Field-of-view limitations in parallel imaging

Accelerated Musculoskeletal Magnetic Resonance Imaging

With a substantial growth in the use of musculoskeletal MRI, there has been a growing need to improve MRI workflow, and faster imaging has been suggested as one of the solutions for a more efficient examination process. Consequently, there have been considerable advances in accelerated MRI scanning methods. This article aims to review the basic principles and applications of accelerated musculoskeletal MRI techniques including widely used conventional acceleration methods, more advanced deep learning-based techniques, and new approaches to reduce scan time. Specifically, conventional accelerated MRI techniques, including parallel imaging, compressed sensing, and simultaneous multislice imaging, and deep learning-based accelerated MRI techniques, including undersampled MR image reconstruction, super-resolution imaging, artifact correction, and generation of unacquired contrast images, are discussed. Finally, new approaches to reduce scan time, including synthetic MRI, novel sequences, and new coil setups and designs, are also reviewed. We believe that a deep understanding of these fast MRI techniques and proper use of combined acceleration methods will synergistically improve scan time and MRI workflow in daily practice. EVIDENCE LEVEL: 3 TECHNICAL EFFICACY: Stage 1.

Aliasing-free reduced field-of-view parallel imaging

PURPOSE

To reconstruct aliasing-free full field-of-view (FOV) images for reduced FOV (rFOV) parallel imaging (PI) with Cartesian and Wave sampling, which suffers from aliasing artifacts using existing PI methods.

THEORY AND METHODS

The sensitivity encoding method (SENSE) was extended to the Soft-SENSE models supporting multiple-set coil sensitivity maps (CSM) and point spread functions (PSF) for Cartesian and Wave sampled rFOV PI, respectively. The multiple-set CSM and PSF were created from full FOV CSM and PSF according to the image folding process induced by rFOV sampling. The Soft-SENSE reconstructions could be solved by the same algorithms for the conventional full FOV SENSE reconstruction.

RESULTS

Soft-SENSE using multiple-set full FOV CSM and PSF successfully reconstruct aliasing-free full FOV image from rFOV PI data with Cartesian and Wave sampling. The proposed rFOV PI enables flexible control of the aliasing and achieves comparable geometry factors as the standard full FOV PI with the same net acceleration factor. Reduced FOV PI improves the computational efficiency of iterative compressed sensing (CS) and PI reconstruction, especially for high-resolution volumetric imaging, thanks to the reduced fast Fourier transform (FFT) size. Moreover, rFOV PI reconstruction provides a potential alternative to the phase oversampling for the FOV aliasing problem.

CONCLUSION

The proposed Soft-SENSE using full FOV CSM and PSF could reconstruct aliasing-free full FOV image for rFOV PI, and make it a viable solution enabling more flexible PI acceleration and effectively improving the computational efficiency of iterative CSPI reconstruction.

Image reconstruction for the rotating RF coil using k-t bin robust principal component analysis (RPCA) method

The recently developed rotating radiofrequency coil (RRFC) technique has been proven to be an alternative solution to phased-array coils for magnetic resonance imaging (MRI). However, most of the image reconstruction methods for the RRFC requires detailed knowledge of coil sensitivity to yield optimal results. In this work, a novel reconstruction algorithm based on Robust Principal Component Analysis (RPCA) with the k-t (k-space-time domain) sparse bin reformation method (or rotating k-t bin method) has been presented to restore images without using dedicated coil sensitivity information. The proposed algorithm recovers images by iteratively removing the artefacts in both temporal and frequency domains caused by the Fourier invariant violation from coil rotation. The data sampling scheme consists of the golden angle (GA) radial k-space and the stepping-mode coil rotation. Simulation results demonstrate the effectiveness of the proposed imaging method for the RRFC-based MR scan.

Accelerating cardiac cine MRI using a deep learning-based ESPIRiT reconstruction

PURPOSE

To propose a novel combined parallel imaging and deep learning-based reconstruction framework for robust reconstruction of highly accelerated 2D cardiac cine MRI data.

METHODS

We propose DL-ESPIRiT, an unrolled neural network architecture that utilizes an extended coil sensitivity model to address SENSE-related field-of-view (FOV) limitations in previously proposed deep learning-based reconstruction frameworks. Additionally, we propose a novel neural network design based on (2+1)D spatiotemporal convolutions to produce more accurate dynamic MRI reconstructions than conventional 3D convolutions. The network is trained on fully sampled 2D cardiac cine datasets collected from 11 healthy volunteers with IRB approval. DL-ESPIRiT is compared against a state-of-the-art parallel imaging and compressed sensing method known as l 1 -ESPIRiT. The reconstruction accuracy of both methods is evaluated on retrospectively undersampled datasets (R = 12) with respect to standard image quality metrics as well as automatic deep learning-based segmentations of left ventricular volumes. Feasibility of DL-ESPIRiT is demonstrated on two prospectively undersampled datasets acquired in a single heartbeat per slice.

RESULTS

The (2+1)D DL-ESPIRiT method produces higher fidelity image reconstructions when compared to l 1 -ESPIRiT reconstructions with respect to standard image quality metrics (P < .001). As a result of improved image quality, segmentations made from (2+1)D DL-ESPIRiT images are also more accurate than segmentations from l 1 -ESPIRiT images.

CONCLUSIONS

DL-ESPIRiT synergistically combines a robust parallel imaging model and deep learning-based priors to produce high-fidelity reconstructions of retrospectively undersampled 2D cardiac cine data acquired with reduced FOV. Although a proof-of-concept is shown, further experiments are necessary to determine the efficacy of DL-ESPIRiT in prospectively undersampled data.

