K-space Sampling Trajectories Research Articles

Improving spreading projection algorithm for rapid k-space sampling trajectories through minimized off-resonance effects and gridding of low frequencies.

Non-Cartesian MRI with long arbitrary readout directions are susceptible to off-resonance artifacts due to patient induced inhomogeneities. This results in degraded image quality with strong signal losses and blurring. Current solutions to address this issue involve correcting the off-resonance artifacts during image reconstruction or reducing inhomogeneities through improved shimming. The recently developed SPARKLING algorithm is extended to drastically diminish off-resonance artifacts by generating temporally smooth k-space sampling patterns. For doing so, the cost function which is optimized in SPARKLING is modified using a temporal weighting factor. Additionally, oversampling of the center of k-space beyond the Nyquist criteria is prevented through the use of gridded sampling in the region, enforced with affine constraints. Prospective k-space data was acquired at 3 T on new trajectories, and we show robustness to inhomogeneities through in silico experiments by adding through artificial degradation of system shimming. Later on, in vivo experiments were carried out to optimize parameters of the new improvements and benchmark the gain in performance. The improved trajectories allowed for the recovery of signal dropouts observed on original SPARKLING acquisitions at larger field inhomogeneities. Furthermore, imposing gridded sampling at the center of k-space provided improved reconstructed image quality with limited artifacts. These advancements allowed us for nearly shorter scan time compared to GRAPPA-p4x1, allowing us to reach 600 µm isotropic resolution in 3D -w imaging in just 3.3 min at 3 T with negligible degradation in image quality.

Stochastic optimization of three-dimensional non-Cartesian sampling trajectory.

Optimizing three-dimensional (3D) k-space sampling trajectories is important for efficient MRI yet presents a challenging computational problem. This work proposes a generalized framework for optimizing 3D non-Cartesian sampling patterns via data-driven optimization. We built a differentiable simulation model to enable gradient-based methods for sampling trajectory optimization. The algorithm can simultaneously optimize multiple properties of sampling patterns, including image quality, hardware constraints (maximum slew rate and gradient strength), reduced peripheral nerve stimulation (PNS), and parameter-weighted contrast. The proposed method can either optimize the gradient waveform (spline-based freeform optimization) or optimize properties of given sampling trajectories (such as the rotation angle of radial trajectories). Notably, the method can optimize sampling trajectories synergistically with either model-based or learning-based reconstruction methods. We proposed several strategies to alleviate the severe nonconvexity and huge computation demand posed by the large scale. The corresponding code is available as an open-source toolbox. We applied the optimized trajectory to multiple applications including structural and functional imaging. In the simulation studies, the image quality of a 3D kooshball trajectory was improved from 0.29 to 0.22 (NRMSE) with Stochastic optimization framework for 3D NOn-Cartesian samPling trajectorY (SNOPY) optimization. In the prospective studies, by optimizing the rotation angles of a stack-of-stars (SOS) trajectory, SNOPY reduced the NRMSE of reconstructed images from 1.19 to 0.97 compared to the best empirical method (RSOS-GR). Optimizing the gradient waveform of a rotational EPI trajectory improved participants' rating of the PNS from "strong" to "mild." SNOPY provides an efficient data-driven and optimization-based method to tailor non-Cartesian sampling trajectories.

Jointly Learning Non-Cartesian k-Space Trajectories and Reconstruction Networks for 2D and 3D MR Imaging through Projection.

