Quantitative susceptibility map reconstruction from MR phase data using bayesian regularization: validation and application to brain imaging

The diagnosis of many neurologic diseases benefits from the ability to quantitatively assess iron in the brain. Paramagnetic iron modifies the magnetic susceptibility causing magnetic field inhomogeneity in MRI. The local field can be mapped using the MR signal phase, which is discarded in a typical image reconstruction. The calculation of the susceptibility from the measured magnetic field is an ill-posed inverse problem. In this work, a bayesian regularization approach that adds spatial priors from the MR magnitude image is formulated for susceptibility imaging. Priors include background regions of known zero susceptibility and edge information from the magnitude image. Simulation and phantom validation experiments demonstrated accurate susceptibility maps free of artifacts. The ability to characterize iron content in brain hemorrhage was demonstrated on patients with cavernous hemangioma. Additionally, multiple structures within the brain can be clearly visualized and characterized. The technique introduces a new quantitative contrast in MRI that is directly linked to iron in the brain.

Morphology enabled dipole inversion for quantitative susceptibility mapping using structural consistency between the magnitude image and the susceptibility map

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.

Calculation of susceptibility through multiple orientation sampling (COSMOS): a method for conditioning the inverse problem from measured magnetic field map to susceptibility source image in MRI

Magnetic susceptibility differs among tissues based on their contents of iron, calcium, contrast agent, and other molecular compositions. Susceptibility modifies the magnetic field detected in the MR signal phase. The determination of an arbitrary susceptibility distribution from the induced field shifts is a challenging, ill-posed inverse problem. A method called "calculation of susceptibility through multiple orientation sampling" (COSMOS) is proposed to stabilize this inverse problem. The field created by the susceptibility distribution is sampled at multiple orientations with respect to the polarization field, B(0), and the susceptibility map is reconstructed by weighted linear least squares to account for field noise and the signal void region. Numerical simulations and phantom and in vitro imaging validations demonstrated that COSMOS is a stable and precise approach to quantify a susceptibility distribution using MRI.

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.

Morphology enabled dipole inversion (MEDI) from a single-angle acquisition: comparison with COSMOS in human brain imaging

Magnetic susceptibility varies among brain structures and provides insights into the chemical and molecular composition of brain tissues. However, the determination of an arbitrary susceptibility distribution from the measured MR signal phase is a challenging, ill-conditioned inverse problem. Although a previous method named calculation of susceptibility through multiple orientation sampling (COSMOS) has solved this inverse problem both theoretically and experimentally using multiple angle acquisitions, it is often impractical to carry out on human subjects. Recently, the feasibility of calculating the brain susceptibility distribution from a single-angle acquisition was demonstrated using morphology enabled dipole inversion (MEDI). In this study, we further improved the original MEDI method by sparsifying the edges in the quantitative susceptibility map that do not have a corresponding edge in the magnitude image. Quantitative susceptibility maps generated by the improved MEDI were compared qualitatively and quantitatively with those generated by calculation of susceptibility through multiple orientation sampling. The results show a high degree of agreement between MEDI and calculation of susceptibility through multiple orientation sampling, and the practicality of MEDI allows many potential clinical applications.

Nonlinear formulation of the magnetic field to source relationship for robust quantitative susceptibility mapping

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.

Clinical quantitative susceptibility mapping (QSM): Biometal imaging and its emerging roles in patient care

Quantitative susceptibility mapping (QSM) has enabled magnetic resonance imaging (MRI) of tissue magnetic susceptibility to advance from simple qualitative detection of hypointense blooming artifacts to precise quantitative measurement of spatial biodistributions. QSM technology may be regarded to be sufficiently developed and validated to warrant wide dissemination for clinical applications of imaging isotropic susceptibility, which is dominated by metals in tissue, including iron and calcium. These biometals are highly regulated as vital participants in normal cellular biochemistry, and their dysregulations are manifested in a variety of pathologic processes. Therefore, QSM can be used to assess important tissue functions and disease. To facilitate QSM clinical translation, this review aims to organize pertinent information for implementing a robust automated QSM technique in routine MRI practice and to summarize available knowledge on diseases for which QSM can be used to improve patient care. In brief, QSM can be generated with postprocessing whenever gradient echo MRI is performed. QSM can be useful for diseases that involve neurodegeneration, inflammation, hemorrhage, abnormal oxygen consumption, substantial alterations in highly paramagnetic cellular iron, bone mineralization, or pathologic calcification; and for all disorders in which MRI diagnosis or surveillance requires contrast agent injection. Clinicians may consider integrating QSM into their routine imaging practices by including gradient echo sequences in all relevant MRI protocols.

