Density compensation functions for spiral MRI

A silent echo-planar spectroscopic imaging readout with high spectral bandwidth MRSI using an ultrasonic gradient axis

PURPOSE

We present a novel silent echo-planar spectroscopic imaging (EPSI) readout, which uses an ultrasonic gradient insert to accelerate MRSI while producing a high spectral bandwidth (20 kHz) and a low sound level.

METHODS

The ultrasonic gradient insert consisted of a single-axis (z-direction) plug-and-play gradient coil, powered by an audio amplifier, and produced 40 mT/m at 20 kHz. The silent EPSI readout was implemented in a phase-encoded MRSI acquisition. Here, the additional spatial encoding provided by this silent EPSI readout was used to reduce the number of phase-encoding steps. Spectroscopic acquisitions using phase-encoded MRSI, a conventional EPSI-readout, and the silent EPSI readout were performed on a phantom containing metabolites with resonance frequencies in the ppm range of brain metabolites (0-4 ppm). These acquisitions were used to determine sound levels, showcase the high spectral bandwidth of the silent EPSI readout, and determine the SNR efficiency and the scan efficiency.

RESULTS

The silent EPSI readout featured a 19-dB lower sound level than a conventional EPSI readout while featuring a high spectral bandwidth of 20 kHz without spectral ghosting artifacts. Compared with phase-encoded MRSI, the silent EPSI readout provided a 4.5-fold reduction in scan time. In addition, the scan efficiency of the silent EPSI readout was higher (82.5% vs. 51.5%) than the conventional EPSI readout.

CONCLUSIONS

We have for the first time demonstrated a silent spectroscopic imaging readout with a high spectral bandwidth and low sound level. This sound reduction provided by the silent readout is expected to have applications in sound-sensitive patient groups, whereas the high spectral bandwidth could benefit ultrahigh-field MR systems.

The future of CMR: All-in-one vs. real-time CMR (Part 2)

Cardiac Magnetic Resonance (CMR) protocols can be lengthy and complex, which has driven the research community to develop new technologies to make these protocols more efficient and patient-friendly. Two different approaches to improving CMR have been proposed, specifically "all-in-one" CMR, where several contrasts and/or motion states are acquired simultaneously, and "real-time" CMR, in which the examination is accelerated to avoid the need for breathholding and/or cardiac gating. The goal of this two-part manuscript is to describe these two different types of emerging rapid CMR protocols. To this end, the vision of all-in-one and real-time imaging are described, along with techniques which have been devised and tested along the pathway of clinical implementation. The pros and cons of the different methods are presented, and the remaining open needs of each are detailed. Part 1 tackles the "All-in-One" approaches, and Part 2 focuses on the "Real-Time" approaches along with an overall summary of these emerging methods.

Design and development of a novel flexible ultra-short echo time (FUSE) sequence

PURPOSE

To present the validation of a new Flexible Ultra-Short Echo time (FUSE) pulse sequence using a short-T2 phantom.

METHODS

FUSE was developed to include a range of RF excitation pulses, trajectories, dimensionalities, and long-T2 suppression techniques, enabling real-time interchangeability of acquisition parameters. Additionally, we developed an improved 3D deblurring algorithm to correct for off-resonance artifacts. Several experiments were conducted to validate the efficacy of FUSE, by comparing different approaches for off-resonance artifact correction, variations in RF pulse and trajectory combinations, and long-T2 suppression techniques. All scans were performed on a 3 T system using an in-house short-T2 phantom. The evaluation of results included qualitative comparisons and quantitative assessments of the SNR and contrast-to-noise ratio.

RESULTS

Using the capabilities of FUSE, we demonstrated that we could combine a shorter readout duration with our improved deblurring algorithm to effectively reduce off-resonance artifacts. Among the different RF and trajectory combinations, the spiral trajectory with the regular half-inc pulse achieves the highest SNRs. The dual-echo subtraction technique delivers better short-T2 contrast and superior suppression of water and agar signals, whereas the off-resonance saturation method successfully suppresses water and lipid signals simultaneously.

CONCLUSION

In this work, we have validated the use of our new FUSE sequence using a short T2 phantom, demonstrating that multiple UTE acquisitions can be achieved within a single sequence. This new sequence may be useful for acquiring improved UTE images and the development of UTE imaging protocols.

Efficient Approximation of Jacobian Matrices Involving a Non-Uniform Fast Fourier Transform (NUFFT)

There is growing interest in learning Fourier domain sampling strategies (particularly for magnetic resonance imaging, MRI) using optimization approaches. For non-Cartesian sampling, the system models typically involve non-uniform fast Fourier transform (NUFFT) operations. Commonly used NUFFT algorithms contain frequency domain interpolation, which is not differentiable with respect to the sampling pattern, complicating the use of gradient methods. This paper describes an efficient and accurate approach for computing approximate gradients involving NUFFTs. Multiple numerical experiments validate the improved accuracy and efficiency of the proposed approximation. As an application to computational imaging, the NUFFT Jacobians were used to optimize non-Cartesian MRI sampling trajectories via data-driven stochastic optimization. Specifically, the sampling patterns were learned with respect to various model-based image reconstruction (MBIR) algorithms. The proposed approach enables sampling optimization for image sizes that are infeasible with standard auto-differentiation methods due to memory limits. The synergistic acquisition and reconstruction design leads to remarkably improved image quality. In fact, we show that model-based image reconstruction methods with suitably optimized imaging parameters can perform nearly as well as CNN-based methods.

Improving D-2-hydroxyglutarate MR spectroscopic imaging in mutant isocitrate dehydrogenase glioma patients with multiplexed RF-receive/B0 -shim array coils at 3 T

MR spectroscopic imaging (MRSI) noninvasively maps the metabolism of human brains. In particular, the imaging of D-2-hydroxyglutarate (2HG) produced by glioma isocitrate dehydrogenase (IDH) mutations has become a key application in neuro-oncology. However, the performance of full field-of-view MRSI is limited by B0 spatial nonuniformity and lipid artifacts from tissues surrounding the brain. Array coils that multiplex RF-receive and B0 -shim electrical currents (AC/DC mixing) over the same conductive loops provide many degrees of freedom to improve B0 uniformity and reduce lipid artifacts. AC/DC coils are highly efficient due to compact design, requiring low shim currents (<2 A) that can be switched fast (0.5 ms) with high interscan reproducibility (10% coefficient of variation for repeat measurements). We measured four tumor patients and five volunteers at 3 T and show that using AC/DC coils in addition to the vendor-provided second-order spherical harmonics shim provides 19% narrower spectral linewidth, 6% higher SNR, and 23% less lipid content for unrestricted field-of-view MRSI, compared with the vendor-provided shim alone. We demonstrate that improvement in MRSI data quality led to 2HG maps with higher contrast-to-noise ratio for tumors that coincide better with the FLAIR-enhancing lesions in mutant IDH glioma patients. Smaller Cramér-Rao lower bounds for 2HG quantification are obtained in tumors by AC/DC shim, corroborating with simulations that predicted improved accuracy and precision for narrower linewidths. AC/DC coils can be used synergistically with optimized acquisition schemes to improve metabolic imaging for precision oncology of glioma patients. Furthermore, this methodology has broad applicability to other neurological disorders and neuroscience.

