Compensation of multi-dimensional selective excitation pulses using measured k-space trajectories

Fast measurement of the gradient system transfer function at 7 T

PURPOSE

In this work, a new method to determine the gradient system transfer function (GSTF) with high frequency resolution and high SNR is presented, using fast and simple phantom measurements. The GSTF is an effective instrument for hardware characterization and calibration, which can be used to correct for gradient distortions, or enhance gradient fidelity.

METHODS

The thin-slice approach for phantom-based measurements of the GSTF is expanded by adding excitations that are shifted after the application of the probing gradient, to capture long-lasting field fluctuations with high SNR. A physics-informed regularization procedure is implemented to derive high-quality transfer functions from a small number of measurements. The resulting GSTFs are evaluated by means of gradient time-course estimation and pre-emphasis of a trapezoidal test gradient on a 7T scanner.

RESULTS

The GSTFs determined with the proposed method capture sharp mechanical resonances with a high level of detail. The measured trapezoidal gradient progressions are authentically reproduced by the GSTF estimations on all three axes. The GSTF-based pre-emphasis considerably improves the gradient fidelity in the plateau phase of the test gradient and almost completely eliminates lingering field oscillations.

CONCLUSION

The presented approach allows fast and simple characterization of gradient field fluctuations caused by long-living eddy current and vibration effects, which become more pronounced at ultrahigh field strengths.

Efficient gradient waveform measurements with variable-prephasing

Accurate measurement of gradient waveform errors can often improve image quality in sequences with time varying readout and excitation waveforms. Self-encoding or offset-slice sequences are commonly used to measure gradient waveforms. However, the self-encoding method requires a long scan time, while the offset-slice method is often low precision, requiring the thickness of the excited slice to be small compared to the maximal k-space encoded by the test waveform. This work introduces a hybrid these methods, called variable-prephasing. Using a straightforward algebraic model, we demonstrate that variable-prephasing improves the precision of the waveform measurement by allowing acquisition of larger slice thicknesses. Experiments in a phantom were used to validate the theoretical predictions, showing that the precision of variable-prephasing gradient waveform measurements improves with increasing slice thickness.

Trajectory correction based on the gradient impulse response function improves high-resolution UTE imaging of the musculoskeletal system

PURPOSE

UTE sequences typically acquire data during the ramping up of the gradient fields, which makes UTE imaging prone to eddy current and system delay effects. The purpose of this work was to use a simple gradient impulse response function (GIRF) measurement to estimate the real readout gradient waveform and to demonstrate that precise knowledge of the gradient waveform is important in the context of high-resolution UTE musculoskeletal imaging.

METHODS

The GIRF was measured using the standard hardware of a 3 Tesla scanner and applied on 3D radial UTE data (TE: 0.14 ms). Experiments were performed on a phantom, in vivo on a healthy knee, and in vivo on patients with spine fractures. UTE images were reconstructed twice, first using the GIRF-corrected gradient waveforms and second using nominal-corrected waveforms, correcting for the low-pass filter characteristic of the gradient chain.

RESULTS

Images reconstructed with the nominal-corrected gradient waveforms exhibited blurring and showed edge artifacts. The blurring and the edge artifacts were reduced when the GIRF-corrected gradient waveforms were used, as shown in single-UTE phantom scans and in vivo dual-UTE gradient-echo scans in the knee. Further, the importance of the GIRF-based correction was indicated in UTE images of the lumbar spine, where thin bone structures disappeared when the nominal correction was employed.

CONCLUSION

The presented GIRF-based trajectory correction method using standard scanner hardware can improve the quality of high-resolution UTE musculoskeletal imaging.

A multi spin echo pulse sequence with optimized excitation pulses and a 3D cone readout for hyperpolarized 13 C imaging

PURPOSE

Imaging tumor metabolism in vivo using hyperpolarized [1-13 C]pyruvate is a promising technique for detecting disease, monitoring disease progression, and assessing treatment response. However, the transient nature of the hyperpolarization and its depletion following excitation limits the available time for imaging. We describe here a single-shot multi spin echo sequence, which improves on previously reported sequences, with a shorter readout time, isotropic point spread function (PSF), and better signal-to-noise ratio.

METHODS

The sequence uses numerically optimized spectrally selective excitation pulses set to the resonant frequencies of pyruvate and lactate and a hyperbolic secant adiabatic refocusing pulse, all applied in the absence of slice selection gradients. The excitation pulses were designed to be resistant to the effects of B0 and B1 field inhomogeneity. The gradient readout uses a 3D cone trajectory composed of 13 cones, all fully refocused and distributed among 7 spin echoes. The maximal gradient amplitude and slew rate were set to 4 G/cm and 20 G/cm/ms, respectively, to demonstrate the feasibility of clinical translation.

RESULTS

The pulse sequence gave an isotropic PSF of 2.8 mm. The excitation profiles of the optimized pulses closely matched simulations and a 46.10 ± 0.04% gain in image SNR was observed compared to a conventional Shinnar-Le Roux excitation pulse. The sequence was demonstrated with dynamic imaging of hyperpolarized [1-13 C]pyruvate and [1-13 C]lactate in vivo.

CONCLUSION

The pulse sequence was capable of dynamic imaging of hyperpolarized 13 C labeled metabolites in vivo with relatively high spatial and temporal resolution and immunity to system imperfections.

Fast quantitative 3D ultrashort echo time MRI of cortical bone using extended cones sampling

PURPOSE

To investigate the effect of stretching sampling window on quantitative 3D ultrashort TE (UTE) imaging of cortical bone at 3 T.

METHODS

Ten bovine cortical bone and 17 human tibial midshaft samples were imaged with a 3T clinical MRI scanner using an 8-channel knee coil. Quantitative 3D UTE imaging biomarkers, including T₁ , T 2 ∗ , magnetization transfer ratio and magnetization transfer modeling, were performed using radial or spiral Cones sampling trajectories with various durations. Errors in UTE-MRI biomarkers as a function of sampling time were evaluated using radial sampling as a reference standard.

