Off-resonance correction of MR images

Design and development of a novel flexible ultra-short echo time (FUSE) sequence

PURPOSE

To present the validation of a new Flexible Ultra-Short Echo time (FUSE) pulse sequence using a short-T2 phantom.

METHODS

FUSE was developed to include a range of RF excitation pulses, trajectories, dimensionalities, and long-T2 suppression techniques, enabling real-time interchangeability of acquisition parameters. Additionally, we developed an improved 3D deblurring algorithm to correct for off-resonance artifacts. Several experiments were conducted to validate the efficacy of FUSE, by comparing different approaches for off-resonance artifact correction, variations in RF pulse and trajectory combinations, and long-T2 suppression techniques. All scans were performed on a 3 T system using an in-house short-T2 phantom. The evaluation of results included qualitative comparisons and quantitative assessments of the SNR and contrast-to-noise ratio.

RESULTS

Using the capabilities of FUSE, we demonstrated that we could combine a shorter readout duration with our improved deblurring algorithm to effectively reduce off-resonance artifacts. Among the different RF and trajectory combinations, the spiral trajectory with the regular half-inc pulse achieves the highest SNRs. The dual-echo subtraction technique delivers better short-T2 contrast and superior suppression of water and agar signals, whereas the off-resonance saturation method successfully suppresses water and lipid signals simultaneously.

CONCLUSION

In this work, we have validated the use of our new FUSE sequence using a short T2 phantom, demonstrating that multiple UTE acquisitions can be achieved within a single sequence. This new sequence may be useful for acquiring improved UTE images and the development of UTE imaging protocols.

Off-resonance artifact correction for MRI: A review

In magnetic resonance imaging (MRI), inhomogeneity in the main magnetic field used for imaging, referred to as off-resonance, can lead to image artifacts ranging from mild to severe depending on the application. Off-resonance artifacts, such as signal loss, geometric distortions, and blurring, can compromise the clinical and scientific utility of MR images. In this review, we describe sources of off-resonance in MRI, how off-resonance affects images, and strategies to prevent and correct for off-resonance. Given recent advances and the great potential of low-field and/or portable MRI, we also highlight the advantages and challenges of imaging at low field with respect to off-resonance.

Deep residual network for off-resonance artifact correction with application to pediatric body MRA with 3D cones

PURPOSE

To enable rapid imaging with a scan time-efficient 3D cones trajectory with a deep-learning off-resonance artifact correction technique.

METHODS

A residual convolutional neural network to correct off-resonance artifacts (Off-ResNet) was trained with a prospective study of pediatric MRA exams. Each exam acquired a short readout scan (1.18 ms ± 0.38) and a long readout scan (3.35 ms ± 0.74) at 3 T. Short readout scans, with longer scan times but negligible off-resonance blurring, were used as reference images and augmented with additional off-resonance for supervised training examples. Long readout scans, with greater off-resonance artifacts but shorter scan time, were corrected by autofocus and Off-ResNet and compared with short readout scans by normalized RMS error, structural similarity index, and peak SNR. Scans were also compared by scoring on 8 anatomical features by two radiologists, using analysis of variance with post hoc Tukey's test and two one-sided t-tests. Reader agreement was determined with intraclass correlation.

RESULTS

The total scan time for long readout scans was on average 59.3% shorter than short readout scans. Images from Off-ResNet had superior normalized RMS error, structural similarity index, and peak SNR compared with uncorrected images across ±1 kHz off-resonance (P < .01). The proposed method had superior normalized RMS error over -677 Hz to +1 kHz and superior structural similarity index and peak SNR over ±1 kHz compared with autofocus (P < .01). Radiologic scoring demonstrated that long readout scans corrected with Off-ResNet were noninferior to short readout scans (P < .05).

CONCLUSION

The proposed method can correct off-resonance artifacts from rapid long-readout 3D cones scans to a noninferior image quality compared with diagnostically standard short readout scans.

Calibration-Free B0 Correction of EPI Data Using Structured Low Rank Matrix Recovery

We introduce a structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in echo planar imaging (EPI) MRI data. We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled Fourier measurements. The temporal profile at each pixel is modeled as a single exponential, which is exploited to fill in the missing entries. We show that the exponential behavior at each pixel, along with the spatial smoothness of the exponential parameters, can be exploited to derive a 3-D annihilation relation in the Fourier domain. This relation translates to a low rank property on a structured multi-fold Toeplitz matrix, whose entries correspond to the measured k-space samples. We introduce a fast two-step algorithm for the completion of the Toeplitz matrix from the available samples. In the first step, we estimate the null space vectors of the Toeplitz matrix using only its fully sampled rows. The null space is then used to estimate the signal subspace, which facilitates the efficient recovery of the time series of images. We finally demonstrate the proposed approach on spherical MR phantom data and human data and show that the artifacts are significantly reduced.

MR fingerprinting with simultaneous T1, T2, and fat signal fraction estimation with integrated B0 correction reduces bias in water T1 and T2 estimates

PURPOSE

MR fingerprinting (MRF) sequences permit efficient T₁ and T₂ estimation in cranial and extracranial regions, but these areas may include substantial fat signals that bias T₁ and T₂ estimates. MRI fat signal fraction estimation is also a topic of active research in itself, but may be complicated by B₀ heterogeneity and blurring during spiral k-space acquisitions, which are commonly used for MRF. An MRF method is proposed that separates fat and water signals, estimates water T₁ and T₂, and accounts for B₀ effects with spiral blurring correction, in a single sequence.