In Vivo Absolute Metabolite Quantification Using a Multiplexed ERETIC-RX Array Coil for Whole-Brain MR Spectroscopic Imaging

BACKGROUND

Absolute quantification of metabolites in MR spectroscopic imaging (MRSI) requires a stable reference signal of known concentration. The Electronic REference To access In vivo Concentrations (ERETIC) has shown great promise but has not been applied in patients and 3D MRSI. ERETIC hardware has not been integrated with receive arrays due to technical challenges, such as coil combination and unwanted coupling between multiple ERETIC and receive channels, for which we developed mitigation strategies.

PURPOSE

To develop absolute quantification for whole-brain MRSI in glioma patients.

STUDY TYPE

Prospective.

POPULATION

Five healthy volunteers and three patients with isocitrate dehydrogenase mutant glioma (27% female). Calibration and coil loading phantoms.

FIELD STRENGTH/SEQUENCE

A 3 T; Adiabatic spin-echo spiral 3D MRSI with real-time motion correction, Fluid Attenuated Inversion Recovery (FLAIR), Gradient Recalled Echo (GRE), Multi-echo Magnetization Prepared Rapid Acquisition of Gradient Echo (MEMPRAGE).

ASSESSMENT

Absolute quantification was performed for five brain metabolites (total N-acetyl-aspartate [NAA]/creatine/choline, glutamine + glutamate, myo-inositol) and the oncometabolite 2-hydroxyglutarate using a custom-built 4x-ERETIC/8x-receive array coil. Metabolite quantification was performed with both EREIC and internal water reference methods. ERETIC signal was transmitted via optical link and used to correct coil loading. Inductive and radiative coupling between ERETIC and receive channels were measured.

STATISTICAL TESTS

ERETIC and internal water methods for metabolite quantification were compared using Bland-Altman (BA) analysis and the nonparametric Mann-Whitney test. P < 0.05 was considered statistically significant.

RESULTS

ERETIC could be integrated in receive arrays and inductive coupling dominated (5-886 times) radiative coupling. Phantoms show proportional scaling of the ERETIC signal with coil loading. The BA analysis demonstrated very good agreement (3.3% ± 1.6%) in healthy volunteers, while there was a large difference (36.1% ± 3.8%) in glioma tumors between metabolite concentrations by ERETIC and internal water quantification.

CONCLUSION

Our results indicate that ERETIC integrated with receive arrays and whole-brain MRSI is feasible for brain metabolites quantification. Further validation is required to probe that ERETIC provides more accurate metabolite concentration in glioma patients.

EVIDENCE LEVEL

2 TECHNICAL EFFICACY: Stage 1.

Real-Time Mapping of Tissue Properties for Magnetic Resonance Fingerprinting

Magnetic resonance fingerprinting (MRF) is a relatively new multi-parametric quantitative imaging method that involves a two-step process: (i) reconstructing a series of time frames from highly-undersampled non-Cartesian spiral k-space data and (ii) pattern matching using the time frames to infer tissue properties (e.g., T 1 and T 2 relaxation times). In this paper, we introduce a novel end-to-end deep learning framework to seamlessly map the tissue properties directly from spiral k-space MRF data, thereby avoiding time-consuming processing such as the non-uniform fast Fourier transform (NUFFT) and the dictionary-based fingerprint matching. Our method directly consumes the non-Cartesian k -space data, performs adaptive density compensation, and predicts multiple tissue property maps in one forward pass. Experiments on both 2D and 3D MRF data demonstrate that quantification accuracy comparable to state-of-the-art methods can be accomplished within 0.5 s, which is 1,100 to 7,700 times faster than the original MRF framework. The proposed method is thus promising for facilitating the adoption of MRF in clinical settings.

Whole-Slab 3D MR Spectroscopic Imaging of the Human Brain With Spiral-Out-In Sampling at 7T

BACKGROUND

Metabolic imaging using proton magnetic resonance spectroscopic imaging (MRSI) has increased the sensitivity and spectral resolution at field strengths of ≥7T. Compared to the conventional Cartesian-based spectroscopic imaging, spiral trajectories enable faster data collection, promising the clinical translation of whole-brain MRSI. Technical considerations at 7T, however, lead to a suboptimal sampling efficiency for the spiral-out (SO) acquisitions, as a significant portion of the trajectory consists of rewinders.

PURPOSE

To develop and implement a spiral-out-in (SOI) trajectory for sampling of whole-brain MRSI at 7T. We hypothesized that SOI will improve the signal-to-noise ratio (SNR) of metabolite maps due to a more efficient acquisition.

STUDY TYPE

Prospective.

SUBJECTS/PHANTOM

Five healthy volunteers (28-38 years, three females) and a phantom.

FIELD STRENGTH/SEQUENCE

Navigated adiabatic spin-echo spiral 3D MRSI at 7T.

ASSESSMENT

A 3D stack of SOI trajectories was incorporated into an adiabatic spin-echo MRSI sequence with real-time motion and shim correction. Metabolite spectral fitting, SNR, and Cramér-Rao lower bound (CRLB) were obtained. We compared the signal intensity and CRLB of three metabolites of tNAA, tCr, and tCho. Peak SNR (PSNR), structure similarity index (SSIM), and signal-to-artifact ratio were evaluated on water maps.

STATISTICAL TESTS

The nonparametric Mann-Whitney U-test was used for statistical testing.

RESULTS

Compared to SO, the SOI trajectory: 1) increased the k-space sampling efficiency by 23%; 2) is less demanding for the gradient hardware, requiring 36% lower Gmax and 26% lower Smax ; 3) increased PSNR of water maps by 4.94 dB (P = 0.0006); 4) resulted in a 29% higher SNR (P = 0.003) and lower CRLB by 26-35% (P = 0.02, tNAA), 35-55% (P = 0.03, tCr), and 22-23% (P = 0.04, tCho), which increased the number of well-fitted voxels (eg, for tCr by 11%, P = 0.03). SOI did not significantly change the signal-to-artifact ratio and SSIM (P = 0.65) compared to SO.

