Volumetric navigators for real-time motion correction in diffusion tensor imaging

A method for motion correction in multicoil imaging applications, involving both data collection and reconstruction, is presented. A bit‐reversed radial acquisition scheme, in conjunction with a rapid self‐calibrated parallel imaging method, Generalized auto‐calibrating partial parallel acquisition (GRAPPA) operator for wider radial bands (GROWL), is used to achieve motion correction at a high temporal resolution. View‐by‐view in‐plane motion correction is achieved in 2D imaging, while 3D motion correction is achieved for every two consecutive slice‐encoding planes in 3D imaging. In the proposed technique, GROWL contributes in two aspects: First, a central k‐space circle/cylinder used as the motion‐free reference is generated from a small number of radial lines/planes; Second, undersampled k‐space regions resulting from rotation and inconsistent (e.g. intraview and nonrigid body) motion can be filled in. When compared with navigator‐based motion correction methods, the proposed method does not prolong scan time and can be applied to short‐TR sequences. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

IIR GRAPPA for parallel MR image reconstruction

Accelerated parallel MRI has advantage in imaging speed, and its image quality has been improved continuously in recent years. This paper introduces a two‐dimensional infinite impulse response model of inverse filter to replace the finite impulse response model currently used in generalized autocalibrating partially parallel acquisitions class image reconstruction methods. The infinite impulse response model better characterizes the correlation of k‐space data points and better approximates the perfect inversion of parallel imaging process, resulting in a novel generalized image reconstruction method for accelerated parallel MRI. This k‐space‐based reconstruction method includes the conventional generalized autocalibrating partially parallel acquisitions class methods as special cases and has a new infinite impulse response data estimation mechanism for effective improvement of image quality. The experiments on in vivo MRI data show that the proposed method significantly reduces reconstruction errors compared with the conventional two‐dimensional generalized autocalibrating partially parallel acquisitions method, particularly at the high acceleration rates. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.     

Robust GRAPPA‐accelerated diffusion‐weighted readout‐segmented (RS)‐EPI

Readout segmentation (RS‐EPI) has been suggested as a promising variant to echo‐planar imaging (EPI) for high‐resolution imaging, particularly when combined with parallel imaging. This work details some of the technical aspects of diffusion‐weighted (DW)‐RS‐EPI, outlining a set of reconstruction methods and imaging parameters that can both minimize the scan time and afford high‐resolution diffusion imaging with reduced distortions. These methods include an efficient generalized autocalibrating partially parallel acquisition (GRAPPA) calibration for DW‐RS‐EPI data without scan time penalty, together with a variant for the phase correction of partial Fourier RS‐EPI data. In addition, the role of pulsatile and rigid‐body brain motion in DW‐RS‐EPI was assessed. Corrupt DW‐RS‐EPI data arising from pulsatile nonlinear brain motion had a prevalence of ～7% and were robustly identified via k‐space entropy metrics. For DW‐RS‐EPI data corrupted by rigid‐body motion, we showed that no blind overlap was required. The robustness of RS‐EPI toward phase errors and motion, together with its minimized distortions compared with EPI, enables the acquisition of exquisite 3 T DW images with matrix sizes close to 512². Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Navigator accuracy requirements for prospective motion correction

Prospective motion correction in MRI is becoming increasingly popular to prevent the image artifacts that result from subject motion. Navigator information is used to update the position of the imaging volume before every spin excitation so that lines of acquired k‐space data are consistent. Errors in the navigator information, however, result in residual errors in each k‐space line. This paper presents an analysis linking noise in the tracking system to the power of the resulting image artifacts. An expression is formulated for the required navigator accuracy based on the properties of the imaged object and the desired resolution. Analytical results are compared with computer simulations and experimental data. Magn Reson Med, 2010. © 2009 Wiley‐Liss, Inc.     