THEORY AND METHODS

A k-space-based fat-water separation method is further extended to unbalanced steady-state free precession MRF with swept echo time. Repeated application of this k-space fat-water separation to demodulated forms of the measured data allows a B₀ map and correction to be approximated. The method is compared with MRF without fat separation across a broad range of fat signal fractions (FSFs), water T₁s and T₂s, and under heterogeneous static fields in simulations, phantoms, and in vivo.

RESULTS

The proposed method's FSF estimates had a concordance correlation coefficient of 0.990 with conventional measurements, and reduced biases in the T₁ and T₂ estimates due to fat signal relative to other MRF sequences by several hundred ms. The B₀ correction improved the FSF, T₁, and T₂ estimation compared to those estimates without correction.

CONCLUSION

The proposed method improves MRF water T₁ and T₂ estimation in the presence of fat and provides accurate FSF estimation with inline B₀ correction.

Magnetic resonance field fingerprinting

PURPOSE

To develop and evaluate the magnetic resonance field fingerprinting method that simultaneously generates T₁ , T₂ , B₀ , and B 1 + maps from a single continuous measurement.

METHODS

An encoding pattern was designed to integrate true fast imaging with steady-state precession (TrueFISP), fast imaging with steady-state precession (FISP), and fast low-angle shot (FLASH) sequence segments with varying flip angles, radio frequency (RF) phases, TEs, and gradient moments in a continuous acquisition. A multistep matching process was introduced that includes steps for integrated spiral deblurring and the correction of intravoxel phase dispersion. The method was evaluated in phantoms as well as in vivo studies in brain and lower abdomen.

RESULTS

Simultaneous measurement of T₁ , T₂ , B₀ , and B 1 + is achieved with T₁ and T₂ subsequently being less afflicted by B₀ and B 1 + variations. Phantom results demonstrate the stability of generated parameter maps. Higher undersampling factors and spatial resolution can be achieved with the proposed method as compared with solely FISP-based magnetic resonance fingerprinting. High-resolution B₀ maps can potentially be further used as diagnostic information.

CONCLUSION

The proposed magnetic resonance field fingerprinting method can estimate T₁ , T₂ , B₀ , and B 1 + maps accurately in phantoms, in the brain, and in the lower abdomen.

Multi-frequency interpolation in spiral magnetic resonance fingerprinting for correction of off-resonance blurring

Magnetic resonance fingerprinting (MRF) pulse sequences often employ spiral trajectories for data readout. Spiral k-space acquisitions are vulnerable to blurring in the spatial domain in the presence of static field off-resonance. This work describes a blurring correction algorithm for use in spiral MRF and demonstrates its effectiveness in phantom and in vivo experiments. Results show that image quality of T1 and T2 parametric maps is improved by application of this correction. This MRF correction has negligible effect on the concordance correlation coefficient and improves coefficient of variation in regions of off-resonance relative to uncorrected measurements.

A simple acquisition strategy to avoid off-resonance blurring in spiral imaging with redundant spiral-in/out k-space trajectories

PURPOSE

The major hurdle to widespread adoption of spiral trajectories has been their poor off-resonance performance. Here we present a self-correcting spiral k-space trajectory that avoids much of the well-known spiral blurring during data acquisition.

THEORY AND METHODS

In comparison with a traditional spiral-out trajectory, the spiral-in/out trajectory has improved off-resonance performance. By combining two spiral-in/out acquisitions, one rotated 180° in k-space compared with the other, multishot spiral-in/out artifacts are eliminated. A phantom was scanned with the center frequency manually tuned 20, 40, 80, and 160 Hz off-resonance with both a spiral-out gradient echo sequence and the redundant spiral-in/out sequence. The phantom was also imaged in an oblique orientation in order to demonstrate improved concomitant gradient field performance of the sequence. Additionally, the trajectory was incorporated into a spiral turbo spin echo sequence for brain imaging.

RESULTS

Phantom studies with manually tuned off-resonance agree well with theoretical calculations, showing that moderate off-resonance is well-corrected by this acquisition scheme. Blur due to concomitant fields is reduced, and good results are obtained in vivo.

CONCLUSION

The redundant spiral-in/out trajectory results in less image blur for a given readout length than a traditional spiral-out scan, reducing the need for complex off-resonance correction algorithms.

Fast higher-order MR image reconstruction using singular-vector separation

Medical resonance imaging (MRI) conventionally relies on spatially linear gradient fields for image encoding. However, in practice various sources of nonlinear fields can perturb the encoding process and give rise to artifacts unless they are suitably addressed at the reconstruction level. Accounting for field perturbations that are neither linear in space nor constant over time, i.e., dynamic higher-order fields, is particularly challenging. It was previously shown to be feasible with conjugate-gradient iteration. However, so far this approach has been relatively slow due to the need to carry out explicit matrix-vector multiplications in each cycle. In this work, it is proposed to accelerate higher-order reconstruction by expanding the encoding matrix such that fast Fourier transform can be employed for more efficient matrix-vector computation. The underlying principle is to represent the perturbing terms as sums of separable functions of space and time. Compact representations with this property are found by singular-vector analysis of the perturbing matrix. Guidelines for balancing the accuracy and speed of the resulting algorithm are derived by error propagation analysis. The proposed technique is demonstrated for the case of higher-order field perturbations due to eddy currents caused by diffusion weighting. In this example, image reconstruction was accelerated by two orders of magnitude.

