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.

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.

Fast 3D contrast enhanced MRI of the liver using temporal resolution acceleration with constrained evolution reconstruction

Time-resolved imaging is crucial for the accurate diagnosis of liver lesions. Current contrast enhanced liver magnetic resonance imaging acquires a few phases in sequential breath-holds. The image quality is susceptible to bolus timing errors, which could result in missing the critical arterial phase. This impairs the detection of malignant tumors that are supplied primarily by the hepatic artery. In addition, the temporal resolution may be too low to reliably separate the arterial phase from the portal venous phase. In this study, a method called temporal resolution acceleration with constrained evolution reconstruction was developed with three-dimensional volume coverage and high-temporal frame rate. Data is acquired using a stack of spirals sampling trajectory combined with a golden ratio view order using an eight-channel coil array. Temporal frames are reconstructed from vastly undersampled data sets using a nonlinear inverse algorithm assuming that the temporal changes are small at short time intervals. Numerical and phantom experimental validation is presented. Preliminary in vivo results demonstrated high spatial resolution dynamic three-dimensional images of the whole liver with high frame rates, from which numerous subarterial phases could be easily identified retrospectively.

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.

Flip angle profile correction for T₁ and T₂ quantification with look-locker inversion recovery 2D steady-state free precession imaging

Fast methods using balanced steady-state free precession have been developed to reduce the scan time of T₁ and T₂ mapping. However, flip angle (FA) profiles created by the short radiofrequency pulses used in steady-state free precession deviate substantially from the ideal rectangular profile, causing T₁ and T₂ mapping errors. The purpose of this study was to develop a FA profile correction for T₁ and T₂ mapping with Look-Locker 2D inversion recovery steady-state free precession and to validate this method using 2D spin echo as a reference standard. Phantom studies showed consistent improvement in T₁ and T₂ accuracy using profile correction at multiple FAs. Over six human calves, profile correction provided muscle T₁ estimates with mean error ranging from excellent (-0.6%) at repetition time/FA = 18 ms/60° to acceptable (6.8%) at repetition time/FA = 4.9 ms/30°, while muscle T₂ estimates were less accurate with mean errors of 31.2% and 47.9%, respectively.

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.

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.

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 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.

A radial self-calibrated (RASCAL) generalized autocalibrating partially parallel acquisition (GRAPPA) method using weight interpolation

A generalized autocalibrating partially parallel acquisition (GRAPPA) method for radial k-space sampling is presented that calculates GRAPPA weights without synthesized or acquired calibration data. Instead, GRAPPA weights are fitted to the undersampled data as if they were the calibration data. Because the relative k-space shifts associated with these GRAPPA weights vary for a radial trajectory, new GRAPPA weights can be resampled for arbitrary shifts through interpolation, which are then used to generate missing projections between the acquired projections. The method is demonstrated in phantoms and in abdominal and brain imaging. Image quality is similar to radial GRAPPA using fully sampled calibration data, and improved relative to a previously described self-calibrated radial GRAPPA technique.

Three-dimensional flow-independent balanced steady-state free precession vessel wall MRI of the popliteal artery: preliminary experience and comparison with flow-dependent black-blood techniques

PURPOSE

To examine the feasibility of flow-independent T2-prepared inversion recovery (T2IR) black-blood (BB) magnetization preparation for three-dimensional (3D) balanced steady-state free precession (SSFP) vessel wall MRI of the popliteal artery, and to evaluate its performance relative to flow-dependent double inversion recovery (DIR), spatial presaturation (SPSAT), and motion-sensitizing magnetization preparation (MSPREP) BB techniques in healthy volunteers.

MATERIALS AND METHODS

Eleven subjects underwent 3D MRI at 1.5 Tesla with four techniques performed in a randomized order. Wall and lumen signal-to-noise ratio (SNR), wall-to-lumen contrast-to-noise ratio (CNR), vessel wall area, and lumen area were measured at proximal, middle, and distal locations of the imaged popliteal artery. Image quality scores based on wall visualization and degree of intraluminal artifacts were also obtained.

RESULTS

In the proximal region, DIR and SPSAT had higher wall SNR and wall-to-lumen CNR than both MSPREP and T2IR. In the middle and distal regions, DIR and SPSAT failed to provide effective blood suppression, whereas MSPREP and T2IR provided adequate black blood contrast with comparable wall-to-lumen CNR and image quality.

CONCLUSION

The feasibility of 3D SSFP imaging of the popliteal vessel wall using flow-independent T2IR was demonstrated with effective blood suppression and good vessel wall visualization. Although DIR and SPSAT are effective for thin slab imaging, MSPREP and T2IR are better suited for 3D thick slab imaging.