Compressed sensing in magnetic resonance imaging essentially involves the optimization of (1) the sampling pattern in k-space under MR hardware constraints and (2) image reconstruction from undersampled k-space data. Recently, deep learning methods have allowed the community to address both problems simultaneously, especially in the non-Cartesian acquisition setting. This work aims to contribute to this field by tackling some major concerns in existing approaches. Particularly, current state-of-the-art learning methods seek hardware compliant k-space sampling trajectories by enforcing the hardware constraints through additional penalty terms in the training loss. Through ablation studies, we rather show the benefit of using a projection step to enforce these constraints and demonstrate that the resulting k-space trajectories are more flexible under a projection-based scheme, which results in superior performance in reconstructed image quality. In 2D studies, our novel method trajectories present an improved image reconstruction quality at a 20-fold acceleration factor on the fastMRI data set with SSIM scores of nearly 0.92-0.95 in our retrospective studies as compared to the corresponding Cartesian reference and also see a 3-4 dB gain in PSNR as compared to earlier state-of-the-art methods. Finally, we extend the algorithm to 3D and by comparing optimization as learning-based projection schemes, we show that data-driven joint learning-based method trajectories outperform model-based methods such as SPARKLING through a 2 dB gain in PSNR and 0.02 gain in SSIM.

B-Spline Parameterized Joint Optimization of Reconstruction and K-Space Trajectories (BJORK) for Accelerated 2D MRI.

Optimizing k-space sampling trajectories is a promising yet challenging topic for fast magnetic resonance imaging (MRI). This work proposes to optimize a reconstruction method and sampling trajectories jointly concerning image reconstruction quality in a supervised learning manner. We parameterize trajectories with quadratic B-spline kernels to reduce the number of parameters and apply multi-scale optimization, which may help to avoid sub-optimal local minima. The algorithm includes an efficient non-Cartesian unrolled neural network-based reconstruction and an accurate approximation for backpropagation through the non-uniform fast Fourier transform (NUFFT) operator to accurately reconstruct and back-propagate multi-coil non-Cartesian data. Penalties on slew rate and gradient amplitude enforce hardware constraints. Sampling and reconstruction are trained jointly using large public datasets. To correct for possible eddy-current effects introduced by the curved trajectory, we use a pencil-beam trajectory mapping technique. In both simulations and in- vivo experiments, the learned trajectory demonstrates significantly improved image quality compared to previous model-based and learning-based trajectory optimization methods for 10× acceleration factors. Though trained with neural network-based reconstruction, the proposed trajectory also leads to improved image quality with compressed sensing-based reconstruction.

Learning-based method for k-space trajectory design in MRI.

Variable density sampling of the k-space in MRI is an integral part of trajectory design. It has been observed that data-driven trajectory design methods provide a better image reconstruction as compared to trajectories obtained from a fixed or a parametric density function. In this paper, a data-driven strategy has been proposed to obtain non-Cartesian continuous k-space sampling trajectories for MRI under the compressed sensing framework (greedy non-Cartesian (GNC)). A stochas-tic version of the algorithm (stochastic greedy non-Cartesian (SGNC)) is also proposed that reduces the computation time. We compare the proposed trajectory with a traveling salesman problem (TSP)-based trajectory and an echo planar imaging-like trajectory obtained by a greedy method called stochastic greedy-Cartesian (SGC) algorithm. The training images are taken from knee images of the fastMRI dataset. It is observed that the proposed algorithms outperform the TSP-based and the SGC trajectories for similar read-out times.

Closed-loop control of k-space sampling via physiologic feedback for cine MRI.

