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, B₀, 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. Magn Reson Med 61:196–204, 2009. © 2008 Wiley‐Liss, Inc.     

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. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.     

Improving susceptibility mapping using a threshold‐based K‐space/image domain iterative reconstruction approach

To improve susceptibility quantification, a threshold‐based k‐space/image domain iterative approach that uses geometric information from the susceptibility map itself as a constraint to overcome the ill‐posed nature of the inverse filter is introduced. Simulations were used to study the accuracy of the method and its robustness in the presence of noise. In vivo data were processed and analyzed using this method. Both simulations and in vivo results show that most streaking artifacts inside the susceptibility map caused by the ill‐defined inverse filter were suppressed by the iterative approach. In simulated data, the bias toward lower mean susceptibility values inside vessels has been shown to decrease from around 10% to 2% when choosing an appropriate threshold value for the proposed iterative method. Typically, three iterations are sufficient for this approach to converge and this process takes less than 30 s to process a 512 × 512 × 256 dataset. This iterative method improves quantification of susceptibility inside vessels and reduces streaking artifacts throughout the brain for data collected from a single‐orientation acquisition. This approach has been applied to vessels alone as well as to vessels and other structures with lower susceptibility to generate whole brain susceptibility maps with significantly reduced streaking artifacts. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc.     

Reconstruction of the orientation distribution function in single‐ and multiple‐shell q‐ball imaging within constant solid angle

q‐Ball imaging is a high‐angular‐resolution diffusion imaging technique that has been proven very successful in resolving multiple intravoxel fiber orientations in MR images. The standard computation of the orientation distribution function (the probability of diffusion in a given direction) from q‐ball data uses linear radial projection, neglecting the change in the volume element along each direction. This results in spherical distributions that are different from the true orientation distribution functions. For instance, they are neither normalized nor as sharp as expected and generally require postprocessing, such as artificial sharpening. In this paper, a new technique is proposed that, by considering the solid angle factor, uses the mathematically correct definition of the orientation distribution function and results in a dimensionless and normalized orientation distribution function expression. Our model is flexible enough so that orientation distribution functions can be estimated either from single q‐shell datasets or by exploiting the greater information available from multiple q‐shell acquisitions. We show that the latter can be achieved by using a more accurate multiexponential model for the diffusion signal. The improved performance of the proposed method is demonstrated on artificial examples and high‐angular‐resolution diffusion imaging data acquired on a 7‐T magnet. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Susceptibility mapping in the human brain using threshold‐based k‐space division

A method for calculating quantitative three‐dimensional susceptibility maps from field measurements acquired using gradient echo imaging at high field is presented. This method is based on division of the three‐dimensional Fourier transforms of high‐pass‐filtered field maps by a simple function that is the Fourier transform of the convolution kernel linking field and susceptibility, and uses k‐space masking to avoid noise enhancement in regions where this function is small. Simulations were used to show that the method can be applied to data acquired from objects that are oriented at one angle or multiple angles with respect to the applied field and that the use of multiple orientations improves the quality of the calculated susceptibility maps. As part of this work, we developed an improved approach for high‐pass filtering of field maps, based on using an arrangement of dipoles to model the fields generated by external structures. This approach was tested on simulated field maps from the substantia nigra and red nuclei. Susceptibility mapping was successfully applied to experimental measurements on a structured phantom and then used to make measurements of the susceptibility of the red nuclei and substantia nigra in healthy subjects at 3 and 7 T. Magn Reson Med 63:1292–1304, 2010. © 2010 Wiley‐Liss, Inc.     

Magnetic susceptibility mapping of brain tissue in vivo using MRI phase data

Phase images in susceptibility‐weighted MRI of brain provide excellent contrast. However, the phase is affected by tissue geometry and orientation relative to the main magnetic field (B₀), and phase changes extend beyond areas of altered susceptibility. Magnetic susceptibility, on the other hand, is an intrinsic tissue property, closely reflecting tissue composition. Therefore, recently developed inverse Fourier‐based methods were applied to calculate susceptibility maps from high‐resolution phase images acquired at a single orientation at 7 T in the human brain (in vivo and fixed) and at 11.7 T in fixed marmoset brain. In susceptibility images, the contrast of cortical layers was more consistent than in phase images and was independent of the structures' orientation relative to B₀. The contrast of iron‐rich deep‐brain structures (red nucleus and substantia nigra) in susceptibility images agreed more closely with iron‐dominated R images than the phase image contrast, which extended outside the structures. The mean susceptibility in these regions was significantly correlated with their estimated iron content. Susceptibility maps calculated using this method overcome the orientation‐dependence and non‐locality of phase image contrast and seem to reflect underlying tissue composition. Susceptibility images should be easier to interpret than phase images and could improve our understanding of the sources of susceptibility contrast. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