Nonrigid motion correction in 3D using autofocusing with localized linear translations

MR scans are sensitive to motion effects due to the scan duration. To properly suppress artifacts from nonrigid body motion, complex models with elements such as translation, rotation, shear, and scaling have been incorporated into the reconstruction pipeline. However, these techniques are computationally intensive and difficult to implement for online reconstruction. On a sufficiently small spatial scale, the different types of motion can be well approximated as simple linear translations. This formulation allows for a practical autofocusing algorithm that locally minimizes a given motion metric--more specifically, the proposed localized gradient-entropy metric. To reduce the vast search space for an optimal solution, possible motion paths are limited to the motion measured from multichannel navigator data. The novel navigation strategy is based on the so-called "Butterfly" navigators, which are modifications of the spin-warp sequence that provides intrinsic translational motion information with negligible overhead. With a 32-channel abdominal coil, sufficient number of motion measurements were found to approximate possible linear motion paths for every image voxel. The correction scheme was applied to free-breathing abdominal patient studies. In these scans, a reduction in artifacts from complex, nonrigid motion was observed.

Application of the fractional Fourier transform to image reconstruction in MRI

The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from concomitant fields, particularly in low-field imaging, or intentionally used for nonlinear encoding. In any of these situations, the second-order component is key, because it constitutes the first step to approximate higher-order fields. We propose to use the fractional Fourier transform for analyzing and reconstructing the object's magnetization under the presence of quadratic fields. The fractional fourier transform provides a precise theoretical framework for this. We show how it can be used for reconstruction and for gaining a better understanding of the quadratic field-induced distortions, including examples of reconstruction for simulated and in vivo data. The obtained images have improved quality compared with standard Fourier reconstructions. The fractional fourier transform opens a new paradigm for understanding the MR signal generated by an object under a quadratic main field or nonlinear encoding.

Fast concomitant gradient field and field inhomogeneity correction for spiral cardiac imaging

Non-Cartesian imaging provides many advantages in terms of flexibility, functionality, and speed. However, a major drawback to these imaging methods is off-resonance distortion artifacts. These artifacts manifest as blurring in spiral imaging. Common techniques that remove the off-resonance field inhomogeneity distortion effects are not sufficient, because the high order concomitant gradient fields are nontrivial for common imaging conditions, such as imaging 5 cm off isocenter in an 1.5 T scanner. Previous correction algorithms are either slow or do not take into account the known effects of concomitant gradient fields along with the field inhomogeneities. To ease the correction, the distortion effects are modeled as a non-stationary convolution problem. In this work, two fast and accurate postgridding algorithms are presented and analyzed. These methods account for both the concomitant field effects and the field inhomogeneities. One algorithm operates in the frequency domain and the other in the spatial domain. To take advantage of their speed and accuracy, the algorithms are applied to a real-time cardiac study and a high-resolution cardiac study. Both of the presented algorithms provide for a practical solution to the off-resonance problem in spiral imaging.

Faster dynamic imaging of speech with field inhomogeneity corrected spiral fast low angle shot (FLASH) at 3 T

PURPOSE

To evaluate the impact of magnetic field inhomogeneity correction on achievable imaging speeds for magnetic resonance imaging (MRI) of articulating oropharyngeal structures during speech and to determine if sufficient acquisition speed is available for visualizing speech structures with real-time MRI.

MATERIALS AND METHODS

We designed a spiral fast low angle shot (FLASH) sequence that combines several acquisition techniques with an advanced image reconstruction approach that includes magnetic field inhomogeneity correction. A simulation study was performed to examine the interaction between imaging speed, image quality, number of spiral shots, and field inhomogeneity correction. Six volunteer subjects were scanned to demonstrate adequate visualization of articulating structures during simple speech samples.

RESULTS

The simulation study confirmed that magnetic field inhomogeneity correction improves the available tradeoff between image quality and speed. Our optimized sequence co-acquires magnetic field maps for image correction and achieves a dynamic imaging rate of 21.4 frames per second, significantly faster than previous studies. Improved visualization of anatomical structures, such as the soft palate, was also seen from the field-corrected reconstructions in data acquired on volunteer subjects producing simple speech samples.

CONCLUSION

Adequate temporal resolution of articulating oropharyngeal structures during speech can be obtained by combining outer volume suppression, multishot spiral imaging, and magnetic field corrected image reconstruction. Correcting for the large, dynamic magnetic field variation in the oropharyngeal cavity improves image quality and allows for higher temporal resolution.

Quantitative sodium imaging with a flexible twisted projection pulse sequence

The quantification of sodium MR images from an arbitrary intensity scale into a bioscale fosters image interpretation in terms of the spatially resolved biochemical process of sodium ion homeostasis. A methodology for quantifying tissue sodium concentration using a flexible twisted projection imaging sequence is proposed that allows for optimization of tradeoffs between readout time, signal-to-noise ratio efficiency, and sensitivity to static field susceptibility artifacts. The gradient amplitude supported by the slew rate at each k-space radius regularizes the readout gradient waveform design to avoid slew rate violation. Static field inhomogeneity artifacts are corrected using a frequency-segmented conjugate phase reconstruction approach, with field maps obtained quickly from coregistered proton imaging. High-quality quantitative sodium images have been achieved in phantom and volunteer studies with real isotropic spatial resolution of 7.5 x 7.5 x 7.5 mm(3) for the slow T(2) component in approximately 8 min on a clinical 3-T scanner. After correcting for coil sensitivity inhomogeneity and water fraction, the tissue sodium concentration in gray matter and white matter was measured to be 36.6 +/- 0.6 micromol/g wet weight and 27.6 +/- 1.2 micromol/g wet weight, respectively.

Dynamic imaging of speech and swallowing with MRI

Dynamic imaging with MRI holds great promise for visualizing soft tissue structures in the oropharyngeal region during speech and swallowing studies. However, MRI suffers from historically slow acquisition speed and sensitivity to significant magnetic susceptibility differences in this region. In this work, we describe our efforts in creating high temporal resolution, serial acquisitions of the muscles of the oropharyngeal region. We describe our imaging approach that leads to acquisition rates of up to 21 frames per second. Additionally, we compare the serial acquisition scheme to gated acquisitions that suffer from temporal blur due to limited repeatability of the dynamic action.