RESULTS

For both bovine and human cortical bone samples, no significant differences were observed for all UTE biomarkers (single-component T 2 ∗ , bicomponent T 2 ∗ and relative fractions, T₁ , magnetization transfer ratio, and magnetization transfer modeling of macromolecular fraction) for spiral sampling windows of 992 µs to 1600 µs compared with a radial sampling window of 688 µs.

CONCLUSION

The total scan time can be reduced by 76% with quantification errors less than 5%. Quantitative UTE-MRI techniques can be greatly accelerated using longer sampling windows without significant quantification errors.

Hyperpolarized 13 C spectroscopic imaging using single-shot 3D sequences with unpaired adiabatic refocusing pulses

Hyperpolarized MRI with 13 C-labeled metabolites has enabled metabolic imaging of tumors in vivo. The heterogeneous nature of tumors and the limited lifetime of the hyperpolarization require high resolution, both temporally and spatially. We describe two sequences that make more efficient use of the 13 C polarization than previously described single-shot 3D sequences. With these sequences, the target metabolite resonances were excited using spectral-spatial pulses and the data acquired using spiral readouts from a series of echoes created using a fast-spin-echo sequence employing adiabatic 180° pulses. The third dimension was encoded with blipped gradients applied in an interleaved order to the echo train. Adiabatic inversion pulses applied in the absence of slice selection gradients allowed acquisition of signal from odd echoes, formed by unpaired adiabatic pulses, as well as from even echoes. The sequences were tested on tumor-bearing mice following intravenous injection of hyperpolarized [1-13 C]pyruvate. [1-13 C] pyruvate and [1-13 C] lactate images were acquired in vivo with a 4 × 4 × 2 cm3 field of view and a 32 × 32 × 16 matrix, leading to a nominal resolution of 1.25 × 1.25 × 1.25 mm3 and an effective resolution of 1.25 × 1.25 × 4.5 mm3 when the z-direction point spread function was taken into account. The acquisition of signal from more echoes also allowed for an improvement in the signal-to-noise ratio for resonances with longer T2 relaxation times. The pulse sequences described here produced hyperpolarized 13 C images with improved resolution and signal-to-noise ratio when compared with similar sequences described previously.

Imperfect magnetic field gradients in radial k-space encoding-Quantification, correction, and parameter dependency

PURPOSE

Sensitivity to imperfections of image-encoding gradient fields may significantly impair widespread use of radial MR data acquisition. Such imperfections can cause individual echo shifts for each spoke acquired in the k-space and may produce severe image artifacts. Therefore, fast and robust methods to quantify and correct for those echo shifts are required.

THEORY AND METHODS

Echo shifts can be induced by inhomogeneities of the static magnetic field (δn_B ) and by imbalances of the imaging gradients (δn_G ) mainly caused by eddy currents. However, mismatch between data acquisition and gradient switching may additionally play a role. From the position of the echo maxima of 2 opposing spokes, δn_G and δn_B can be determined and corrected by adapting the read-dephasing gradient accordantly. This approach was implemented on MR-systems of different field strengths, gradient systems, and vendors, and the dependencies of echo shift and acquisition parameters were analyzed. Data sets of phantoms and of mice under in vivo conditions were obtained using RF-spoiled 2D radial-FLASH.

RESULTS

The presented method allowed for echo-shift detection and correction of < 1 data point, significantly improving the image quality in vitro and in vivo. Moreover, the method separated the effect of imbalanced gradients from those of magnetic inhomogeneities. The observed echo shifts were MR system-specifically dependent on acquisition parameters such as gradient strengths and dwell time.

CONCLUSIONS

By acquiring 12 spokes for a certain set of acquisition parameters, the proposed method successfully corrects echo shift-related image artifacts independently of the MR system.

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

PURPOSE

To evaluate the impact of MR gradient system imperfections and limitations for the quantitative mapping of short T2* signals performed by ultrashort echo time (UTE) acquisition approach.

MATERIALS AND METHODS

The measurement of short T2* signals from a phantom and a healthy volunteer study (8 subjects of average age 28 ± 4 years) were performed on a 3T scanner. The characteristics of the gradient system were obtained using calibration method performed directly on the measured subject or phantom. This information was used to calculate the actual sampling trajectory with the help of a parametric eddy current model. The actual sample positions were used to reconstruct corrected images and compared with uncorrected data.

RESULTS

Comparison of both approaches, i.e., without and with correction of k-space sampling trajectories revealed substantial improvement when correction was applied. The phantom experiments demonstrate substantial in-plane signal intensity variations for uncorrected sampling trajectories. In the case of the volunteer study, this led to significant differences in relative proton density (RPD) estimation between the uncorrected and corrected data (P = 0.0117 by Wilcoxon matched-pairs test) and provides for about ~15% higher values for short T2* components of white matter (WM) in the case of uncorrected images.

CONCLUSION

The imperfection of the applied gradients could induce errors in k-space data sampling which further propagates into the fidelity of the UTE images and jeopardizes precision of quantification. However, the study proved that measurement of gradient errors together with correction of sample positions can contribute to increased accuracy and unbiased characterization of short T2* signals.

Estimating and eliminating the excitation errors in bipolar gradient composite excitations caused by radiofrequency-gradient delay: Example of bipolar spokes pulses in parallel transmission

Purpose

To eliminate a slice‐position–dependent excitation error commonly observed in bipolar‐gradient composite excitations such as spokes pulses in parallel transmission.