Estimation error bound for GRAPPA diffusion-weighted MRI

In recent years, diffusion weight magnetic resonance imaging (DW-MRI) has become one of the most important MRI imaging modalities. The importance of the DW-MRI grew thanks to the combination of parallel magnetic resonance imaging (pMRI) techniques with the echo-planar imaging (EPI), which minimize scan time and lead to reduced distortion, allowing the DW-MRI to become a routine clinical exam. Additionally, this has brought various new parameters that influence image quality and biomarkers used in DW-MRI. This work aims to investigate the effects of these parameters on the estimation quality, by using the Cramér-Rao bound tool, which gives analytical expressions of the lower limit on the estimation error variance of different DW-MRI variables when using the pMRI technique. In particular, these bounds will be used to study and optimize the impact of different factors of generalized autocalibrating partially parallel acquisition (GRAPPA) technique and system parameters on the estimation quality of the desired clinical metrics. Moreover, the obtained results of this study can be exploited and adapted in all human body DW-MRI clinical routines, further improving disease diagnosis, and tractography studies.

Parallel magnetic resonance image reconstruction from a single-element parametric amplifier

In magnetic resonance imaging (MRI), acquisition speed is always an important issue. In this paper, we propose a promising technique to achieve parallel MRI (pMRI) on a single-channel spectrometer, using a novel Wireless Amplified Nuclear MR Detector (WAND) for spatial encoding in image reconstruction. For this, a planar structure double frequency WAND is designed and fabricated, where two of its frequencies - 'signal', ω1 and 'idler', ω2 are effectively utilized as two separate "channels" for accelerated acquisition. We provided a thorough background needed for the method and subsequently parallel imaging algorithms. Sum-of-Squares (SoS) reconstruction and GeneRalized Autocalibrating Partially Parallel Acquisition (GRAPPA) reconstruction are used to reconstruct as well as to analyze the SNR in the resulting images and validate our hypothesis. Experimental results using phantom datasets demonstrate that the proposed method of parallel imaging yield a better sensitivity for the combined images ('idler' + 'signal') than the sensitivity acquired for each individual image and thus significantly improving the reconstruction quality with optimal signal-to-noise ratio. We also demonstrated the achievable acceleration factor of this approach.

Improving GRAPPA reconstruction using joint nonlinear kernel mapped and phase conjugated virtual coils

To improve the reconstruction condition and alleviate the noise amplification of GRAPPA reconstruction by aggregating the phase conjugated and nonlinear kernel mapped coils with the original physical coil. Nonlinear GRAPPA (NL-GRAPPA) is a kernel-based non-iterative approach which can reduce noise-induced error in GRAPPA reconstruction. And virtual conjugate coil (VCC) embeds the conjugate symmetric property of k-space into GRAPPA data synthesis to improve reconstruction condition. This work proposed NL-VCC-GRAPPA to jointly utilize the nonlinear mapped virtual coil and phase conjugated virtual coil to further reduce noise amplification in parallel imaging. In vivo static and dynamic 2D imaging accelerated by uniform undersampling schemes were performed to evaluate the proposed method in terms of visual image quality, root-mean-square-error (RMSE), and geometry factor (g-factor). The effects of acceleration factors, calibration data size and kernel shape on the proposed model were also separately analyzed and discussed. The proposed method illustrated improved visual image quality evidenced by reduced retrospective RMSE and prospective g-factor comparing with conventional GRAPPA and the recently proposed iterative SENSE-LORAKS reconstructions. Although a larger amount of calibration data and smaller kernel size were required to stabilize the calibration of fourfold extended kernel for the proposed method, it was non-iterative and relatively insensitive to parameter adjustment in the applications. The proposed NL-VCC-extension to conventional GRAPPA brings visible improvements for imaging scenarios accelerated by the widely available uniform undersampling schemes in a practically efficient manner without iteration.

ENLIVE: An Efficient Nonlinear Method for Calibrationless and Robust Parallel Imaging

Robustness against data inconsistencies, imaging artifacts and acquisition speed are crucial factors limiting the possible range of applications for magnetic resonance imaging (MRI). Therefore, we report a novel calibrationless parallel imaging technique which simultaneously estimates coil profiles and image content in a relaxed forward model. Our method is robust against a wide class of data inconsistencies, minimizes imaging artifacts and is comparably fast, combining important advantages of many conceptually different state-of-the-art parallel imaging approaches. Depending on the experimental setting, data can be undersampled well below the Nyquist limit. Here, even high acceleration factors yield excellent imaging results while being robust to noise and the occurrence of phase singularities in the image domain, as we show on different data. Moreover, our method successfully reconstructs acquisitions with insufficient field-of-view. We further compare our approach to ESPIRiT and SAKE using spin-echo and gradient echo MRI data from the human head and knee. In addition, we show its applicability to non-Cartesian imaging on radial FLASH cardiac MRI data. Using theoretical considerations, we show that ENLIVE can be related to a low-rank formulation of blind multi-channel deconvolution, explaining why it inherently promotes low-rank solutions.

Recent advances in parallel imaging for MRI

Magnetic Resonance Imaging (MRI) is an essential technology in modern medicine. However, one of its main drawbacks is the long scan time needed to localize the MR signal in space to generate an image. This review article summarizes some basic principles and recent developments in parallel imaging, a class of image reconstruction techniques for shortening scan time. First, the fundamentals of MRI data acquisition are covered, including the concepts of k-space, undersampling, and aliasing. It is demonstrated that scan time can be reduced by sampling a smaller number of phase encoding lines in k-space; however, without further processing, the resulting images will be degraded by aliasing artifacts. Nearly all modern clinical scanners acquire data from multiple independent receiver coil arrays. Parallel imaging methods exploit properties of these coil arrays to separate aliased pixels in the image domain or to estimate missing k-space data using knowledge of nearby acquired k-space points. Three parallel imaging methods-SENSE, GRAPPA, and SPIRiT-are described in detail, since they are employed clinically and form the foundation for more advanced methods. These techniques can be extended to non-Cartesian sampling patterns, where the collected k-space points do not fall on a rectangular grid. Non-Cartesian acquisitions have several beneficial properties, the most important being the appearance of incoherent aliasing artifacts. Recent advances in simultaneous multi-slice imaging are presented next, which use parallel imaging to disentangle images of several slices that have been acquired at once. Parallel imaging can also be employed to accelerate 3D MRI, in which a contiguous volume is scanned rather than sequential slices. Another class of phase-constrained parallel imaging methods takes advantage of both image magnitude and phase to achieve better reconstruction performance. Finally, some applications are presented of parallel imaging being used to accelerate MR Spectroscopic Imaging.

