Simultaneous Acquisition Of Spatial Harmonics Research Articles

Multiple-coil k-space interpolation enhances resolution in single-shot spatiotemporal MRI.

Spatio-temporal encoding (SPEN) experiments can deliver single-scan MR images without folding complications and with robustness to chemical shift and susceptibility artifacts. Further resolution improvements are shown to arise by relying on multiple receivers, to interpolate the sampled data along the low-bandwidth dimension. The ensuing multiple-sensor interpolation is akin to recently introduced SPEN interleaving procedures, albeit without requiring multiple shots. By casting SPEN's spatial rasterization in k-space, it becomes evident that local k-data interpolations enabled by multiple receivers are akin to real-space interleaving of SPEN images. The practical implementation of such a resolution-enhancing procedure becomes similar to those normally used in simultaneous acquisition of spatial harmonics or sensitivity encoding, yet relaxing these methods' fold-over constraints. Experiments validating the theoretical expectations were carried out on phantoms and human volunteers on a 3T scanner. The experiments showed the expected resolution enhancement, at no cost to the sequence's complexity. With the addition of multibanding and stimulated echo procedures, 48-slice full-brain coverage could be recorded free from distortions at submillimeter resolution, in 3 s. Super-resolved SPEN with SENSE (SUSPENSE) achieves the goals of multishot SPEN interleaving delivering single-shot submillimeter in-plane resolutions in scanners equipped with suitable multiple sensors. Magn Reson Med 79:796-805, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Joint image reconstruction and sensitivity estimation in SENSE (JSENSE)

Parallel magnetic resonance imaging (pMRI) using multichannel receiver coils has emerged as an effective tool to reduce imaging time in various applications. However, the issue of accurate estimation of coil sensitivities has not been fully addressed, which limits the level of speed enhancement achievable with the technology. The self-calibrating (SC) technique for sensitivity extraction has been well accepted, especially for dynamic imaging, and complements the common calibration technique that uses a separate scan. However, the existing method to extract the sensitivity information from the SC data is not accurate enough when the number of data is small, and thus erroneous sensitivities affect the reconstruction quality when they are directly applied to the reconstruction equation. This paper considers this problem of error propagation in the sequential procedure of sensitivity estimation followed by image reconstruction in existing methods, such as sensitivity encoding (SENSE) and simultaneous acquisition of spatial harmonics (SMASH), and reformulates the image reconstruction problem as a joint estimation of the coil sensitivities and the desired image, which is solved by an iterative optimization algorithm. The proposed method was tested on various data sets. The results from a set of in vivo data are shown to demonstrate the effectiveness of the proposed method, especially when a rather large net acceleration factor is used.

K-space in the clinic.

Magnetic resonance imaging (MRI) sequences are characterized by both radio frequency (RF) pulses and time-varying gradient magnetic fields. The RF pulses manipulate the alignment of the resonant nuclei and thereby generate a measurable signal. The gradient fields spatially encode the signals so that those arising from one location in an excited slice of tissue may be distinguished from those arising in another location. These signals are collected and mapped into an array called k-space that represents the spatial frequency content of the imaged object. Spatial frequencies indicate how rapidly an image feature changes over a given distance. It is the action of the gradient fields that determines where in the k-space array each data point is located, with the order in which k-space points are acquired being described by the k-space trajectory. How signals are mapped into k-space determines much of the spatial, temporal, and contrast resolution of the resulting images and scan duration. The objective of this article is to provide an understanding of k-space as is needed to better understand basic research in MRI and to make well-informed decisions about clinical protocols. Four major classes of trajectories-echo planar imaging (EPI), standard (non-EPI) rectilinear, radial, and spiral-are explained. Parallel imaging techniques SMASH (simultaneous acquisition of spatial harmonics) and SENSE (sensitivity encoding) are also described.

A four-element phased array coil for high resolution and parallel MR imaging of the knee.

A four-element phased array coil for MR imaging of the knee was designed, built and tested for clinical use at 1.5 Tesla. In routine imaging, it provides over twofold increase in signal-to-noise (SNR) compared to two commercially available knee coils, and supports higher spatial image resolution. The phased array knee coil was also tested for its compatibility with parallel MR imaging that reduces imaging time by several folds over conventional MR technique. Results obtained using SiMultaneous Acquisition of Spatial Harmonics (SMASH) technique shows that our phased array knee coil can be used with parallel MR imaging. These improvements may enhance knee diagnosis with higher image quality and reduced scan time.