Theory and Methods

An undesired timing delay between subpulses in the composite pulse and their bipolar slice‐selective gradient is hypothesized to cause the error. A mathematical model is presented here to relate this mismatch to an induced slice‐position–dependent phase difference between the subpulses. A new navigator method is proposed to measure the timing mismatch and eliminate the error. This is demonstrated at 7 Tesla with flip‐angle maps measured by a presaturation turbo‐flash sequence and in vivo images acquired by a simultaneous multislice/echo‐planar imaging (SMS‐EPI) sequence.

Results

Error‐free flip‐angle maps were obtained in two ways: 1) by correcting the time delay directly and 2) by applying the corresponding slice‐position–dependent phase differences to the subpulses. This confirms the validity of the mathematical description. The radiofrequency (RF)‐gradient delay measured by the navigator method was of 6.3 μs, which agreed well with the estimate from flip‐angle maps at different delay times. By applying the timing correction, accurately excited EPI images were acquired with bipolar dual‐spokes SMS‐2 excitations.

Conclusion

An effective correction is proposed to mitigate slice‐position–dependent errors in bipolar composite excitations caused by undesired RF‐gradient timing delays. Magn Reson Med 78:1883–1890, 2017. © 2016 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‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made.

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.

A new sequence for shaped voxel spectroscopy in the human brain using 2D spatially selective excitation and parallel transmission

Spatially selective excitation in two dimensions (2D-SSE) utilizing parallel transmission was applied as a means to acquire signal from voxels adapted to the anatomy of interest for in vivo (1) H MR spectroscopy. A novel method to select spectroscopy voxels with arbitrary shapes in two dimensions was investigated. An on-off scheme with an adiabatic slice selective inversion pulse preceding a 2D-SSE pulse together with a segmented inward spiral excitation k-space trajectory enabled rapid free induction decay acquisitions. Performance of the sequence was evaluated in simulations, phantom experiments, and in vivo measurements at 3 T. High spatial fidelity of the excitation profile was achieved for different target shapes and with little off-resonance deterioration. Metabolite concentrations in human brain determined with the new sequence were quantified with Cramér-Rao lower bounds less than 20%. They were in the physiological range and did not deviate systematically from results acquired with a conventional SPECIAL sequence. In conclusion, a new approach for shaped voxel MRS in the human brain is presented, which complements existing sequences. Simulations show that 2D-SSE pulses yield reduced chemical shift artifact when compared with conventional localization methods. Copyright © 2016 John Wiley & Sons, Ltd.

A dual K-space UNFOLD method for 3D functional brain imaging: A preliminary study

PURPOSE

To investigate a method of dual k-space unaliasing by Fourier-encoding the overlaps using the temporal dimension (DUNFOLD), a novel technique for high temporal resolution 3D functional brain imaging.

METHODS

Two different methods of unaliasing by Fourier-encoding the overlaps using the temporal dimension (UNFOLD), excitation UNFOLD (XUNFOLD) and acquisition UNFOLD, were merged to obtain a DUNFOLD. The feasibility of the DUNFOLD technique was examined by using a phantom and comparing its result to that of the previous XUNFOLD method. A high temporal resolution 3D functional brain imaging study was also performed, focusing on the microvascular response. Three different temporal resolutions, 20s, 10s and 5s, were tested with a spatial resolution of 0.6(3) mm3 to evaluate the method. The vascular regions of interest were selected for data analysis.

RESULTS

The DUNFOLD method achieved a temporal resolution approximately four times greater than those of the UNFOLD and XUNFOLD methods, without apparent signal degradation. The vascular responses in the visual cortex were obtained with high spatiotemporal resolution by using the DUNFOLD method during visual stimulation. For small vessels, the percentage change in the signal reached 18%.

CONCLUSION

The proposed DUNFOLD method yields a temporal resolution higher than those of the previous UNFOLD and XUNFOLD methods. The conclusions are likely to be important for functional imaging studies, especially those targeting cerebral vascular responsiveness.

Accurate Measurement of Magnetic Resonance Imaging Gradient Characteristics

Recently, gradient performance and fidelity has become of increasing interest, as the fidelity of the magnetic resonance (MR) image is somewhat dependent on the fidelity of the gradient system. In particular, for high fidelity non-Cartesian imaging, due to non-fidelity of the gradient system, it becomes necessary to know the actual k-space trajectory as opposed to the requested trajectory. In this work we show that, by considering the gradient system as a linear time-invariant system, the gradient impulse response function (GIRF) can be reliably measured to a relatively high degree of accuracy with a simple setup, using a small phantom and a series of simple experiments. It is shown experimentally that the resulting GIRF is able to predict actual gradient performance with a high degree of accuracy. The method captures not only the frequency response but also gradient timing errors and artifacts due to mechanical vibrations of the gradient system. Some discussion is provided comparing the method presented here with other analogous methods, along with limitations of these methods.

Parallel transmission RF pulse design for eddy current correction at ultra high field

Multidimensional spatially selective RF pulses have been used in MRI applications such as B₁ and B₀ inhomogeneities mitigation. However, the long pulse duration has limited their practical applications. Recently, theoretical and experimental studies have shown that parallel transmission can effectively shorten pulse duration without sacrificing the quality of the excitation pattern. Nonetheless, parallel transmission with accelerated pulses can be severely impeded by hardware and/or system imperfections. One of such imperfections is the effect of the eddy current field. In this paper, we first show the effects of the eddy current field on the excitation pattern and then report an RF pulse the design method to correct eddy current fields caused by the RF coil and the gradient system. Experimental results on a 7 T human eight-channel parallel transmit system show substantial improvements on excitation patterns with the use of eddy current correction. Moreover, the proposed model-based correction method not only demonstrates comparable excitation patterns as the trajectory measurement method, but also significantly improves time efficiency.