Optimized parallel imaging for dynamic PC‐MRI with multidirectional velocity encoding

Phase contrast MRI with multidirectional velocity encoding requires multiple acquisitions of the same k‐space lines to encode the underlying velocities, which can considerably lengthen the total scan time. To reduce scan time, parallel imaging is often applied. In dynamic phase contrast MRI using standard generalized autocalibrating partially parallel acquisitions (GRAPPA), several central k‐spaces for autocalibration of the reconstruction (autocalibrating signal lines (ACS)) are typically acquired, separately for each velocity direction and each cardiac timeframe, for calculating the reconstruction weights. To further accelerate data acquisition, we developed two methods, which calculated weights with a substantially reduced number of ACSl lines. The effects on image quality and flow quantification were compared to fully sampled data, standard GRAPPA, and time‐interleaved sampling scheme in combination with generalized autocalibrating partially parallel acquisitions (TGRAPPA). The results show that the two proposed methods can clearly improve scan efficiency while maintaining image quality and accuracy of measured flow or myocardial tissue velocities. Compared to TGRAPPA, the proposed methods were more accurate in evaluating flow velocity. In conclusion, the proposed reconstruction strategies are promising for dynamic multidirectionally encoded acquisitions and can easily be implemented using the standard GRAPPA reconstruction algorithm. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Generalized GRAPPA operators for wider spiral bands: Rapid self‐calibrated parallel reconstruction for variable density spiral MRI

A rapid and self‐calibrated parallel imaging reconstruction method is proposed for undersampled variable density spiral datasets. A set of generalized GRAPPA for wider readout line operators are used to expand each acquired spiral line into a wider spiral band, therefore fulfilling Nyquist sampling criterion throughout the k‐space. The calibration of generalized GRAPPA for wider readout line operators is performed using the fully sampled central k‐space region. The resulting generalized GRAPPA for wider readout line operator weights are adaptively regularized to minimize the error in the newly‐generated data at different k‐space locations. Simulation and experimental results demonstrate that the technique can be used either to achieve a significant acceleration and/or to reduce off‐resonance artifacts due to a shorten readout duration. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

Parallel reconstruction using null operations

A novel iterative k‐space data‐driven technique, namely parallel reconstruction using null operations (PRUNO), is presented for parallel imaging reconstruction. In PRUNO, both data calibration and image reconstruction are formulated into linear algebra problems based on a generalized system model. An optimal data calibration strategy is demonstrated by using singular value decomposition, and an iterative conjugate‐gradient approach is proposed to efficiently solve missing k‐space samples during reconstruction. With its generalized formulation and precise mathematical model, PRUNO reconstruction yields good accuracy, flexibility, and stability. Both computer simulation and in vivo studies have shown that PRUNO produces much better reconstruction quality than generalized autocalibrating partially parallel acquisition (GRAPPA), especially under high accelerating rates. With the aid of PRUNO reconstruction, ultra‐high accelerating parallel imaging can be performed with decent image quality. For example, we have done successful PRUNO reconstruction at a reduction factor of 6 (effective factor of 4.44) with eight coils and only a few autocalibration signal lines. Magn Reson Med, 2011. © 2011 Wiley Periodicals, Inc.     

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 ?₁‐wavelet regularization are also demonstrated. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Non‐Cartesian parallel imaging reconstruction

Non‐Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non‐Cartesian trajectories can enable more efficient coverage of k‐space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be used to reconstruct images from undersampled Cartesian data, non‐Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the nonhomogeneous sensitivities of multi‐coil phased arrays. This review will begin with an overview of non‐Cartesian k‐space trajectories and their sampling properties, followed by an in‐depth discussion of several selected non‐Cartesian parallel imaging algorithms. Three representative non‐Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non‐Cartesian generalized autocalibrating partially parallel acquisition (GRAPPA), and Iterative Self‐Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non‐Cartesian parallel imaging will be covered. J. Magn. Reson. Imaging 2014;40:1022–1040 . © 2014 Wiley Periodicals, Inc.     

3D radial sampling and 3D affine transform‐based respiratory motion correction technique for free‐breathing whole‐heart coronary MRA with 100% imaging efficiency