Usefulness of the simultaneous acquisition of spatial harmonics technique during MRI of the shoulder.

The simultaneous acquisition of spatial harmonics (SMASH) technique is a parallel imaging technique that uses fewer echoes than conventional techniques to obtain the desired resolution. Production of images occurs more quickly with parallel imaging than with conventional imaging. This study assesses the usefulness of the SMASH technique for MRI of the shoulder. SUBJECTS AND METHODS. Five experienced musculoskeletal radiologists prospectively interpreted MRIs of the shoulder in 50 consecutive patients. All patients underwent a complete MRI examination of the shoulder on a 1.5-T commercially available scanner. Axial fat-saturated proton density-weighted, coronal T1-weighted, and coronal and sagittal fat-saturated T2-weighted sequences were performed. Patients also underwent SMASH T2-weighted imaging in the coronal and sagittal planes. Coronal and sagittal SMASH T2-weighted imaging took approximately 50% as long to complete compared with conventional T2-weighted imaging. Each radiologist interpreted MRIs of the shoulder without knowing whether the images were obtained using the SMASH or the fat-saturated T2-weighted technique. Twenty-eight of the 50 patients also underwent subsequent arthroscopy, and the results were compared with MRI interpretations based on SMASH and fat-saturated T2-weighted images. We found no intraobserver variability between the interpretations of SMASH imaging and the interpretations of fat-saturated T2-weighted imaging. Of the 28 patients who also underwent subsequent arthroscopy, 19 were found to have full-thickness supraspinatus tendon tears and nine had superior labral anterior-to-posterior lesions. All arthroscopic findings correlated with prospective MRI interpretations. SMASH imaging allows significant time savings compared with fat-saturated T2-weighted MRI. We found that the use of the SMASH technique did not affect the MRI interpretation or the clinical outcome of patients.

SMASH navigators.

The additional data acquired when using multiple receiver coils is commonly used to improve SNR or reduce acquisition times. It may also be used to remove image artifacts by selectively replacing corrupt data. In the present study, a correction scheme is presented based on simultaneous acquisition of spatial harmonics (SMASH) that enables detection and correction of motion artifacts caused by 2D translations. Newly measured data is compared with predictions from previously measured data by making negative and positive spatial harmonics. Differences are attributed to motion occurring in the interval between the acquisition of separate phase encode lines and correction parameters are determined. Two types of rigid body motion are considered: 1) object and coil array move, and 2) object only moves, since each causes different phase errors in k-space. Simulation, phantom, and volunteer experiments demonstrate the validity of the technique.

Using UNFOLD to remove artifacts in parallel imaging and in partial-Fourier imaging.

In dynamic MRI, it is often difficult to achieve the acquisition speed required to resolve or freeze the temporal variations of the imaged object. Several MRI methods aim at speeding up the image acquisition process. Through assumptions and/or prior knowledge, these dynamic MRI methods allow part of the needed data to be calculated instead of acquired. For example, partial-Fourier imaging assumes that phase varies smoothly within the object, and parallel imaging (e.g., simultaneous acquisition of spatial harmonics (SMASH) and sensitivity encoding (SENSE)) uses prior knowledge about receiver-coil sensitivity. While these methods accelerate acquisition, they can introduce artifacts or amplify noise in doing so. The present work aims at accelerating image acquisition significantly, while introducing almost no artifacts or noise amplification. It is shown here that new, extra information is gained if dynamic MRI methods are modified so that the sampling function changes in specific ways from time-frame to time-frame. In other words, the set of k-space locations that are acquired (instead of calculated) changes with time. The present temporal strategy, based on the UNaliasing by Fourier-encoding the Overlaps in the temporaL Dimension (UNFOLD) method, can be incorporated into common dynamic MRI methods. Results with partial-Fourier, SMASH, and SENSE imaging are presented here, where UNFOLD's contribution is to very significantly reduce the artifact and/or amplified noise content. Used in this way, UNFOLD contributes indirectly, rather than directly to the improvement in image acquisition speed, as it allows companion methods to operate properly at greater acceleration settings than would otherwise be feasible.

On the UNFOLD method.