Z intensity-weighted position self-respiratory gating method for free-breathing 3D cardiac CINE imaging

A free-breathing 3D cine steady-state free precession (SSFP) technique was developed using the z intensity-weighted position (ZIP) which is the center of mass of a projection along the slice direction as a respiratory gating signal. The ZIP signal was continuously acquired using a slice encoded k-space center sampling in every TR. The performance of this gating method was compared with a method using the k-space center signal (KC) and with conventional 2D breath-hold cine SSFP in healthy subjects by measuring image quality and left ventricular function. The preliminary data obtained here demonstrated that the ZIP gating method provided superior respiratory motion artifact suppression when compared to the KC gating and provided left ventricular ejection fractions, and end-diastolic and end-systolic volumes similar to those obtained with the breath-hold 2D cine SSFP acquisition.

A fast Edge-preserving Bayesian reconstruction method for Parallel Imaging applications in cardiac MRI

Among recent parallel MR imaging reconstruction advances, a Bayesian method called Edge-preserving Parallel Imaging reconstructions with GRAph cuts Minimization (EPIGRAM) has been demonstrated to significantly improve signal-to-noise ratio when compared with conventional regularized sensitivity encoding method. However, EPIGRAM requires a large number of iterations in proportion to the number of intensity labels in the image, making it computationally expensive for high dynamic range images. The objective of this study is to develop a Fast EPIGRAM reconstruction based on the efficient binary jump move algorithm that provides a logarithmic reduction in reconstruction time while maintaining image quality. Preliminary in vivo validation of the proposed algorithm is presented for two-dimensional cardiac cine MR imaging and three-dimensional coronary MR angiography at acceleration factors of 2-4. Fast EPIGRAM was found to provide similar image quality to EPIGRAM and maintain the previously reported signal-to-noise ratio improvement over regularized sensitivity encoding method, while reducing EPIGRAM reconstruction time by 25-50 times.

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.

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.

Unambiguous identification of superparamagnetic iron oxide particles through quantitative susceptibility mapping of the nonlinear response to magnetic fields

Superparamagnetic iron oxide (SPIO) particles generate signal void regions on gradient echo images due to their strong magnetization. In practice, the signal void region might be indistinguishable from that generated by air. However, the response of SPIO to an externally applied magnetic field is nonlinear. Magnetization of SPIO saturates at around 1 T while magnetization of water and air increase linearly with field strength. Phantom experiment and mice experiments demonstrated the feasibility of a nonambiguous identification of superparamagnetic contrast agents.

Effect of blood flow on double inversion recovery vessel wall MRI of the peripheral arteries: quantitation with T2 mapping and comparison with flow-insensitive T2-prepared inversion recovery imaging

Blood suppression in the lower extremities using flow-reliant methods such as double inversion recovery may be problematic due to slow blood flow. T(2) mapping using fast spin echo (FSE) acquisition was utilized to quantitate the effectiveness of double inversion recovery blood suppression in 13 subjects and showed that 25 +/- 12% of perceived vessel wall pixels in the popliteal arteries contained artifactual blood signal. To overcome this problem, a flow-insensitive T(2)-prepared inversion recovery sequence was implemented and optimal timing parameters were calculated for FSE acquisition. Black blood vessel wall imaging of the popliteal and femoral arteries was performed using two-dimensional T(2)-prepared inversion recovery-FSE in the same 13 subjects. Comparison with two-dimensional double inversion recovery-FSE showed that T(2)-prepared inversion recovery-FSE reduced wall-mimicking blood artifacts that inflated double inversion recovery-FSE vessel wall area measurements in the popliteal artery.

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.

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.

Free-breathing 3-dimensional steady-state free precession coronary magnetic resonance angiography: comparison of four navigator gating techniques

This work compared the performance of four navigator gating algorithms [accept/reject (A/R), diminishing variance algorithm (DVA), phase ordering with automatic window selection (PAWS) and retrospective gating (RETRO)] in suppressing respiratory motion artifacts in free-breathing 3D balanced steady-state free precession coronary MRA. In 10 volunteers, the right coronary artery (RCA) or the left anterior descending artery (LAD) was imaged (both if time permitted) at 1.5 T with the four gating techniques in random order. Vessel signal, vessel contrast and motion suppression were scored by the consensus of two blinded readers. In 15 imaged vessels (nine RCA and six LAD), PAWS provided significantly better image quality than A/R (P<.05), DVA (P=.02) and RETRO (P=.002). While the quality difference between A/R and DVA was not statistically significant, both algorithms yielded significantly better image quality than RETRO. PAWS and DVA were the most efficient algorithms, providing an approximately 20% and 40% relative increase in average navigator efficiency compared to A/R and RETRO, respectively.