHARP

Sophisticated harmonic artifact reduction for phase data (SHARP) is a method to remove background field contributions in MRI phase images, which is an essential processing step for quantitative susceptibility mapping (QSM). To perform SHARP, a spherical kernel radius and a regularization parameter need to be defined. In this study, we carried out an extensive analysis of the effect of these two parameters on the corrected phase images and on the reconstructed susceptibility maps. As a result of the dependence of the parameters on acquisition and processing characteristics, we propose a new SHARP scheme with generalized parameters. The new SHARP scheme uses a high-pass filtering approach to define the regularization parameter. We employed the variable-kernel SHARP (V-SHARP) approach, using different maximum radii (R_m ) between 1 and 15 mm and varying regularization parameters (f) in a numerical brain model. The local root-mean-square error (RMSE) between the ground-truth, background-corrected field map and the results from SHARP decreased towards the center of the brain. RMSE of susceptibility maps calculated with a spatial domain algorithm was smallest for R_m between 6 and 10 mm and f between 0 and 0.01 mm^-1 , and for maps calculated with a Fourier domain algorithm for R_m between 10 and 15 mm and f between 0 and 0.0091 mm^-1 . We demonstrated and confirmed the new parameter scheme in vivo. The novel regularization scheme allows the use of the same regularization parameter irrespective of other imaging parameters, such as image resolution. Copyright © 2016 John Wiley & Sons, Ltd.

Overview of quantitative susceptibility mapping

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.

A 24-channel shim array for the human spinal cord: Design, evaluation, and application

PURPOSE

A novel multichannel shim array is introduced to improve MRI and spectroscopic studies of the human spinal cord.

METHODS

Twenty-four-channel shim and 8-channel transceiver arrays were designed to insert into the patient bed table to lie in close proximity to the subject's spine. The reference field patterns of each of the shim channels (Hz/A) were determined empirically via gradient echo field mapping and subsequently used to demonstrate shim performance at 3 Tesla using an ex vivo phantom, which incorporated a fixed human spine. The shim was further demonstrated on five healthy volunteers.

RESULTS

Application of the shim to the ex vivo phantom reduced the standard deviation of the field over the spinal volume of interest (123.4 cm³ ) from an original 51.3 Hz down to 32.5 Hz, amounting to an improvement in field homogeneity of 36.6%. In vivo, the spine shim resulted in an average improvement in field homogeneity of 63.8 ± 15.4%.

CONCLUSION

The localized spine shim offers a promising new means of correcting magnetic field distortion in the spinal cord. Magn Reson Med 76:1604-1611, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

Dual-pathway multi-echo sequence for simultaneous frequency and T2 mapping

PURPOSE

To present a dual-pathway multi-echo steady state sequence and reconstruction algorithm to capture T2, T2(∗) and field map information.

METHODS

Typically, pulse sequences based on spin echoes are needed for T2 mapping while gradient echoes are needed for field mapping, making it difficult to jointly acquire both types of information. A dual-pathway multi-echo pulse sequence is employed here to generate T2 and field maps from the same acquired data. The approach might be used, for example, to obtain both thermometry and tissue damage information during thermal therapies, or susceptibility and T2 information from a same head scan, or to generate bonus T2 maps during a knee scan.

RESULTS

Quantitative T2, T2(∗) and field maps were generated in gel phantoms, ex vivo bovine muscle, and twelve volunteers. T2 results were validated against a spin-echo reference standard: A linear regression based on ROI analysis in phantoms provided close agreement (slope/R(2)=0.99/0.998). A pixel-wise in vivo Bland-Altman analysis of R2=1/T2 showed a bias of 0.034 Hz (about 0.3%), as averaged over four volunteers. Ex vivo results, with and without motion, suggested that tissue damage detection based on T2 rather than temperature-dose measurements might prove more robust to motion.

CONCLUSION

T2, T2(∗) and field maps were obtained simultaneously, from the same datasets, in thermometry, susceptibility-weighted imaging and knee-imaging contexts.

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.