The influence of radial undersampling schemes on compressed sensing reconstruction in breast MRI

Fast imaging applications in magnetic resonance imaging (MRI) frequently involve undersampling of k‐space data to achieve the desired temporal resolution. However, high temporal resolution images generated from undersampled data suffer from aliasing artifacts. In radial k‐space sampling, this manifests as undesirable streaks that obscure image detail. Compressed sensing reconstruction has been shown to reduce such streak artifacts, based on the assumption of image sparsity. Here, compressed sensing is implemented with three different radial sampling schemes (golden‐angle, bit‐reversed, and random sampling), which are compared over a range of spatiotemporal resolutions. The sampling methods are implemented in static scenarios where different undersampling patterns could be compared. Results from point spread function studies, simulations, phantom and in vivo experiments show that the choice of radial sampling pattern influences the quality of the final image reconstructed by the compressed sensing algorithm. While evenly undersampled radial trajectories are best for specific temporal resolutions, golden‐angle radial sampling results in the least overall error when various temporal resolutions are considered. Reduced temporal fluctuations from aliasing artifacts in golden‐angle sampling translates to improved compressed sensing reconstructions overall. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.     

Spectral decomposition of susceptibility artifacts for spectral‐spatial radiofrequency pulse design

Susceptibility induced signal loss is a limitation in gradient echo functional MRI. The through‐plane artifact in axial slices is particularly problematic due to the inferior position of air cavities in the brain. Spectral‐spatial radiofrequency pulses have recently been shown to reduce signal loss in a single excitation. The pulses were successfully demonstrated assuming a linear relationship between susceptibility gradient and frequency, however, the exact frequency and spatial distribution of the susceptibility gradient in the brain is unknown. We present a spiral spectroscopic imaging sequence with a time‐shifted radiofrequency pulse that can spectrally decompose the through‐plane susceptibility gradient for spectral‐spatial radiofrequency pulse design. Maps of the through‐plane susceptibility gradient as a function of frequency were generated for the human brain at 3T. We found that the linear relationship holds well for the whole brain with an optimal slope of ?1.0 μT/m/Hz. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.     

An efficient gridding reconstruction method for multishot non‐Cartesian imaging with correction of off‐resonance artifacts

An efficient iterative gridding reconstruction method with correction of off‐resonance artifacts was developed, which is especially tailored for multiple‐shot non‐Cartesian imaging. The novelty of the method lies in that the transformation matrix for gridding (T) was constructed as the convolution of two sparse matrices, among which the former is determined by the sampling interval and the spatial distribution of the off‐resonance frequencies and the latter by the sampling trajectory and the target grid in the Cartesian space. The resulting T matrix is also sparse and can be solved efficiently with the iterative conjugate gradient algorithm. It was shown that, with the proposed method, the reconstruction speed in multiple‐shot non‐Cartesian imaging can be improved significantly while retaining high reconstruction fidelity. More important, the method proposed allows tradeoff between the accuracy and the computation time of reconstruction, making customization of the use of such a method in different applications possible. The performance of the proposed method was demonstrated by numerical simulation and multiple‐shot spiral imaging on rat brain at 4.7 T. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

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. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.     

Bayesian algorithm using spatial priors for multiexponential T(2) relaxometry from multiecho spin echo MRI

Multiexponential T₂ relaxometry is a powerful research tool for detecting brain structural changes due to demyelinating diseases such as multiple sclerosis. However, because of unusually high signal‐to‐noise ratio requirement compared with other MR modalities and ill‐posedness of the underlying inverse problem, the T₂ distributions obtained with conventional approaches are frequently prone to noise effects. In this article, a novel multivoxel Bayesian algorithm using spatial prior information is proposed. This prior takes into account the expectation that volume fractions and T₂ relaxation times of tissue compartments change smoothly within coherent brain regions. Three‐dimensional multiecho spin echo MRI data were collected from five healthy volunteers at 1.5 T and myelin water fraction maps were obtained using the conventional and proposed algorithms. Compared with the conventional method, the proposed method provides myelin water fraction maps with improved depiction of brain structures and significantly lower coefficients of variance in white matter. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.     