ESPIRiT--an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA

PURPOSE

Parallel imaging allows the reconstruction of images from undersampled multicoil data. The two main approaches are: SENSE, which explicitly uses coil sensitivities, and GRAPPA, which makes use of learned correlations in k-space. The purpose of this work is to clarify their relationship and to develop and evaluate an improved algorithm.

THEORY AND METHODS

A theoretical analysis shows: (1) The correlations in k-space are encoded in the null space of a calibration matrix. (2) Both approaches restrict the solution to a subspace spanned by the sensitivities. (3) The sensitivities appear as the main eigenvector of a reconstruction operator computed from the null space. The basic assumptions and the quality of the sensitivity maps are evaluated in experimental examples. The appearance of additional eigenvectors motivates an extended SENSE reconstruction with multiple maps, which is compared to existing methods.

RESULTS

The existence of a null space and the high quality of the extracted sensitivities are confirmed. The extended reconstruction combines all advantages of SENSE with robustness to certain errors similar to GRAPPA.

CONCLUSION

In this article the gap between both approaches is finally bridged. A new autocalibration technique combines the benefits of both.

Application of direct virtual coil to dynamic contrast-enhanced MRI and MR angiography with data-driven parallel imaging

PURPOSE

To demonstrate the feasibility of direct virtual coil (DVC) in the setting of 4D dynamic imaging used in multiple clinical applications.

THEORY AND METHODS

Three dynamic imaging applications were chosen: pulmonary perfusion, liver perfusion, and peripheral MR angiography (MRA), with 18, 11, and 10 subjects, respectively. After view-sharing, the k-space data were reconstructed twice: once with channel-by-channel (CBC) followed by sum-of-squares coil combination and once with DVC. Images reconstructed using CBC and DVC were compared and scored based on overall image quality by two experienced radiologists using a five-point scale.

RESULTS

The CBC and DVC showed similar image quality in image domain. Time course measurements also showed good agreement in the temporal domain. CBC and DVC images were scored as equivalent for all pulmonary perfusion cases, all liver perfusion cases, and four of the 10 peripheral MRA cases. For the remaining six peripheral MRA cases, DVC were scored as slightly better (not clinically significant) than the CBC images by Radiologist A and as equivalent by Radiologist B.

CONCLUSION

For dynamic contrast-enhanced MR applications, it is clinically feasible to reduce image reconstruction time while maintaining image quality and time course measurement using the DVC technique.

State-of-the-art MRI techniques in neuroradiology: principles, pitfalls, and clinical applications

This article reviews the most relevant state-of-the-art magnetic resonance (MR) techniques, which are clinically available to investigate brain diseases. MR acquisition techniques addressed include notably diffusion imaging (diffusion-weighted imaging (DWI), diffusion tensor imaging (DTI), and diffusion kurtosis imaging (DKI)) as well as perfusion imaging (dynamic susceptibility contrast (DSC), arterial spin labeling (ASL), and dynamic contrast enhanced (DCE)). The underlying models used to process these images are described, as well as the theoretic underpinnings of quantitative diffusion and perfusion MR imaging-based methods. The technical requirements and how they may help to understand, classify, or follow-up neurological pathologies are briefly summarized. Techniques, principles, advantages but also intrinsic limitations, typical artifacts, and alternative solutions developed to overcome them are discussed. In this article, we also review routinely available three-dimensional (3D) techniques in neuro MRI, including state-of-the-art and emerging angiography sequences, and briefly introduce more recently proposed 3D quantitative neuro-anatomy sequences, and new technology, such as multi-slice and multi-transmit imaging.

Comparison of phase-constrained parallel MRI approaches: Analogies and differences

PURPOSE

Phase-constrained parallel MRI approaches have the potential for significantly improving the image quality of accelerated MRI scans. The purpose of this study was to investigate the properties of two different phase-constrained parallel MRI formulations, namely the standard phase-constrained approach and the virtual conjugate coil (VCC) concept utilizing conjugate k-space symmetry.

METHODS

Both formulations were combined with image-domain algorithms (SENSE) and a mathematical analysis was performed. Furthermore, the VCC concept was combined with k-space algorithms (GRAPPA and ESPIRiT) for image reconstruction. In vivo experiments were conducted to illustrate analogies and differences between the individual methods. Furthermore, a simple method of improving the signal-to-noise ratio by modifying the sampling scheme was implemented.

RESULTS

For SENSE, the VCC concept was mathematically equivalent to the standard phase-constrained formulation and therefore yielded identical results. In conjunction with k-space algorithms, the VCC concept provided more robust results when only a limited amount of calibration data were available. Additionally, VCC-GRAPPA reconstructed images provided spatial phase information with full resolution.

CONCLUSIONS

Although both phase-constrained parallel MRI formulations are very similar conceptually, there exist important differences between image-domain and k-space domain reconstructions regarding the calibration robustness and the availability of high-resolution phase information.

An L1-norm phase constraint for half-Fourier compressed sensing in 3D MR imaging

OBJECTIVE

In most half-Fourier imaging methods, explicit phase replacement is used. In combination with parallel imaging, or compressed sensing, half-Fourier reconstruction is usually performed in a separate step. The purpose of this paper is to report that integration of half-Fourier reconstruction into iterative reconstruction minimizes reconstruction errors.

MATERIALS AND METHODS

The L1-norm phase constraint for half-Fourier imaging proposed in this work is compared with the L2-norm variant of the same algorithm, with several typical half-Fourier reconstruction methods. Half-Fourier imaging with the proposed phase constraint can be seamlessly combined with parallel imaging and compressed sensing to achieve high acceleration factors.

RESULTS

In simulations and in in-vivo experiments half-Fourier imaging with the proposed L1-norm phase constraint enables superior performance both reconstruction of image details and with regard to robustness against phase estimation errors.