A Novel Multiparametric Approach to 3D Quantitative MRI of the Brain

Magnetic Resonance properties of tissues can be quantified in several respects: relaxation processes, density of imaged nuclei, magnetism of environmental molecules, etc. In this paper, we propose a new comprehensive approach to obtain 3D high resolution quantitative maps of arbitrary body districts, mainly focusing on the brain. The theory presented makes it possible to map longitudinal (R1), pure transverse (R2) and free induction decay ([Formula: see text]) rates, along with proton density (PD) and magnetic susceptibility (χ), from a set of fast acquisition sequences in steady-state that are highly insensitive to flow phenomena. A novel denoising scheme is described and applied to the acquired datasets to enhance the signal to noise ratio of the derived maps and an information theory approach compensates for biases from radio frequency (RF) inhomogeneities, if no direct measure of the RF field is available. Finally, the results obtained on sample brain scans of healthy controls and multiple sclerosis patients are presented and discussed.

Improved estimation of myelin water fraction using complex model fitting

In gradient echo (GRE) imaging, three compartment water modeling (myelin water, axonal water and extracellular water) in white matter has been demonstrated to show different frequency shifts that depend on the relative orientation of fibers and the B0 field. This finding suggests that in GRE-based myelin water imaging, a signal model may need to incorporate frequency offset terms and become a complex-valued model. In the current study, three different signal models and fitting approaches (a magnitude model fitted to magnitude data, a complex model fitted to magnitude data, and a complex model fitted to complex data) were investigated to address the reliability of each model in the estimation of the myelin water signal. For the complex model fitted to complex data, a new fitting approach that does not require background phase removal was proposed. When the three models were compared, the results from the new complex model fitting showed the most stable parameter estimation.

Quantitative susceptibility mapping by inversion of a perturbation field model: correlation with brain iron in normal aging

There is increasing evidence that iron deposition occurs in specific regions of the brain in normal aging and neurodegenerative disorders such as Parkinson's, Huntington's, and Alzheimer's disease. Iron deposition changes the magnetic susceptibility of tissue, which alters the MR signal phase, and allows estimation of susceptibility differences using quantitative susceptibility mapping (QSM). We present a method for quantifying susceptibility by inversion of a perturbation model, or "QSIP." The perturbation model relates phase to susceptibility using a kernel calculated in the spatial domain, in contrast to previous Fourier-based techniques. A tissue/air susceptibility atlas is used to estimate B0 inhomogeneity. QSIP estimates in young and elderly subjects are compared to postmortem iron estimates, maps of the Field-Dependent Relaxation Rate Increase, and the L1-QSM method. Results for both groups showed excellent agreement with published postmortem data and in vivo FDRI: statistically significant Spearman correlations ranging from Rho=0.905 to Rho=1.00 were obtained. QSIP also showed improvement over FDRI and L1-QSM: reduced variance in susceptibility estimates and statistically significant group differences were detected in striatal and brainstem nuclei, consistent with age-dependent iron accumulation in these regions.

Quantitative susceptibility mapping: current status and future directions

Quantitative susceptibility mapping (QSM) is a new technique for quantifying magnetic susceptibility. It has already found various applications in quantifying in vivo iron content, calcifications and changes in venous oxygen saturation. The accuracy of susceptibility mapping is dependent on several factors. In this review, we evaluate the entire process of QSM from data acquisition to individual data processing steps. We also show preliminary results of several new concepts introduced in this review in an attempt to improve the quality and accuracy for certain steps. The uncertainties in estimating susceptibility differences using susceptibility maps, phase images, and T2* maps are analyzed and compared. Finally, example clinical applications are presented. We conclude that QSM holds great promise in quantifying iron and becoming a standard clinical tool.

Quantitative susceptibility mapping in the abdomen as an imaging biomarker of hepatic iron overload

PURPOSE

The purpose of this work was to develop and demonstrate feasibility and initial clinical validation of quantitative susceptibility mapping (QSM) in the abdomen as an imaging biomarker of hepatic iron overload.

