Off-resonance correction using an estimated linear time map

Images acquired in the presence of magnetic field deviations and reconstructed without taking into account the off-resonance, are distorted and corrupted with artifacts. Several post-processing algorithms have been developed for correcting the distortion when it is not possible to fix the field inhomogeneities. These off-resonance correction methods are, in general, slow and computing intensive. To make them faster they are usually adapted to a particular situation or approximated. One of these approximations is to assume that the field map is linear. Although this assumption makes the algorithm fast and robust it is not well suited for arbitrary field maps. On the other hand, there are k-space trajectories with an almost linear time map (time at which each k-space value is acquired), such as 2DFT and EPI. This paper presents an algorithm for off-resonance correction based on a linear time map approximation. This approximation allows a fast algorithm that takes advantage of the almost linearity of the time map and uses the whole field map to correct the images. The proposed correction algorithm reduces the off-resonance induced artifacts while being fast. The linear approximation of the time map needs to be done only once for each trajectory because it does not depend on the acquired image or field map data. The method can also be extended to a multi-plane approximation for sequences with more complex time maps.     

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.     

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. ASP 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 recon- struction. 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.     

Multi-frequency interpolation in spiral magnetic resonance fingerprinting for correction of off-resonance blurring

Magnetic resonance fingerprinting (MRF) pulse sequences often employ spiral trajectories for data readout. Spiral k-space acquisitions are vulnerable to blurring in the spatial domain in the presence of static field off-resonance. This work describes a blurring correction algorithm for use in spiral MRF and demonstrates its effectiveness in phantom and in vivo experiments. Results show that image quality of T1 and T2 parametric maps is improved by application of this correction. This MRF correction has negligible effect on the concordance correlation coefficient and improves coefficient of variation in regions of off-resonance relative to uncorrected measurements.     

Flow properties of fast three-dimensional sequences for MR angiography

To reduce the scan time of time of flight or phase contrast angiography sequences, fast three-dimensional k-space trajectories can be employed. The best 3D trajectory depends on tolerable scan time, readout time, geometric flexibility, flow/motion properties and others. A formalism for flow/motion sensitivity comparison based on the velocity k-space behavior is presented. It consists in finding the velocity k-space position as a function of the spatial k-space position. The trajectories are compared graphically by their velocity k-space maps, with simulations and with an objective computed index. The flow/motion properties of various 3D trajectories (cones, spiral-pr hybrid, spherical stack of spirals, 3DFT, 3D echo-planar, and shells) were determined. In terms of flow/motion sensitivity the cones trajectory is the best, however, it is difficult to use it for anisotropic resolutions or fields of view. Tolerating more flow sensitivity, the stack of spirals trajectory offers more geometric flexibility.     

Improved matrix inversion in image plane parallel MRI

A new 3D parallel magnetic resonance imaging (MRI) method named Generalized Unaliasing Incorporating Support constraint and sensitivity Encoding (GUISE) is presented. GUISE allows direct image recovery from arbitrary Cartesian k-space trajectories. However, periodic k-space sampling patterns are considered for reconstruction efficiency. Image recovery methods such as 2D SENSE (SENSitivity Encoding) and 2D CAIPIRINHA (Controlled Aliasing In Parallel Imaging Results IN Higher Acceleration) are special instances of GUISE where specific restrictions are placed on the k-space sampling patterns used. It is shown that the sampling pattern has large impacts on the image reconstruction error due to noise. An efficient sampling pattern design method that incorporates prior knowledge of object support and coil sensitivity profile is proposed. It requires no experimental trials and could be used in clinical imaging. Comparison of the proposed sampling pattern design method with 2D SENSE and 2D CAIPIRINHA are made based on both simulation and experiment results. It is seen that this new adaptive sampling pattern design method results in a lower noise level in reconstructions due to better exploitation of the coil sensitivity variation and object support constraint. In addition, elimination of the non-object region from reconstruction potentially allows an acceleration factor higher than the number of receiver coils used.     