LEVEL OF EVIDENCE

1 Technical Efficacy: Stage 5 J. Magn. Reson. Imaging 2017;46:951-971.

Nonlinear regularization for per voxel estimation of magnetic susceptibility distributions from MRI field maps

Magnetic susceptibility is an important physical property of tissues, and can be used as a contrast mechanism in magnetic resonance imaging (MRI). Recently, targeting contrast agents by conjugation with signaling molecules and labeling stem cells with contrast agents have become feasible. These contrast agents are strongly paramagnetic, and the ability to quantify magnetic susceptibility could allow accurate measurement of signaling and cell localization. Presented here is a technique to estimate arbitrary magnetic susceptibility distributions by solving an ill-posed inversion problem from field maps obtained in an MRI scanner. Two regularization strategies are considered: conventional Tikhonov regularization and a sparsity promoting nonlinear regularization using the l(1) norm. Proof of concept is demonstrated using numerical simulations, phantoms, and in a stroke model in a rat. Initial experience indicates that the nonlinear regularization better suppresses noise and streaking artifacts common in susceptibility estimation.

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.

Cerebral microbleeds: burden assessment by using quantitative susceptibility mapping

PURPOSE

To assess quantitative susceptibility mapping (QSM) for reducing the inconsistency of standard magnetic resonance (MR) imaging sequences in measurements of cerebral microbleed burden.

MATERIALS AND METHODS

This retrospective study was HIPAA compliant and institutional review board approved. Ten patients (5.6%) were selected from among 178 consecutive patients suspected of having experienced a stroke who were imaged with a multiecho gradient-echo sequence at 3.0 T and who had cerebral microbleeds on T2*-weighted images. QSM was performed for various ranges of echo time by using both the magnitude and phase components in the morphology-enabled dipole inversion method. Cerebral microbleed size was measured by two neuroradiologists on QSM images, T2*-weighted images, susceptibility-weighted (SW) images, and R2* maps calculated by using different echo times. The sum of susceptibility over a region containing a cerebral microbleed was also estimated on QSM images as its total susceptibility. Measurement differences were assessed by using the Student t test and the F test; P < .05 was considered to indicate a statistically significant difference.

RESULTS

When echo time was increased from approximately 20 to 40 msec, the measured cerebral microbleed volume increased by mean factors of 1.49 ± 0.86 (standard deviation), 1.64 ± 0.84, 2.30 ± 1.20, and 2.30 ± 1.19 for QSM, R2*, T2*-weighted, and SW images, respectively (P < .01). However, the measured total susceptibility with QSM did not show significant change over echo time (P = .31), and the variation was significantly smaller than any of the volume increases (P < .01 for each).

CONCLUSION

The total susceptibility of a cerebral microbleed measured by using QSM is a physical property that is independent of echo time.

MEDI+0: Morphology enabled dipole inversion with automatic uniform cerebrospinal fluid zero reference for quantitative susceptibility mapping

PURPOSE

To develop a quantitative susceptibility mapping (QSM) method with a consistent zero reference using minimal variation in cerebrospinal fluid (CSF) susceptibility.

THEORY AND METHODS

The ventricular CSF was automatically segmented on the R2* map. An L₂ -regularization was used to enforce CSF susceptibility homogeneity within the segmented region, with the averaged CSF susceptibility as the zero reference. This regularization for CSF homogeneity was added to the model used in a prior QSM method (morphology enabled dipole inversion [MEDI]). Therefore, the proposed method was referred to as MEDI+0 and compared with MEDI in a numerical simulation, in multiple sclerosis (MS) lesions, and in a reproducibility study in healthy subjects.

RESULTS

In both the numerical simulations and in vivo experiments, MEDI+0 not only decreased the susceptibility variation within the ventricular CSF, but also suppressed the artifact near the lateral ventricles. In the simulation, MEDI+0 also provided more accurate quantification compared to MEDI in the globus pallidus, substantia nigra, corpus callosum, and internal capsule. MEDI+0 measurements of MS lesion susceptibility were in good agreement with those obtained by MEDI. Finally, both MEDI+0 and MEDI showed good and similar intrasubject reproducibility.

CONCLUSION

QSM with a minimal variation in ventricular CSF is viable to provide a consistent zero reference while improving image quality. Magn Reson Med 79:2795-2803, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Quantitative mapping of cerebral metabolic rate of oxygen (CMRO2 ) using quantitative susceptibility mapping (QSM)

PURPOSE

To quantitatively map cerebral metabolic rate of oxygen ( CMRO2) and oxygen extraction fraction ( OEF) in human brains using quantitative susceptibility mapping (QSM) and arterial spin labeling-measured cerebral blood flow (CBF) before and after caffeine vasoconstriction.