High-resolution spiral imaging on a whole-body 7T scanner with minimized image blurring

High-resolution (approximately 0.22 mm) images are preferably acquired on whole-body 7T scanners to visualize minianatomic structures in human brain. They usually need long acquisition time ( approximately 12 min) in three-dimensional scans, even with both parallel imaging and partial Fourier samplings. The combined use of both fast imaging techniques, however, leads to occasionally visible undersampling artifacts. Spiral imaging has an advantage in acquisition efficiency over rectangular sampling, but its implementations are limited due to image blurring caused by a strong off-resonance effect at 7T. This study proposes a solution for minimizing image blurring while keeping spiral efficient. Image blurring at 7T was, first, quantitatively investigated using computer simulations and point-spread functions. A combined use of multishot spirals and ultrashort echo time acquisitions was then employed to minimize off-resonance-induced image blurring. Experiments on phantoms and healthy subjects were performed on a whole-body 7T scanner to show the performance of the proposed method. The three-dimensional brain images of human subjects were obtained at echo time = 1.18 ms, resolution = 0.22 mm (field of view = 220 mm, matrix size = 1024), and in-plane spiral shots = 128, using a home-developed ultrashort echo time sequence (acquisition-weighted stack of spirals). The total acquisition time for 60 partitions at pulse repetition time = 100 ms was 12.8 min without use of parallel imaging and partial Fourier sampling. The blurring in these spiral images was minimized to a level comparable to that in gradient-echo images with rectangular acquisitions, while the spiral acquisition efficiency was maintained at eight. These images showed that spiral imaging at 7T was feasible.

A new distortion model for strong inhomogeneity problems in echo-planar MRI

This paper proposes a new distortion model for strong inhomogeneity problems in echo planar imaging (EPI). Fast imaging sequences in magnetic resonance imaging (MRI), such as EPI, are very important in applications where temporal resolution or short total acquisition time is essential. Unfortunately, fast imaging sequences are very sensitive to variations in the homogeneity of the main magnetic field. The inhomogeneity leads to geometrical distortions and intensity changes in the image reconstructed via fast Fourier transform. Also, under strong inhomogeneity, the accelerated intravoxel dephase may overly attenuate signals coming from regions with higher inhomogeneity variations. Moreover, coarse discretization schemes for the inhomogeneity are not able to cope with this problem, producing discretization artifacts when large inhomogeneity variations occur. Most of the existing models do not attempt to solve this problem. In this paper, we propose a modification of the discrete distortion model to incorporate the effects of the intravoxel inhomogeneity and to minimize the discretization artifacts. As a result, these problems are significantly reduced. Extensive experiments are shown to demonstrate the achieved improvements. Also, the performance of the new model is evaluated for conjugate phase, least squares method (minimized iteratively using conjugated gradients), and regularized methods (using a total variation penalty).

Joint estimation and correction of geometric distortions for EPI functional MRI using harmonic retrieval

Magnetic resonance imaging (MRI) uses applied spatial variations in the magnetic field to encode spatial position. Therefore, nonuniformities in the main magnetic field can cause image distortions. In order to correct the image distortions, it is desirable to simultaneously acquire data with a field map in registration. We propose a joint estimation (JE) framework with a fast, noniterative approach using harmonic retrieval (HR) methods, combined with a multi-echo echo-planar imaging (EPI) acquisition. The connection with HR establishes an elegant framework to solve the JE problem through a sequence of 1-D HR problems in which efficient solutions are available. We also derive the condition on the smoothness of the field map in order for HR techniques to recover the image with high signal-to-noise ratio. Compared to other dynamic field mapping methods, this method is not constrained by the absolute level of the field inhomogeneity over the slice, but relies on a generous pixel-to-pixel smoothness. Moreover, this method can recover image, field map, and T2* map simultaneously.

Iterative off-resonance and signal decay estimation and correction for multi-echo MRI

Signal dephasing due to field inhomogeneity and signal decay due to transverse relaxation lead to perturbations of the Fourier encoding commonly applied in magnetic resonance imaging. Hence, images acquired with long readouts suffer from artifacts such as blurring, distortion, and intensity variation. These artifacts can be removed in reconstruction, usually based on separately collected information in form of field and relaxation maps. In this work, a recently proposed gridding-based algorithm for off-resonance correction is extended to also address signal decay. It is integrated into a new fixed-point iteration, which permits the joint estimation of an image and field and relaxation maps from multi-echo acquisitions. This approach is then applied in simulations and in vivo experiments and demonstrated to improve both images and maps. The rapid convergence of the fixed-point iteration in combination with the efficient gridding-based correction promises to render the running time of such a joint estimation acceptable.

Current trends and challenges in MRI acquisitions to investigate brain function

Functional magnetic resonance imaging (fMRI) studies using the blood oxygenation level dependent (BOLD) response have become a widely used tool for noninvasive assessment of functional organization of the brain. Yet the technique is still fairly new, with many significant challenges remaining. Capitalizing on additional contrast mechanisms available with MRI, several other functional imaging techniques have been developed that potentially provide improved quantification or specificity of neuronal function. This article reviews the challenges and the current state of the art in MRI-based methods of imaging cognitive function.

Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients

Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method.

Effect on BOLD sensitivity due to susceptibility-induced echo time shift in spiral-in based functional MRI

Susceptibility artifacts induced by the magnetic field inhomogeneity exist near the air/tissue interfaces at the ventral brain in functional magnetic resonance imaging (fMRI). These susceptibility artifacts will cause geometric distortions and signal loss in reconstructed images. Additionally, the in-plane susceptibility gradients will cause a shift in effective echo time, and therefore influence the blood-oxygen-level dependent (BOLD) sensitivity since it is proportional to effective echo time. In this work, we examine the effective echo time shift and the change of the BOLD sensitivity based on susceptibility gradients. The analysis results show that there are regions, such as the orbitofrontal cortex, that suffer from significant loss of BOLD sensitivity using spiral-in trajectory in BOLD fMRI.