Motion correction properties of the shells k-space trajectory

The feasibility of a k-space trajectory that samples data on a set of 3D shells is demonstrated with phantom and volunteer experiments. Details of an interleaved multi-shot, helical spiral pulse sequence and a gridding reconstruction algorithm that uses Voronoi diagrams are provided. The motion-correction properties of the shells k-space trajectory are described. It is shown that when used in conjunction with three point markers, k-space data acquired with the shells trajectory provide a generalization of the RINGLET method, allowing for correction of arbitrary rigid-body motion with six degrees of freedom. Use of dedicated navigator echoes or redundant acquisitions of k-space data are not required. Retrospective motion correction is demonstrated with controlled phantom experiments and with seven healthy human volunteers. The motion correction is shown to improve the images, both qualitatively and quantitatively with a metric calculated from image entropy. Advantages and challenges of the shells trajectory are discussed, with particular attention to acquisition efficiency.     

MR image reconstruction of sparsely sampled 3D k-space data by projection-onto-convex sets

In many rapid three-dimensional (3D) magnetic resonance (MR) imaging applications, such as when following a contrast bolus in the vasculature using a moving table technique, the desired k-space data cannot be fully acquired due to scan time limitations. One solution to this problem is to sparsely sample the data space. Typically, the central zone of k-space is fully sampled, but the peripheral zone is partially sampled. We have experimentally evaluated the application of the projection-onto-convex sets (POCS) and zero-filling (ZF) algorithms for the reconstruction of sparsely sampled 3D k-space data. Both a subjective assessment (by direct image visualization) and an objective analysis [using standard image quality parameters such as global and local performance error and signal-to-noise ratio (SNR)] were employed. Compared to ZF, the POCS algorithm was found to be a powerful and robust method for reconstructing images from sparsely sampled 3D k-space data, a practical strategy for greatly reducing scan time. The POCS algorithm reconstructed a faithful representation of the true image and improved image quality with regard to global and local performance error, with respect to the ZF images. SNR, however, was superior to ZF only when more than 20% of the data were sparsely sampled. POCS-based methods show potential for reconstructing fast 3D MR images obtained by sparse sampling.     

Phase-constrained parallel MR image reconstruction

A generalized method for phase-constrained parallel MR image reconstruction is presented that combines and extends the concepts of partial-Fourier reconstruction and parallel imaging. It provides a framework for reconstructing images employing either or both techniques and for comparing image quality achieved by varying k-space sampling schemes. The method can be used as a parallel image reconstruction with a partial-Fourier reconstruction built in. It can also be used with trajectories not readily handled by straightforward combinations of partial-Fourier and SENSE-like parallel reconstructions, including variable-density, and non-Cartesian trajectories. The phase constraint specifies a better-conditioned inverse problem compared to unconstrained parallel MR reconstruction alone. This phase-constrained parallel MRI reconstruction offers a one-step alternative to the standard combination of homodyne and SENSE reconstructions with the added benefit of flexibility of sampling trajectory. The theory of the phase-constrained approach is outlined, and its calibration requirements and limitations are discussed. Simulations, phantom experiments, and in vivo experiments are presented.     

A 3D trajectory for undersampling k-space in MRSI applications

Magnetic resonance spectroscopic imaging (MRSI) is a noninvasive technique for producing spatially localized spectra. MRSI presents the important challenge of reducing the scan time while maintaining the spatial resolution. The preferred approach for this is to use time-varying readout gradients to collect the spatial and chemical-shift information. Fast, three-dimensional (3D) spatial encoded methods also reduce the scan time. Despite the existence of several new and faster 3D encoded methods, or k-space trajectories, for magnetic resonance imaging (MRI), only stack of spirals and echo planar have been studied in 3D MRSI. A novel formulation for designing fast, 3D k-space trajectory applicable to 3D MRSI is presented. This approach is simple and consists of rays expanding from the origin of k-space into a revolving sphere, collecting spectral data of all 3D spatial k-space at different times in the same scan. This article describes this new method and presents some results of its application to 3D MRSI. This technique allows some degree of undersampling; hence, it is possible to reconstruct high-quality undersampled spectroscopic imaging in order to recognize different compounds in short scan times. Additionally, the method is tested in regular 3D MRI. This proposed method can also be used for dynamic undersampled imaging.     

k-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics

Biomedical applications of photoacoustics, in particular photoacoustic tomography, require efficient models of photoacoustic propagation that can incorporate realistic properties of soft tissue, such as acoustic inhomogeneities both for purposes of simulation and for use in model-based image reconstruction methods. k-space methods are well suited to modeling high-frequency acoustics applications as they require fewer mesh points per wavelength than conventional finite element and finite difference models, and larger time steps can be taken without a loss of stability or accuracy. They are also straightforward to encode numerically, making them appealing as a general tool. The rationale behind k-space methods and the k-space approach to the numerical modeling of photoacoustic waves in fluids are covered in this paper. Three existing k-space models are applied to photoacoustics and demonstrated with examples: an exact model for homogeneous media, a second-order model that can take into account heterogeneous media, and a first-order model that can incorporate absorbing boundary conditions.     