CONCLUSION

The performance and feasibility of half-Fourier imaging with the proposed L1-norm phase constraint is reported. Its seamless combination with parallel imaging and compressed sensing enables use of greater acceleration in 3D MR imaging.

Fast pediatric 3D free-breathing abdominal dynamic contrast enhanced MRI with high spatiotemporal resolution

PURPOSE

To develop a method for fast pediatric 3D free-breathing abdominal dynamic contrast enhanced (DCE) magnetic resonance imaging (MRI) and investigate its clinical feasibility.

MATERIALS AND METHODS

A combined locally low rank parallel imaging method with soft gating is proposed for free-breathing DCE MRI acquisition. With Institutional Review Board (IRB) approval and informed consent/assent, 23 consecutive pediatric patients were recruited for this study. Free-breathing DCE MRI with ∼1 mm(3) spatial resolution and a 6.5-sec frame rate was acquired on a 3T scanner. Undersampled data were reconstructed with a compressed sensing method without motion correction (FB-CS) and the proposed method (FB-LR). A follow-up respiratory-triggered acquisition (RT-CS) was performed as a reference standard. The reconstructed images were evaluated independently by two radiologists. Wilcoxon tests were performed to test the hypothesis that there was no significant difference between different reconstructions. Quantitative evaluation of contrast dynamics was also performed.

RESULTS

The mean score of overall image quality of FB-LR was 4.0 on a 5-point scale, significantly better (P < 0.05) than FB-CS reconstruction (mean score 2.9), and similar to RT-CS (mean score 4.1). FB-LR also matched the temporal fidelity of contrast dynamics with a root mean square error less than 5%.

CONCLUSION

Fast 3D free-breathing DCE MRI with high scan efficiency and image quality similar to respiratory-triggered acquisition is feasible in a pediatric clinical setting.

Image reconstruction in k-space from MR data encoded with ambiguous gradient fields

PURPOSE

In this work, the limits of image reconstruction in k-space are explored when non-bijective gradient fields are used for spatial encoding.

THEORY

The image space analogy between parallel imaging and imaging with non-bijective encoding fields is partially broken in k-space. As a consequence, it is hypothesized and proven that ambiguities can only be resolved partially in k-space, and not completely as is the case in image space.

METHODS

Image-space and k-space based reconstruction algorithms for multi-channel radiofrequency data acquisitions are programmed and tested using numerical simulations as well as in vivo measurement data.

RESULTS

The hypothesis is verified based on an analysis of reconstructed images. It is found that non-bijective gradient fields have the effect that densely sampled autocalibration data, used for k-space reconstruction, provide less information than a separate scan of the receiver coil sensitivity maps, used for image space reconstruction. Consequently, in k-space only the undersampling artifact can be unfolded, whereas in image space, it is also possible to resolve aliasing that is caused by the non-bijectivity of the gradient fields.

CONCLUSION

For standard imaging, reconstruction in image space and in k-space is nearly equivalent, whereas there is a fundamental difference with practical consequences for the selection of image reconstruction algorithms when non-bijective encoding fields are involved.

Myocardial arterial spin labeling perfusion imaging with improved sensitivity

BACKGROUND

Myocardial arterial spin labeling (ASL) is a noninvasive MRI based technique that is capable of measuring myocardial blood flow (MBF) in humans. It suffers from poor sensitivity to MBF due to high physiological noise (PN). This study aims to determine if the sensitivity of myocardial ASL to MBF can be improved by reducing image acquisition time, via parallel imaging.

METHODS

Myocardial ASL scans were performed in 7 healthy subjects at rest using flow-sensitive alternating inversion recovery (FAIR) tagging and balanced steady state free precession (SSFP) imaging. Sensitivity encoding (SENSE) with a reduction factor of 2 was used to shorten each image acquisition from roughly 300 ms per heartbeat to roughly 150 ms per heartbeat. A paired Student's t-test was performed to compare measurements of myocardial blood flow (MBF) and physiological noise (PN) from the reference and accelerated methods.

RESULTS

The measured PN (mean ± standard deviation) was 0.20 ± 0.08 ml/g/min for the reference method and 0.08 ± 0.05 ml/g/min for the accelerated method, corresponding to a 60% reduction. PN measured from the accelerated method was found to be significantly lower than that of the reference method (p=0.0059). There was no significant difference between MBF measured from the accelerated and reference ASL methods (p=0.7297).

CONCLUSIONS

In this study, significant PN reduction was achieved by shortening the acquisition window using parallel imaging with no significant impact on the measured MBF. This indicates an improvement in sensitivity to MBF and may also enable the imaging of subjects with higher heart rates and imaging during systole.

Radial k-t SPIRiT: autocalibrated parallel imaging for generalized phase-contrast MRI

PURPOSE

To extend SPIRiT to additionally exploit temporal correlations for highly accelerated generalized phase-contrast MRI and to compare the performance of the proposed radial k-t SPIRiT method relative to frame-by-frame SPIRiT and radial k-t GRAPPA reconstruction for velocity and turbulence mapping in the aortic arch.

THEORY AND METHODS

Free-breathing navigator-gated two-dimensional radial cine imaging with three-directional multi-point velocity encoding was implemented and fully sampled data were obtained in the aortic arch of healthy volunteers. Velocities were encoded with three different first gradient moments per axis to permit quantification of mean velocity and turbulent kinetic energy. Velocity and turbulent kinetic energy maps from up to 14-fold undersampled data were compared for k-t SPIRiT, frame-by-frame SPIRiT, and k-t GRAPPA relative to the fully sampled reference.

RESULTS

Using k-t SPIRiT, improvements in magnitude and velocity reconstruction accuracy were found. Temporally resolved magnitude profiles revealed a reduction in spatial blurring with k-t SPIRiT compared with frame-by-frame SPIRiT and k-t GRAPPA for all velocity encodings, leading to improved estimates of turbulent kinetic energy.

CONCLUSION

k-t SPIRiT offers improved reconstruction accuracy at high radial undersampling factors and hence facilitates the use of generalized phase-contrast MRI for routine use.