THEORY AND METHODS

In general, QSM is faced with the challenges of background field removal and dipole inversion. Respiratory motion, the presence of fat, and severe iron overload further complicate QSM in the abdomen. We propose a technique for QSM in the abdomen that addresses these challenges. Data were acquired from 10 subjects without hepatic iron overload and 33 subjects with known or suspected iron overload. The proposed technique was used to estimate the susceptibility map in the abdomen, from which hepatic iron overload was measured. As a reference, spin-echo data were acquired for R2-based LIC estimation. Liver R2* was measured for correlation with liver susceptibility estimates.

RESULTS

Correlation between susceptibility and R2-based LIC estimation was R(2) = 0.76 at 1.5 Tesla (T) and R(2) = 0.83 at 3T. Furthermore, high correlation between liver susceptibility and liver R2* (R(2) = 0.94 at 1.5T; R(2) = 0.93 at 3T) was observed.

CONCLUSION

We have developed and demonstrated initial validation of QSM in the abdomen as an imaging biomarker of hepatic iron overload.

2D harmonic filtering of MR phase images in multicenter clinical setting: toward a magnetic signature of cerebral microbleeds

Cerebral microbleeds (CMBs) have emerged as a new imaging marker of small vessel disease. Composed of hemosiderin, CMBs are paramagnetic and can be detected with MRI sequences sensitive to magnetic susceptibility (typically, gradient recalled echo T2* weighted images). Nevertheless, their identification remains challenging on T2* magnitude images because of confounding structures and lesions. In this context, T2* phase image may play a key role in better characterizing CMBs because of its direct relationship with local magnetic field variations due to magnetic susceptibility difference. To address this issue, susceptibility-based imaging techniques were proposed, such as Susceptibility Weighted Imaging (SWI) and Quantitative Susceptibility Mapping (QSM). But these techniques have not yet been validated for 2D clinical data in multicenter settings. Here, we introduce 2DHF, a fast 2D phase processing technique embedding both unwrapping and harmonic filtering designed for data acquired in 2D, even with slice-to-slice inconsistencies. This method results in internal field maps which reveal local field details due to magnetic inhomogeneity within the region of interest only. This technique is based on the physical properties of the induced magnetic field and should yield consistent results. A synthetic phantom was created for numerical simulations. It simulates paramagnetic and diamagnetic lesions within a 'brain-like' tissue, within a background. The method was evaluated on both this synthetic phantom and multicenter 2D datasets acquired in standardized clinical setting, and compared with two state-of-the-art methods. It proved to yield consistent results on synthetic images and to be applicable and robust on patient data. As a proof-of-concept, we finally illustrate that it is possible to find a magnetic signature of CMBs and CMCs on internal field maps generated with 2DHF on 2D clinical datasets that give consistent results with CT-scans in a subsample of 10 subjects acquired with both modalities.

Background field removal by solving the Laplacian boundary value problem

The removal of the background magnetic field is a critical step in generating phase images and quantitative susceptibility maps, which have recently been receiving increasing attention. Although it is known that the background field satisfies Laplace's equation, the boundary values of the background field for the region of interest have not been explicitly addressed in the existing methods, and they are not directly available from MRI measurements. In this paper, we assume simple boundary conditions and remove the background field by explicitly solving the boundary value problems of Laplace's or Poisson's equation. The proposed Laplacian boundary value (LBV) method for background field removal retains data near the boundary and is computationally efficient. Tests on a numerical phantom and an experimental phantom showed that LBV was more accurate than two existing methods.

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.

Effective digitized spatial size of unit dipole field in Quantitative Susceptibility Mapping

Quantitative Susceptibility Mapping (QSM) calculates a distribution of tissue magnetic susceptibility difference in vivo using measured magnetic field perturbation. The magnetic field perturbation can be approximated in first order by convolution of the susceptibility distribution with a spatial unit dipole field. Since the convolution has to be done in all space, a novel technique using harmonic properties of the dipole field is introduced to confine the calculation within the measurable region. However, discretized dipole field does not satisfy the harmonic property near its orign. Here, we investigate an effective spatial size of the dipole field in relation with the nonharmonic property using Shepp-Logan phantoms including partial volume effects. This study suggests that the dipole field can be effectively restricted to 15 voxels in diameter and that this value relates with the nonharmonic region of the discretized dipole field. Moreover, the effective size in a real space is scaled with a spatial resolution of a QSM experiment.