BackgroundSegmented cine cardiac MRI combines data from multiple heartbeats to achieve high spatiotemporal resolution cardiac images, yet predefined k-space segmentation trajectories can lead to suboptimal k-space sampling. In this work, we developed and evaluated an autonomous and closed-loop control system for radial k-space sampling (ARKS) to increase sampling uniformity.MethodsThe closed-loop system autonomously selects radial k-space sampling trajectory during live segmented cine MRI and attempts to optimize angular sampling uniformity by selecting views in regions of k-space that were not previously well-sampled. Sampling uniformity and the ability to detect cardiac phase in vivo was assessed using ECG data acquired from 10 normal subjects in an MRI scanner. The approach was then implemented with a fast gradient echo sequence on a whole-body clinical MRI scanner and imaging was performed in 4 healthy volunteers. The closed-loop k-space trajectory was compared to random, uniformly distributed and golden angle view trajectories via measurement of k-space uniformity and the point spread function. Lastly, an arrhythmic dataset was used to evaluate a potential application of the approach.ResultsThe autonomous trajectory increased k-space sampling uniformity by 15±7%, main lobe point spread function (PSF) signal intensity by 6±4%, and reduced ringing relative to golden angle sampling. When implemented, the autonomous pulse sequence prescribed radial view angles faster than the scan TR (0.98 ± 0.01 ms, maximum = 1.38 ms) and increased k-space sampling mean uniformity by 10±11%, decreased uniformity variability by 44±12%, and increased PSF signal ratio by 6±6% relative to golden angle sampling.ConclusionThe closed-loop approach enables near-uniform radial sampling in a segmented acquisition approach which was higher than predetermined golden-angle radial sampling. This can be utilized to increase the sampling or decrease the temporal footprint of an acquisition and the closed-loop framework has the potential to be applied to patients with complex heart rhythms.

Tilted-CAIPI for highly accelerated distortion-free EPI with point spread function (PSF) encoding.

To develop a method for fast distortion- and blurring-free imaging. EPI with point-spread-function (PSF) mapping can achieve distortion- and blurring-free imaging at a cost of long acquisition time. In this study, an acquisition/reconstruction technique, termed "tilted-CAIPI," is proposed to achieve >20× acceleration for PSF-EPI. The proposed method systematically optimized the k-space sampling trajectory with B0 -inhomogeneity-informed reconstruction, to exploit the inherent signal correlation in PSF-EPI and take full advantage of coil sensitivity. Susceptibility-induced phase accumulation is regarded as an additional encoding that is estimated by calibration data and integrated into reconstruction. Self-navigated phase correction was developed to correct shot-to-shot phase variation in diffusion imaging. Tilted-CAIPI was implemented at 3T, with incorporation of partial Fourier and simultaneous multislice to achieve further accelerations. T2 -weighted, T2* -weighted, and diffusion-weighted imaging experiments were conducted to evaluate the proposed method. The ability of tilted-CAIPI to provide highly accelerated imaging without distortion and blurring was demonstrated through in vivo brain experiments, where only 8 shots per simultaneous slice group were required to provide high-quality, high-SNR imaging at 0.8-1 mm resolution. Tilted-CAIPI achieved fast distortion- and blurring-free imaging with high SNR. Whole-brain T2 -weighted, T2* -weighted, and diffusion imaging can be obtained in just 15-60 s.

Influence of k-space trajectory corrections on proton density mapping with ultrashort echo time imaging: Application for imaging of short T2 components in white matter

PurposeTo evaluate the impact of MR gradient system imperfections and limitations for the quantitative mapping of short T2* signals performed by ultrashort echo time (UTE) acquisition approach. Materials and methodsThe measurement of short T2* signals from a phantom and a healthy volunteer study (8 subjects of average age 28 ± 4 years) were performed on a 3T scanner. The characteristics of the gradient system were obtained using calibration method performed directly on the measured subject or phantom. This information was used to calculate the actual sampling trajectory with the help of a parametric eddy current model. The actual sample positions were used to reconstruct corrected images and compared with uncorrected data. ResultsComparison of both approaches, i.e., without and with correction of k-space sampling trajectories revealed substantial improvement when correction was applied. The phantom experiments demonstrate substantial in-plane signal intensity variations for uncorrected sampling trajectories. In the case of the volunteer study, this led to significant differences in relative proton density (RPD) estimation between the uncorrected and corrected data (P = 0.0117 by Wilcoxon matched-pairs test) and provides for about ~15% higher values for short T2* components of white matter (WM) in the case of uncorrected images. ConclusionThe imperfection of the applied gradients could induce errors in k-space data sampling which further propagates into the fidelity of the UTE images and jeopardizes precision of quantification. However, the study proved that measurement of gradient errors together with correction of sample positions can contribute to increased accuracy and unbiased characterization of short T2* signals.