Cardiovascular magnetic resonance artefacts

The multitude of applications offered by CMR make it an increasing popular modality to study the heart and the surrounding vessels. Nevertheless the anatomical complexity of the chest, together with cardiac and respiratory motion, and the fast flowing blood, present many challenges which can possibly translate into imaging artefacts. The literature is wide in terms of papers describing specific MR artefacts in great technical detail. In this review we attempt to summarise, in a language accessible to a clinical readership, some of the most common artefacts found in CMR applications. It begins with an introduction of the most common pulse sequences, and imaging techniques, followed by a brief section on typical cardiovascular applications. This leads to the main section on common CMR artefacts with examples, a short description of the mechanisms behind them, and possible solutions.

Parallel MR imaging

Parallel imaging is a robust method for accelerating the acquisition of magnetic resonance imaging (MRI) data, and has made possible many new applications of MR imaging. Parallel imaging works by acquiring a reduced amount of k-space data with an array of receiver coils. These undersampled data can be acquired more quickly, but the undersampling leads to aliased images. One of several parallel imaging algorithms can then be used to reconstruct artifact-free images from either the aliased images (SENSE-type reconstruction) or from the undersampled data (GRAPPA-type reconstruction). The advantages of parallel imaging in a clinical setting include faster image acquisition, which can be used, for instance, to shorten breath-hold times resulting in fewer motion-corrupted examinations. In this article the basic concepts behind parallel imaging are introduced. The relationship between undersampling and aliasing is discussed and two commonly used parallel imaging methods, SENSE and GRAPPA, are explained in detail. Examples of artifacts arising from parallel imaging are shown and ways to detect and mitigate these artifacts are described. Finally, several current applications of parallel imaging are presented and recent advancements and promising research in parallel imaging are briefly reviewed.

Sparse Methods for Biomedical Data

Following recent technological revolutions, the investigation of massive biomedical data with growing scale, diversity, and complexity has taken a center stage in modern data analysis. Although complex, the underlying representations of many biomedical data are often sparse. For example, for a certain disease such as leukemia, even though humans have tens of thousands of genes, only a few genes are relevant to the disease; a gene network is sparse since a regulatory pathway involves only a small number of genes; many biomedical signals are sparse or compressible in the sense that they have concise representations when expressed in a proper basis. Therefore, finding sparse representations is fundamentally important for scientific discovery. Sparse methods based on the [Formula: see text] norm have attracted a great amount of research efforts in the past decade due to its sparsity-inducing property, convenient convexity, and strong theoretical guarantees. They have achieved great success in various applications such as biomarker selection, biological network construction, and magnetic resonance imaging. In this paper, we review state-of-the-art sparse methods and their applications to biomedical data.

Improved parallel MR imaging using a coefficient penalized regularization for GRAPPA reconstruction

A novel coefficient penalized regularization method for generalized autocalibrating partially parallel acquisitions (GRAPPA) reconstruction is developed for improving MR image quality. In this method, the fitting coefficients of the source data are weighted with different penalty factors, which are highly dependent upon the relative displacements from the source data to the target data in k-space. The imaging data from both phantom testing and in vivo MRI experiments demonstrate that the coefficient penalized regularization method in GRAPPA reconstruction is able to reduce noise amplification to a greater degree. Therefore, the method enhances the quality of images significantly when compared to the previous least squares and Tikhonov regularization methods.

Coil compression for accelerated imaging with Cartesian sampling

MRI using receiver arrays with many coil elements can provide high signal-to-noise ratio and increase parallel imaging acceleration. At the same time, the growing number of elements results in larger datasets and more computation in the reconstruction. This is of particular concern in 3D acquisitions and in iterative reconstructions. Coil compression algorithms are effective in mitigating this problem by compressing data from many channels into fewer virtual coils. In Cartesian sampling there often are fully sampled k-space dimensions. In this work, a new coil compression technique for Cartesian sampling is presented that exploits the spatially varying coil sensitivities in these nonsubsampled dimensions for better compression and computation reduction. Instead of directly compressing in k-space, coil compression is performed separately for each spatial location along the fully sampled directions, followed by an additional alignment process that guarantees the smoothness of the virtual coil sensitivities. This important step provides compatibility with autocalibrating parallel imaging techniques. Its performance is not susceptible to artifacts caused by a tight imaging field-of-view. High quality compression of in vivo 3D data from a 32 channel pediatric coil into six virtual coils is demonstrated.

Temporal filtering effects in dynamic parallel MRI

Autocalibrated parallel MRI methods such as TSENSE or k-t SENSE have been presented for dynamic imaging studies as they are able to provide images with high temporal resolution. One key element of these techniques is the temporal averaging of the undersampled raw data to obtain an unaliased image. This image represents the temporal average (also known as direct current, DC) and is used to derive the reconstruction parameters. In this work, we show that aliasing artifacts can be introduced in the DC signal obtained from the undersampled raw data. These artifacts lead to undesired temporal filtering effects when the DC signal is used for coil sensitivity calibration or when the DC signal is subtracted from the raw data. It is demonstrated that the temporal filtering effects can be reduced significantly by filtering the DC signal.

SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space

A new approach to autocalibrating, coil-by-coil parallel imaging reconstruction, is presented. It is a generalized reconstruction framework based on self-consistency. The reconstruction problem is formulated as an optimization that yields the most consistent solution with the calibration and acquisition data. The approach is general and can accurately reconstruct images from arbitrary k-space sampling patterns. The formulation can flexibly incorporate additional image priors such as off-resonance correction and regularization terms that appear in compressed sensing. Several iterative strategies to solve the posed reconstruction problem in both image and k-space domain are presented. These are based on a projection over convex sets and conjugate gradient algorithms. Phantom and in vivo studies demonstrate efficient reconstructions from undersampled Cartesian and spiral trajectories. Reconstructions that include off-resonance correction and nonlinear l(1)-wavelet regularization are also demonstrated.