The navigator gating and slice tracking approach currently used for respiratory motion compensation during free‐breathing coronary magnetic resonance angiography (MRA) has low imaging efficiency (typically 30–50%), resulting in long imaging times. In this work, a novel respiratory motion correction technique with 100% scan efficiency was developed for free‐breathing whole‐heart coronary MRA. The navigator signal was used as a reference respiratory signal to segment the data into six bins. 3D projection reconstruction k‐space sampling was used for data acquisition and enabled reconstruction of low resolution images within each respiratory bin. The motion between bins was estimated by image registration with a 3D affine transform. The data from the different respiratory bins was retrospectively combined after motion correction to produce the final image. The proposed method was compared with a traditional navigator gating approach in nine healthy subjects. The proposed technique acquired whole‐heart coronary MRA with 1.0 mm³ isotropic spatial resolution in a scan time of 6.8 ± 0.9 min, compared with 16.2 ± 2.8 min for the navigator gating approach. The image quality scores, and length, diameter and sharpness of the right coronary artery (RCA), left anterior descending coronary artery (LAD), and left circumflex coronary artery (LCX) were similar for both approaches (P > 0.05 for all), but the proposed technique reduced scan time by a factor of 2.5. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

Highly k‐t‐space–accelerated phase‐contrast MRI

The purpose of this study was to combine a recently introduced spatiotemporal parallel imaging technique, PEAK‐GRAPPA (parallel MRI with extended and averaged generalized autocalibrating partially parallel acquisition), with two‐dimensional (2D) cine phase‐contrast velocity mapping. Phase‐contrast MRI was applied to measure the blood flow in the thoracic aorta and the myocardial motion of the left ventricle. To evaluate the performance of different reconstruction methods, fully acquired k‐space data sets were used to compare conventional parallel imaging using GRAPPA with reduction factors of R = 2–6 and PEAK‐GRAPPA as well as sliding window reconstruction with reduction factors R = 2–12 (net acceleration factors up to 5.2). PEAK‐GRAPPA reconstruction resulted in improved image quality with considerably reduced artifacts, which was also supported by error analysis. To analyze potential blurring or low‐pass filtering effects of spatiotemporal PEAK‐GRAPPA, the velocity time courses of aortic flow and myocardial tissue motion were evaluated and compared with conventional image reconstructions. Quantitative comparisons of blood flow velocities and pixel‐wise correlation analysis of velocities highlight the potential of PEAK‐GRAPPA for highly accelerated dynamic phase‐contrast velocity mapping. Magn Reson Med 60:1169–1177, 2008. © 2008 Wiley‐Liss, Inc.     

Diffusion weighted vertical gradient and spin echo

In this work, diffusion weighting and parallel imaging is combined with a vertical gradient and spin echo data readout. This sequence was implemented and evaluated on healthy volunteers using a 1.5 and a 3 T whole‐body MR system. As the vertical gradient and spin echo trajectory enables a higher k‐space velocity in the phase‐encoding direction than single‐shot echo planar imaging, the geometrical distortions are reduced. When combined with parallel imaging such as generalized autocalibrating partially parallel acquisition, the geometric distortions are reduced even further, while also keeping the minimum echo time reasonably low. However, this combination of a diffusion preparation and multiple refocusing pulses during the vertical gradient and spin echo readout, generally violates the Carr–Purcell–Meiboom–Gill condition, which leads to interferences between echo pathways. To suppress the stimulated echo pathway, refocusing pulses with a sharper slice profiles and an odd/even crusher variation scheme were implemented and evaluated. Being a single‐shot acquisition technique, the reconstructed images are robust to rigid‐body head motion and spatially varying brain motion, both of which are common sources of artifacts in diffusion MRI. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.     

Quantitative T*2‐mapping based on multi‐slice multiple gradient echo flash imaging: Retrospective correction for subject motion effects

Numerous clinical and research applications for quantitative mapping of the effective transverse relaxation time T*₂ have been described. Subject motion can severely deteriorate the quality and accuracy of results. A correction method for T*₂ maps acquired with multi‐slice multiple gradient echo FLASH imaging is presented, based on acquisition repetition with reduced spatial resolution (and consequently reduced acquisition time) and weighted averaging of both data sets, choosing weighting factors individually for each k‐space line to reduce the influence of motion. In detail, the procedure is based on the fact that motion artifacts reduce the correlation between acquired and exponentially fitted data. A target data set is constructed in image space, choosing the data yielding best correlation from the two acquired data sets. The k‐space representation of the target is subsequently approximated as linear combination of original raw data, yielding the required weighting factors. As this method only requires a single acquisition repetition with reduced spatial resolution, it can be employed on any clinical system offering a suitable sequence with export of modulus and phase images. Experimental results show that the method works well for sparse motion, but fails for strong motion affecting the same k‐space lines in both acquisitions. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