Advanced three-dimensional tailored RF pulse design in volume selective parallel excitation

Volume selective excitation has a variety of uses in clinical magnetic resonance imaging, but can suffer from insufficient excitation accuracy and impractically long pulse duration in ultra-high field applications. Based on recently-developed parallel transmission techniques, an optimized 3D tailored radio-frequency RF (TRF) pulse, designed with a novel 3D adaptive trajectory, is proposed to improve and accelerate volume selective excitation. The trajectory is designed to be regular-shaped and adaptively stretched according to the size of a 3D k-space "trajectory container." The container is designed to hold most of the RF energy deposition responsible for the desired pattern in the excitation k-space in the use of the blurring patterns caused by the multichannel sensitivity maps. The proposed method can also be used to reduce both global and peak RF energy required during excitation. The feasibility of this method is confirmed by simulations of ultra-high field cases.

Rapid measurement and correction of phase errors from B0 eddy currents: impact on image quality for non-Cartesian imaging

Non-Cartesian imaging sequences and navigational methods can be more sensitive to scanner imperfections that have little impact on conventional clinical sequences, an issue which has repeatedly complicated the commercialization of these techniques by frustrating transitions to multicenter evaluations. One such imperfection is phase errors caused by resonant frequency shifts from eddy currents induced in the cryostat by time-varying gradients, a phenomenon known as B(0) eddy currents. These phase errors can have a substantial impact on sequences that use ramp sampling, bipolar gradients, and readouts at varying azimuthal angles. We present a method for measuring and correcting phase errors from B(0) eddy currents and examine the results on two different scanner models. This technique yields significant improvements in image quality for high-resolution joint imaging on certain scanners. This result suggests that correcting short-time B(0) eddy currents that do not affect conventional clinical sequences may simplify the adoption of non-Cartesian methods.

Simple method for MR gradient system characterization and k-space trajectory estimation

Fast imaging trajectories are used in MRI to speed up the acquisition process, but imperfections in the gradient system create artifacts in the reconstructed images. Artifacts result from the deviation between k-space trajectories achieved on the scanner and their original prescription. Measuring or approximating actual k-space trajectories with predetermined gradient timing delays reduces the artifacts, but are generally based on a specific trajectory and scan orientation. A single linear time-invariant characterization of the gradient system provides a method to predict k-space trajectories scanned in arbitrary orientations through convolution. This is done efficiently, by comparing the Fourier transforms of the input and measured waveforms of a single high-bandwidth test gradient waveform. This new method is tested for spiral, interleaved echo-planar, and three-dimensional cones imaging, demonstrating its ability to reduce reconstructed image artifacts for various k-space trajectories.

Robust spatially selective excitation using radiofrequency pulses adapted to the effective spatially encoding magnetic fields

Multidimensional spatially selective excitation (SSE) has stimulated a variety of useful applications in magnetic resonance imaging and magnetic resonance spectroscopy, which have regained considerable interest after the recent introduction of parallel excitation. For SSE, radiofrequency pulses are designed specifically for certain time-courses of spatially encoding magnetic fields (SEM) which are applied simultaneously with the radiofrequency pulses. However, experimental imperfections of gradient-systems and undesired SEM field contributions often prevent the correct co-action of radiofrequency pulses and gradient-waveforms and therefore degrade the fidelity of excitation patterns, especially for parallel excitation. To cope with such imperfections, a classical measurement of k-space-trajectories can be performed followed by an adaptation of the SSE-pulses. However, this method is limited to linear SEM field distributions, which are describable in the k-space-formalism. Hence, this work presents a more sophisticated method consisting in a spatially resolved measurement of the temporal phase evolution of the transverse magnetization. This exhaustive phase information can be incorporated into pulse-design algorithms to compensate even for undesired spatially nonlinear, dynamic SEM field contributions. Both approaches are assessed in various experimental scenarios and individual benefits and limitations are discussed. The adaptation of SSE-pulses to experimentally achieved calibration data turned out to be very beneficial, and especially the novel spatially resolved method exhibited high potential for robust SSE even in adverse experimental setups.

Fast, simple gradient delay estimation for spiral MRI

Timing delays between data acquisition and gradient transmission result in image degradation. This is especially true in spiral MRI, where delays can alter data in a nonuniform manner, generating significant artifact in the reconstructed data. The many methods that exist to mitigate these delays or measure the k-space coordinates require long measurement times, complicated analysis, specialized phantoms or hardware, or significant changes to the sequence of interest. A fast and simple method is proposed to measure delays on each gradient channel. It requires only minimal modification to an existing spiral sequence and can be used to measure independent delays on three gradient channels and any scan subject within six sequence repetition times. The effectiveness and accuracy of this method are analyzed.

Non-Cartesian sampled centric scan SPRITE imaging with magnetic field gradient and B0(t) field measurements for MRI in the vicinity of metal structures

This paper proposes the possibility of spatially resolved MRI measurements undertaken inside metallic cells. MRI has been rarely usable inside conducting vessels due to the eddy currents in the walls caused by switching magnetic field gradients, which render most advanced MRI pulse sequences impossible. We propose magnetic field gradient waveform monitoring (MFGM) for MRI of samples inside metallic cells. In this work the MFGM method was extended to measure the B(0) field temporal evolution associated with gradient waveforms. MFGM was used to observe and correct eddy current effects associated with a metallic cell. High quality centric scan SPRITE images result from such corrections. MRI of samples held under pressure, most notably rock core samples, traditionally employs cells that are non-magnetic and fabricated from polymeric materials. The natural material for high-pressure MRI is however non-ferromagnetic metal given their high tensile strengths and high thermal conductivity. MRI measurement of macroscopic samples at high pressure would be generally possible if metallic pressure vessels could be employed. This study will form the basis of new MRI compatible metallic pressure vessels, which will permit MRI of macroscopic systems at high pressure.

Characterizing and correcting gradient errors in non-cartesian imaging: Are gradient errors linear time-invariant (LTI)?

