3D sensitivity encoded ellipsoidal MR spectroscopic imaging of gliomas at 3T

Purpose

The goal of this study was to implement time efficient data acquisition and reconstruction methods for 3D magnetic resonance spectroscopic imaging (MRSI) of gliomas at a field strength of 3T using parallel imaging techniques.

Methods

The point spread functions, signal to noise ratio (SNR), spatial resolution, metabolite intensity distributions and Cho:NAA ratio of 3D ellipsoidal, 3D sensitivity encoding (SENSE) and 3D combined ellipsoidal and SENSE (e-SENSE) k-space sampling schemes were compared with conventional k-space data acquisition methods.

Results

The 3D SENSE and e-SENSE methods resulted in similar spectral patterns as the conventional MRSI methods. The Cho:NAA ratios were highly correlated (P<.05 for SENSE and P<.001 for e-SENSE) with the ellipsoidal method and all methods exhibited significantly different spectral patterns in tumor regions compared to normal appearing white matter. The geometry factors ranged between 1.2 and 1.3 for both the SENSE and e-SENSE spectra. When corrected for these factors and for differences in data acquisition times, the empirical SNRs were similar to values expected based upon theoretical grounds. The effective spatial resolution of the SENSE spectra was estimated to be same as the corresponding fully sampled k-space data, while the spectra acquired with ellipsoidal and e-SENSE k-space samplings were estimated to have a 2.36–2.47-fold loss in spatial resolution due to the differences in their point spread functions.

Conclusion

The 3D SENSE method retained the same spatial resolution as full k-space sampling but with a 4-fold reduction in scan time and an acquisition time of 9.28 min. The 3D e-SENSE method had a similar spatial resolution as the corresponding ellipsoidal sampling with a scan time of 4:36 min. Both parallel imaging methods provided clinically interpretable spectra with volumetric coverage and adequate SNR for evaluating Cho, Cr and NAA.     

Real-time imaging with radial GRAPPA: Implementation on a heterogeneous architecture for low-latency reconstructions

Combination of non-Cartesian trajectories with parallel MRI permits to attain unmatched acceleration rates when compared to traditional Cartesian MRI during real-time imaging. However, computationally demanding reconstructions of such imaging techniques, such as k-space domain radial generalized auto-calibrating partially parallel acquisitions (radial GRAPPA) and image domain conjugate gradient sensitivity encoding (CG-SENSE), lead to longer reconstruction times and unacceptable latency for online real-time MRI on conventional computational hardware. Though CG-SENSE has been shown to work with low-latency using a general purpose graphics processing unit (GPU), to the best of our knowledge, no such effort has been made for radial GRAPPA. Radial GRAPPA reconstruction, which is robust even with highly undersampled acquisitions, is not iterative, requiring only significant computation during initial calibration while achieving good image quality for low-latency imaging applications. In this work, we present a very fast, low-latency, reconstruction framework based on a heterogeneous system using multi-core CPUs and GPUs. We demonstrate an implementation of radial GRAPPA that permits reconstruction times on par with or faster than acquisition of highly accelerated datasets in both cardiac and dynamic musculoskeletal imaging scenarios. Acquisition and reconstruction times are reported.     

Phase gradient imaging for positive contrast generation to superparamagnetic iron oxide nanoparticle-labeled targets in magnetic resonance imaging

Positive contrast imaging methods produce enhanced signal at large magnetic field gradient in magnetic resonance imaging. Several postprocessing algorithms, such as susceptibility gradient mapping and phase gradient mapping methods, have been applied for positive contrast generation to detect the cells targeted by superparamagnetic iron oxide nanoparticles. In the phase gradient mapping methods, smoothness condition has to be satisfied to keep the phase gradient unwrapped. Moreover, there has been no discussion about the truncation artifact associated with the algorithm of differentiation that is performed in k-space by the multiplication with frequency value. In this work, phase gradient methods are discussed by considering the wrapping problem when the smoothness condition is not satisfied. A region-growing unwrapping algorithm is used in the phase gradient image to solve the problem. In order to reduce the truncation artifact, a cosine function is multiplied in the k-space to eliminate the abrupt change at the boundaries. Simulation, phantom and in vivo experimental results demonstrate that the modified phase gradient mapping methods may produce improved positive contrast effects by reducing truncation or wrapping artifacts.     