GRAPPA operator for wider radial bands (GROWL) with optimally regularized self‐calibration

A self‐calibrated parallel imaging reconstruction method is proposed for azimuthally undersampled radial dataset. A generalized auto‐calibrating partially parallel acquisition (GRAPPA) operator is used to widen each radial view into a band consisting of several parallel lines, followed by a standard regridding procedure. Self‐calibration is achieved by regridding the central k‐space region, where Nyquist criterion is satisfied, to a rotated Cartesian grid. During the calibration process, an optimal Tikhonov regularization factor is introduced to reduce the error caused by the small k‐space area of the self‐calibration region. The method was applied to phantom and in vivo datasets acquired with an eight‐element coil array, using 32‐64 radial views with 256 readout samples. When compared with previous radial parallel imaging techniques, GRAPPA operator for wider radial bands (GROWL) provides a significant speed advantage since calibration is carried out using the fully sampled k‐space center. A further advantage of GROWL is its applicability to arbitrary‐view angle ordering schemes. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Novel reconstruction method for three‐dimensional axial continuously moving table whole‐body magnetic resonance imaging featuring autocalibrated parallel imaging GRAPPA

Continuously moving table MR imaging has been successfully evaluated for whole‐body tumor staging and metastasis screening. In previous studies it was demonstrated that three‐dimensional (3D) slab‐selective excitation with lateral readout can provide very efficient k‐space coverage when the longitudinal field of view (FOV) is limited. To reduce respiratory artifacts, data acquisition in the thoracoabdominal region of the patient typically must be performed during one single breath hold. This consequently restricts acquisition time and thus spatial resolution. In this work, a novel reconstruction method is introduced for axial 3D moving table data acquisition with lateral readout. The method features table position correction completely in k‐space and is compatible with autocalibrated parallel imaging (GRAPPA). Parallel imaging can be applied to increase spatial resolution while maintaining the breath‐holding time. A sophisticated protocol for whole‐body moving table MRI was developed. The impact of gradient nonlinearity on the featured imaging method was evaluated in phantom and volunteer experiments. Finally, the protocol was optimized toward minimizing residual artifacts. Moving table whole‐body MRI with lateral readout was performed in 5 healthy volunteers and was compared with lateral readout data acquired with a GRAPPA accelerated protocol providing increased spatial resolution. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Compressed‐sensing motion compensation (CosMo): A joint prospective–retrospective respiratory navigator for coronary MRI

Prospective right hemidiaphragm navigator (NAV) is commonly used in free‐breathing coronary MRI. The NAV results in an increase in acquisition time to allow for resampling of the motion‐corrupted k‐space data. In this study, we are presenting a joint prospective–retrospective NAV motion compensation algorithm called compressed‐sensing motion compensation (CosMo). The inner k‐space region is acquired using a prospective NAV; for the outer k‐space, a NAV is only used to reject the motion‐corrupted data without reacquiring them. Subsequently, those unfilled k‐space lines are retrospectively estimated using compressed sensing reconstruction. We imaged right coronary artery in nine healthy adult subjects. An undersampling probability map and sidelobe‐to‐peak ratio were calculated to study the pattern of undersampling, generated by NAV. Right coronary artery images were then retrospectively reconstructed using compressed‐sensing motion compensation for gating windows between 3 and 10 mm and compared with the ones fully acquired within the gating windows. Qualitative imaging score and quantitative vessel sharpness were calculated for each reconstruction. The probability map and sidelobe‐to‐peak ratio show that the NAV generates a random undersampling k‐space pattern. There were no statistically significant differences between the vessel sharpness and subjective score of the two reconstructions. Compressed‐sensing motion compensation could be an alternative motion compensation technique for free‐breathing coronary MRI that can be used to reduce scan time. Magn Reson Med, 2011. © 2011 Wiley Periodicals, Inc.     