Breathheld autocalibrated phase-contrast imaging

PURPOSE

To compare generalized autocalibrating partially parallel acquisitions (GRAPPA), modified sensitivity encoding (mSENSE), and SENSE in phase-contrast magnetic resonance imaging (PC-MRI) applications.

MATERIALS AND METHODS

Aliasing of the torso can occur in PC-MRI applications. If the data are further undersampled for parallel imaging, SENSE can be problematic in correctly unaliasing signals due to coil sensitivity maps that do not match that of the aliased volume. Here, a method for estimating coil sensitivities in flow applications is described. Normal volunteers (n = 5) were scanned on a 1.5 T MRI scanner and underwent PC-MRI scans using GRAPPA, mSENSE, SENSE, and conventional PC-MRI acquisitions. Peak velocity and flow through the aorta and pulmonary artery were evaluated.

RESULTS

Bland-Altman statistics for flow in the aorta and pulmonary artery acquired with mSENSE and GRAPPA methods (R = 2 and R = 3 cases) have comparable mean differences to flow acquired with conventional PC-MRI. GRAPPA and mSENSE PC-MRI have more robust measurements than SENSE when there is aliasing artifact caused by insufficient coil sensitivity maps. For peak velocity, there are no considerable differences among the mSENSE, GRAPPA, and SENSE reconstructions and are comparable to conventional PC-MRI.

CONCLUSION

Flow measurements of images reconstructed with autocalibration techniques have comparable agreement with conventional PC-MRI and provide robust measurements in the presence of wraparound.

Parallel imaging artifacts in body magnetic resonance imaging

OBJECTIVE

To familiarize the reader with the fundamental concepts of partial parallel imaging (PPI); to review the technical aspects of PPI including calibration scan, coil geometry, and field of view (FOV); and to illustrate artifacts related to parallel imaging and describe solutions to minimize their negative impact.

RESULTS

PPI has led to a significant advance in body magnetic resonance imaging by reducing the time required to generate an image without loss of spatial resolution. Although PPI can improve image quality, it is not free of artifacts, which can result in significant image degradation. Knowledge of these artifacts and how to minimize their effect is important to optimize the use of parallel imaging for specific body magnetic resonance imaging applications.

CONCLUSIONS

The reader will be introduced to the fundamental principles of PPI. Common imaging characteristics of PPI artifacts will be displayed with an emphasis on those seen with image-based methods, the principles behind their generation presented, and measures to minimize their negative impact will be proposed.

Elliptical magnetic resonance spectroscopic imaging with GRAPPA for imaging brain tumors at 3 T

Magnetic Resonance Spectroscopic Imaging (MRSI) is a technique for imaging spatial variation of metabolites and has been very useful in characterizing biochemical changes associated with disease as well as response to therapy in malignant pathologies. This work presents a self-calibrated undersampling to accelerate 3D elliptical MRSI and an extrapolation-reconstruction algorithm based on the GRAPPA method. The accelerated MRSI technique was tested in three volunteers and five brain tumor patients. Acceleration allowed larger spatial coverage and consequently, less lipid contamination in spectra, compared to fully sampled acquisition within the same scantime. Metabolite concentrations measured from the accelerated acquisitions were in good agreement with measurements obtained from fully sampled MRSI scans.

Regionally optimized reconstruction for partially parallel imaging in MRI applications

Based on the conventional SENSE and GRAPPA, a regionally optimized reconstruction method is developed for reduced noise and artifact level in partially parallel imaging. In this regionally optimized reconstruction, the field-of-view (FOV) is divided into a number of small regions. Over every small region, the noise amplification and data fitting error can be balanced and minimized locally by taking advantage of spatial correlation of neighboring pixels in reconstruction. The full FOV image can be obtained by "region-by-region" reconstruction. Compared with the conventional SENSE, this method gives better performance in the regions where there are pixels with high SENSE g-factors. Compared with GRAPPA, it is better in the regions where all the pixels have low SENSE g-factors. In this work, we applied the regionally optimized reconstruction in four important imaging experiments: brain, spine, breast, and cardiac. It was demonstrated in these experiments that the overall image quality using this regionally optimized reconstruction is better than that using the conventional SENSE or GRAPPA.

High temporal resolution functional MRI using parallel echo volumar imaging

PURPOSE

To combine parallel imaging with 3D single-shot acquisition (echo volumar imaging, EVI) in order to acquire high temporal resolution volumar functional MRI (fMRI) data.

MATERIALS AND METHODS

An improved EVI sequence was associated with parallel acquisition and field of view reduction in order to acquire a large brain volume in 200 msec. Temporal stability and functional sensitivity were increased through optimization of all imaging parameters and Tikhonov regularization of parallel reconstruction. Two human volunteers were scanned with parallel EVI in a 1.5T whole-body MR system, while submitted to a slow event-related auditory paradigm.

RESULTS

Thanks to parallel acquisition, the EVI volumes display a low level of geometric distortions and signal losses. After removal of low-frequency drifts and physiological artifacts, activations were detected in the temporal lobes of both volunteers and voxelwise hemodynamic response functions (HRF) could be computed. On these HRF different habituation behaviors in response to sentence repetition could be identified.

CONCLUSION

This work demonstrates the feasibility of high temporal resolution 3D fMRI with parallel EVI. Combined with advanced estimation tools, this acquisition method should prove useful to measure neural activity timing differences or study the nonlinearities and nonstationarities of the BOLD response.

Fast four-dimensional coronary MR angiography with k-t GRAPPA

PURPOSE

To investigate the effectiveness of k-t GRAPPA for accelerating four-dimensional (4D) coronary MRA in comparison with GRAPPA and the feasibility of combining variable density undersampling with conventional k-t GRAPPA (k-t(2) GRAPPA) to alleviate the overhead of acquiring autocalibration signals.

MATERIALS AND METHODS

The right coronary artery of nine healthy volunteers was scanned at 1.5 Tesla. The 4D k-space datasets were fully acquired and subsequently undersampled to simulate partially parallel acquisitions, namely, GRAPPA, k-t GRAPPA, and k-t(2) GRAPPA. Comparisons were made between the images reconstructed from full k-space datasets and those reconstructed from undersampled k-space datasets.