A graphical formalism is presented, showing that "UNaliasing by Fourier-encoding the Overlaps Using the temporaL Dimension" (UNFOLD) is equivalent to sampling k-t-space in a sheared grid pattern. Discrete regular sampling in k-t-space leads to periodic replication of the support region in x-f-space. Thus, the maximum acceleration achievable by UNFOLD is equivalent to the maximum packing of support regions in x-f-space. When the support region is separable along the x and f axes, the reconstruction can be performed separately for each k. UNFOLD can be combined with SiMultaneous Acquisition of Spatial Harmonics (SMASH) to further accelerate acquisition. However, a straightforward combination of the methods has been shown to result in a size restriction, which limits the portion of the field of view (FOV) with a larger temporal bandwidth to only a quarter of the FOV. Two solutions are presented to overcome this restriction.

Recent advances in image reconstruction, coil sensitivity calibration, and coil array design for SMASH and generalized parallel MRI.

Parallel magnetic resonance imaging (MRI) techniques use spatial information from arrays of radiofrequency (RF) detector coils to accelerate imaging. A number of parallel MRI techniques have been described in recent years, and numerous clinical applications are currently being explored. The advent of practical parallel imaging presents various challenges for image reconstruction and RF system design. Recent advances in tailored SiMultaneous Acquisition of Spatial Harmonics (SMASH) image reconstructions are summarized. These advances enable robust SMASH imaging in arbitrary image planes with a wide range of coil array geometries. A generalized formalism is described which may be used to understand the relations between SMASH and SENSE, to derive typical implementations of each as special cases, and to form hybrid techniques combining some of the advantages of both. Accurate knowledge of coil sensitivities is crucial for parallel MRI, and errors in calibration represent one of the most common and the most pernicious sources of error in parallel image reconstructions. As one example, motion of the patient and/or the coil array between the sensitivity reference scan and the accelerated acquisition can lead to calibration errors and reconstruction artifacts. Self-calibrating parallel MRI approaches that address this problem by eliminating the need for external sensitivity references are reviewed. The ultimate achievable signal-to-noise ratio (SNR) for parallel MRI studies is closely tied to the geometry and sensitivity patterns of the coil arrays used for spatial encoding. Several parallel imaging array designs that depart from the traditional model of overlapped adjacent loop elements are described.

Improved spatial harmonic selection for SMASH image reconstructions.

The fitting of coil sensitivity functions to spatial harmonics is central to image reconstructions using the simultaneous acquisition of spatial harmonics (SMASH) technique. It has previously been shown that the selection of the set of spatial harmonics used in a SMASH reconstruction can have a noticeable effect on the quality of the reconstructed image. However, a mechanism for automatic selection of the best set of harmonics in any particular situation has not been provided. In this work, a modification to the SMASH reconstruction procedure is introduced that allows the use of a weighted average of all possible harmonics in a reconstruction. The new reconstruction procedure is shown to allow automatic selection of the spatial harmonics and substantially improve SNR for both phantom and in vivo images.

Coil-by-coil image reconstruction with SMASH.

The SiMultaneous Acquisition of Spatial Harmonics (SMASH) technique uses linear combinations of undersampled datasets from the component coils of an RF coil array to reconstruct fully sampled composite datasets in reduced imaging times. In previously reported implementations, SMASH reconstructions were designed to reproduce the images that would otherwise be obtained by simple sums of fully gradient encoded component coil images. This strategy has left SMASH images vulnerable to phase cancellation artifacts when the sensitivities of RF coil array elements are not suitably phase-aligned. In fully gradient encoded imaging schemes these artifacts can be eliminated using a variety of methods for combining the individual coil images, including matched filter combinations as well as sum of squares combinations. Until now, these reconstruction schemes have been unavailable to SMASH reconstructions as SMASH produced a final composite image directly from the raw component coil k-space datasets. This article demonstrates a modification to SMASH that allows reconstruction of a full set of accelerated individual component coil images by fitting component coil sensitivity functions to a complete set of spatial harmonics tailored for each coil in the array. Standard component coil combinations applied to the individual reconstructed images produce final composite images free of phase cancellation artifacts.

Contrast-enhanced 3D MR angiography with simultaneous acquisition of spatial harmonics: A pilot study.

A partially parallel image acquisition technique, simultaneous acquisition of spatial harmonics, or SMASH, was used to increase the spatial and/or temporal resolution in contrast material-enhanced three-dimensional magnetic resonance angiography of the abdominal aorta and renal arteries. In eight healthy subjects, the breath-hold duration was halved at constant spatial resolution, or the spatial resolution was doubled at fixed breath-hold duration, with a 30%-55% reduction in the signal-to-noise ratio but otherwise preserved or improved image quality.