Optimizing Spatially Localized NMR

Fourier-series windowing, a technique used to obtain spatially localized in vivo NMR spectra, is extended to fields-of-view containing a number of arbitrarily shaped regions of interest. For each volume, k-space weighting functions are derived and then combined to give an overall k-space sampling pattern - the number of signal acquisitions per phase-encoding vector - which can then be used to obtain spatially localized spectra of optimal sensitivity, consistent with a specified degree of localization. The technique is compared with the related methods of chemical-shift imaging and spectral localization by imaging.     

Improved SNR in linear reordered 2D bSSFP imaging using variable flip angles

This article presents a variable flip-angle approach for balanced steady-state free precession (bSSFP) imaging, which allows increases in signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) while keeping specific absorption rate (SAR) constant or reduces SAR for given CNR and SNR. The gain in SNR is achieved by utilizing the higher signal in the transient phase. Flip-angle variation during the echo train is realized using a trigonometric function with M steps (ramp length). Variation is combined with a linear k-space reordering such that outer parts of k-space are sampled using a lower flip angle α_min, while the central part of k-space is acquired with a higher flip angle α_max. No additional preparation or dummy cycles are applied prior to data acquisition. Several variation schemes with different starting flip angles α_min and ramp length M are considered. For example, using α_min=1° and M=96, α_max can be set to 47° without exceeding SAR limits at 3 T and gaining up to 50% in SNR, while, conventionally, α=34° is the maximal possible flip angle. Resolution seems unaffected in volunteer imaging. In all cases, no transient artifacts due to flip-angle variation were observed. This article demonstrates the use of flip-angle variations in bSSFP to increase SNR and CNR while keeping SAR constant, which is especially important at higher field strengths. Flip-angle variation can also be combined with other methods such as parallel imaging techniques for further SAR reduction.     

Parallel imaging with 3D TPI trajectory: SNR and acceleration benefits

Three-dimensional (3D) twisted projection imaging (TPI) trajectory has a unique advantage in sodium (²³Na) imaging on clinical MRI scanners at 1.5 or 3 T, generating a high signal-to-noise ratio (SNR) with a short acquisition time (∼10 min). Parallel imaging with an array of coil elements transits SNR benefits from small coil elements to acquisition efficiency by sampling partial k-space. This study investigates the feasibility of parallel sodium imaging with emphases on SNR and acceleration benefits provided by the 3D TPI trajectory. Computer simulations were used to find available acceleration factors and noise amplification. Human head studies were performed on clinical 1.5/3-T scanners with four-element coil arrays to verify simulation outcomes. In in vivo studies, proton (¹H) data, however, were acquired for concept–proof purpose. The sensitivity encoding (SENSE) method with the conjugate gradient algorithm was used to reconstruct images from accelerated TPI-SENSE data sets. Self-calibration was employed to estimate coil sensitivities. Noise amplification in TPI-SENSE was evaluated using multiple noise trials. It was found that the acceleration factor was as high as 5.53 (corresponding to acceleration number 2×3, ring-by-rotation), with a small image error of 6.9% when TPI projections were reduced in both polar (ring) and azimuthal (rotation) directions. The average noise amplification was as low as 98.7%, or 27% lower than Cartesian SENSE at that acceleration factor. The 3D nature of both TPI trajectory and coil sensitivities might be responsible for the high acceleration and low noise amplification. Consequently, TPI-SENSE may have potential advantages for parallel sodium imaging.     

Negative U-centers and defect superconductivity

A connection between the formation of defect bipolarons (i.e. U-centers or U-bipolarons) and superconductivity in high-T_csuperconductors (HTSC) is considered in two pairing limits of carriers in realr- andk-spaces. The irrelevance ofr-space U-bipolarons to superconductivity is motivated. It is shown that the formation ofk-space U-bipolarons and their subsequent attractive single particle and pair condensation lead to depressed (in comparison with lattice bipolarons) superconductivity due to a large mass of such U-bipolarons. It is argued that the coexistence ofk-space lattice bipolarons andr-space U-bipolarons leads to the shift of the maximum of the concentration dependenceT_c(n)to higher carrier concentrations, in accordance with the observations in HTSC.     