RESULTS

k-t GRAPPA significantly reduced artifacts compared with GRAPPA and high acceleration factors were achieved with only minimal sacrifices in vessel depiction. k-t(2) GRAPPA could further increase imaging speed without significant losses in image quality.

CONCLUSION

By exploiting high-degree spatiotemporal correlations during the rest period of a cardiac cycle, k-t GRAPPA and k-t(2) GRAPPA can greatly increase data acquisition efficiency and, therefore, are promising solutions for fast 4D coronary MRA.

Comparison of parallel acquisition techniques generalized autocalibrating partially parallel acquisitions (GRAPPA) and modified sensitivity encoding (mSENSE) in functional MRI (fMRI) at 3T

PURPOSE

To evaluate the parallel acquisition techniques, generalized autocalibrating partially parallel acquisitions (GRAPPA) and modified sensitivity encoding (mSENSE), and determine imaging parameters maximizing sensitivity toward functional activation at 3T.

MATERIALS AND METHODS

A total of eight imaging protocols with different parallel imaging techniques (GRAPPA and mSENSE) and reduction factors (R = 1, 2, 3) were compared at different matrix sizes (64 and 128) with respect to temporal noise characteristics, artifact behavior, and sensitivity toward functional activation.

RESULTS

Echo planar imaging (EPI) with GRAPPA and a reduction factor of 2 revealed similar image quality and sensitivity than full k-space EPI. A higher incidence of artifacts and a marked sensitivity loss occurred at R = 3. Even though the same eight-channel head coil was used for signal detection in all experiments, GRAPPA generally showed more benign patterns of spatially-varying noise amplification, and mSENSE was also more susceptible to residual unfolding artifacts than GRAPPA.

CONCLUSION

At 3T and a reduction factor of 2, parallel imaging can be used with only little penalty with regard to sensitivity. With our implementation and coil setup the performance of GRAPPA was clearly superior to mSENSE. Thus, it seems advisable to pay special attention to the employed parallel imaging method and its implementation.

Influence of multichannel combination, parallel imaging and other reconstruction techniques on MRI noise characteristics

The statistical properties of background noise such as its standard deviation and mean value are frequently used to estimate the original noise level of the acquired data. This requires the knowledge of the statistical intensity distribution of the background signal, that is, the probability density of the occurrence of a certain signal intensity. The influence of many new MRI techniques and, in particular, of various parallel-imaging methods on the noise statistics has neither been rigorously investigated nor experimentally demonstrated yet. In this study, the statistical distribution of background noise was analyzed for MR acquisitions with a single-channel and a 32-channel coil, with sum-of-squares (SoS) and spatial-matched-filter (SMF) data combination, with and without parallel imaging using k-space and image-domain algorithms, with real-part and conventional magnitude reconstruction and with several reconstruction filters. Depending on the imaging technique, the background noise could be described by a Rayleigh distribution, a noncentral chi-distribution or the positive half of a Gaussian distribution. In particular, the noise characteristics of SoS-reconstructed multichannel acquisitions (with k-space-based parallel imaging or without parallel imaging) differ substantially from those with image-domain parallel imaging or SMF combination. These effects must be taken into account if mean values or standard deviations of background noise are employed for data analysis such as determination of local noise levels. Assuming a Rayleigh distribution as in conventional MR images or a noncentral chi-distribution for all multichannel acquisitions is invalid in general and may lead to erroneous estimates of the signal-to-noise ratio or the contrast-to-noise ratio.

Comparison of reconstruction accuracy and efficiency among autocalibrating data-driven parallel imaging methods

The class of autocalibrating "data-driven" parallel imaging (PI) methods has gained attention in recent years due to its ability to achieve high quality reconstructions even under challenging imaging conditions. The aim of this work was to perform a formal comparative study of various data-driven reconstruction techniques to evaluate their relative merits for certain imaging applications. A total of five different reconstruction methods are presented within a consistent theoretical framework and experimentally compared in terms of the specific measures of reconstruction accuracy and efficiency using one-dimensional (1D)-accelerated Cartesian datasets. It is shown that by treating the reconstruction process as two discrete phases, a calibration phase and a synthesis phase, the reconstruction pathway can be tailored to exploit the computational advantages available in certain data domains. A new "split-domain" reconstruction method is presented that performs the calibration phase in k-space (k(x), k(y)) and the synthesis phase in a hybrid (x, k(y)) space, enabling highly accurate 2D neighborhood reconstructions to be performed more efficiently than previously possible with conventional techniques. This analysis may help guide the selection of PI methods for a given imaging task to achieve high reconstruction accuracy at minimal computational expense.

SSFP and GRE phase contrast imaging using a three-echo readout

A technique for rapid in-plane phase-contrast imaging with high signal-to-noise ratio (SNR) is described. Velocity-encoding is achieved by oscillating the readout gradient, such that each 2DFT phase-encode is acquired three times following a single RF slice-selective excitation. Three images are reconstructed, from which both flow velocity and local resonance offset are calculated. This technique is compatible with both gradient-recalled echo (GRE) and balanced steady-state free precession (SSFP) imaging using a single steady-state. The proposed technique enables 1D velocity mapping with 40% higher temporal resolution and 80% higher SNR, compared to conventional PC-MRI using bipolar velocity-encoding gradient pulses.