Iterative image reconstruction model including susceptibility gradients combined with Z-shimming gradients in fMRI

Magnetic susceptibility artifacts, including both image distortions and signal losses, exist near air/tissue interfaces in the ventral brain in standard blood oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI). Although several acquisition-based approaches exist to address the signal losses, they require increased acquisition time or patient customization. In this work, we propose a statistical estimation model that includes the effects of magnetic field gradients (both within-plane and through-plane gradients) and uses an iterative reconstruction algorithm to reconstruct images corrected for both magnetic field distortion and signal losses. Besides, we combine our reconstruction approach with a recently proposed MRI sequence with Z-shimming gradient between the spiral-in and spiral-out acquisition to enhance the compensation for signal losses. Therefore, we extend our forward MR signal model to include the physics of Susceptibility-induced magnetic Field (SF), Susceptibility-induced magnetic Field Gradients (SFG), and the application of the data acquisition technique with Z-shimming Gradients (ZShG). The results show that not only signal distortions but also significant signal losses can be compensated by considering both the modeling of field-inhomogeneity effects along with the acquisition using Z-shimming.

An iterative reconstruction technique for geometric distortion-corrected segmented echo-planar imaging

In this article, we present a modified interleaved segmented echo-planar imaging (SEPI) sequence with a center-out k-space trajectory that is especially designed for susceptibility-weighted imaging applications. We introduce a simple and efficient technique to phase correct the acquired SEPI data in the presence of moderate field inhomogeneities. This phase correction reduces the distortion in the phase-encoding direction without requiring an extra reference scan. With the use of a center-out k-space trajectory and a low-spatial-frequency phase map, phase discontinuities between segments can be eliminated, in principle, iteratively using a fast Fourier transform from the center segment to the outermost segment in k-space. With an extra echo added in front of the echo train, neither phase unwrapping nor an extra reference scan is required to obtain a low-spatial-frequency phase map. The method is shown to remove blurring and reduce geometric distortion caused by phase changes from echo to echo in both phantom and human data. The method is most useful for high-resolution imaging applications and moderate factors of speed improvement.

Fast joint reconstruction of dynamic R2* and field maps in functional MRI

Blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) is conventionally done by reconstructing T(2)(*)-weighted images. However, since the images are unitless they are nonquantifiable in terms of important physiological parameters. An alternative approach is to reconstruct R(2)(*) maps which are quantifiable and have comparable BOLD contrast as T(2)(*)-weighted images. However, conventional R(2)(*) mapping involves long readouts and ignores relaxation during readout. Another problem with fMRI imaging is temporal drift/fluctuations in off-resonance. Conventionally, a field map is collected at the start of the fMRI study to correct for off-resonance, ignoring any temporal changes. Here, we propose a new fast regularized iterative algorithm that jointly reconstructs R(2)(*) and field maps for all time frames in fMRI data. To accelerate the algorithm we linearize the MR signal model, enabling the use of fast regularized iterative reconstruction methods. The regularizer was designed to account for the different resolution properties of both R(2)(*) and field maps and provide uniform spatial resolution. For fMRI data with the same temporal frame rate as data collected for T(2)(*)-weighted imaging the resulting R(2)(*) maps performed comparably to T(2)(*)-weighted images in activation detection while also correcting for spatially global and local temporal changes in off-resonance.

Semiautomatic off-resonance correction in spiral imaging

Spiral scanning is a promising MRI method, but one limitation is that off-resonance effects can cause image blurring. Most current off-resonance correction methods for spiral imaging require an accurate field map, which is difficult to obtain in many applications. Automatic methods can perform off-resonance correction without acquiring a field map. However, these methods are computationally inefficient and relatively prone to estimation error. This study describes a new semiautomatic off-resonance correction method that combines an automatic method with a low resolution field map acquisition for off-resonance correction in spiral scanning. Experiments demonstrate that this method is more robust than conventional automatic off-resonance correction and can provide more accurate off-resonance correction than conventional field map based methods. The proposed method is also computationally efficient and has been implemented for online reconstruction.

Joint estimation of water/fat images and field inhomogeneity map

Water/fat separation in the presence of B 0 field inhomogeneity is a problem of considerable practical importance in MRI. This article describes two complementary methods for estimating the water/fat images and the field inhomogeneity map from Dixon-type acquisitions. One is based on variable projection (VARPRO) and the other on linear prediction (LP). The VARPRO method is very robust and can be used in low signal-to-noise ratio conditions because of its ability to achieve the maximum-likelihood solution. The LP method is computationally more efficient, and is shown to perform well under moderate levels of noise and field inhomogeneity. These methods have been extended to handle multicoil acquisitions by jointly solving the estimation problem for all the coils. Both methods are analyzed and compared and results from several experiments are included to demonstrate their performance.