DATA CONCLUSION

SOI provided more efficient MRSI at 7T compared to SO, which improved the data quality and metabolite quantification.

LEVEL OF EVIDENCE

1 TECHNICAL EFFICACY STAGE: 2.

Revealing the mechanisms behind novel auditory stimuli discrimination: An evaluation of silent functional MRI using looping star

Looping Star is a near‐silent, multi‐echo, 3D functional magnetic resonance imaging (fMRI) technique. It reduces acoustic noise by at least 25dBA, with respect to gradient‐recalled echo echo‐planar imaging (GRE‐EPI)‐based fMRI. Looping Star has successfully demonstrated sensitivity to the cerebral blood‐oxygen‐level‐dependent (BOLD) response during block design paradigms but has not been applied to event‐related auditory perception tasks. Demonstrating Looping Star's sensitivity to such tasks could (a) provide new insights into auditory processing studies, (b) minimise the need for invasive ear protection, and (c) facilitate the translation of numerous fMRI studies to investigations in sound‐averse patients. We aimed to demonstrate, for the first time, that multi‐echo Looping Star has sufficient sensitivity to the BOLD response, compared to that of GRE‐EPI, during a well‐established event‐related auditory discrimination paradigm: the “oddball” task. We also present the first quantitative evaluation of Looping Star's test–retest reliability using the intra‐class correlation coefficient. Twelve participants were scanned using single‐echo GRE‐EPI and multi‐echo Looping Star fMRI in two sessions. Random‐effects analyses were performed, evaluating the overall response to tones and differential tone recognition, and intermodality analyses were computed. We found that multi‐echo Looping Star exhibited consistent sensitivity to auditory stimulation relative to GRE‐EPI. However, Looping Star demonstrated lower test–retest reliability in comparison with GRE‐EPI. This could reflect differences in functional sensitivity between the techniques, though further study is necessary with additional cognitive paradigms as varying cognitive strategies between sessions may arise from elimination of acoustic scanner noise.

Accelerating Non-Cartesian MRI Reconstruction Convergence Using k-Space Preconditioning

We propose a k-space preconditioning formulation for accelerating the convergence of iterative Magnetic Resonance Imaging (MRI) reconstructions from non-uniformly sampled k-space data. Existing methods either use sampling density compensations which sacrifice reconstruction accuracy, or circulant preconditioners which increase per-iteration computation. Our approach overcomes both shortcomings. Concretely, we show that viewing the reconstruction problem in the dual formulation allows us to precondition in k-space using density-compensation-like operations. Using the primal-dual hybrid gradient method, the proposed preconditioning method does not have inner loops and are competitive in accelerating convergence compared to existing algorithms. We derive l2 -optimized preconditioners, and demonstrate through experiments that the proposed method converges in about ten iterations in practice.

Acquisition strategies for spatially resolved magnetic resonance detection of hyperpolarized nuclei

Hyperpolarization is an emerging method in magnetic resonance imaging that allows nuclear spin polarization of gases or liquids to be temporarily enhanced by up to five or six orders of magnitude at clinically relevant field strengths and administered at high concentration to a subject at the time of measurement. This transient gain in signal has enabled the non-invasive detection and imaging of gas ventilation and diffusion in the lungs, perfusion in blood vessels and tissues, and metabolic conversion in cells, animals, and patients. The rapid development of this method is based on advances in polarizer technology, the availability of suitable probe isotopes and molecules, improved MRI hardware and pulse sequence development. Acquisition strategies for hyperpolarized nuclei are not yet standardized and are set up individually at most sites depending on the specific requirements of the probe, the object of interest, and the MRI hardware. This review provides a detailed introduction to spatially resolved detection of hyperpolarized nuclei and summarizes novel and previously established acquisition strategies for different key areas of application.

Short-T2 MRI: Principles and recent advances

Among current modalities of biomedical and diagnostic imaging, MRI stands out by virtue of its versatile contrast obtained without ionizing radiation. However, in various cases, e.g., water protons in tissues such as bone, tendon, and lung, MRI performance is limited by the rapid decay of resonance signals associated with short transverse relaxation times T₂ or T₂*. Efforts to address this shortcoming have led to a variety of specialized short-T₂ techniques. Recent progress in this field expands the choice of methods and prompts fresh considerations with regard to instrumentation, data acquisition, and signal processing. In this review, the current status of short-T₂ MRI is surveyed. In an attempt to structure the growing range of techniques, the presentation highlights overarching concepts and basic methodological options. The most frequently used approaches are described in detail, including acquisition strategies, image reconstruction, hardware requirements, means of introducing contrast, sources of artifacts, limitations, and applications.

Content-aware compressive magnetic resonance image reconstruction

This paper describes an adaptive approach to regularizing model-based reconstructions in magnetic resonance imaging to account for local structure or image content. In conjunction with common models like wavelet and total variation sparsity, this content-aware regularization avoids oversmoothing or compromising image features while suppressing noise and incoherent aliasing from accelerated imaging. To evaluate this regularization approach, the experiments reconstruct images from single- and multi-channel, Cartesian and non-Cartesian, brain and cardiac data. These reconstructions combine common analysis-form regularizers and autocalibrating parallel imaging (when applicable). In most cases, the results show widespread improvement in structural similarity and peak-signal-to-error ratio relative to the fully sampled images. These results suggest that this content-aware regularization can preserve local image structures such as edges while providing denoising power superior to sparsity-promoting or sparsity-reweighted regularization.

Density-weighted concentric circle trajectories for high resolution brain magnetic resonance spectroscopic imaging at 7T

PURPOSE

Full-slice magnetic resonance spectroscopic imaging at ≥7 T is especially vulnerable to lipid contaminations arising from regions close to the skull. This contamination can be mitigated by improving the point spread function via higher spatial resolution sampling and k-space filtering, but this prolongs scan times and reduces the signal-to-noise ratio (SNR) efficiency. Currently applied parallel imaging methods accelerate magnetic resonance spectroscopic imaging scans at 7T, but increase lipid artifacts and lower SNR-efficiency further. In this study, we propose an SNR-efficient spatial-spectral sampling scheme using concentric circle echo planar trajectories (CONCEPT), which was adapted to intrinsically acquire a Hamming-weighted k-space, thus termed density-weighted-CONCEPT. This minimizes voxel bleeding, while preserving an optimal SNR.