Centric scan SPRITE magnetic resonance imaging

Two rapid, pure phase encode, centric scan, Single Point Ramped Imaging with T₁-Enhancement (SPRITE) MRI methods are described. Each retains the benefits of the standard SPRITE method, most notably the ability to image short T₂^* systems, while increasing the sensitivity and generality of the technique. The Spiral-SPRITE method utilizes a modified Archimedean spiral k-space trajectory. The Conical-SPRITE method utilizes a system of spirals mapped to conical surfaces to sample the k-space cube. The sampled k-space points are naturally Cartesian grid points, eliminating the requirement of a re-gridding procedure prior to image reconstruction. The effects of transient state behaviour on image resolution and signal/noise are explored.     

SPRITE MRI with Prepared Magnetization and Centrick-Space Sampling

A technique for imaging materials with short transverse relaxation times and prepared longitudinal magnetization is proposed. The technique is single-point ramped imaging withT₁-enhancement (SPRITE) MRI with centrick-space sampling. The effects of transient state behavior on image resolution and signal/noise are estimated. Centric sampling in the basic SPRITE sequence gives increased signal-to-noise and permits a quantitative determination of the MR parameters associated with longitudinal spin preparation. Spin-lock and inversion recovery preparation experiments are presented.     

Smoothly Clipped Absolute Deviation (SCAD) regularization for compressed sensing MRI Using an augmented Lagrangian scheme

PurposeCompressed sensing (CS) provides a promising framework for MR image reconstruction from highly undersampled data, thus reducing data acquisition time. In this context, sparsity-promoting regularization techniques exploit the prior knowledge that MR images are sparse or compressible in a given transform domain. In this work, a new regularization technique was introduced by iterative linearization of the non-convex smoothly clipped absolute deviation (SCAD) norm with the aim of reducing the sampling rate even lower than it is required by the conventional l₁ norm while approaching an l₀ norm.Materials and MethodsThe CS-MR image reconstruction was formulated as an equality-constrained optimization problem using a variable splitting technique and solved using an augmented Lagrangian (AL) method developed to accelerate the optimization of constrained problems. The performance of the resulting SCAD-based algorithm was evaluated for discrete gradients and wavelet sparsifying transforms and compared with its l₁-based counterpart using phantom and clinical studies. The k-spaces of the datasets were retrospectively undersampled using different sampling trajectories. In the AL framework, the CS-MRI problem was decomposed into two simpler sub-problems, wherein the linearization of the SCAD norm resulted in an adaptively weighted soft thresholding rule with a sparsity enhancing effect.ResultsIt was demonstrated that the proposed regularization technique adaptively assigns lower weights on the thresholding of gradient fields and wavelet coefficients, and as such, is more efficient in reducing aliasing artifacts arising from k-space undersampling, when compared to its l₁-based counterpart.ConclusionThe SCAD regularization improves the performance of l₁-based regularization technique, especially at reduced sampling rates, and thus might be a good candidate for some applications in CS-MRI.     

Cardiac magnetic resonance imaging using radial k-space sampling and self-calibrated partial parallel reconstruction

Radial sampling has been demonstrated to be potentially useful in cardiac magnetic resonance imaging because it is less susceptible to motion than Cartesian sampling. Nevertheless, its capability of imaging acceleration remains limited by undersampling-induced streaking artifacts. In this study, a self-calibrated reconstruction method was developed to suppress streaking artifacts for highly accelerated parallel radial acquisitions in cardiac magnetic resonance imaging. Two- (2D) and three-dimensional (3D) radial k-space data were collected from a phantom and healthy volunteers. Images reconstructed using the proposed method and the conventional regridding method were compared based on statistical analysis on a four-point scale imaging scoring. It was demonstrated that the proposed method can effectively remove undersampling streaking artifacts and significantly improve image quality (P<.05). With the use of the proposed method, image score (1–4, 1=poor, 2=good, 3=very good, 4=excellent) was improved from 2.14 to 3.34 with the use of an undersampling factor of 4 and from 1.09 to 2.5 with the use of an undersampling factor of 8. Our study demonstrates that the proposed reconstruction method is effective for highly accelerated cardiac imaging applications using parallel radial acquisitions without calibration data.     