Non-Cartesian and rapid imaging sequences are more sensitive to scanner imperfections such as gradient delays and eddy currents. These imperfections vary between scanners and over time and can be a significant impediment to successful implementation and eventual adoption of non-Cartesian techniques by scanner manufacturers. Differences between the k-space trajectory desired and the trajectory actually acquired lead to misregistration and reduction in image quality. While early calibration methods required considerable scan time, more recent methods can work more quickly by making certain approximations. We examine a rapid gradient calibration procedure applied to multiecho three-dimensional projection reconstruction (3DPR) acquisitions in which the calibration runs as part of every scan. After measuring the trajectories traversed for excitations on each of the orthogonal gradient axes, trajectories for the oblique projections actually acquired during the scan are synthesized as linear combinations of these measurements. The ability to do rapid calibration depends on the assumption that gradient errors are linear and time-invariant (LTI). This work examines the validity of these assumptions and shows that the assumption of linearity is reasonable, but that gradient errors can vary over short time periods (due to changes in gradient coil temperature) and thus it is important to use calibration data matched to the scan data.

Parallel excitation in the human brain at 9.4 T counteracting k-space errors with RF pulse design

Multidimensional spatially selective radiofrequency (RF) pulses have been proposed as a method to mitigate transmit B1 inhomogeneity in MR experiments. These RF pulses, however, have been considered impractical for many years because they typically require very long RF pulse durations. The recent development of parallel excitation techniques makes it possible to design multidimensional RF pulses that are short enough for use in actual experiments. However, hardware and experimental imperfections can still severely alter the excitation patterns obtained with these accelerated pulses. In this note, we report at 9.4 T on a human eight-channel transmit system, substantial improvements in two-dimensional excitation pattern accuracy obtained when measuring k-space trajectories prior to parallel transmit RF pulse design (acceleration x4). Excitation patterns based on numerical simulations closely reproducing the experimental conditions were in good agreement with the experimental results.

Pure phase encode magnetic field gradient monitor

Numerous methods have been developed to measure MRI gradient waveforms and k-space trajectories. The most promising new strategy appears to be magnetic field monitoring with RF microprobes. Multiple RF microprobes may record the magnetic field evolution associated with a wide variety of imaging pulse sequences. The method involves exciting one or more test samples and measuring the time evolution of magnetization through the FIDs. Two critical problems remain. The gradient waveform duration is limited by the sample T(2)*, while the k-space maxima are limited by gradient dephasing. The method presented is based on pure phase encode FIDs and solves the above two problems in addition to permitting high strength gradient measurement. A small doped water phantom (1-3 mm droplet, T(1), T(2), T(2)* < 100 micros) within a microprobe is excited by a series of closely spaced broadband RF pulses each followed by FID single point acquisition. Two trial gradient waveforms have been chosen to illustrate the technique, neither of which could be measured by the conventional RF microprobe measurement. The first is an extended duration gradient waveform while the other illustrates the new method's ability to measure gradient waveforms with large net area and/or high amplitude. The new method is a point monitor with simple implementation and low cost hardware requirements.

Estimation of k-space trajectories in spiral MRI

For non-Cartesian data acquisition in MRI, k-space trajectory infidelity due to eddy current effects and other hardware imperfections will blur and distort the reconstructed images. Even with the shielded gradients and eddy current compensation techniques of current scanners, the deviation between the actual k-space trajectory and the requested trajectory remains a major reason for image artifacts in non-Cartesian MRI. It is often not practical to measure the k-space trajectory for each imaging slice. It has been reported that better image quality is achieved in radial scanning by correcting anisotropic delays on different physical gradient axes. In this article the delay model is applied in spiral k-space trajectory estimation to reduce image artifacts. Then a novel estimation method combining the anisotropic delay model and a simple convolution eddy current model further reduces the artifact level in spiral image reconstruction. The root mean square error and peak error in both phantom and in vivo images reconstructed using the estimated trajectories are reduced substantially compared to the results achieved by only tuning delays. After a one-time calibration, it is thus possible to get an accurate estimate of the spiral trajectory and a high-quality image reconstruction for an arbitrary scan plane.

Self-gated Fourier velocity encoding

Self-gating is investigated to improve the velocity resolution of real-time Fourier velocity encoding measurements in the absence of a reliable electrocardiogram waveform (e.g., fetal magnetic resonance or severe arrhythmia). Real-time flow data are acquired using interleaved k-space trajectories which share a common path near the origin of k-space. These common data provide a rapid self-gating signal that can be used to combine the interleaved data. The combined interleaves cover a greater area of k-space than a single real-time acquisition, thereby providing higher velocity resolution for a given aliasing velocity and temporal resolution. For example, this approach provided velocity spectra with a temporal resolution of 19 ms and velocity resolution of 22 cm/s over an 818 cm/s field-of-view. The method was validated experimentally using a computer-controlled pulsatile flow apparatus and applied in vivo to measure aortic-valve flow in a healthy volunteer.

Spatiotemporal magnetic field monitoring for MR

MR experiments frequently rely on signal encoding by the application of magnetic fields that vary in both space and time. The accurate interpretation of the resulting signals often requires knowledge of the exact spatiotemporal field evolution during the experiment. To better fulfill this need, a new approach is presented that enables measuring the field evolution concurrently with any MR sequence. Miniature NMR probes are used to monitor the MR phase evolution around the object under investigation. Based on these data, a global phase model is calculated that can then be used as a basis for processing the actual image or spectroscopic data. The new method is demonstrated by MRI of a phantom, using spin-warp, spiral, and EPI trajectories. Throughout, the monitoring results enabled highly accurate image reconstruction, even in the presence of massive gradient imperfections.