THEORY AND METHODS

Trajectories were theoretically derived and verified in phantoms as well as in the human brain via measurements of five volunteers (single-slice, field-of-view 220 × 220 mm2 , matrix 64 × 64, scan time 6 min) with free induction decay magnetic resonance spectroscopic imaging. Density-weighted-CONCEPT was compared to (a) the originally proposed CONCEPT with equidistant circles (here termed e-CONCEPT), (b) elliptical phase-encoding, and (c) 5-fold Controlled Aliasing In Parallel Imaging Results IN Higher Acceleration accelerated elliptical phase-encoding.

RESULTS

By intrinsically sampling a Hamming-weighted k-space, density-weighted-CONCEPT removed Gibbs-ringing artifacts and had in vivo +9.5%, +24.4%, and +39.7% higher SNR than e-CONCEPT, elliptical phase-encoding, and the Controlled Aliasing In Parallel Imaging Results IN Higher Acceleration accelerated elliptical phase-encoding (all P < 0.05), respectively, which lead to improved metabolic maps.

CONCLUSION

Density-weighted-CONCEPT provides clinically attractive full-slice high-resolution magnetic resonance spectroscopic imaging with optimal SNR at 7T. Magn Reson Med 79:2874-2885, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Super-resolution reconstruction in frequency, image, and wavelet domains to reduce through-plane partial voluming in MRI

PURPOSE

To compare and evaluate the use of super-resolution reconstruction (SRR), in frequency, image, and wavelet domains, to reduce through-plane partial voluming effects in magnetic resonance imaging.

METHODS

The reconstruction of an isotropic high-resolution image from multiple thick-slice scans has been investigated through techniques in frequency, image, and wavelet domains. Experiments were carried out with thick-slice T2-weighted fast spin echo sequence on the Academic College of Radiology MRI phantom, where the reconstructed images were compared to a reference high-resolution scan using peak signal-to-noise ratio (PSNR), structural similarity image metric (SSIM), mutual information (MI), and the mean absolute error (MAE) of image intensity profiles. The application of super-resolution reconstruction was then examined in retrospective processing of clinical neuroimages of ten pediatric patients with tuberous sclerosis complex (TSC) to reduce through-plane partial voluming for improved 3D delineation and visualization of thin radial bands of white matter abnormalities.

RESULTS

Quantitative evaluation results show improvements in all evaluation metrics through super-resolution reconstruction in the frequency, image, and wavelet domains, with the highest values obtained from SRR in the image domain. The metric values for image-domain SRR versus the original axial, coronal, and sagittal images were PSNR = 32.26 vs 32.22, 32.16, 30.65; SSIM = 0.931 vs 0.922, 0.924, 0.918; MI = 0.871 vs 0.842, 0.844, 0.831; and MAE = 5.38 vs 7.34, 7.06, 6.19. All similarity metrics showed high correlations with expert ranking of image resolution with MI showing the highest correlation at 0.943. Qualitative assessment of the neuroimages of ten TSC patients through in-plane and out-of-plane visualization of structures showed the extent of partial voluming effect in a real clinical scenario and its reduction using SRR. Blinded expert evaluation of image resolution in resampled out-of-plane views consistently showed the superiority of SRR compared to original axial and coronal image acquisitions.

CONCLUSIONS

Thick-slice 2D T2-weighted MRI scans are part of many routine clinical protocols due to their high signal-to-noise ratio, but are often severely affected by through-plane partial voluming effects. This study shows that while radiologic assessment is performed in 2D on thick-slice scans, super-resolution MRI reconstruction techniques can be used to fuse those scans to generate a high-resolution image with reduced partial voluming for improved postacquisition processing. Qualitative and quantitative evaluation showed the efficacy of all SRR techniques with the best results obtained from SRR in the image domain. The limitations of SRR techniques are uncertainties in modeling the slice profile, density compensation, quantization in resampling, and uncompensated motion between scans.

α-trideuteromethyl[15N]glutamine: A long-lived hyperpolarized perfusion marker

PURPOSE

We characterized the performance of a novel hyperpolarized perfusion marker, α-trideuteromethyl[15N]glutamine, for direct comparison with a 13C-based hyperpolarized perfusion marker, [13C, 15N2]urea.

METHODS

A hardware platform and pulse sequence for in vivo 15N experiments were established. Hyperpolarized solutions of α-trideuteromethyl[15N]glutamine and [13C, 15N2]urea were injected into healthy male Lewis rats. Kidney slice images were acquired using a single-shot spiral readout. Both compounds were compared to determine in vivo signal lifetime and tracer distribution. Mass spectrometry was performed to evaluate excretion of the compound.

RESULTS

Compared with 13C-labeled urea, a significantly increased signal lifetime was observed. While the urea signal was gone after 90 s, decay of the glutamine compound was sufficiently slow to obtain a quantifiable signal, even after 5 min. The glutamine derivative showed strong localization in the kidneys with little background signal. Effective T1 of α-trideuteromethyl[15N]glutamine was approximately eight-fold higher than that of urea. Mass spectrometry results confirmed rapid excretion within the time scale of the measurement.

CONCLUSION

Hyperpolarized α-trideuteromethyl[15N]glutamine is a highly promising candidate for renal studies because of its long signal lifetime, strong localization and rapid excretion. Magn Reson Med 76:1900-1904, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

Magnetic Resonance Sequences and Rapid Acquisition for MR-Guided Interventions

Interventional MR uses rapid imaging to guide diagnostic and therapeutic procedures. One of the attractions of MR-guidance is the abundance of inherent contrast mechanisms available. Dynamic procedural guidance with real-time imaging has pushed the limits of MR technology, demanding rapid acquisition and reconstruction paired with interactive control and device visualization. This article reviews the technical aspects of real-time MR sequences that enable MR-guided interventions.

Comparison of acquisition schemes for hyperpolarised ¹³C imaging

The aim of this study was to characterise and compare widely used acquisition strategies for hyperpolarised (13)C imaging. Free induction decay chemical shift imaging (FIDCSI), echo-planar spectroscopic imaging (EPSI), IDEAL spiral chemical shift imaging (ISPCSI) and spiral chemical shift imaging (SPCSI) sequences were designed for two different regimes of spatial resolution. Their characteristics were studied in simulations and in tumour-bearing rats after injection of hyperpolarised [1-(13)C]pyruvate on a clinical 3-T scanner. Two or three different sequences were used on the same rat in random order for direct comparison. The experimentally obtained lactate signal-to-noise ratio (SNR) in the tumour matched the simulations. Differences between the sequences were mainly found in the encoding efficiency, gradient demand and artefact behaviour. Although ISPCSI and SPCSI offer high encoding efficiencies, these non-Cartesian trajectories are more prone than EPSI and FIDCSI to artefacts from various sources. If the encoding efficiency is sufficient for the desired application, EPSI has been proven to be a robust choice. Otherwise, faster spiral acquisition schemes are recommended. The conclusions found in this work can be applied directly to clinical applications.