Surface nanostructure effects on optical properties of Pb(Zr x Ti1−x )O3 thin films

Optical scattering properties of nanostructured matter have crucial impact on performance efficiency of various photonic components, such as waveguides, display elements, and solar cells. In this paper, diffuse transmission properties of nanocrystalline Pb(Zr _x Ti_1?x )O₃ thin films with a high refractive index of ~2.5 and optical transmittance are presented. Thin films with a thicknesses ranging from 50 to 500 nm were studied using integrating sphere technique and results were compared to simulations performed by a scalar scattering theory. Thin films were deposited by pulsed laser deposition at room temperature on MgO(100) substrates and post-annealed at a temperature of 800 °C. Structural phase evolution-induced surface effects, which introduced periodicity on the film surface, cause the definite diffuse elements in transmission spectra of the films. Low and evenly distributed scattering amplitudes in k-space were seen for highly tetragonal- or trigonal-oriented films with non-textured surfaces, which led to low diffuse transmission values (T _D ≈ 5 %), while confined and increased scattering amplitudes in k-space were seen for tetragonal–trigonal-oriented films, with phase co-existence, which led to microstructure-induced textured surfaces and increased diffuse transmission values (T _D ≈ 50 %). For highly textured surfaces, scattering amplitudes distributed in tilted ellipsoid shape in k-space was observed. Difference between modeled and measured values was 3.8 % in maximum.     

Wavelet-based edge correlation incorporated iterative reconstruction for undersampled MRI

Undersampling k-space is an effective way to decrease acquisition time for MRI. However, aliasing artifacts introduced by undersampling may blur the edges of magnetic resonance images, which often contain important information for clinical diagnosis. Moreover, k-space data is often contaminated by the noise signals of unknown intensity. To better preserve the edge features while suppressing the aliasing artifacts and noises, we present a new wavelet-based algorithm for undersampled MRI reconstruction. The algorithm solves the image reconstruction as a standard optimization problem including a ?₂ data fidelity term and ?₁ sparsity regularization term. Rather than manually setting the regularization parameter for the ?₁ term, which is directly related to the threshold, an automatic estimated threshold adaptive to noise intensity is introduced in our proposed algorithm. In addition, a prior matrix based on edge correlation in wavelet domain is incorporated into the regularization term. Compared with nonlinear conjugate gradient descent algorithm, iterative shrinkage/thresholding algorithm, fast iterative soft-thresholding algorithm and the iterative thresholding algorithm using exponentially decreasing threshold, the proposed algorithm yields reconstructions with better edge recovery and noise suppression.     

Non-Iterative Regularized reconstruction Algorithm for Non-CartesiAn MRI: NIRVANA

We introduce a novel noniterative algorithm for the fast and accurate reconstruction of nonuniformly sampled MRI data. The proposed scheme derives the reconstructed image as the nonuniform inverse Fourier transform of a compensated dataset. We derive each sample in the compensated dataset as a weighted linear combination of a few measured k-space samples. The specific k-space samples and the weights involved in the linear combination are derived such that the reconstruction error is minimized. The computational complexity of the proposed scheme is comparable to that of gridding. At the same time, it provides significantly improved accuracy and is considerably more robust to noise and undersampling. The advantages of the proposed scheme makes it ideally suited for the fast reconstruction of large multidimensional datasets, which routinely arise in applications such as f-MRI and MR spectroscopy. The comparisons with state-of-the-art algorithms on numerical phantoms and MRI data clearly demonstrate the performance improvement.     

Nature of pairing in high Tc oxide superconductors

In connection with the unique structural features of the recently discovered high T_c YBa₂Cu₃O₇ and (La,Ba)₂CuO₄ we show that in such a multi-narrow-band system the opposite-spin interband pairs can function concurrently as both antiferromagnetic real pairs in x-space and Cooper pairs in k-space. So, contrary to the usually depairing Coulomb pseudotential μ¹ considered in traditional superconductors, the intra-atomic Coulomb repulsive interactions in a multiband system result in a positive contribution to Cooper pairing and enhance the conventional boson-mediated (electron-phonon and/or electron-exciton) superconductivity.     