Three‐dimensional MR‐encephalography: Fast volumetric brain imaging using rosette trajectories

MR‐Encephalography (MREG) is a technique that allows real time observation of functional changes in the brain that appears within 100 msec. The high sampling rate is achieved at the cost of some spatial resolution. The article describes a novel imaging method for fast three‐dimensional‐MR‐encephalography whole brain coverage based on rosette trajectories and the use of multiple small receiver coils. The technique allows the observation of changes in brain physiology at very high temporal resolution. A highly undersampled three‐dimensional rosette trajectory is chosen, to perform single shot acquisition of k‐space data within 23 msec. By using a 32‐channel head coil array and regularized nonuniform Fourier transformation reconstruction, the spatial resolution is sufficient to detect even subtle centers of activation (e.g. human MT+). The method was applied to visual block design paradigms and compared with echo planar imaging‐based functional MRI. As a proof‐of‐principle of the method's ability to detect local differences in the hemodynamic response functions, the analyzed MR‐encephalography data revealed a spatially dependent delay of the arrival of the blood oxygenation level dependent response within the visual cortex. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

Optimal magnetic susceptibility matching in 3D

When an object is inserted into the strong homogeneous magnetic field of a magnetic resonance magnet, its intrinsic relative susceptibility can cause unwanted local magnetic field inhomogeneities in the space surrounding the object. As is known, this effect can be partially countered by selectively adding material layers with opposing sign in susceptibility to the part. The determination of an optimal magnetic susceptibility distribution is an inverse problem, in which the susceptibility‐induced inhomogeneity of the magnetic field inside a region of interest is reduced by redistributing the placement of materials in the design domain. This article proposes an efficient numerical topology optimization method for obtaining an optimal magnetic susceptibility distribution, in particular, for which the induced spatial magnetic field inhomogeneity is minimized. Using a material density function as a design variable, the value of the magnetic field inside a computational domain is determined using a finite element method. The first‐order sensitivity of the objective function is calculated using an adjoint equation method. Numerical examples on a variety of design domain geometries illustrate the effectiveness of the optimization method. The method is of specific interest for the design of interventional magnetic resonance devices. It is a particularly useful method if passive shimming of magnetic resonance equipment is aimed for. Magn Reson Med 69:1146–1156, 2013. © 2012 Wiley Periodicals, Inc.     

Correlation methods for the centering, rotation, and alignment of functional brain images

Simple methods are described using correlation analysis to rotate functional brain images to a standard vertical orientation, identify the antero-posterior centerline, and align multiple images from the same brain level. Image rotation and centering are performed by determining the angle of rotation and centerline coordinate that result in maximal left-right correlation. Testing of this method on sets of multiple images acquired simultaneously through different brain levels suggests that the optimal rotation can be determined within 1 degree and the centerline within 0.3 mm. Spatial alignment of two or more images from the same brain level of a single subject is accomplished by finding the translation and rotation that yield the highest correlation between the images. Testing of the alignment method on sets of simultaneously acquired images at multiple brain levels suggests that the optimal translation can be determined within 0.45-0.69 mm and the optimal rotation within 0.8 degrees. These methods are completely objective and can easily be automated.     

Improved temporal resolution in cardiac imaging using through‐time spiral GRAPPA

Previous work has shown that the use of radial GRAPPA for the reconstruction of undersampled real‐time free‐breathing cardiac data allows for frame rates of up to 30 images/s. It is well known that the spiral trajectory offers a higher scan efficiency compared to radial trajectories. For this reason, we have developed a novel through‐time spiral GRAPPA method and demonstrate its application to real‐time cardiac imaging. By moving from the radial trajectory to the spiral trajectory, the temporal resolution can be further improved at lower acceleration factors compared to radial GRAPPA. In addition, the image quality is improved compared to those generated using the radial trajectory due to the lower acceleration factor. Here, we show that 2D frame rates of up to 56 images/s can be achieved using this parallel imaging method with the spiral trajectory. Magn Reson Med, 2011. © 2011 Wiley Periodicals, Inc.     