Highly accelerated cardiovascular MR imaging using many channel technology: concepts and clinical applications

Cardiovascular magnetic resonance imaging (CVMRI) is of proven clinical value in the non-invasive imaging of cardiovascular diseases. CVMRI requires rapid image acquisition, but acquisition speed is fundamentally limited in conventional MRI. Parallel imaging provides a means for increasing acquisition speed and efficiency. However, signal-to-noise (SNR) limitations and the limited number of receiver channels available on most MR systems have in the past imposed practical constraints, which dictated the use of moderate accelerations in CVMRI. High levels of acceleration, which were unattainable previously, have become possible with many-receiver MR systems and many-element, cardiac-optimized RF-coil arrays. The resulting imaging speed improvements can be exploited in a number of ways, ranging from enhancement of spatial and temporal resolution to efficient whole heart coverage to streamlining of CVMRI work flow. In this review, examples of these strategies are provided, following an outline of the fundamentals of the highly accelerated imaging approaches employed in CVMRI. Topics discussed include basic principles of parallel imaging; key requirements for MR systems and RF-coil design; practical considerations of SNR management, supported by multi-dimensional accelerations, 3D noise averaging and high field imaging; highly accelerated clinical state-of-the art cardiovascular imaging applications spanning the range from SNR-rich to SNR-limited; and current trends and future directions.

Reconstruction in image space using basis functions for partially parallel imaging

General theory of a new reconstruction technique for partially parallel imaging (PPI) is presented in this study. Reconstruction in Image space using Basis functions (RIB) is based on the general principle that the PPI reconstruction in image space can be represented by a pixel-wise weighted summation of the aliased images directly from undersampled data. By assuming that these weighting coefficients for unaliasing can be approximated from the linear combination of a few predefined basis functions, RIB is capable of reconstructing the image within an arbitrary region. This paper discusses the general theory of RIB and its relationship to the classical reconstruction method, GRAPPA. The presented experiments demonstrate RIB with several MRI applications. It is shown that the performance of RIB is comparable to that of GRAPPA. In some cases, RIB shows advantages of increasing reconstruction efficiency, suppressing artifacts and alleviating the nonuniformity of noise distribution. It is anticipated that RIB would be especially useful for cardiac and prostate imaging, where the field of view during data acquisition is required to be much larger than the region of interest.

Measurement of signal-to-noise ratios in MR images: influence of multichannel coils, parallel imaging, and reconstruction filters

PURPOSE

To evaluate the validity of different approaches to determine the signal-to-noise ratio (SNR) in MRI experiments with multi-element surface coils, parallel imaging, and different reconstruction filters.

MATERIALS AND METHODS

Four different approaches of SNR calculation were compared in phantom measurements and in vivo based on: 1) the pixel-by-pixel standard deviation (SD) in multiple repeated acquisitions; 2) the signal statistics in a difference image; and 3) and 4) the statistics in two separate regions of a single image employing either the mean value or the SD of background noise. Different receiver coil systems (with one and eight channels), acquisitions with and without parallel imaging, and five different reconstruction filters were compared.

RESULTS

Averaged over all phantom measurements, the deviations from the reference value provided by the multiple-acquisitions method are 2.7% (SD 1.6%) for the difference method, 37.7% (25.9%) for the evaluation of the mean value of background noise, and 34.0% (38.1%) for the evaluation of the SD of background noise.

CONCLUSION

The conventionally determined SNR based on separate signal and noise regions in a single image will in general not agree with the true SNR measured in images after the application of certain reconstruction filters, multichannel reconstruction, or parallel imaging.

Noise distribution in SENSE- and GRAPPA-reconstructed images: a computer simulation study

This work presents a descriptive study of noise distributions in images reconstructed according to the parallel imaging methods SENSE and GRAPPA. In the computer simulations, two different settings were used for describing an object. The first setting included a synthetic object and eight complex-valued coil sensitivities. In the second setting, a complex-valued in vitro object, composed of four individual coil images, was used. After adding noise and subsampling k-space for each coil image, reconstruction was performed according to SENSE, with and without regularization, and GRAPPA for different reduction factors. A set of images was created for three different reduction factors. Noise distributions were determined for each data set and compared with each other. The results of this study show that the noise distributions in SENSE- and GRAPPA-reconstructed images differ. The noise in images reconstructed according to GRAPPA has a more uniform spatial distribution compared with SENSE-reconstructed images, in which the noise varies regionally according to the geometry factor. The noise distribution in SENSE-reconstructed images using regularization showed a similar but lowered pattern of noise compared with images reconstructed according to SENSE without regularization.

Clinical multishot DW-EPI through parallel imaging with considerations of susceptibility, motion, and noise

Geometric distortions and poor image resolution are well known shortcomings of single-shot echo-planar imaging (ss-EPI). Yet, due to the motion immunity of ss-EPI, it remains the most common sequence for diffusion-weighted imaging (DWI). Moreover, both navigated DW interleaved EPI (iEPI) and parallel imaging (PI) methods, such as sensitivity encoding (SENSE) and generalized autocalibrating parallel acquisitions (GRAPPA), can improve the image quality in EPI. In this work, DW-EPI accelerated by PI is proposed as a self-calibrated and unnavigated form of interleaved acquisition. The PI calibration is performed on the b = 0 s/mm2 data and applied to each shot in the rest of the DW data set, followed by magnitude averaging. Central in this study is the comparison of GRAPPA and SENSE in the presence of off-resonances and motion. The results show that GRAPPA is more robust than SENSE against both off-resonance and motion-related artifacts. The SNR efficiency was also investigated, and it is shown that the SNR/scan time ratio is equally high for one- to three-shot high-resolution diffusion scans due to the shortened EPI readout train length. The image quality improvements without SNR efficiency loss, together with motion tolerance, make the GRAPPA-driven DW-EPI sequence clinically attractive.

Magnetic resonance angiography of chest and abdomen at 3 T

During the past decade, contrast-enhanced magnetic resonance angiography (CE-MRA) has been proven to be a powerful tool to visualize the thoracoabdominal vasculature and, consequently, has become a widely accepted noninvasive imaging modality. With the more recent introduction of high-field whole-body magnetic resonance scanners, a further improvement of diagnostic accuracy can be expected. General considerations for performing high-resolution CE-MRA at higher field strength include the benefits of higher signal-to-noise ratio and an improved contrast between vascular and background tissues. Although there are many positive attributes for performing CE-MRA at 3 T, there are also some tradeoffs, such as static magnetic field inhomogeneity and increase in specific absorption rate. This review describes the main technical innovations of advanced CE-MRA techniques at 3 T, illustrated by characteristic cases.