Four-shot non-cartesian trajectories for k-space sampling in MRI

This paper considers the problem of designing trajectories for scanning k-space in MRI. Various cartesian and non-cartesian trajectories such as rectangular, spiral, radial, etc. have been proposed in the literature. Non-cartesian trajectories are observed to perform optimally in terms of scan time and reduced artifacts in the constructed image. Novel k-space sampling trajectories that use sinusoidal smooth functions and four RF excitations (four-shots) have been proposed here. Simulations on Shepp–Logan phantom image show that the proposed trajectory provides slightly better peak signal-to-noise ratio compared to the commonly used spiral trajectory .

Super-resolution intracranial quiescent interval slice-selective magnetic resonance angiography.

To evaluate the combination of nonenhanced quiescent-interval slice-selective (QISS) magnetic resonance angiography (MRA) with super-resolution reconstruction for portraying the intracranial arteries. The intracranial arteries of seven volunteers were imaged at 3T using QISS MRA acquired with a flow-compensated fast low-angle shot (FLASH) readout and thin overlapping slices. The impacts of super-resolution reconstruction and various acquisition parameters on the delineation of intracranial arteries were quantified using four metrics: arterial-to-background contrast-to-noise ratio (CNR), arterial-to-background contrast, arterial sharpness, and arterial full-width-at-half-maximum (FWHM). Three-dimensional time-of-flight (TOF) MRA was also acquired. For similar voxel sizes, QISS MRA displayed the intracranial arteries with an arterial-to-background contrast that exceeded 3D TOF MRA by 59-84%, depending on the k-space sampling trajectory (P < 0.001). Super-resolution reconstruction improved CNR, contrast, and sharpness, while reducing arterial FWHM (P < 0.001). Cardiac triggering provided minimal benefits, while Cartesian sampling provided higher CNR than radial sampling for multishot QISS (P < 0.05). Scan time for a complete intracranial MRA was <90 s using an ungated single-shot QISS acquisition. Thin, overlapping-slice QISS leveraging super-resolution reconstruction is a flexible approach for intracranial MRA that provides competitive image quality to standard-of-care 3D TOF, with the potential for reduced sensitivity to in-plane flow saturation and motion artifacts. Magn Reson Med 79:683-691, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

K-space trajectory mapping and its application for ultrashort Echo time imaging

MR images are affected by system delays and gradient field imperfections which induce discrepancies between prescribed and actual k-space trajectories. This could be even more critical for non-Cartesian data acquisitions where even a small deviation from the assumed k-space trajectory results in severe image degradation and artifacts. Knowledge of the actual k-space trajectories is therefore crucial and can be incorporated in the reconstruction of high quality non-Cartesian images. A novel MR method for the calibration of actual gradient waveforms was developed using a combination of phase encoding increments and subsequent detection of the exact time point at which the corresponding trajectory is crossing the k-space origin. The measured sets of points were fitted to a parametrical model to calculate the complete actual acquisition trajectory. Measurements performed on phantoms and volunteers, positioned both in- and off-isocenter of the magnet, clearly demonstrate the improvement in reconstructed ultrashort echo time (UTE) images, when information from calibration of k-space sampling trajectories is employed in the MR image reconstruction procedure. The unique feature of the proposed method is its robustness and simple experimental setup, making it suitable for quick acquisition trajectory calibration procedures e.g. for non-Cartesian radial fast imaging.

3D Cartesian MRI with compressed sensing and variable view sharing using complementary poisson-disc sampling.