Ultrashort echo time (UTE) imaging using gradient pre-equalization and compressed sensing

Ultrashort echo time (UTE) imaging is a well-known technique used in medical MRI, however, the implementation of the sequence remains non-trivial. This paper introduces UTE for non-medical applications and outlines a method for the implementation of UTE to enable accurate slice selection and short acquisition times. Slice selection in UTE requires fast, accurate switching of the gradient and r.f. pulses. Here a gradient "pre-equalization" technique is used to optimize the gradient switching and achieve an effective echo time of 10μs. In order to minimize the echo time, k-space is sampled radially. A compressed sensing approach is used to minimize the total acquisition time. Using the corrections for slice selection and acquisition along with novel image reconstruction techniques, UTE is shown to be a viable method to study samples of cork and rubber with a shorter signal lifetime than can typically be measured. Further, the compressed sensing image reconstruction algorithm is shown to provide accurate images of the samples with as little as 12.5% of the full k-space data set, potentially permitting real time imaging of short T2(*) materials.

High-speed spiral imaging technique for an atomic force microscope using a linear quadratic Gaussian controller

This paper demonstrates a high-speed spiral imaging technique for an atomic force microscope (AFM). As an alternative to traditional raster scanning, an approach of gradient pulsing using a spiral line is implemented and spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes to the X and Y-axes of the AFM's piezoelectric tube scanner (PTS). Due to these single-frequency sinusoidal input signals, the scanning process can be faster than that of conventional raster scanning. A linear quadratic Gaussian controller is designed to track the reference sinusoid and a vibration compensator is combined to damp the resonant mode of the PTS. An internal model of the reference sinusoidal signal is included in the plant model and an integrator for the system error is introduced in the proposed control scheme. As a result, the phase error between the input and output sinusoids from the X and Y-PTSs is reduced. The spirals produced have particularly narrow-band frequency measures which change slowly over time, thereby making it possible for the scanner to achieve improved tracking and continuous high-speed scanning rather than being restricted to the back and forth motion of raster scanning. As part of the post-processing of the experimental data, a fifth-order Butterworth filter is used to filter noises in the signals emanating from the position sensors and a Gaussian image filter is used to filter the images. A comparison of images scanned using the proposed controller (spiral) and the AFM PI controller (raster) shows improvement in the scanning rate using the proposed method.

Structured errors in reconstruction methods for Non-Cartesian MR data

BACKGROUND

Reconstruction methods for Non-Cartesian magnetic resonance imaging have often been analyzed using the root mean square error (RMSE). However, RMSE is not able to measure the level of structured error associated with the reconstruction process.

METHODS

An index for geometric information loss was presented using the 2D autocorrelation function. The performances of Least Squares Non Uniform Fast Fourier Transform (LS-NUFFT) and gridding reconstruction (GR) methods were compared. The Direct Summation method (DS) was used as reference. For both methods, RMSE and the loss in geometric information were calculated using a digital phantom and a hyperpolarized (13)C dataset.

RESULTS

The performance of the geometric information loss index was analyzed in the presence of noise. Comparing to GR, LS-NUFFT obtained a lower RMSE, but its error image appeared more structured. This was observed in both phantom and in vivo experiments.

DISCUSSION

The evaluation of geometric information loss together with the reconstruction error was important for an appropriate performance analysis of the reconstruction methods. The use of geometric information loss was helpful to determine that LS-NUFFT loses relevant information in the reconstruction process, despite the low RMSE.

Regularization techniques on least squares non-uniform fast Fourier transform

Non-Cartesian acquisition strategies are widely used in MRI to dramatically reduce the acquisition time while at the same time preserving the image quality. Among non-Cartesian reconstruction methods, the least squares non-uniform fast Fourier transform (LS_NUFFT) is a gridding method based on a local data interpolation kernel that minimizes the worst-case approximation error. The interpolator is chosen using a pseudoinverse matrix. As the size of the interpolation kernel increases, the inversion problem may become ill-conditioned. Regularization methods can be adopted to solve this issue. In this study, we compared three regularization methods applied to LS_NUFFT. We used truncated singular value decomposition (TSVD), Tikhonov regularization and L₁-regularization. Reconstruction performance was evaluated using the direct summation method as reference on both simulated and experimental data. We also evaluated the processing time required to calculate the interpolator. First, we defined the value of the interpolator size after which regularization is needed. Above this value, TSVD obtained the best reconstruction. However, for large interpolator size, the processing time becomes an important constraint, so an appropriate compromise between processing time and reconstruction quality should be adopted.

Evaluation of partial k-space strategies to speed up time-domain EPR imaging

Narrow-line spin probes derived from the trityl radical have led to the development of fast in vivo time-domain EPR imaging. Pure phase-encoding imaging modalities based on the single-point imaging scheme have demonstrated the feasibility of three-dimensional oximetric images with functional information in minutes. In this article, we explore techniques to improve the temporal resolution and circumvent the relatively short biological half-lives of trityl probes using partial k-space strategies. There are two main approaches: one involves the use of the Hermitian character of the k-space by which only part of the k-space is measured and the unmeasured part is generated using the Hermitian symmetry. This approach is limited in success by the accuracy of numerical estimate of the phase roll in the k-space that corrupts the Hermiticy. The other approach is to measure only a judicially chosen reduced region of k-space (a centrosymmetric ellipsoid region) that more or less accounts for >70% of the k-space energy. Both of these aspects were explored in Fourier transform-EPR imaging with a doubling of scan speed demonstrated by considering ellipsoid geometry of the k-space. Partial k-space strategies help improve the temporal resolution in studying fast dynamics of functional aspects in vivo with infused spin probes.

Automatic off-resonance correction in spiral imaging with piecewise linear autofocus

Off-resonance generates blurring artifacts in spiral images. Applications that often utilize spiral trajectories, such as fine-resolution imaging and rapid scanning, typically preclude the measurement of accurate field maps needed for effective off-resonance correction. Automatic deblurring, or autofocus, algorithms have been developed to estimate the field map directly from the corrupted data prior to off-resonance correction, eliminating the need for field map measurements. These algorithms rely in whole or in part on optimizing an objective function, and suffer from problems related to the accurate minimization and utility of the function. Here, a new method is presented to correct off-resonance blurring automatically without an objective function using a piecewise linear framework. Local linear field maps are estimated with a combination of k-space spectral analysis and mapdrift, an image feature-based correlation technique, for subsequent piecewise linear deblurring. This approach enables field map estimation without optimization, provides accurate off-resonance correction, is suitable for low signal-to-noise ratio and fine-resolution applications, and does not require access to the raw data. Deblurred images from fine-resolution spiral scans of a phantom and healthy volunteers at 3T show that the proposed method can be superior to conventional autofocus and comparable to field map-based correction.