METHODS

Using the multiecho, three-dimensional gradient echo sequence and an oral bolus of 200 mg caffeine, whole brain CMRO2 and OEF were mapped at 3-mm isotropic resolution on 13 healthy subjects. The QSM-based CMRO2 was compared with an R2*-based CMRO2 to analyze the regional consistency within cortical gray matter (CGM) with the scaling in the R2* method set to provide same total CMRO2 as the QSM method for each subject.

RESULTS

Compared to precaffeine, susceptibility increased (5.1 ± 1.1 ppb; P < 0.01) and CBF decreased (-23.6 ± 6.7 ml/100 g/min; P < 0.01) at 25-min postcaffeine in CGM. This corresponded to a CMRO2 of 153.0 ± 26.4 μmol/100 g/min with an OEF of 33.9 ± 9.6% and 54.5 ± 13.2% (P < 0.01) pre- and postcaffeine, respectively, at CGM, and a CMRO2 of 58.0 ± 26.6 μmol/100 g/min at white matter. CMRO2 from both QSM- and R2*-based methods showed good regional consistency (P > 0.05), but quantitation of R2*-based CMRO2 required an additional scaling factor.

CONCLUSION

QSM can be used with perfusion measurements pre- and postcaffeine vascoconstriction to map CMRO2 and OEF.

Respiratory and cardiac self-gated free-breathing cardiac CINE imaging with multiecho 3D hybrid radial SSFP acquisition

A respiratory and cardiac self-gated free-breathing three-dimensional cine steady-state free precession imaging method using multiecho hybrid radial sampling is presented. Cartesian mapping of the k-space center along the slice encoding direction provides intensity-weighted position information, from which both respiratory and cardiac motions are derived. With in plan radial sampling acquired at every pulse repetition time, no extra scan time is required for sampling the k-space center. Temporal filtering based on density compensation is used for radial reconstruction to achieve high signal-to-noise ratio and contrast-to-noise ratio. High correlation between the self-gating signals and external gating signals is demonstrated. This respiratory and cardiac self-gated, free-breathing, three-dimensional, radial cardiac cine imaging technique provides image quality comparable to that acquired with the multiple breath-hold two-dimensional Cartesian steady-state free precession technique in short-axis, four-chamber, and two-chamber orientations. Functional measurements from the three-dimensional cardiac short axis cine images are found to be comparable to those obtained using the standard two-dimensional technique.

Flow compensated quantitative susceptibility mapping for venous oxygenation imaging

PURPOSE

Venous blood oxygen saturation is an indicator of brain oxygen consumption and can be measured directly from quantitative susceptibility mapping (QSM) by deconvolving the MR phase signal. However, accurate estimation of the susceptibility of blood may be affected by flow induced phase in the presence of imaging gradient and the inhomogeneous susceptibility field gradient. The purpose of this study is to correct the flow induced error in QSM for improved venous oxygenation quantification.

METHODS

Flow compensation is proposed for QSM by using a fully flow compensated multi-echo gradient echo sequence for data acquisition. A quadratic fit of the phase with respect to echo time is employed for the flow phase in the presence of inhomogeneity field gradients. Phantom and in vivo experiments were carried out to validate the proposed method.

RESULTS

Phantom experiments demonstrated reduced error in the estimated field map and susceptibility map. Initial data in in vivo human imaging demonstrated improvements in the quantitative susceptibility map and in the estimated venous oxygen saturation values.

CONCLUSION

Flow compensated multi-echo acquisition and an adaptive-quadratic fit of the phase images improves the quantitative susceptibility map of blood flow. The improved vein susceptibility enables in vivo measurement of venous oxygen saturation throughout the brain.

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.

Reducing the object orientation dependence of susceptibility effects in gradient echo MRI through quantitative susceptibility mapping

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. 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 quantitative susceptibility mapping, 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 quantitative susceptibility mapping, these blooming artifacts, including their dependence on object orientation, were reduced, and the material susceptibilities were quantified.

Preconditioned total field inversion (TFI) method for quantitative susceptibility mapping

PURPOSE

To investigate systematic errors in traditional quantitative susceptibility mapping (QSM) where background field removal and local field inversion (LFI) are performed sequentially, to develop a total field inversion (TFI) QSM method to reduce these errors, and to improve QSM quality in the presence of large susceptibility differences.

THEORY AND METHODS

The proposed TFI is a single optimization problem which simultaneously estimates the background and local fields, preventing error propagation from background field removal to QSM. To increase the computational speed, a new preconditioner is introduced and analyzed. TFI is compared with the traditional combination of background field removal and LFI in a numerical simulation and in phantom, 5 healthy subjects, and 18 patients with intracerebral hemorrhage.