Excitonic polariton dispersion in CuBr determined by resonant Raman scattering under two-photon excitation of excitonic molecules

The excitonic polariton dispersion in wide k-space for k∥[111] is measured through the two-photon-resonant Raman scattering with the use of the double beam excitation technique. The k-linear effect, the heavy and light masses and the polariton effect of the Z_1,2 exciton are clarified.     

Image registration guided,sparsity constrained reconstructions for dynamic MRI

It is generally a challenging task to reconstruct dynamic magnetic resonance (MR) images with high spatial and high temporal resolutions, especially with highly incomplete k-space sampling. In this work, a novel method that combines a non-rigid image registration technique with sparsity-constrained image reconstruction is introduced. Employing a multi-resolution free-form deformation technique with B-spline interpolations, the non-rigid image registration accurately models the complex deformations of the physiological dynamics, and provides artifact-suppressed high spatial-resolution predictions. Based on these prediction images, the sparsity-constrained data fidelity-enforced image reconstruction further improves the reconstruction accuracy. When compared with the k-t FOCUSS with motion estimation/motion compensation (MEMC) technique on volunteer scans, the proposed method consistently outperforms in both the spatial and the temporal accuracy with variously accelerated k-space sampling. High fidelity reconstructions for dynamic systolic phases with reduction factor of 10 and cardiac perfusion series with reduction factor of 3 are presented.     

Post-processing central k-space subtraction for high-resolution arterial peripheral MR angiography

Peripheral MR angiography requires high resolution and arterial contrast. Neither can be obtained simultaneously due to the short arterial phase of the contrast agent. To improve temporal resolution, keyhole imaging was developed, which combines high resolution and arterial k-spaces at the time of image acquisition. Here, a related approach is introduced for image post-processing in the Fourier domain. It is demonstrated that simple substitution of the central k-space with low-resolution data leads to severe distortion. Hence, a dedicated calculation scheme is necessary for composite k-space post-processing. A solution is presented for high-resolution arterial peripheral MR angiography that uses subtraction of venous intensities from the central high-resolution k-space. The calculations in the Fourier domain do not require interpolations between the different resolutions. High-resolution steady-state MR angiography, which exhibits contrast-enhanced arteries and veins at an isotropic resolution of 0.65 mm, and standard resolution arterial first-pass MR angiography were combined to obtain images with the resolution of the steady-state images and arterial contrast. Numerical simulations on software phantoms are presented. The operation of the method is demonstrated in five patients.     

Retrospectively gated cardiac cine imaging with temporal and spatial acceleration

Parallel imaging methods are routinely used to accelerate the image acquisition process in cardiac cine imaging. The addition of a temporal acceleration method, whereby k-space is sampled differently for different time frames, has been shown in prior work to improve image quality as compared to parallel imaging by itself. However, such temporal acceleration strategies prove difficult to combine with retrospectively gated cine imaging. The only currently published method to feature such combination, by Hansen et al. [Magn Reson Med 55 (2006) 85-91] tends to be associated with prohibitively long reconstruction times. The goal of the present work was to develop a retrospectively gated cardiac cine method that features both parallel imaging and temporal acceleration, capable of achieving significant acceleration factors on commonly available hardware and associated with reconstruction times short enough for practical use in a clinical context.Seven cardiac patients and a healthy volunteer were recruited and imaged, with acceleration factors of 3.5 or 4.5, using an eight-channel product cardiac array on a 1.5-T system. The prescribed FOV value proved slightly too small in three patients, and one of the patients had a bigemini condition. Despite these additional challenges, good-quality results were obtained for all slices and all patients, with a reconstruction time of 0.98±0.07 s per frame, or about 20 s for a 20-frame slice, using a single processor on a single PC. As compared to using parallel imaging by itself, the addition of a temporal acceleration strategy provided much resistance to artifacts.