Toward online reconstruction of quantitative susceptibility maps: superfast dipole inversion

Magnetic susceptibility is an intrinsic tissue property that recently became measureable in vivo by a magnetic-resonance based technique called quantitative susceptibility mapping (QSM). Although QSM may be performed without additional acquisition time, for example, in the course of the well-established susceptibility weighted imaging, the applicability of QSM is currently hampered by the numerical complexity and computational cost associated with the reconstruction procedure. This work introduces a novel QSM framework called superfast dipole inversion which allows rapid online reconstruction of susceptibility maps from wrapped raw gradient-echo phase data. The algorithm relies on the extension and combination of several recent algorithms involving the precalculation of convolution kernels and the correction of inversion artifacts. Reconstruction of three-dimensional high resolution susceptibility maps of the human brain was achieved with superfast dipole inversion in less than 20 s on a conventional workstation computer. Thus, superfast dipole inversion opens the door to an implementation of QSM on MR scanner hardware as well as to the routine reconstruction of large cohorts of datasets.

Quantitative susceptibility mapping for investigating subtle susceptibility variations in the human brain

Quantitative susceptibility mapping (QSM) is a novel magnetic resonance-based technique that determines tissue magnetic susceptibility from measurements of the magnetic field perturbation. Due to the ill-posed nature of this problem, regularization strategies are generally required to reduce streaking artifacts on the computed maps. The present study introduces a new algorithm for calculating the susceptibility distribution utilizing a priori information on its regional homogeneity derived from gradient echo phase images and analyzes the impact of erroneous a priori information on susceptibility map fidelity. The algorithm, Homogeneity Enabled Incremental Dipole Inversion (HEIDI), was investigated with a special focus on the reconstruction of subtle susceptibility variations in a numerical model and in volunteer data and was compared with two recently published approaches, Thresholded K-space Division (TKD) and Morphology Enabled Dipole Inversion (MEDI). HEIDI resulted in susceptibility maps without streaking artifacts and excellent depiction of subtle susceptibility variations in most regions. By investigating HEIDI susceptibility maps acquired with the volunteers' heads in different orientations, it was demonstrated that the apparent magnetic susceptibility distribution of human brain tissue considerably depends on the direction of the main magnetic field.

Selective depiction of susceptibility transitions using Laplace-filtered phase maps

In this work, we aim to demonstrate the ability of Laplace-filtered three-dimensional (3D) phase maps to selectively depict the susceptibility transitions in an object. To realize this goal, it is first shown that both the Laplace derivative of the z component of the static magnetic field in an object and the Laplacian of the corresponding phase distribution may be expected to be zero in regions of constant or linearly varying susceptibility and to be nonzero when there is an abrupt change in susceptibility, for instance, at a single point, a ridge, an interface, an edge or a boundary. Next, a method is presented by which the Laplace derivative of a 3D phase map can be directly extracted from the complex data, without the need for phase unwrapping or subtraction of a reference image. The validity of this approach and of the theory behind it is subsequently demonstrated by simulations and phantom experiments with exactly known susceptibility distributions. Finally, the potential of the Laplace derivative analysis is illustrated by simulations with a Shepp-Logan digital brain phantom and experiments with a gel phantom containing positive and negative focal susceptibility deviations.

A novel background field removal method for MRI using projection onto dipole fields (PDF)

For optimal image quality in susceptibility-weighted imaging and accurate quantification of susceptibility, it is necessary to isolate the local field generated by local magnetic sources (such as iron) from the background field that arises from imperfect shimming and variations in magnetic susceptibility of surrounding tissues (including air). Previous background removal techniques have limited effectiveness depending on the accuracy of model assumptions or information input. In this article, we report an observation that the magnetic field for a dipole outside a given region of interest (ROI) is approximately orthogonal to the magnetic field of a dipole inside the ROI. Accordingly, we propose a nonparametric background field removal technique based on projection onto dipole fields (PDF). In this PDF technique, the background field inside an ROI is decomposed into a field originating from dipoles outside the ROI using the projection theorem in Hilbert space. This novel PDF background removal technique was validated on a numerical simulation and a phantom experiment and was applied in human brain imaging, demonstrating substantial improvement in background field removal compared with the commonly used high-pass filtering method.