RESULTS

Compared with the traditional method projection onto dipole fields+LFI, preconditioned TFI substantially reduced error in QSM along the air-tissue boundaries in simulation, generated high-quality in vivo QSM within similar processing time, and suppressed streaking artifacts in intracerebral hemorrhage QSM. Moreover, preconditioned TFI was capable of generating QSM for the entire head including the brain, air-filled sinus, skull, and fat.

CONCLUSION

Preconditioned total field inversion improves the accuracy of QSM over the traditional method where background and local fields are separately estimated. Magn Reson Med 78:303-315, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Accuracy of the morphology enabled dipole inversion (MEDI) algorithm for quantitative susceptibility mapping in MRI

Determining the susceptibility distribution from the magnetic field measured in a magnetic resonance (MR) scanner is an ill-posed inverse problem, because of the presence of zeroes in the convolution kernel in the forward problem. An algorithm called morphology enabled dipole inversion (MEDI), which incorporates spatial prior information, has been proposed to generate a quantitative susceptibility map (QSM). The accuracy of QSM can be validated experimentally. However, there is not yet a rigorous mathematical demonstration of accuracy for a general regularized approach or for MEDI specifically. The error in the susceptibility map reconstructed by MEDI is expressed in terms of the acquisition noise and the error in the spatial prior information. A detailed analysis demonstrates that the error in the susceptibility map reconstructed by MEDI is bounded by a linear function of these two error sources. Numerical analysis confirms that the error of the susceptibility map reconstructed by MEDI is on the same order of the noise in the original MRI data, and comprehensive edge detection will lead to reduced model error in MEDI. Additional phantom validation and human brain imaging demonstrated the practicality of the MEDI method.

Age and sex related differences in subcortical brain iron concentrations among healthy adults

Age and sex can influence brain iron levels. We studied the influence of these variables on deep gray matter magnetic susceptibilities. In 183 healthy volunteers (44.7 ± 14.2 years, range 20-69, ♀ 49%), in vivo quantitative susceptibility mapping (QSM) at 1.5T was performed to estimate brain iron accumulation in the following regions of interest (ROIs): caudate nucleus (Cd), putamen (Pt), globus pallidus (Gp), thalamus (Th), pulvinar (Pul), red nucleus (Rn), substantia nigra (Sn) and the cerebellar dentate nuclei (Dn). We gauged the influence of age and sex on magnetic susceptibility by specifying a series of structural equation models. The distributions of susceptibility varied in degree across the structures, conforming to histologic findings (Hallgren and Sourander, 1958), with the highest degree of susceptibility in the Gp and the lowest in the Th. Iron increase correlated across several ROIs, which may reflect an underlying age-related process. Advanced age was associated with a particularly strong linear rise of susceptibility in the striatum. Nonlinear age trends were found in the Rn, where they were the most pronounced, followed by the Pul and Sn, while minimal nonlinear trends were observed for the Pt, Th, and Dn. Moreover, sex related variations were observed, so that women showed lower levels of susceptibility in the Sn after accounting for age. Regional susceptibility of the Pul increased linearly with age in men but exhibited a nonlinear association with age in women with a leveling off starting from midlife. Women expected to be post menopause (+51 years) showed lower total magnetic susceptibility in the subcortical gray matter. The current report not only is consistent with previous reports of age related variations of brain iron, but also adds to the current knowledge by reporting age-related changes in less studied, smaller subcortical nuclei. This is the first in-vivo report to show lower total subcortical brain iron levels selectively in women from midlife, compared to men and younger women. These results encourage further assessment of sex differences in brain iron. We anticipate that age and sex are important co-factors to take into account when establishing a baseline level for differentiating pathologic neurodegeneration from healthy aging. The variations in regional susceptibility reported herein should be evaluated further using a longitudinal study design to determine within-person changes in aging.

Magnetic susceptibility anisotropy: cylindrical symmetry from macroscopically ordered anisotropic molecules and accuracy of MRI measurements using few orientations

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.