Simple phase method for measurement of magnetic field gradient waveforms

Magnetic field gradients play a fundamental role in MR imaging and localized spectroscopy. The MRI experiment, in particular fast MRI, relies on precise gradient switching, which has become more demanding with the constantly growing number of fast imaging techniques. Here we present a simple MR method to measure the behavior of a magnetic field gradient waveform in an MR scanner. The method employs excitation of a thin slice, followed by application of the studied gradient and simultaneous FID acquisition. Measurements of different gradient waveforms were performed with a spherical phantom filled with doped water and positioned at the isocenter of the gradient set. The presented experiments demonstrate the capability of the technique to measure different gradient waveforms with an estimated error of less than 200 microT/m.

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.

Reducing gradient imperfections for spiral magnetic resonance spectroscopic imaging

Spiral k-space magnetic resonance spectroscopic imaging (MRSI) requires high performance from gradient hardware systems. During the readout phase, oscillating gradients are continuously played out, which can cause undesired effects. These effects on the quality of SI data are non-intuitive because of their time-varying nature. In this work we describe the effects of undesirable gradient performance on SI. Measurements of the true readout trajectories were performed and the results were then used in the reconstruction process. The effects of these imperfections resulted in a spatially and spectrally varying amplitude and frequency modulation. The use of the measured trajectories in the reconstruction process yielded an up to 20% increase in signal amplitude recovery.

Spatial localization in nuclear magnetic resonance spectroscopy

The ability to select a discrete region within the body for signal acquisition is a fundamental requirement of in vivo NMR spectroscopy. Ideally, it should be possible to tailor the selected volume to coincide exactly with the lesion or tissue of interest, without loss of signal from within this volume or contamination with extraneous signals. Many techniques have been developed over the past 25 years employing a combination of RF coil properties, static magnetic field gradients and pulse sequence design in an attempt to meet these goals. This review presents a comprehensive survey of these techniques, their various advantages and disadvantages, and implications for clinical applications. Particular emphasis is placed on the reliability of the techniques in terms of signal loss, contamination and the effect of nuclear relaxation and J-coupling. The survey includes techniques based on RF coil and pulse design alone, those using static magnetic field gradients, and magnetic resonance spectroscopic imaging. Although there is an emphasis on techniques currently in widespread use (PRESS, STEAM, ISIS and MRSI), the review also includes earlier techniques, in order to provide historical context, and techniques that are promising for future use in clinical and biomedical applications.

Dual-echo spiral in/in acquisition method for reducing magnetic susceptibility artifacts in blood-oxygen-level-dependent functional magnetic resonance imaging

MRI signal dropout in gradient recalled echo acquisitions limits the capability of blood-oxygen-level-dependent functional magnetic resonance imaging (fMRI) to study activation tasks that involve the orbitofrontal, temporal, and basal areas of the brain where significant macroscopic magnetic susceptibility differences exist. Among the various approaches aimed to address this issue, the acquisition method based on spiral in/out trajectories is one of the most time-efficient and effective techniques. In this study, we extended further the spiral in/out approach into 3D acquisition and compared the effectiveness of the different spiral in/out trajectory combinations in reducing signal dropout. The activation results from whole brain fMRI studies using complex finger tapping and breath-holding tasks demonstrate that the acquisition method based on dual-echo spiral in/in (DSPIN) trajectories is the most favorable. The DSPIN acquisition method has the following advantages: (1) It reduces most effectively signal dropout in the brain where magnetic susceptibility inhomogeneity is problematic and significantly improves the sensitivity to detect functional activations in those regions. (2) It significantly improves SNR in the whole brain by dual echo averaging without compromising functional contrast. (3) There is no reduction in time-efficiency and spatial resolution.

Strategies for inner volume 3D fast spin echo magnetic resonance imaging using nonselective refocusing radio frequency pulses

Fast spin echo (FSE) trains elicited by nonselective "hard" refocusing radio frequency (RF) pulses have been proposed as a means to enable application of FSE methods for high-resolution 3D magnetic resonance imaging (MRI). Hard-pulse FSE (HPFSE) trains offer short (3-4 ms) echo spacings, but are unfortunately limited to imaging the entire sample within the coil sensitivity thus requiring lengthy imaging times, consequently limiting clinical application. In this work we formulate and analyze two general-purpose combinations of 3D HPFSE with inner volume (IV) MR imaging to circumvent this limitation. The first method employs a 2D selective RF excitation followed by the HPFSE train and focuses on required properties of the spatial excitation profile with respect to limiting RF pulse duration in the 5-6 ms range. The second method employs two orthogonally selective 1D RF excitations (a 90x degrees - 180y degrees pair) to generate an echo from magnetization within the volume defined by their intersection. Subsequent echoes are formed via the HPFSE train, placing the focus of the method on (a) avoiding spurious echoes that may arise from transverse magnetization located outside the slab intersection when it is unavoidably affected by the nonselective refocusing pulses and (b) avoiding signal losses due to the necessarily different spacing (in time) of the RF pulse applications. The performance of each method is experimentally measured using Carr-Purcell-Meiboom-Gill (CPMG) multi-echo imaging, enabling examination of the magnetization evolution throughout the echo train. The methods as implemented achieve 95% to 97% outer volume signal suppression, and higher suppression appears to be well within reach, by further refinement of the selective RF excitations. Example images of the human brain and spine are presented with each technique. We conclude that the SNR efficiency of volume imaging in conjunction with the short echo spacing afforded by hard pulse trains enables high-resolution 3D HPFSE MRI of a small field-of-view (FOV) with minimal aliasing artifact.