Fast frequency selective MR imaging

With the proposed fast frequency selective MR imaging (FFSMRI) method, we focused on the elimination of all off-resonance components from the image of the observed object. To maintain imaging speed and simultaneously achieve good frequency selectivity, MRI was divided into two steps: signal acquisition and postprocessing. After the preliminary phase in which we determine imaging parameters, MRI takes place; the signal from the same object is successively acquired M times. As a result, we obtain M partial signals in k-space, from which we calculate the image of the observed object in postprocessing phase, after signal acquisition has been completed. With proper selection of parameters, it is possible to exclude from the image a majority of off-resonance components present in the observed object. However, we can decide to keep only a chosen off-resonance component in the image and eliminate all other components, including the on-resonance component and thus producing a different image from the same acquisition. The experiments with Fe(OH)(3) and oil showed that signal-to-noise ratio (SNR) can be improved by about a factor of four. The proposed FFSMRI method is suitable for frequency selective MR imaging and quantitative measurements in dynamic MRI where exclusion of off-resonance components can improve the reliability of measurement.     

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.     

High-flip-angle slice-selective parallel RF transmission with 8 channels at 7 T

At high magnetic field, B(1)(+) non-uniformity causes undesired inhomogeneity in SNR and image contrast. Parallel RF transmission using tailored 3D k-space trajectory design has been shown to correct for this problem and produce highly uniform in-plane magnetization with good slice selection profile within a relatively short excitation duration. However, at large flip angles the excitation k-space based design method fails. Consequently, several large-flip-angle parallel transmission designs have recently been suggested. In this work, we propose and demonstrate a large-flip-angle parallel excitation design for 90 degrees and 180 degrees spin-echo slice-selective excitations that mitigate severe B(1)(+) inhomogeneity. The method was validated on an 8-channel transmit array at 7T using a water phantom with B(1)(+) inhomogeneity similar to that seen in human brain in vivo. Slice-selective excitations with parallel RF systems offer means to implement conventional high-flip excitation sequences without a severe pulse-duration penalty, even at very high B(0) field strengths where large B(1)(+) inhomogeneity is present.     

Visually weighted reconstruction of compressive sensing MRI

Compressive sensing (CS) enables the reconstruction of a magnetic resonance (MR) image from undersampled data in k-space with relatively low-quality distortion when compared to the original image. In addition, CS allows the scan time to be significantly reduced. Along with a reduction in the computational overhead, we investigate an effective way to improve visual quality through the use of a weighted optimization algorithm for reconstruction after variable density random undersampling in the phase encoding direction over k-space. In contrast to conventional magnetic resonance imaging (MRI) reconstruction methods, the visual weight, in particular, the region of interest (ROI), is investigated here for quality improvement. In addition, we employ a wavelet transform to analyze the reconstructed image in the space domain and fully utilize data sparsity over the spatial and frequency domains. The visual weight is constructed by reflecting the perceptual characteristics of the human visual system (HVS), and then applied to ?₁ norm minimization, which gives priority to each coefficient during the reconstruction process. Using objective quality assessment metrics, it was found that an image reconstructed using the visual weight has higher local and global quality than those processed by conventional methods.     

Truncation artifact reduction in spectroscopic imaging using a dual-density spiral k-space trajectory

Truncation artifacts arise in magnetic resonance spectroscopic imaging (MRSI) of the human brain due to limited coverage of k-space necessitated by low SNR of metabolite signal and limited scanning time. In proton MRSI of the head, intense extra-cranial lipid signals “bleed” into brain regions, thereby contaminating signals of metabolites therein. This work presents a data acquisition strategy for reducing truncation artifact based on extended k-space coverage achieved with a dual-SNR strategy. Using the fact that the SNR in k-space increases monotonically with sampling density, dual-SNR is achieved in an efficient manner with a dual-density spiral k-space trajectory that permits a smooth transition from high density to low density. The technique is demonstrated to be effective in reducing “bleeding” of extra-cranial lipid signals while preserving the SNR of metabolites in the brain.     