High-field (9.4 T) MRI of brain dysmyelination by quantitative mapping of magnetic susceptibility

The multilayered myelin sheath wrapping around nerve axons is essential for proper functioning of the central nervous system. Abnormal myelination leads to a wide range of neurological diseases and developmental disorders. Non-invasive imaging of myelin content is of great clinical importance. The present work demonstrated that loss of myelin in the central nervous system of the shiverer mouse results in a dramatic reduction of magnetic susceptibility in white matter axons. The reduction resulted in a near extinction of susceptibility contrast between gray and white matter. Quantitative magnetic susceptibility imaging and diffusion tensor imaging were conducted on a group of control and shiverer mice at 9.4 T. We measured the resonance frequency distribution of the whole brain for each mouse. Magnetic susceptibility maps were computed and compared between the two groups. It was shown that the susceptibility contrast between gray and white matter was reduced by 96% in the shiverer compared to the controls. Diffusion measurements further confirmed intact fiber pathways in the shiverer mice, ruling out the possibility of axonal injury and its potential contribution to the altered susceptibility. As an autosomal recessive mutation, shiverer is characterized by an almost total lack of central nervous system myelin. Our data provide new evidences indicating that myelin is the predominant source of susceptibility differences between deep gray and white matter observed in magnetic resonance imaging. More importantly, the present study suggests that quantitative magnetic susceptibility is a potential endogenous biomarker for myelination.

Differentiation between diamagnetic and paramagnetic cerebral lesions based on magnetic susceptibility mapping

PURPOSE

Identification of calcifications and hemorrhages is essential for the etiological diagnosis of cerebral lesions. The purpose of this work was to develop a robust method for characterization of para- and diamagnetic intracerebral lesions based on clinical gradient-echo magnetic resonance phase data acquired at 1.5 Tesla.

METHODS

The magnetic susceptibility distribution of biological tissue produces a distinct magnetic field pattern, which is directly reflected in gradient-echo magnetic resonance phase images. Compared to brain parenchyma, iron-laden tissues are more paramagnetic, whereas mineralized tissues usually possess more diamagnetic susceptibilities. Magnetic resonance phase data were inverted to the underlying susceptibility distribution utilizing additional geometrical information about the lesions, which was obtained from the gradient-echo magnitude signal void corresponding to the lesions. Clinical magnetic resonance exams of three patients with multiple brain lesions (total n = 70) were processed and evaluated. For one patient, the results were validated by an additionally available computed tomography scan. Numerical simulations were conducted to evaluate the robustness of the method.

RESULTS

The obtained susceptibility maps showed impressive delineation of lesions, vessels, and potentially iron-laden tissue. Compensation of the nonlocal field perturbations was clearly discernable on the susceptibility maps. In all cases, discrimination of para- from diamagnetic lesions was achieved and the results were confirmed by the additional computed tomography. The numerical simulations demonstrated that robust determination of the total magnetic moment of lesions is possible. Thus, the proposed method is able to yield quantitative values for the minimum magnetic susceptibility of lesions.

CONCLUSIONS

A method has been developed for noninvasive, semiautomatic characterization of brain lesions based on magnetic resonance imaging data. Initial clinical results demonstrated that the proposed technique can be applied to diagnosis of lesions with calcifications or hemorrhages. If confirmed by larger studies, it bears the potential to obviate the need for confirmation with computed tomography.

Quantitative imaging of intrinsic magnetic tissue properties using MRI signal phase: an approach to in vivo brain iron metabolism?