Hybrid two-dimensional navigator correction: a new technique to suppress respiratory-induced physiological noise in multi-shot echo-planar functional MRI

A troublesome source of physiological noise in functional magnetic resonance imaging (fMRI) is due to the spatio-temporal modulation of the magnetic field in the brain caused by normal subject respiration. fMRI data acquired using echo-planar imaging are very sensitive to these respiratory-induced frequency offsets, which cause significant geometric distortions in images. Because these effects increase with main magnetic field, they can nullify the gains in statistical power expected by the use of higher magnetic fields. As a study of existing navigator correction techniques for echo-planar fMRI has shown that further improvements can be made in the suppression of respiratory-induced physiological noise, a new hybrid two-dimensional (2D) navigator is proposed. Using a priori knowledge of the slow spatial variations of these induced frequency offsets, 2D field maps are constructed for each shot using spatial frequencies between +/-0.5 cm(-1) in k-space. For multi-shot fMRI experiments, we estimate that the improvement of hybrid 2D navigator correction over the best performance of one-dimensional navigator echo correction translates into a 15% increase in the volume of activation, 6% and 10% increases in the maximum and average t-statistics, respectively, for regions with high t-statistics, and 71% and 56% increases in the maximum and average t-statistics, respectively, in regions with low t-statistics due to contamination by residual physiological noise.

Field inhomogeneity correction based on gridding reconstruction for magnetic resonance imaging

Spatial variations of the main field give rise to artifacts in magnetic resonance images if disregarded in reconstruction. With non-Cartesian k-space sampling, they often lead to unacceptable blurring. Data from such acquisitions are usually reconstructed with gridding methods and optionally restored with various correction methods. Both types of methods essentially face the same basic problem of adequately approximating an exponential function to enable an efficient processing with fast Fourier transforms. Nevertheless, they have commonly addressed it differently so far. In the present work, a unified approach is pursued. The principle behind gridding methods is first generalized to nonequispaced sampling in both domains and then applied to field inhomogeneity correction. Three new algorithms, which are compatible with a direct conjugate phase and an iterative algebraic reconstruction, are derived in this way from a straightforward embedding of the data into a higher dimensional space. Their evaluation in simulations and phantom experiments with spiral k-space sampling shows that one of them promises to provide a favorable compromise between fidelity and complexity compared with existing algorithms. Moreover, it allows a simple choice of key parameters involved in approximating an exponential function and a balance between the accuracy of reconstruction and correction.

Fast automatic linear off-resonance correction method for spiral imaging

Field inhomogeneity and susceptibility variations, coupled with a long readout, can result in image blurring in spiral imaging. Many correction methods based on a priori off-resonance information, such as an acquired field map, have been proposed in the literature. Automatic off-resonance correction methods are alternative approaches that estimate a field map from the image data themselves. In this paper we propose a fast automatic off-resonance correction method that performs linear correction without acquiring a field map. The method requires only about two times the total computation time compared to image reconstruction by gridding. It can also be used in combination with a full field map automatic off-resonance correction method to increase the extent of correction. The method is demonstrated by in vivo coronary artery imaging.

Noise reduction and convergence of Bayesian algorithms with blobs based on the Huber function and median root prior

Iterative image reconstruction algorithms have the potential to produce low noise images. Early stopping of the iteration process is problematic because some features of the image may converge slowly. On the other hand, there may be noise build-up with increased number of iterations. Therefore, we examined the stabilizing effect of using two different prior functions as well as image representation by blobs so that the number of iterations could be increased without noise build-up. Reconstruction was performed of simulated phantoms and of real data acquired by positron emission tomography. Image quality measures were calculated for images reconstructed with or without priors. Both priors stabilized the iteration process. The first prior based on the Huber function reduced the noise without significant loss of contrast recovery of small spots, but the drawback of the method was the difficulty in finding optimal values of two free parameters. The second method based on a median root prior has only one Bayesian parameter which was easy to set, but it should be taken into account that the image resolution while using that prior has to be chosen sufficiently high not to cause the complete removal of small spots. In conclusion, the Huber penalty function gives accurate and low noise images, but it may be difficult to determine the parameters. The median root prior method is not quite as accurate but may be used if image resolution is increased.

Conjugate phase MRI reconstruction with spatially variant sample density correction

A new image reconstruction method to correct for the effects of magnetic field inhomogeneity in non-Cartesian sampled magnetic resonance imaging (MRI) is proposed. The conjugate phase reconstruction method, which corrects for phase accumulation due to applied gradients and magnetic field inhomogeneity, has been commonly used for this case. This can lead to incomplete correction, in part, due to the presence of gradients in the field inhomogeneity function. Based on local distortions to the k-space trajectory from these gradients, a spatially variant sample density compensation function is introduced as part of the conjugate phase reconstruction. This method was applied to both simulated and experimental spiral imaging data and shown to produce more accurate image reconstructions. Two approaches for fast implementation that allow the use of fast Fourier transforms are also described. The proposed method is shown to produce fast and accurate image reconstructions for spiral sampled MRI.

Iterative RF pulse design for multidimensional, small-tip-angle selective excitation

The excitation k-space perspective on small-tip-angle selective excitation has facilitated RF pulse designs in a range of MR applications. In this paper, k-space-based design of multidimensional RF pulses is formulated as a quadratic optimization problem, and solved efficiently by the iterative conjugate-gradient (CG) algorithm. Compared to conventional design approaches, such as the conjugate-phase (CP) method, the new design approach is beneficial in several regards. It generally produces more accurate excitation patterns. The improvement is particularly significant when k-space is undersampled, and it can potentially shorten pulse lengths. A prominent improvement in accuracy is also observed when large off-resonance gradients are present. A further boost in excitation accuracy can be accomplished in regions of interest (ROIs) if they are specified together with "don't-care" regions. The density compensation function (DCF) is no longer required. In addition, regularization techniques allow control over integrated and peak pulse power.

Three-dimensional breathhold SSFP coronary MRA: A comparison between 1.5T and 3.0T

PURPOSE

To assess the feasibility of three-dimensional breathhold coronary magnetic resonance angiography (MRA) at 3.0T using the steady-state free precession (SSFP) sequence, and quantify the signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) gains of coronary MRA from 1.5T to 3.0T using whole-body and phased-array cardiac coils as the signal receiver.