To enable robust, high spatio-temporal-resolution three-dimensional Cartesian MRI using a scheme incorporating a novel variable density random k-space sampling trajectory allowing flexible and retrospective selection of the temporal footprint with compressed sensing (CS). A complementary Poisson-disc k-space sampling trajectory was designed to allow view sharing and varying combinations of reduced view sharing with CS from the same prospective acquisition. These schemes were used for two-point Dixon-based dynamic contrast-enhanced MRI (DCE-MRI) of the breast and abdomen. Results were validated in vivo with a novel approach using variable-flip-angle data, which was retrospectively accelerated using the same methods but offered a ground truth. In breast DCE-MRI, the temporal footprint could be reduced 2.3-fold retrospectively without introducing noticeable artifacts, improving depiction of rapidly enhancing lesions. Further, experiments with variable-flip-angle data showed that reducing view sharing improved accuracy in reconstruction and T1 mapping. In abdominal MRI, 2.3-fold and 3.6-fold reductions in temporal footprint allowed reduced motion artifacts. The complementary-Poisson-disc k-space sampling trajectory allowed a retrospective spatiotemporal resolution tradeoff using CS and view sharing, imparting robustness to motion and contrast enhancement. The technique was also validated using a novel approach of fully acquired variable-flip-angle acquisition. Magn Reson Med 77:1774-1785, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

LORAKS makes better SENSE: Phase-constrained partial fourier SENSE reconstruction without phase calibration.

Parallel imaging and partial Fourier acquisition are two classical approaches for accelerated MRI. Methods that combine these approaches often rely on prior knowledge of the image phase, but the need to obtain this prior information can place practical restrictions on the data acquisition strategy. In this work, we propose and evaluate SENSE-LORAKS, which enables combined parallel imaging and partial Fourier reconstruction without requiring prior phase information. The proposed formulation is based on combining the classical SENSE model for parallel imaging data with the more recent LORAKS framework for MR image reconstruction using low-rank matrix modeling. Previous LORAKS-based methods have successfully enabled calibrationless partial Fourier parallel MRI reconstruction, but have been most successful with nonuniform sampling strategies that may be hard to implement for certain applications. By combining LORAKS with SENSE, we enable highly accelerated partial Fourier MRI reconstruction for a broader range of sampling trajectories, including widely used calibrationless uniformly undersampled trajectories. Our empirical results with retrospectively undersampled datasets indicate that when SENSE-LORAKS reconstruction is combined with an appropriate k-space sampling trajectory, it can provide substantially better image quality at high-acceleration rates relative to existing state-of-the-art reconstruction approaches. The SENSE-LORAKS framework provides promising new opportunities for highly accelerated MRI. Magn Reson Med 77:1021-1035, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Accelerated and motion-robust in vivo T2 mapping from radially undersampled data using bloch-simulation-based iterative reconstruction.

Development of a quantitative transverse relaxation time (T2)-mapping platform that operates at clinically feasible timescales by employing advanced image reconstruction of radially undersampled multi spin-echo (MSE) datasets. Data was acquired on phantom and in vivo at 3 Tesla using MSE protocols employing radial k-space sampling trajectories. In order to overcome the nontrivial spin evolution associated with MSE protocols, a numerical signal model was precalculated based on Bloch simulations of the actual pulse-sequence scheme used in the acquisition process. This signal model was subsequently incorporated into an iterative model-based image reconstruction process, producing T2 and proton-density maps. T2 maps of phantom and in vivo brain were successfully constructed, closely matching values produced by a single spin-echo reference scan. High-resolution mapping was also performed for the spinal cord in vivo, differentiating the underlying gray/white matter morphology. The presented MSE data-processing framework offers reliable mapping of T2 relaxation values in a ∼ 5-minute timescale, free of user- and scanner-dependent variations. The use of radial k-space sampling provides further advantages in the form of high immunity to irregular physiological motion, as well as enhanced spatial resolutions, owing to its inherent ability to perform alias-free limited field-of-view imaging.

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

Radial imaging techniques, such as projection-reconstruction (PR), are used in magnetic resonance imaging (MRI) for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function (PSF). In this paper, a shaking projection (SP) k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. A SP trajectory has the same aliasing character when using half sampling frequency (or half data) for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling reconstruction. Furthermore, this method can be applied to three-dimensional (3D) hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.