Simultaneous phase unwrapping and removal of chemical shift (SPURS) using graph cuts: application in quantitative susceptibility mapping

Quantitative susceptibility mapping (QSM) is a magnetic resonance imaging technique that reveals tissue magnetic susceptibility. It relies on having a high quality field map, typically acquired with a relatively long echo spacing and long final TE. Applications of QSM outside the brain require the removal of fat contributions to the total signal phase. However, current water/fat separation methods applied on typical data acquired for QSM suffer from three issues: inadequacy when using large echo spacing, over-smoothing of the field maps and high computational cost. In this paper, the general phase wrap and chemical shift problem is formulated using a single species fitting and is solved using graph cuts with conditional jump moves. This method is referred as simultaneous phase unwrapping and removal of chemical shift (SPURS). The result from SPURS is then used as the initial guess for a voxel-wise iterative decomposition of water and fat with echo asymmetric and least-squares estimation (IDEAL). The estimated 3-D field maps are used to compute QSM in body regions outside of the brain, such as the liver. Experimental results show substantial improvements in field map estimation, water/fat separation and reconstructed QSM compared to two existing water/fat separation methods on 1.5T and 3T magnetic resonance human data with long echo spacing and rapid field map variation.

In vivo quantification of contrast agent concentration using the induced magnetic field for time-resolved arterial input function measurement with MRI

For pharmacokinetic modeling of tissue physiology, there is great interest in measuring the arterial input function (AIF) from dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) using paramagnetic contrast agents. Due to relaxation effects, the measured signal is a nonlinear function of the injected contrast agent concentration and depends on sequence parameters, system calibration, and time-of-flight effects, making it difficult to accurately measure the AIF during the first pass. Paramagnetic contrast agents also affect susceptibility and modify the magnetic field in proportion to their concentration. This information is contained in the MR signal phase which is discarded in a typical image reconstruction. However, quantifying AIF through contrast agent susceptibility induced phase changes is made difficult by the fact that the induced magnetic field is nonlocal and depends upon the contrast agent spatial distribution and thus on organ and vessel shapes. In this article, the contrast agent susceptibility was quantified through inversion of magnetic field shifts using a piece-wise constant model. Its feasibility is demonstrated by a determination of the AIF from the susceptibility-induced field changes of an intravenous bolus. After in vitro validation, a time-resolved two-dimensional (2D) gradient echo scan, triggered to diastole, was performed in vivo on the aortic arch during a bolus injection of 0.1 mmol/kg Gd-DTPA. An approximate geometrical model of the aortic arch constructed from the magnitude images was used to calculate the spatial variation of the field associated with the bolus. In 14 subjects, Gd concentration curves were measured dynamically (one measurement per heart beat) and indirectly validated by independent 2D cine phase contrast flow rate measurements. Flow rate measurements using indicator conservation with this novel quantitative susceptibility imaging technique were found to be in good agreement with those obtained from the cine phase contrast measurements in all subjects. Contrary to techniques that rely on intensity, the accuracy of this signal phase based method is insensitive to factors influencing signal intensity such as flip angle, coil sensitivity, relaxation changes, and time-of-flight effects extending the range of pulse sequences and contrast doses for which quantitative DCE-MRI can be applied.

Cerebral metabolic rate of oxygen (CMRO2 ) mapping by combining quantitative susceptibility mapping (QSM) and quantitative blood oxygenation level-dependent imaging (qBOLD)

PURPOSE

To map the cerebral metabolic rate of oxygen (CMRO₂ ) by estimating the oxygen extraction fraction (OEF) from gradient echo imaging (GRE) using phase and magnitude of the GRE data.

THEORY AND METHODS

3D multi-echo gradient echo imaging and perfusion imaging with arterial spin labeling were performed in 11 healthy subjects. CMRO₂ and OEF maps were reconstructed by joint quantitative susceptibility mapping (QSM) to process GRE phases and quantitative blood oxygen level-dependent (qBOLD) modeling to process GRE magnitudes. Comparisons with QSM and qBOLD alone were performed using ROI analysis, paired t-tests, and Bland-Altman plot.

RESULTS

The average CMRO₂ value in cortical gray matter across subjects were 140.4 ± 14.9, 134.1 ± 12.5, and 184.6 ± 17.9 μmol/100 g/min, with corresponding OEFs of 30.9 ± 3.4%, 30.0 ± 1.8%, and 40.9 ± 2.4% for methods based on QSM, qBOLD, and QSM+qBOLD, respectively. QSM+qBOLD provided the highest CMRO₂ contrast between gray and white matter, more uniform OEF than QSM, and less noisy OEF than qBOLD.

CONCLUSION

Quantitative CMRO₂ mapping that fits the entire complex GRE data is feasible by combining QSM analysis of phase and qBOLD analysis of magnitude.

Multiple sclerosis lesion geometry in quantitative susceptibility mapping (QSM) and phase imaging

PURPOSE

To demonstrate the phase and quantitative susceptibility mapping (QSM) patterns created by solid and shell spatial distributions of magnetic susceptibility in multiple sclerosis (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 Institutional Review Board (IRB)-approved MRI study to identify the 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.