Using the axis of rotation of polar navigator echoes to rapidly measure 3D rigid-body motion

An improved technique to prospectively correct three-dimensional rigid-body motion using polar spherical navigator (pNAV) echoes is presented. The technique is based on acquiring pNAVs of an object in a baseline and rotated position and determining the axis of rotation (AOR) between data sets, thereby reducing 3D rotations to a 2D, planar rotation. Finding the AOR is simplified by prerotating the baseline trajectory, which forces the axis to lie within a specific polar region of a spherical shell in k-space. Orbital navigator echoes are interpolated from the pNAV data in planes orthogonal to the AOR and cross-correlated to determine the 2D rotation. The rotation about the AOR is used in conjunction with its orientation to calculate the overall 3D rotation. The pNAV-AOR technique was tested for its precision, accuracy, and processing speed in detecting compound rotations and translations of varying magnitude. In comparison to the spherical navigator echo technique, the pNAV-AOR technique is noniterative, fast, and independent of rotation magnitude and direction. At low SNR, the technique can detect compound rotations to 0.5 degrees accuracy in an estimated 100 msec, indicating that prospective 3D rigid-body motion correction may be feasible with this technique.

Calibration of gradient propagation delays for accurate two-dimensional radiofrequency pulses

Hardware-related delays between the requested and actual start times of the gradient waveforms on each physical axis are of particular importance for multidimensional selective excitation in which the synchronization of gradient and radiofrequency (RF) waveforms is critical. A method is proposed for the accurate calibration of gradient propagation delays to optimize the spatial accuracy of 2D RF pulses, although the results may also be used to reduce artifacts in other MR techniques. The sensitivity of 2D RF pulses to uncorrected time shifts between the gradient and RF waveforms was exploited to calibrate accurately the propagation delays on each physical gradient axis. This was achieved using a technique that relates the effect of gradient delays in the component waveforms of a constant-angular rate spiral k-space trajectory 2D RF pulse to the spatial location of the subsequent excitation profile. Comparison was also made with a procedure based on a previously described k-space plotting method, showing broad agreement, but with some discrepancies that illustrate the value of a self-referenced correction method for multidimensional RF pulses.

Calibration of echo-planar 2D-selective RF excitation pulses

Echo-planar radiofrequency (RF) pulses (EPP) are increasingly being used for 2D-selective excitation in MRI. Pulse schemes of this kind are susceptible to eddy-current effects, timing imperfections, and anisotropy of the gradient system. As a consequence, practical EPP implementations have been restricted to robust fly-back strategies that use only every other leg of the echo-planar trajectory for RF transmission. The present work is dedicated to enabling forward-backward EPP with RF transmission during each k-space segment, hence doubling the pulses' time efficiency. This is accomplished by comprehensive pulse calibration based on preparatory measurements of the system imperfections, including potential gradient anisotropy. The effectiveness of the method is demonstrated in vitro and in vivo. By doubling the speed of k-space coverage, the proposed method enhances the potential of EPP for numerous applications. For example, motion-sensitive techniques benefit from shorter feasible echo times (TEs) and improved excitation profiles resulting from reduced in-pulse motion. In sequences with fast repetition, shorter EPP help reduce the overall scan duration. Alternatively, the higher time efficiency of forward-backward EPP can enhance their spatial selectivity.

Real-time Fourier velocity encoding: An in vivo evaluation

PURPOSE

To compare in vivo real-time Fourier velocity encoding (FVE), spectral-Doppler ultrasound, and phase-contrast (PC) magnetic-resonance (MR) imaging.

MATERIALS AND METHODS

In vivo velocity spectra were measured in the suprarenal and infrarenal aorta and the hepatic segment of the inferior vena cava of eight normal volunteers using FVE, and compared to similar measurements using Doppler ultrasound and gated PC MR imaging. In vivo waveforms were compared qualitatively according to flow pattern appearance (number, shape, and position of velocity peaks) and quantitatively according to peak velocity.

RESULTS

Good agreement was obtained between peak velocities measured in vitro using FVE and PC MR imaging (R(2) = 0.99, P = 2.10(-6), slope = 0.97 +/- 0.05). Qualitatively, the FVE and ultrasound measurements agreed closely in the majority of in vivo cases (excellent or good in 21/24 cases) while the PC MR method resolved fewer velocity peaks due to the inherent temporal averaging of cardiac-gated studies (excellent or good agreement with FVE in 13/24 cases). Quantitatively, the FVE measurement of peak velocity correlated strongly with both ultrasound (R(2) = 0.71, P = 2.10(-7), slope = 0.81 +/- 0.08) and PC MR (R(2) = 0.85, P = 2.10(-10), slope = 1.04 +/- 0.08).

CONCLUSION

Real-time MR assessment of blood-flow velocity correlated well with spectral Doppler ultrasound. Such new methods may allow hemodynamic information to be acquired in vessels inaccessible to ultrasound or in patients for whom respiratory compensation is not possible.

Optimizing spherical navigator echoes for three-dimensional rigid-body motion detection

Spherical navigator (SNAV) echoes show promise in correcting for three-dimensional rigid-body motion. In this paper, several important parameters in the design and performance of the SNAV technique are discussed, including a novel sampling strategy, the optimal k-space radius and sampling density of the navigator, and the execution of the SNAV trajectory by the scanner hardware. A variable-sampling density (VSD) helical-spiral SNAV trajectory, which can acquire data on the entire spherical shell without exceeding the maximum slew rate of the scanner, is presented. To ensure that the VSD SNAV trajectory was properly executed by the scanner hardware, the gradient waveforms were verified using a self-encoding technique. The ability of the VSD SNAV to measure rotational and translational motion was studied with in vitro experiments at various k-space radii and sampling densities. The results of this study show that the best accuracy was attained at k-space radii of 1.4 and 1.6 cm(-1), with 2400 to 4000 samples acquired over the sphere.