Performance analysis for magnetic resonance imaging with nonlinear encoding fields

Nonlinear spatial encoding fields for magnetic resonance imaging (MRI) hold great promise to improve on the linear gradient approaches by, for example, enabling reduced imaging times. Imaging schemes that employ general nonlinear encoding fields are difficult to analyze using traditional measures. In particular, the resolution is spatially varying, characterized by a position-dependent point spread function (PSF). Likewise, the use of nonlinear encoding fields creates an additional spatial dependence on the signal-to-noise ratio (SNR). Although the two properties of resolution and SNR are linked, in this work we focus on the latter. To this end, we examine the pixel variance, which requires a computation that is often not feasible for nonlinear encoding schemes. This paper presents a general formulation for the performance analysis of imaging schemes using arbitrary encoding fields. The analysis leads to the derivation of a practical and computationally efficient performance metric, which is demonstrated through simulation examples.

Reduced field of view MRI with rapid, B1-robust outer volume suppression

MRI scans are inefficient when the size of the anatomy under investigation is small relative to the subject's full extent. The field of view must be expanded, and acquisition times accordingly prolonged. Shorter scans are feasible with reduced field of view imaging (rFOV) using outer volume suppression (OVS), a magnetization preparation sequence that attenuates signal outside a region of interest (ROI). This work presents a new OVS sequence with a cylindrical ROI, short duration, and improved tolerance for B(1)+ inhomogeneity. The sequence consists of a nonselective adiabatic tipdown pulse, which provides B(1)+-robust signal suppression, and a fast 2D spiral cylindrical tipback pulse. Analysis of the Bloch equations with transverse initial magnetization reveals a conjugate symmetric constraint for tipback pulses with small flip angles. This property is exploited to achieve two-shot performance from the single-shot tipback pulse. The OVS sequence is validated in phantoms and in vivo with multislice spiral imaging at 3 T. The relative signal-to-noise ratio efficiency of the proposed sequence was 98% in a phantom and 75-90% in vivo. The effectiveness is demonstrated with cardiovascular rFOV imaging, which exhibits improved resolution and reduced artifacts compared to conventional, full field of view imaging.

Efficient sample density estimation by combining gridding and an optimized kernel

The reconstruction of non-Cartesian k-space trajectories often requires the estimation of nonuniform sampling density. Particularly for 3D, this calculation can be computationally expensive. The method proposed in this work combines an iterative algorithm previously proposed by Pipe and Menon (Magn Reson Med 1999;41:179-186) with the optimal kernel design previously proposed by Johnson and Pipe (Magn Reson Med 2009;61:439-447). The proposed method shows substantial time reductions in estimating the densities of center-out trajectories, when compared with that of Johnson. It is demonstrated that, depending on the trajectory, the proposed method can provide reductions in execution time by factors of 12 to 85. The method is also shown to be robust in areas of high trajectory overlap, when compared with two analytical density estimation methods, producing a 10-fold increase in accuracy in one case. Initial conditions allow the proposed method to converge in fewer iterations and are shown to be flexible in terms of the accuracy of information supplied. The proposed method is not only one of the fastest and most accurate algorithms, it is also completely generic, allowing any arbitrary trajectory to be density compensated extemporaneously. The proposed method is also simple and can be implemented on parallel computing platforms in a straightforward manner.

Spiral phyllotaxis: the natural way to construct a 3D radial trajectory in MRI

While radial 3D acquisition has been discussed in cardiac MRI for its excellent results with radial undersampling, the self-navigating properties of the trajectory need yet to be exploited. Hence, the radial trajectory has to be interleaved such that the first readout of every interleave starts at the top of the sphere, which represents the shell covering all readouts. If this is done sub-optimally, the image quality might be degraded by eddy current effects, and advanced density compensation is needed. In this work, an innovative 3D radial trajectory based on a natural spiral phyllotaxis pattern is introduced, which features optimized interleaving properties: (1) overall uniform readout distribution is preserved, which facilitates simple density compensation, and (2) if the number of interleaves is a Fibonacci number, the interleaves self-arrange such that eddy current effects are significantly reduced. These features were theoretically assessed in comparison with two variants of an interleaved Archimedean spiral pattern. Furthermore, the novel pattern was compared with one of the Archimedean spiral patterns, with identical density compensation, in phantom experiments. Navigator-gated whole-heart coronary imaging was performed in six healthy volunteers. High reduction of eddy current artifacts and overall improvement in image quality were achieved with the novel trajectory.

Spiral demystified

Spiral acquisition schemes offer unique advantages such as flow compensation, efficient k-space sampling and robustness against motion that make this option a viable choice among other non-Cartesian sampling schemes. For this reason, the main applications of spiral imaging lie in dynamic magnetic resonance imaging such as cardiac imaging and functional brain imaging. However, these advantages are counterbalanced by practical difficulties that render spiral imaging quite challenging. Firstly, the design of gradient waveforms and its hardware requires specific attention. Secondly, the reconstruction of such data is no longer straightforward because k-space samples are no longer aligned on a Cartesian grid. Thirdly, to take advantage of parallel imaging techniques, the common generalized autocalibrating partially parallel acquisitions (GRAPPA) or sensitivity encoding (SENSE) algorithms need to be extended. Finally, and most notably, spiral images are prone to particular artifacts such as blurring due to gradient deviations and off-resonance effects caused by B(0) inhomogeneity and concomitant gradient fields. In this article, various difficulties that spiral imaging brings along, and the solutions, which have been developed and proposed in literature, will be reviewed in detail.

High efficiency, low distortion 3D diffusion tensor imaging with variable density spiral fast spin echoes (3D DW VDS RARE)

We present an acquisition and reconstruction method designed to acquire high resolution 3D fast spin echo diffusion tensor images while mitigating the major sources of artifacts in DTI-field distortions, eddy currents and motion. The resulting images, being 3D, are of high SNR, and being fast spin echoes, exhibit greatly reduced field distortions. This sequence utilizes variable density spiral acquisition gradients, which allow for the implementation of a self-navigation scheme by which both eddy current and motion artifacts are removed. The result is that high resolution 3D DTI images are produced without the need for eddy current compensating gradients or B(0) field correction. In addition, a novel method for fast and accurate reconstruction of the non-Cartesian data is employed. Results are demonstrated in the brains of normal human volunteers.