Design and optimization for variable rate selective excitation using an analytic RF scaling function

At higher B(0) fields, specific absorption rate (SAR) deposition increases. Due to maximum SAR limitation, slice coverage decreases and/or scan time increases. Conventional selective RF pulses are played out in conjunction with a time independent field gradient. Variable rate selective excitation (VERSE) is a technique that modifies the original RF and gradient waveforms such that slice profile is unchanged. The drawback is that the slice profile for off-resonance spins is distorted. A new VERSE algorithm based on modeling the scaled waveforms as a Fermi function is introduced. It ensures that system related constraints of maximum gradient amplitude and slew rate are not exceeded. The algorithm can be used to preserve the original RF pulse duration while minimizing SAR and peak b1 or to minimize the RF pulse duration. The design is general and can be applied to any symmetrical or asymmetrical RF waveform. The algorithm is demonstrated by using it to (a) minimize the SAR of a linear phase RF pulse, (b) minimize SAR of a hyperbolic secant RF pulse, and (c) minimize the duration of a linear phase RF pulse. Images with a T1-FLAIR (T1 FLuid Attenuated Inversion Recovery) sequence using a conventional and VERSE adiabatic inversion RF pulse are presented. Comparison of images and scan parameters for different anatomies and coils shows increased scan coverage and decreased SAR with the VERSE inversion RF pulse, while image quality is preserved.     

Real-time dynamic vocal tract imaging using an accelerated spiral GRE sequence and low rank plus sparse reconstruction

PurposeTo develop a real-time dynamic vocal tract imaging method using an accelerated spiral GRE sequence and low rank plus sparse reconstruction.MethodsSpiral k-space sampling has high data acquisition efficiency and thus is suited for real-time dynamic imaging; further acceleration can be achieved by undersampling k-space and using a model-based reconstruction. Low rank plus sparse reconstruction is a promising method with fast computation and increased robustness to global signal changes and bulk motion, as the images are decomposed into low rank and sparse terms representing different dynamic components. However, the combination with spiral scanning has not been well studied. In this study an accelerated spiral GRE sequence was developed with an optimized low rank plus sparse reconstruction and compared with L1-SPIRiT and XD-GRASP methods. The off-resonance was also corrected using a Chebyshev approximation method to reduce blurring on a frame-by-frame basis.ResultsThe low rank plus sparse reconstruction method is sensitive to the weights of the low rank and sparse terms. The optimized reconstruction showed advantages over other methods with reduced aliasing and improved SNR. With the proposed method, spatial resolution of 1.3*1.3 mm² with 150 mm field-of-view (FOV) and temporal resolution of 30 frames-per-second (fps) was achieved with good image quality. Blurring was reduced using the Chebyshev approximation method.ConclusionThis work studies low rank plus sparse reconstruction using the spiral trajectory and demonstrates a new method for dynamic vocal tract imaging which can benefit studies of speech disorders.     

Improving excitation and inversion accuracy by optimized RF pulse using genetic algorithm

In this study, a Genetic Algorithm (GA) is introduced to optimize the multidimensional spatial selective RF pulse to reduce the passband and stopband errors of excitation profile while limiting the transition width. This method is also used to diminish the nonlinearity effect of the Bloch equation for large tip angle excitation pulse design. The RF pulse is first designed by the k-space method and then coded into float strings to form an initial population. GA operators are then applied to this population to perform evolution, which is an optimization process. In this process, an evaluation function defined as the sum of the reciprocal of passband and stopband errors is used to assess the fitness value of each individual, so as to find the best individual in current generation. It is possible to optimize the RF pulse after a number of iterations. Simulation results of the Bloch equation show that in a 90 degrees excitation pulse design, compared with the k-space method, a GA-optimized RF pulse can reduce the passband and stopband error by 12% and 3%, respectively, while maintaining the transition width within 2 cm (about 12% of the whole 32 cm FOV). In a 180 degrees inversion pulse design, the passband error can be reduced by 43%, while the transition is also kept at 2 cm in a whole 32 cm FOV.