Tailored SMASH image reconstructions for robust in vivo parallel MR imaging

The simultaneous acquisition of spatial harmonics (SMASH) imaging technique uses spatial information from an array of RF coils to substitute for omitted encoding gradient steps and thereby to accelerate MR image acquisition. Since SMASH image reconstructions rely on the accurate generation of sinusoidally varying composite sensitivity functions to emulate the spatial modulations produced by gradients, the technique was originally believed to be limited to certain image planes or coil array configurations which were particularly suited to the generation of spatial harmonics. Several key improvements to the SMASH reconstruction procedure are described, taking advantage of various degrees of freedom in the spatial harmonic fit. The use of tailored fitting procedures, in combination with a numerical conditioning approach based on new observations about noise propagation in the fit, are shown to allow high-quality SMASH image reconstructions in oblique and double-oblique image planes, both in phantoms and in high-resolution cardiac MR images. Magn Reson Med 44:243–251, 2000. © 2000 Wiley-Liss, Inc.

SMASH imaging with an eight element multiplexed RF coil array.

SMASH (SiMultaneous Acquisition of Spatial Harmonics) is a technique which can be used to acquire multiple lines of k-space in parallel, by using spatial information from a radiofrequency coil array to perform some of the encoding normally produced by gradients. Using SMASH, imaging speed can be increased up to a maximum acceleration factor equal to the number of coil array elements. This work is a feasibility study which examines the use of SMASH with specialized coil array and data reception hardware to achieve previously unattainable accelerations. An eight element linear SMASH array was designed to operate in conjunction with a time domain multiplexing system to examine the effectiveness of SMASH imaging with as much as eightfold acceleration factors. Time domain multiplexing allowed the multiple independent array elements to be sampled through a standard single-channel receiver. SMASH-reconstructed images using this system were compared with reference images, and signal to noise ratio and reconstruction artifact power were measured as a function of acceleration factor. Results of the imaging experiments showed an almost constant SNR for SMASH acceleration factors of up to eight. Artifact power remained low within this range of acceleration factors. This study demonstrates that efficient SMASH imaging at high acceleration factors is feasible using appropriate hardware, and that time domain multiplexing is a convenient strategy to provide the multiple channels required for rapid imaging with large arrays.

An analytical SMASH procedure (ASP) for sensitivity-encoded MRI.

The simultaneous acquisition of spatial harmonics (SMASH) method of imaging with detector arrays can reduce the number of phase-encoding steps, and MRI scan time several-fold. The original approach utilized numerical gradient-descent fitting with the coil sensitivity profiles to create a set of composite spatial harmonics to replace the phase-encoding steps. Here, an analytical approach for generating the harmonics is presented. A transform is derived to project the harmonics onto a set of sensitivity profiles. A sequence of Fourier, Hilbert, and inverse Fourier transform is then applied to analytically eliminate spatially dependent phase errors from the different coils while fully preserving the spatial-encoding. By combining the transform and phase correction, the original numerical image reconstruction method can be replaced by an analytical SMASH procedure (ASP). The approach also allows simulation of SMASH imaging, revealing a criterion for the ratio of the detector sensitivity profile width to the detector spacing that produces optimal harmonic generation. When detector geometry is suboptimal, a group of quasi-harmonics arises, which can be corrected and restored to pure harmonics. The simulation also reveals high-order harmonic modulation effects, and a demodulation procedure is presented that enables application of ASP to a large numbers of detectors. The method is demonstrated on a phantom and humans using a standard 4-channel phased-array MRI system.

Coronary arteries.

Coronary angiography (CA) is presently considered the gold standard for the assessment of the coronary arteries. However, the presence of ionizing radiation, its invasiveness and the small associated risk of morbidity prompted long ago the development of more patient-friendly imaging modalities. A promising technique, magnetic resonance imaging (MRI), has been regarded as the major modality in the coming decade. Although still in its infancy qualitatively, its flexibility and non-invasiveness opens the door for a comprehensive evaluation of the heart and the coronary arteries in one single sitting with high anatomical definition and excellent soft tissue contrast capabilities, double-oblique tomographic sections and the possibility to quantify an innumerable number of cardiovascular physiological parameters. Numerous ideas have been assessed, comprising breath-hold and free-breathing two-dimensional and three-dimensional measurements. New ongoing trials with intravascular contrast agents may provide for all these techniques the long-awaited essential boost for reliable magnetic resonance coronary angiography (MRCA). Introduction of parallel MRI acquisition techniques, such as simultaneous acquisition of spatial harmonics (SMASH) and sensitivity encoding (SENSE) may provide the speed enhancement required to shorten imaging time for all techniques explored to date.