Convolution kernel design and efficient algorithm for sampling density correction

Sampling density compensation is an important step in non-cartesian image reconstruction. One of the common techniques to determine weights that compensate for differences in sampling density involves a convolution. A new convolution kernel is designed for sampling density attempting to minimize the error in a fully reconstructed image. The resulting weights obtained using this new kernel are compared with various previous methods, showing a reduction in reconstruction error. A computationally efficient algorithm is also presented that facilitates the calculation of the convolution of finite kernels. Both the kernel and the algorithm are extended to 3D.

Iterative off-resonance and signal decay estimation and correction for multi-echo MRI

Signal dephasing due to field inhomogeneity and signal decay due to transverse relaxation lead to perturbations of the Fourier encoding commonly applied in magnetic resonance imaging. Hence, images acquired with long readouts suffer from artifacts such as blurring, distortion, and intensity variation. These artifacts can be removed in reconstruction, usually based on separately collected information in form of field and relaxation maps. In this work, a recently proposed gridding-based algorithm for off-resonance correction is extended to also address signal decay. It is integrated into a new fixed-point iteration, which permits the joint estimation of an image and field and relaxation maps from multi-echo acquisitions. This approach is then applied in simulations and in vivo experiments and demonstrated to improve both images and maps. The rapid convergence of the fixed-point iteration in combination with the efficient gridding-based correction promises to render the running time of such a joint estimation acceptable.

Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients

Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method.

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

Three-dimensional (3D) twisted projection imaging (TPI) trajectory has a unique advantage in sodium ((23)Na) imaging on clinical MRI scanners at 1.5 or 3 T, generating a high signal-to-noise ratio (SNR) with a short acquisition time (approximately 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 ((1)H) 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 x 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.

Acquisition-weighted stack of spirals for fast high-resolution three-dimensional ultra-short echo time MR imaging

Ultra-short echo time (UTE) MRI requires both short excitation ( approximately 0.5 ms) and short acquisition delay (<0.2 ms) to minimize T(2)-induced signal decay. These requirements currently lead to low acquisition efficiency when high resolution (<1 mm) is pursued. A novel pulse sequence, acquisition-weighted stack of spirals (AWSOS), is proposed here to acquire high-resolution three-dimensional (3D) UTE images with short scan time ( approximately 72 s). The AWSOS sequence uses variable-duration slice encoding to minimize T(2) decay, separates slice thickness from in-plane resolution to reduce the number of slice encodings, and uses spiral trajectories to accelerate in-plane data collections. T(2)- and off-resonance induced slice widening and image blurring were calculated from 1.5 to 7 Tesla (T) through point spread function. Computer simulations were performed to optimize spiral interleaves and readout times. Phantom scans and in vivo experiments on human heads were implemented on a clinical 1.5T scanner (G(max) = 40 mT/m, S(max) = 150 T/m/s). Accounting for the limits on B(1) maximum, specific absorption rate (SAR), and the lowered amplitude of slab-select gradient, a sinc radiofrequency (RF) pulse of 0.8ms duration and 1.5 cycles was found to produce a flat slab profile. High in-plane resolution (0.86 mm) images were obtained for the human head using echo time (TE) = 0.608 ms and total shots = 720 (30 slice-encodings x 24 spirals). Compared with long-TE (10 ms) images, the ultrashort-TE AWSOS images provided clear visualization of short-T(2) tissues such as the nose cartilage, the eye optic nerve, and the brain meninges and parenchyma.

Self-calibrating GRAPPA operator gridding for radial and spiral trajectories

Self-calibrating GRAPPA operator gridding (GROG) is a method by which non-Cartesian MRI data can be gridded using spatial information from a multichannel coil array without the need for an additional calibration dataset. Using self-calibrating GROG, the non-Cartesian datapoints are shifted to nearby k-space locations using parallel imaging weight sets determined from the datapoints themselves. GROG employs the GRAPPA Operator, a special formulation of the general reconstruction method GRAPPA, to perform these shifts. Although GROG can be used to grid undersampled datasets, it is important to note that this method uses parallel imaging only for gridding, and not to reconstruct artifact-free images from undersampled data. The innovation introduced here, namely, self-calibrating GROG, allows the shift operators to be calculated directly out of the non-Cartesian data themselves. This eliminates the need for an additional calibration dataset, which reduces the imaging time and also makes the GROG reconstruction more robust by removing possible inconsistencies between the calibration and non-Cartesian datasets. Simulated and in vivo examples of radial and spiral datasets gridded using self-calibrating GROG are compared to images gridded using the standard method of convolution gridding.

Multispectral imaging with three-dimensional rosette trajectories

Two-dimensional intersecting k-space trajectories have previously been demonstrated to allow fast multispectral imaging. Repeated sampling of k-space points leads to destructive interference of the signal coming from the off-resonance spectral peaks; on-resonance data reconstruction yields images of the on-resonance peak, with some of the off-resonance energy being spread as noise in the image. A shift of the k-space data by a given off-resonance frequency brings a second frequency of interest on resonance, allowing the reconstruction of a second spectral peak from the same k-space data. Given the higher signal-to-noise per unit time characteristic of a 3D acquisition, we extended the concept of intersecting trajectories to three dimensions. A 3D, rosette-like pulse sequence was designed and implemented on a clinical 1.5T scanner. An iterative density compensation function was developed to weight the 3D intersecting trajectories before Fourier transformation. Three volunteers were scanned using this sequence and separate fat and water images were reconstructed from the same imaging dataset.

Varying kernel-extent gridding reconstruction for undersampled variable-density spirals

Nonuniform, non-Cartesian k-space trajectories enable fast scanning with reduced motion and flow artifacts. In such cases, the data are usually convolved with a kernel and resampled onto a Cartesian grid before reconstruction. For trajectories such as undersampled variable-density spirals, the mainlobe width of the kernel for undersampled high spatial frequencies has to be larger to limit the amount of aliasing energy. Continuously varying the kernel extent is time consuming. By dividing k-space into several annuli and using appropriate mainlobe widths for each, the aliasing energy and noise can be reduced at the expense of lower resolution towards the edge of the field of view (FOV). Resolution can instead be preserved at the center of the FOV, which is expected to be free of artifacts, without any artifact reduction. The image reconstructed from each annulus can be deapodized separately. The method can be applied to most k-space trajectories used in MRI.