MATERIALS AND METHODS

Eight healthy volunteers were scanned on 1.5T and 3.0T whole-body systems using the SSFP sequence. Numerical simulations were performed for the SSFP sequence to optimize the flip angle and predict signal enhancement from 1.5T to 3.0T. Coronary artery images were acquired with the whole-body coil in transmit-receive mode or transmit-only with phased-array cardiac coil receivers.

RESULTS

In vivo studies of the same volunteer group at both field strengths showed increases of 87% in SNR and 83% in CNR from 1.5T to 3.0T using a whole-body coil as the signal receiver. The corresponding increases using phased-array receivers were 53% in SNR and 92% in CNR. However, image quality at 3.0T was more variable than 1.5T, with increased susceptibility artifacts and local brightening as the result of increased B(0) and B(1) inhomogeneities.

CONCLUSION

Coronary MRA at 3.0T using a three-dimensional breathhold SSFP sequence is feasible. Improved SNR at 3.0T warrants the use of coronary MRA with faster acquisition and/or improved spatial resolution. Further investigations are required to improve the consistency of image quality and signal uniformity at 3.0T.

Method for bias field correction of brain T1-weighted magnetic resonance images minimizing segmentation error

This work presents a new algorithm (nonuniform intensity correction; NIC) for correction of intensity inhomogeneities in T1-weighted magnetic resonance (MR) images. The bias field and a bias-free image are obtained through an iterative process that uses brain tissue segmentation. The algorithm was validated by means of realistic phantom images and a set of 24 real images. The first evaluation phase was based on a public domain phantom dataset, used previously to assess bias field correction algorithms. NIC performed similar to previously described methods in removing the bias field from phantom images, without introduction of degradation in the absence of intensity inhomogeneity. The real image dataset was used to compare the performance of this new algorithm to that of other widely used methods (N3, SPM'99, and SPM2). This dataset included both low and high bias field images from two different MR scanners of low (0.5 T) and medium (1.5 T) static fields. Using standard quality criteria for determining the goodness of the different methods, NIC achieved the best results, correcting the images of the real MR dataset, enabling its systematic use in images from both low and medium static field MR scanners. A limitation of our method is that it might fail if the bias field is so high that the initial histogram does not show bimodal distribution for white and gray matter.

Experiments with the nonlinear and chaotic behaviour of the multiplicative algebraic reconstruction technique (MART) algorithm for computed tomography

Among the iterative reconstruction algorithms for tomography, the multiplicative algebraic reconstruction technique (MART) has two advantages that make it stand out from other algorithms: it confines the image (and therefore the projection data) to the convex hull of the patient, and it maximizes entropy. In this paper, we have undertaken a series of experiments to determine the importance of MART nonlinearity to image quality. Variants of MART were implemented aiming to exploit and exaggerate the nonlinear properties of the algorithm. We introduce the Power MART, Boxcar Averaging MART and Bouncing MART algorithms. Power MART is linked to the relaxation concept. Its behaviour is similar to that of the chaos of a logistic equation. There appears to be an antagonism between increasing nonlinearity and noise in the projection data. The experiments confirm our general observation that regularization as a means of solving simultaneous linear equations that are underdetermined is suboptimal: it does not necessarily select the correct image from the hyperplane of solutions, and so does not maximize the image quality:x-ray dose ratio. Our investigations prove that there is scope to optimize CT algorithms and thereby achieve greater dose reduction.

Dynamic field map estimation using a spiral-in/spiral-out acquisition

The long readout times of single-shot acquisitions and the high field strengths desired for functional MRI (fMRI) using blood oxygenation level-dependent (BOLD) contrast make functional scans sensitive to magnetic field inhomogeneity. If it is not corrected during image reconstruction, field inhomogeneity can cause geometric distortions in the images when Cartesian k-space trajectories are used or blurring with spiral acquisitions. Many traditional methods to correct for field inhomogeneity distortions rely on a static field map measured with the use of images that are themselves distorted. In this work, we employ a regularized least-squares approach to jointly estimate both the undistorted image and field map at each acquisition using a spiral-in/spiral-out pulse sequence. Simulation and phantom studies show that this method is accurate and stable over a time series. Human functional studies show that the jointly estimated field map may be more accurate than standard field map estimates in the presence of respiration-induced phase oscillations, leading to better detection of functional activation. The proposed method measures a dynamic field map that accurately tracks magnetic field drift and respiration-induced phase oscillations during the course of a functional study.

Fast Spiral two-point Dixon technique using block regional off-resonance correction

The Spiral two-point Dixon (Spiral 2PD) technique has recently been proposed as a method for unambiguous water-fat decomposition in spiral imaging. It also corrects for off-resonance blurring artifacts using only two data sets. In the Spiral 2PD technique, several predetermined off-resonance frequencies are tested to both separate water and fat signals and deblur the decomposed images. Unfortunately, the algorithm is computationally quite intensive since the range of tested frequencies must be set sufficiently large to span the full range of anticipated B(0) variation over the scanned objects. The block regional off-resonance correction (BRORC) algorithm corrects for off-resonance blurring artifacts block by block through the reconstructed image and usually provides several times higher computational efficiency than the conventional frequency-segmented off-resonance correction algorithm. This work shows that both water-fat decomposition and blurring artifact correction can be performed block by block using two spiral images with different TEs and that this new technique (BRORC-Spiral2PD technique) significantly improves the computational efficiency of other Spiral 2PD algorithms, opening new opportunities for spiral imaging.