Virtual coil concept for improved parallel MRI employing conjugate symmetric signals

A new approach for utilizing conjugate k‐space symmetry for improved parallel MRI performance is presented. By generating virtual coils containing conjugate symmetric k‐space signals from actual coils, additional image‐ and coil‐phase information can be incorporated into the reconstruction process for parallel acquisition techniques. In that way the reconstruction conditions are improved, resulting in less noise enhancement. In particular in combination with generalized autocalibrating partially parallel acquisitions (GRAPPA), the virtual coil concept represents a practical approach since no explicit spatial phase information is required. In addition, the influence of phase variations originating from the complex receiver coils as well as from the background is investigated. It is shown that there exist background phase distributions yielding an optimized pMRI reconstruction. Magn Reson Med 61:93–102, 2009. © 2008 Wiley‐Liss, Inc.     

Nonrigid retrospective respiratory motion correction in whole‐heart coronary MRA

A nonrigid retrospective respiratory motion correction scheme is presented for whole‐heart coronary imaging with interleaved acquisition of motion information. The quasi‐periodic nature of breathing is exploited to populate a 3D nonrigid motion model from low‐resolution 2D imaging slices acquired interleaved with a segmented 3D whole‐heart coronary scan without imposing scan time penalty. Reconstruction and motion correction are based on inversion of a generalized encoding equation. Therein, a forward model describes the transformation from the motion free image to the motion distorted k‐space data, which includes nonrigid spatial transformations. The effectiveness of the approach is demonstrated on 10 healthy volunteers using free‐breathing coronary whole‐heart scans. Although conventional respiratory‐gated acquisitions with 5‐mm gating window resulted in an average gating efficiency of 51% ± 11%, nonrigid motion correction allowed for gate‐free acquisitions, and hence scan time reduction by a factor of two without significant penalty in image quality. Image scores and quantitative image quality measures for the left coronary arteries showed no significant differences between 5‐mm gated and gate‐free acquisitions with motion correction. For the right coronary artery, slightly reduced image quality in the motion corrected gate‐free scan was observed as a result of the close vicinity of anatomical structures with different motion characteristics. Magn Reson Med, 2011. © 2011 Wiley Periodicals, Inc.     

Real‐time motion correction for high‐resolution larynx imaging

Motion—both rigid‐body and nonrigid—is the main limitation to in vivo, high‐resolution larynx imaging. In this work, a new real‐time motion compensation algorithm is introduced. Navigator data are processed in real time to compute the displacement information, and projections are corrected using phase modulation in k‐space. Upon automatic feedback, the system immediately reacquires the data most heavily corrupted by nonrigid motion, i.e., the data whose corresponding projections could not be properly corrected. This algorithm overcomes the shortcomings of the so‐called diminishing variance algorithm by combining it with navigator‐based rigid‐body motion correction. Because rigid‐body motion correction is performed first, continual bulk motion no longer impedes nor prevents the convergence of the algorithm. Phantom experiments show that the algorithm properly corrects for translations and reacquires data corrupted by nonrigid motion. Larynx imaging was performed on healthy volunteers, and substantial reduction of motion artifacts caused by bulk shift, swallowing, and coughing was achieved. Magn Reson Med, 2011. © 2011 Wiley‐Liss, Inc.     

Model‐based reconstruction for cardiac cine MRI without ECG or breath holding

This paper describes an acquisition and reconstruction strategy for cardiac cine MRI that does not require the use of electrocardiogram or breath holding. The method has similarities with self‐gated techniques as information about cardiac and respiratory motion is derived from the imaging sequence itself; here, by acquiring the center k‐space line at the beginning of each segment of a balanced steady‐state free precession sequence. However, the reconstruction step is fundamentally different: a generalized reconstruction by inversion of coupled systems is used instead of conventional gating. By correcting for nonrigid cardiac and respiratory motion, generalized reconstruction by inversion of coupled systems (GRICS) uses all acquired data, whereas gating rejects data acquired in certain motion states. The method relies on the processing and analysis of the k‐space central line data: local information from a 32‐channel cardiac coil is used in order to automatically extract eigenmodes of both cardiac and respiratory motion. In the GRICS framework, these eigenmodes are used as driving signals of a motion model. The motion model is defined piecewise, so that each cardiac phase is reconstructed independently. Results from six healthy volunteers, with various slice orientations, show improved image quality compared to combined respiratory and cardiac gating. Magn Reson Med 63:1247–1257, 2010. © 2010 Wiley‐Liss, Inc.