An efficient MR image reconstruction method for arbitrary K-space trajectories without density compensation

Non-Cartesian sampling is widely used for fast magnetic resonance imaging (MRI). The well known gridding method usually requires density compensation to adjust the non-uniform sampling density, which is a major source of reconstruction error. Minimum-norm least square (MNLS) reconstruction, on the other hand, does not need density compensation, but requires intensive computations. In this paper, a new version of MNLS reconstruction method is developed using maximum likelihood and is speeded up by incorporating novel non-uniform fast Fourier transform (NUFFT) and bi-conjugate gradient fast Fourier transform (BCG-FFT) techniques. Studies on computer-simulated phantoms and a physically scanned phantom show improved reconstruction accuracy and signal-to-noise ratio compared to gridding method. The method is shown applicable to arbitrary k-space trajectory. Furthermore, we find that the method in fact performs un-blurring in the image space as an equivalent of density compensation in the k-space. Equalizing MNLS solution with gridding algorithm leads to new approaches of finding optimal density compensation functions (DCF). The method has been applied to radially encoded cardiac imaging on small animals. Reconstructed dynamic images of an in vivo mouse heart are shown.

Field inhomogeneity correction based on gridding reconstruction for magnetic resonance imaging

Spatial variations of the main field give rise to artifacts in magnetic resonance images if disregarded in reconstruction. With non-Cartesian k-space sampling, they often lead to unacceptable blurring. Data from such acquisitions are usually reconstructed with gridding methods and optionally restored with various correction methods. Both types of methods essentially face the same basic problem of adequately approximating an exponential function to enable an efficient processing with fast Fourier transforms. Nevertheless, they have commonly addressed it differently so far. In the present work, a unified approach is pursued. The principle behind gridding methods is first generalized to nonequispaced sampling in both domains and then applied to field inhomogeneity correction. Three new algorithms, which are compatible with a direct conjugate phase and an iterative algebraic reconstruction, are derived in this way from a straightforward embedding of the data into a higher dimensional space. Their evaluation in simulations and phantom experiments with spiral k-space sampling shows that one of them promises to provide a favorable compromise between fidelity and complexity compared with existing algorithms. Moreover, it allows a simple choice of key parameters involved in approximating an exponential function and a balance between the accuracy of reconstruction and correction.

Flow SS-PARSE: a new method for rapid imaging and mapping of blood flow velocity

A new method for flow velocity mapping of blood is presented here. Instead of the conventional approach of employing two images (velocity sensitive and control) to generate velocity information, in the new method the velocity is determined directly by solving an inverse problem. This technique is an application of single shot - parameter assessment by retrieval from signal encoding (SS-PARSE). Simulations have been done to demonstrate the feasibility of the method. The velocity measurement range of the prototype version is from -50cm/s to 50cm/s, roughly appropriate for future applications in blood flow measurement of carotid arteries.

Deconvolution-interpolation gridding (DING): accurate reconstruction for arbitrary k-space trajectories

A simple iterative algorithm, termed deconvolution-interpolation gridding (DING), is presented to address the problem of reconstructing images from arbitrarily-sampled k-space. The new algorithm solves a sparse system of linear equations that is equivalent to a deconvolution of the k-space with a small window. The deconvolution operation results in increased reconstruction accuracy without grid subsampling, at some cost to computational load. By avoiding grid oversampling, the new solution saves memory, which is critical for 3D trajectories. The DING algorithm does not require the calculation of a sampling density compensation function, which is often problematic. DING's sparse linear system is inverted efficiently using the conjugate gradient (CG) method. The reconstruction of the gridding system matrix is simple and fast, and no regularization is needed. This feature renders DING suitable for situations where the k-space trajectory is changed often or is not known a priori, such as when patient motion occurs during the scan. DING was compared with conventional gridding and an iterative reconstruction method in computer simulations and in vivo spiral MRI experiments. The results demonstrate a stable performance and reduced root mean square (RMS) error for DING in different k-space trajectories.

Improving Non-Cartesian MRI Reconstruction through Discontinuity Subtraction

Non-Cartesian sampling is widely used for fast magnetic resonance imaging (MRI). Accurate and fast image reconstruction from non-Cartesian k-space data becomes a challenge and gains a lot of attention. Images provided by conventional direct reconstruction methods usually bear ringing, streaking, and other leakage artifacts caused by discontinuous structures. In this paper, we tackle these problems by analyzing the principal point spread function (PSF) of non-Cartesian reconstruction and propose a leakage reduction reconstruction scheme based on discontinuity subtraction. Data fidelity in k-space is enforced during each iteration. Multidimensional nonuniform fast Fourier transform (NUFFT) algorithms are utilized to simulate the k-space samples as well as to reconstruct images. The proposed method is compared to the direct reconstruction method on computer-simulated phantoms and physical scans. Non-Cartesian sampling trajectories including 2D spiral, 2D and 3D radial trajectories are studied. The proposed method is found useful on reducing artifacts due to high image discontinuities. It also improves the quality of images reconstructed from undersampled data.

Basis function cross-correlations for Robustk-space sample density compensation, with application to the design of radiofrequency excitations

The problem of k-space sample density compensation is restated as the normalization of the independent information that can be expressed by the ensemble of Fourier basis functions corresponding to the trajectory. Specifically, multiple samples (complex exponential functions) may be contributing to each independent information element (independent basis function). Normalization can be accomplished by solving a linear system based on the cross-correlation matrix of the underlying Fourier basis functions. The solution to this system is straightforward and can be obtained without resorting to discretization since the cross-correlations of Fourier basis functions are analytically known. Furthermore, no restrictions are placed on the k-space trajectory and its point-spread function. Additionally, the linear system can be used to elucidate key trade-offs involved in k-space trajectory design. The approach can be used to compensate samples acquired for image reconstruction or designed for low flip angle radiofrequency (RF) excitation. Here it is demonstrated for the latter application, using reversed spiral trajectories. In this case the linear system approach enables one to easily incorporate additional constraints such as smoothness to the solution. For typical RF excitation durations (<20 ms) it is shown that density compensation can even be achieved without numerical iteration.

Fast automatic linear off-resonance correction method for spiral imaging

Field inhomogeneity and susceptibility variations, coupled with a long readout, can result in image blurring in spiral imaging. Many correction methods based on a priori off-resonance information, such as an acquired field map, have been proposed in the literature. Automatic off-resonance correction methods are alternative approaches that estimate a field map from the image data themselves. In this paper we propose a fast automatic off-resonance correction method that performs linear correction without acquiring a field map. The method requires only about two times the total computation time compared to image reconstruction by gridding. It can also be used in combination with a full field map automatic off-resonance correction method to increase the extent of correction. The method is demonstrated by in vivo coronary artery imaging.