Combination of complex‐based and magnitude‐based multiecho water‐fat separation for accurate quantification of fat‐fraction

Multipoint water–fat separation techniques rely on different water–fat phase shifts generated at multiple echo times to decompose water and fat. Therefore, these methods require complex source images and allow unambiguous separation of water and fat signals. However, complex‐based water–fat separation methods are sensitive to phase errors in the source images, which may lead to clinically important errors. An alternative approach to quantify fat is through “magnitude‐based” methods that acquire multiecho magnitude images. Magnitude‐based methods are insensitive to phase errors, but cannot estimate fat‐fraction greater than 50%. In this work, we introduce a water–fat separation approach that combines the strengths of both complex and magnitude reconstruction algorithms. A magnitude‐based reconstruction is applied after complex‐based water–fat separation to removes the effect of phase errors. The results from the two reconstructions are then combined. We demonstrate that using this hybrid method, 0–100% fat‐fraction can be estimated with improved accuracy at low fat‐fractions. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

Echo‐planar imaging with prospective slice‐by‐slice motion correction using active markers

Head motion is a fundamental problem in functional magnetic resonance imaging and is often a limiting factor in its clinical implementation. This work presents a rigid‐body motion correction strategy for echo‐planar imaging sequences that uses micro radiofrequency coil “active markers” for real‐time, slice‐by‐slice prospective correction. Before the acquisition of each echo‐planar imaging‐slice, a short tracking pulse‐sequence measures the positions of three active markers integrated into a headband worn by the subject; the rigid‐body transformation that realigns these markers to their initial positions is then fed back to dynamically update the scan‐plane, maintaining it at a fixed orientation relative to the head. Using this method, prospectively‐corrected echo‐planar imaging time series are acquired on volunteers performing in‐plane and through‐plane head motions, with results demonstrating increased image stability over conventional retrospective image‐realignment. The benefit of this improved image stability is assessed in a blood oxygenation level dependent functional magnetic resonance imaging application. Finally, a non‐rigid‐body distortion‐correction algorithm is introduced to reduce the remaining signal variation. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

An improved coverage and spatial resolution—using dual injection dynamic contrast‐enhanced (ICE‐DICE) MRI: A novel dynamic contrast‐enhanced technique for cerebral tumors

A new dual temporal resolution‐based, high spatial resolution, pharmacokinetic parametric mapping method is described ‐ improved coverage and spatial resolution using dual injection dynamic contrast‐enhanced (ICE‐DICE) MRI. In a dual‐bolus dynamic contrast‐enhanced‐MRI acquisition protocol, a high temporal resolution prebolus is followed by a high spatial resolution main bolus to allow high spatial resolution parametric mapping for cerebral tumors. The measured plasma concentration curves from the dual‐bolus data were used to reconstruct a high temporal resolution arterial input function. The new method reduces errors resulting from uncertainty in the temporal alignment of the arterial input function, tissue response function, and sampling grid. The technique provides high spatial resolution 3D pharmacokinetic maps (voxel size 1.0 × 1.0 × 2.0 mm³) with whole brain coverage and greater parameter accuracy than that was possible with the conventional single temporal resolution methods. High spatial resolution imaging of brain lesions is highly desirable for small lesions and to support investigation of heterogeneity within pathological tissue and peripheral invasion at the interface between diseased and normal brain. The new method has the potential to be used to improve dynamic contrast‐enhanced‐MRI techniques in general. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.     

Quality assessment of high angular resolution diffusion imaging data using bootstrap on Q-ball reconstruction

Purpose:

To develop a bootstrap method to assess the quality of High Angular Resolution Diffusion Imaging (HARDI) data using Q‐Ball imaging (QBI) reconstruction.

Materials and Methods:

HARDI data were re‐shuffled using regular bootstrap with jackknife sampling. For each bootstrap dataset, the diffusion orientation distribution function (ODF) was estimated voxel‐wise using QBI reconstruction based on spherical harmonics functions. The reproducibility of the ODF was assessed using the Jensen‐Shannon divergence (JSD) and the angular confidence interval was derived for the first and the second ODF maxima. The sensitivity of the bootstrap method was evaluated on a human subject by adding synthetic noise to the data, by acquiring a map of image signal‐to‐noise ratio (SNR) and by varying the echo time and the b‐value.

Results:

The JSD was directly linked to the image SNR. The impact of echo times and b‐values was reflected by both the JSD and the angular confidence interval, proving the usefulness of the bootstrap method to evaluate specific features of HARDI data.

Conclusion:

The bootstrap method can effectively assess the quality of HARDI data and can be used to evaluate new hardware and pulse sequences, perform multifiber probabilistic tractography, and provide reliability metrics to support clinical studies. J. Magn. Reson. Imaging 2011;33:1194–1208. © 2011 Wiley‐Liss, Inc.