Single point measurements of magnetic field gradient waveform

Pulsed magnetic field gradients are fundamental to spatial encoding and diffusion weighting in magnetic resonance. The ideal pulsed magnetic field gradient should have negligible rise and fall times, however, there are physical limits to how fast the magnetic field gradient may change with time. Finite gradient switching times, and transient, secondary, induced magnetic field gradients (eddy currents) alter the ideal gradient waveform and may introduce a variety of undesirable image artifacts. We have developed a new method to measure the complete magnetic field gradient waveform. The measurement employs a heavily doped test sample with short MR relaxation times (T(1), T(2), and T(2)(*)<100 micros) and a series of closely spaced broadband radiofrequency excitations, combined with single point data acquisition. This technique, a measure of evolving signal phase, directly determines the magnetic field gradient waveform experienced by the test sample. The measurement is sensitive to low level transient magnetic fields produced by eddy currents and other short and long time constant non-ideal gradient waveform behaviors. Data analysis is particularly facile permitting a very ready experimental check of gradient performance.

Reduction of spectral ghost artifacts in high-resolution echo-planar spectroscopic imaging of water and fat resonances

Echo-planar spectroscopic imaging (EPSI) can be used for fast spectroscopic imaging of water and fat resonances at high resolution to improve structural and functional imaging. Because of the use of oscillating gradients during the free induction decay (FID), spectra obtained with EPSI are often degraded by Nyquist ghost artifacts arising from the inconsistency between the odd and even echoes. The presence of the spectral ghost lines causes errors in the evaluation of the true spectral lines, and this degrades images derived from high-resolution EPSI data. A technique is described for reducing the spectral ghost artifacts in EPSI of water and fat resonances, using echo shift and zero-order phase corrections. These corrections are applied during the data postprocessing. This technique is demonstrated with EPSI data acquired from human brains and breasts at 1.5 Tesla and from a water phantom at 4.7 Tesla. Experimental results indicate that the present approach significantly reduces the intensities of spectral ghosts. This technique is most useful in conjunction with high-resolution EPSI of water and fat resonances, but is less applicable to EPSI of metabolites due to the complexity of the spectra.

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.

Single-shot curved slice imaging

The feasibility of imaging a curved slice with a single-shot technique so that the reconstructed image shows an un-warping of the slice is examined. This could be of practical importance when the anatomical structures of interest can be more efficiently covered with curved slices than with a series of flat planes. One possible example of such a structure is the cortex of the human brain. Functional imaging would especially benefit from this technique because several planar images can be replaced by a few curved slice images. A method is introduced that is based on multidimensional pulses to excite the desired curved slice profile. A GRASE imaging sequence is then applied that is tailored to the k-space representation of the curved slice. This makes it possible to capture the in-plane information of the slice with a single-shot technique. The method presented is limited to slices that are straight along one axis and can be approximated by a polygon. Reconstruction is performed using a simple numeric Fourier integration along the curved slice. This leads to an image that shows the desired un-warped representation of the slice. Experimental results obtained with this method from healthy volunteers are presented and demonstrate the feasibility of the proposed technique.

Correction of physiologically induced global off-resonance effects in dynamic echo-planar and spiral functional imaging

In functional magnetic resonance imaging, a rapid method such as echo-planar (EPI) or spiral is used to collect a dynamic series of images. These techniques are sensitive to changes in resonance frequency which can arise from respiration and are more significant at high magnetic fields. To decrease the noise from respiration-induced phase and frequency fluctuations, a simple correction of the "dynamic off-resonance in k-space" (DORK) was developed. The correction uses phase information from the center of k-space and a navigator echo and is illustrated with dynamic scans of single-shot and segmented EPI and, for the first time, spiral imaging of the human brain at 7 T. Image noise in the respiratory spectrum was measured with an edge operator. The DORK correction significantly reduced respiration-induced noise (image shift for EPI, blurring for spiral, ghosting for segmented acquisition). While spiral imaging was found to exhibit less noise than EPI before correction, the residual noise after the DORK correction was comparable. The correction is simple to apply and can correct for other sources of frequency drift and fluctuations in dynamic imaging.

Off-centered spiral trajectories

The quality of spiral images depends on the accuracy of the k-space sampling locations. Although newer gradient systems can provide more accurate gradient waveforms, the sampling positions can be significantly distorted by timing misregistration between data acquisition and gradient systems. Even after the timing of data acquisition is tuned, minor residual errors can still cause shading artifacts which are problematic for quantitative MR applications such as phase-contrast flow quantitation. These timing errors can ideally be corrected by measuring the actual k-space trajectory, but trajectory measurement requires additional data acquisition and scan time. Therefore, off-centered spiral trajectories which are more robust against timing errors are proposed and applied to the phase-contrast method. The new trajectories turn shading artifacts into a slowly varying linear phase in reconstructed images without affecting the magnitude of images.

Functional MRI of the human motor cortex using single-shot, multiple gradient-echo spiral imaging

In this study, we combined the advantages of a fast multi-slice spiral imaging approach with a multiple gradient-echo sampling scheme at high magnetic field strength to improve quantification of BOLD and inflow effects and to estimate T2* relaxation times in functional brain imaging. Eight echoes are collected with echo time (TE) ranging from 5 to 180 ms. Acquisition time per slice and echo time is 25 ms for a nominal resolution of 4 x 4 x 4 mm3. Evaluation of parameter images during rest and stimulation yields no significant activation on the inflow sensitive spin-density images (rho or I0-maps) whereas clear activation patterns in primary human motor cortex (M1) and supplementary motor area (SMA) are detected on BOLD sensitive T2*-maps. The calculation of relaxation times and rates of the activated areas over all subjects yields an average T2* +/- standard deviation (SD) of 46.1+/-4.5 ms (R2* of 21.8+/-2.2 s(-1)) and an average increase (deltaT2* +/- SD) of 0.93+/-0.47 ms (deltaR2* of -0.4+/-0.14 s(-1)). Our findings demonstrate the usefulness of a multiple gradient echo data acquisition approach in separating various vascular contributions to brain activation in fMRI.