Tailored SMASH image reconstructions for robust in vivo parallel MR imaging.

The simultaneous acquisition of spatial harmonics (SMASH) imaging technique uses spatial information from an array of RF coils to substitute for omitted encoding gradient steps and thereby to accelerate MR image acquisition. Since SMASH image reconstructions rely on the accurate generation of sinusoidally varying composite sensitivity functions to emulate the spatial modulations produced by gradients, the technique was originally believed to be limited to certain image planes or coil array configurations which were particularly suited to the generation of spatial harmonics. Several key improvements to the SMASH reconstruction procedure are described, taking advantage of various degrees of freedom in the spatial harmonic fit. The use of tailored fitting procedures, in combination with a numerical conditioning approach based on new observations about noise propagation in the fit, are shown to allow high-quality SMASH image reconstructions in oblique and double-oblique image planes, both in phantoms and in high-resolution cardiac MR images. Magn Reson Med 44:243-251, 2000.

Description of parallel imaging in MRI using multiple coils.

A general formulation for parallel imaging using multiple coils is derived from the Fourier transform of coil sensitivity functions. This formulation provides a unified account for developed parallel imaging techniques such as subencoding, simultaneous acquisition of spatial harmonics (SMASH), and sensitivity encoding (SENSE), and indicates a guideline for coil configuration and k-space sampling in parallel imaging. The views that can be acquired simultaneously in parallel imaging have to be contained in the spatial frequency band of coil sensitivity functions.

Sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE RIP).

A new parallel imaging technique was implemented which can result in reduced image acquisition times in MRI. MR data is acquired in parallel using an array of receiver coils and then reconstructed simultaneously with multiple processors. The method requires the initial estimation of the 2D sensitivity profile of each coil used in the receiver array. These sensitivity profiles are then used to partially encode the images of interest. A fraction of the total number of k-space lines is consequently acquired and used in a parallel reconstruction scheme, allowing for a substantial reduction in scanning and display times. This technique is in the family of parallel acquisition schemes such as simultaneous acquisition of spatial harmonics (SMASH) and sensitivity encoding (SENSE). It extends the use of the SMASH method to allow the placement of the receiver coil array around the object of interest, enabling imaging of any plane within the volume of interest. In addition, this technique permits the arbitrary choice of the set of k-space lines used in the reconstruction and lends itself to parallel reconstruction, hence allowing for real-time rendering. Simulated results with a 16-fold increase in temporal resolution are shown, as are experimental results with a 4-fold increase in temporal resolution. Magn Reson Med 44:301-308, 2000.

Resolution enhancement in single-shot imaging using simultaneous acquisition of spatial harmonics (SMASH).

Spatial resolution in single-shot imaging is limited by signal attenuation due to relaxation of transverse magnetization. This effect can be reduced by minimizing acquisition times through the use of short interecho spacings. However, the minimum interecho spacing is constrained by limits on gradient switching rates, radiofrequency (RF) power deposition and RF pulse length. Recently, simultaneous acquisition of spatial harmonics (SMASH) has been introduced as a method to acquire magnetic resonance images at increased speeds using a reduced number of phase-encoding gradient steps by extracting spatial information contained in an RF coil array. In this study, it is shown that SMASH can be used to reduce the effects of relaxation, resulting in single-shot images with increased spatial resolution without increasing imaging time. After a brief theoretical discussion, two strategies to reduce signal attenuation and increase spatial resolution in single-shot imaging are introduced and their performance is evaluated in phantom studies. In vivo single-shot echoplanar imaging (EPI), BURST, and half-Fourier single-shot turbo spin-echo (HASTE) images are then presented demonstrating the practical implementation of these resolution enhancement strategies. Images acquired with SMASH show increased spatial resolution and improved image quality when compared with images obtained with the conventional acquisitions. The general principles presented for imaging with SMASH can also be applied to other partially parallel imaging techniques.