Dixon techniques in spiral trajectories with off-resonance correction: A new approach for fat signal suppression without spatial-spectral RF pulses

Spiral imaging has recently gained acceptance in MR applications requiring rapid data acquisition. One of the main disadvantages of spiral imaging, however, is blurring artifacts that result from off-resonance effects. Spatial-spectral (SPSP) pulses are commonly used to suppress those spins that are chemically shifted from water and lead to off-resonance artifacts. However, SPSP pulses may produce nonuniform fat signal suppression or unwanted water signal suppression when applied in the presence of B(0) field inhomogeneities. Dixon techniques have been developed as methods for water-fat signal decomposition in rectilinear sampling schemes since they can produce unequivocal water-fat signal decomposition even in the presence of B(0) inhomogeneities. This article demonstrates that three-point and two-point Dixon techniques can be extended to conventional spiral and variable-density spiral data acquisitions for unambiguous water-fat decomposition with off-resonance blurring correction. In the spiral three-point Dixon technique, water-fat signal decomposition and image deblurring are performed based on the frequency maps that are directly derived from the acquired images. In the spiral two-point Dixon technique, several predetermined frequencies are tested to create a frequency map. The newly proposed techniques can achieve more effective and more uniform fat signal suppression when compared to the conventional spiral acquisition method with SPSP pulses.

Novel interleaved spiral imaging motion correction technique using orbital navigators

Although spiral imaging seldom produces apparent artifacts related to flow, it remains sensitive to rapid object motion. In this article, a new correction method is presented for rapid rigid body motion in interleaved spiral imaging. With this technique, an identical circular navigator k-space trajectory is linked to each spiral trajectory. Data inconsistency due to both rotation and translation among spiral interleaves can be corrected by evaluating the magnitudes and phases of the data contained in the navigator "ring." Further, it is difficult to create a frequency field map for off-resonance correction when an object moves during a scan, because there is motion-dependent misregistration between the two images acquired with different TEs. However, this difficulty can be overcome by combining the motion-correction method with a recently proposed technique (off-resonance correction using variable-density spirals (ORC-VDS)), thereby enabling both motion compensation and off-resonance correction with no additional scanning.

Functional magnetic resonance imaging: a review of methodological aspects and clinical applications

This paper gives an overview of the recent literature on methodological developments of functional magnetic resonance imaging (fMRI) and recent trends in clinical applications. With the recent introduction of high-field systems and methodological developments leading to more robust signal behavior, fMRI is in a transition state from a research modality for use by experts to a standard procedure with useful applications in patient management. Compared to the use in neuroscientific research, which is often based on BOLD techniques alone, the application in patients is distinguished by a multiparametric characterization of the brain using a combination of several techniques. Neuronal fiber tracking based on diffusion anisotropy measurements, in particular, has already turned out to provide relevant supplementary information to the BOLD-based cortical activation maps.

Fast, iterative image reconstruction for MRI in the presence of field inhomogeneities

In magnetic resonance imaging, magnetic field inhomogeneities cause distortions in images that are reconstructed by conventional fast Fourier trasform (FFT) methods. Several noniterative image reconstruction methods are used currently to compensate for field inhomogeneities, but these methods assume that the field map that characterizes the off-resonance frequencies is spatially smooth. Recently, iterative methods have been proposed that can circumvent this assumption and provide improved compensation for off-resonance effects. However, straightforward implementations of such iterative methods suffer from inconveniently long computation times. This paper describes a tool for accelerating iterative reconstruction of field-corrected MR images: a novel time-segmented approximation to the MR signal equation. We use a min-max formulation to derive the temporal interpolator. Speedups of around 60 were achieved by combining this temporal interpolator with a nonuniform fast Fourier transform with normalized root mean squared approximation errors of 0.07%. The proposed method provides fast, accurate, field-corrected image reconstruction even when the field map is not smooth.

Direct comparison of 3D spiral vs. Cartesian gradient-echo coronary magnetic resonance angiography

While 3D thin-slab coronary magnetic resonance angiography (MRA) has traditionally been performed using a Cartesian acquisition scheme, spiral k-space data acquisition offers several potential advantages. However, these strategies have not been directly compared in the same subjects using similar methodologies. Thus, in the present study a comparison was made between 3D coronary MRA using Cartesian segmented k-space gradient-echo and spiral k-space data acquisition schemes. In both approaches the same spatial resolution was used and data were acquired during free breathing using navigator gating and prospective slice tracking. Magnetization preparation (T(2) preparation and fat suppression) was applied to increase the contrast. For spiral imaging two different examinations were performed, using one or two spiral interleaves, during each R-R interval. Spiral acquisitions were found to be superior to the Cartesian scheme with respect to the signal-to-noise ratio (SNR) and contrast-to-noise-ratio (CNR) (both P < 0.001) and image quality. The single spiral per R-R interval acquisition had the same total scan duration as the Cartesian acquisition, but the single spiral had the best image quality and a 2.6-fold increase in SNR. The double-interleaf spiral approach showed a 50% reduction in scanning time, a 1.8-fold increase in SNR, and similar image quality when compared to the standard Cartesian approach. Spiral 3D coronary MRA appears to be preferable to the Cartesian scheme. The increase in SNR may be "traded" for either shorter scanning times using multiple consecutive spiral interleaves, or for enhanced spatial resolution.

Reversed spiral MR imaging

Reversed spiral imaging is discussed as an approach that provides strong intrinsic T *(2) contrast without the need for long repetition times. In comparison to the conventional forward spiral method, the T *(2) contrast achieved by reversing the spiral k-space trajectory is similar and differs only for very fast relaxing species. The flow and motion sensitivity of the reversed approach is the same if flow compensation is applied, except for a flow-dependent voxel shift and the sign of the artifact pattern. By simulations as well as phantom and in vivo experiments, it is shown that the image quality in reversed spiral imaging is comparable to that obtained with the forward spiral method.