Strategies for rapid in vivo 1H and hyperpolarized 13C MR spectroscopic imaging

In vivo MRSI is an important imaging modality that has been shown in numerous research studies to give biologically relevant information for assessing the underlying mechanisms of disease and for monitoring response to therapy. The increasing availability of high field scanners and multichannel radiofrequency coils has provided the opportunity to acquire in vivo data with significant improvements in sensitivity and signal to noise ratio. These capabilities may be used to shorten acquisition time and provide increased coverage. The ability to acquire rapid, volumetric MRSI data is critical for examining heterogeneity in metabolic profiles and for relating serial changes in metabolism within the same individual during the course of the disease. In this review we discuss the implementation of strategies that use alternative k-space sampling trajectories and parallel imaging methods in order to speed up data acquisition. The impact of such methods is demonstrated using three recent examples of how these methods have been applied. These are to the acquisition of robust 3D 1H MRSI data within 5–10min at a field strength of 3T, to obtaining higher sensitivity for 1H MRSI at 7T and to using ultrafast volumetric and dynamic 13C MRSI for monitoring the changes in signals that occur following the injection of hyperpolarized 13C agents.

Effects of 3D sampling in (k, t)-space on temporal qualities of dynamic MRI

3D (kx, ky, t)-space analysis is invoked to provide insights into dynamic magnetic resonance imaging (DMRI) with arbitrary k-space sampling trajectories. The effects of 3D sampling in (kx, ky, t) are analyzed theoretically and verified with computer simulation. The analyses show that a 3D sampling pattern that is more isotropic in (kx, ky, t)-space and denser around the (kx=0, ky=0, t)-line likely results in improved temporal qualities of DMRI. The isotropy of 3D sampling is quantified using Voronoi 3D cells and the isoperimetric theorem. This 3D sampling perspective provides a theoretical framework for understanding the temporal qualities of various DMRI methods.

K-space Inherited Parallel Acquisition (KIPA): application on dynamic magnetic resonance imaging thermometry

In this study, a novel method for dynamic parallel image acquisition and reconstruction is presented. In this method, called k-space inherited parallel acquisition (KIPA), localized reconstruction coefficients are used to achieve higher reduction factors, and lower noise and artifact levels compared to that of generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction. In KIPA, the full k-space for the first frame and the partial k-space for later frames are required to reconstruct a whole series of images. Reconstruction coefficients calculated for different segments of k-space from the first frame data set are used to estimate missing k-space lines in corresponding k-space segments of other frames. The local determination of KIPA reconstruction coefficients is essential to adjusting them according to the local signal-to-noise ratio characteristics of k-space data. The proposed algorithm is applicable to dynamic imaging with arbitrary k-space sampling trajectories. Simulations of magnetic resonance thermometry using the KIPA method with a reduction factor of 6 and using dynamic imaging studies of human subjects with reduction factors of 4 and 6 have been performed to prove the feasibility of our method and to show apparent improvement in image quality in comparison with GRAPPA for dynamic imaging.

Reduced aliasing artifacts using variable-density k-space sampling trajectories.

A variable-density k-space sampling method is proposed to reduce aliasing artifacts in MR images. Because most of the energy of an image is concentrated around the k-space center, aliasing artifacts will contain mostly low-frequency components if the k-space is uniformly undersampled. On the other hand, because the outer k-space region contains little energy, undersampling that region will not contribute severe aliasing artifacts. Therefore, a variable-density trajectory may sufficiently sample the central k-space region to reduce low-frequency aliasing artifacts and may undersample the outer k-space region to reduce scan time and to increase resolution. In this paper, the variable-density sampling method was implemented for both spiral imaging and two-dimensional Fourier transform (2DFT) imaging. Simulations, phantom images and in vivo cardiac images show that this method can significantly reduce the total energy of aliasing artifacts. In general, this method can be applied to all types of k-space sampling trajectories.