Quantitative susceptibility mapping (QSM) based on gradient echo (GRE) magnetic resonance phase data is a novel technique for non-invasive assessment of magnetic tissue susceptibility differences. The method is expected to be an important means to determine iron distributions in vivo and may, thus, be instrumental for elucidating the physiological role of iron and disease-related iron concentration changes associated with various neurological and psychiatric disorders. This study introduces a framework for QSM and demonstrates calculation of reproducible and orientation-independent susceptibility maps from GRE data acquired at 3T. The potential of these susceptibility maps to perform anatomical imaging is investigated, as well as the ability to measure the venous blood oxygen saturation level in large vessels, and to assess the local tissue iron concentration. In order to take into account diamagnetic susceptibility contributions induced by myelin, a correction scheme for susceptibility based iron estimation is demonstrated. The findings suggest that susceptibility contrast, and therewith also phase contrast, are not only linked to the storage iron concentration but are also significantly influenced by other sources such as myelin. After myelin correction the linear dependence between magnetic susceptibilities and previously published iron concentrations from post mortem studies was significantly improved. Finally, a comparison between susceptibility maps and processed phase images indicated that caution should be exercised when drawing conclusions about iron concentrations when directly assessing processed phase information.

Microdevice's susceptibility difference based MRI positioning system, a preliminary investigation

A positioning technique for an endovascular microdevice propelled by magnetic force inside a magnetic resonance imaging (MRI) system is being developed. Positioning options are presented and a magnetic positioning technique is described in more details. Since a magnetic positioning system is deeply dependent on the quality of the measurement modality, we describe the main magnetic field measurement techniques that can be used inside an MRI. Finally, we propose a magnetic positioning system using MRI phase images to measure the magnetic distortion induced by the ferromagnetic body. Positioning results on a 1010/1020 carbon steel, 1.5875 mm diameter sphere with gradient echo phase images are presented.

Magnetic susceptibility quantitation with MRI by solving boundary value problems

Magnetic susceptibility measurement is of considerable research interest in MRI and MRS. A rigorous method was previously developed to quantify the susceptibility of an arbitrarily shaped uniform object in an inhomogeneous external field. However, it requires using the field distribution information on a spherical surface or shell in the surrounding homogeneous medium enclosing the object. In this work, a new approach was developed through solving the boundary value problems of the Laplace equation, which has an advantage that the boundary providing the necessary field distribution information can have an arbitrary shape. This method has been validated on rectangular boundaries with both numerical simulation as well as experimental data. It has also been realized that MRI provides an experimental means of solving some boundary value problems of partial differential equations, if proper boundary condition can be set up.

Averaging of harmonic physical fields over an annular region enclosing field sources

Fields such as temperature, current density, and static electromagnetic fields in regions with no field sources are harmonic functions that satisfy the Laplace equation. Such functions on a sphere have a well-known mean value property. A new mean value property is derived for fields that are harmonic on an annular region, with the field sources enclosed by the inner boundary. Some examples are discussed.

Magnetic susceptibility quantification for arbitrarily shaped objects in inhomogeneous fields

Magnetic susceptibility measurement has wide-ranging applications in MR technical development and medical applications. A general susceptibility quantitation method for objects of arbitrary shapes in inhomogeneous magnetic fields is presented in this study. Based on the mean value properties of magnetic fields, the polarizing magnetic field at the location of interest inside an object can be exactly obtained in situ from the field values on a spherical surface enclosing the object. With numerical computation of the self-demagnetizing field and correction of contact shifts, magnetic susceptibilities were quantitatively measured for CuSO(4) phantoms based on their MR gradient echo phase maps.

Significant precision improvement for temperature mapping

MR temperature measurements are important for applications such as the evaluation of thermal therapies and radiofrequency (RF) coil heating effects. In this work the spherical mean value (SMV) method has been applied to significantly improve the precision of MR temperature mapping in a homogeneous gel phantom. Temperature-increase maps of the phantom were obtained with three-dimensional (3D) MR phase difference mapping after heating with the RF coil. The temperature-increase distribution in most regions in the phantom is a harmonic function with the mean value property. Based on this property, the precision of temperature-increase maps was improved up to sixfold with the SMV method. Comparison of this method with conventional smoothing, further precision improvement, and the in vivo application of the SMV method are discussed.