Beat phenomena of oscillating readouts.

PURPOSE: To demonstrate slowly varying, erroneous magnetic field gradients for oscillating readouts due to the mechanically resonant behavior of gradient systems. METHODS: Projections of a static phantom were acquired using a one-dimensional (1D) EPI sequence with varying EPI frequencies ranging from 1121 to 1580 Hz on clinical 3T systems (30 mT/m, 200 T/m/s). Phase due to static B0 inhomogeneities was eliminated by a complex division of two separate scans with different polarities of the EPI readout. The temporal evolution of phase was evaluated and related to the mechanical resonances of the gradient systems derived from the gradient modulation transfer function. Additionally, the impact of temporally varying mechanical resonance effects on EPI was evaluated using an echo-planar spectroscopic imaging sequence. RESULTS: A beat phenomenon resulting in a slowly varying phase was observed. Its temporal frequency was given by the difference between the EPI frequency and the mechanical resonance frequency of the activated gradient axis. The maximum erroneous, oscillating phase during phase encoding was ±0.5 rad for an EPI frequency of 1281 Hz. Echo-planar spectroscopic imaging images showed the resulting time-dependent stretching/compression of the FOV. CONCLUSION: Oscillating readouts such as those used in EPI can result in low-frequency, erroneous phase contributions, which are explained by the beat phenomenon. Therefore, EPI phase-correction approaches may need to include beat effects for accurate image reconstruction.

Toward accurate and fast velocity quantification with 3D ultrashort TE phase-contrast imaging.

PURPOSE: Traditional phase-contrast MRI is affected by displacement artifacts caused by non-synchronized spatial- and velocity-encoding time points. The resulting inaccurate velocity maps can affect the accuracy of derived hemodynamic parameters. This study proposes and characterizes a 3D radial phase-contrast UTE (PC-UTE) sequence to reduce displacement artifacts. Furthermore, it investigates the displacement of a standard Cartesian flow sequence by utilizing a displacement-free synchronized-single-point-imaging MR sequence (SYNC-SPI) that requires clinically prohibitively long acquisition times. METHODS: 3D flow data was acquired at 3T at three different constant flow rates and varying spatial resolutions in a stenotic aorta phantom using the proposed PC-UTE, a Cartesian flow sequence, and a SYNC-SPI sequence as reference. Expected displacement artifacts were calculated from gradient timing waveforms and compared to displacement values measured in the in vitro flow experiments. RESULTS: The PC-UTE sequence reduces displacement and intravoxel dephasing, leading to decreased geometric distortions and signal cancellations in magnitude images, and more spatially accurate velocity quantification compared to the Cartesian flow acquisitions; errors increase with velocity and higher spatial resolution. CONCLUSION: PC-UTE MRI can measure velocity vector fields with greater accuracy than Cartesian acquisitions (although pulsatile fields were not studied) and shorter scan times than SYNC-SPI. As such, this approach is superior to traditional Cartesian 3D and 4D flow MRI when spatial misrepresentations cannot be tolerated, for example, when computational fluid dynamics simulations are compared to or combined with in vitro or in vivo measurements, or regional parameters such as wall shear stress are of interest.

Doing more with less: How to design a good subgroup governance model for the air pollution transport network in "2+26" cities of China?

Air pollution shares the attributes of significant spatial spillover effects and environmental public goods, leading to the territorial governance model that easily falls into a state of failure. Despite a growing number of studies on the local spatial spillover effect of air pollution, scant evidence currently exists on its global spatial association effect and a good subgroup governance model. Based on a panel data set of the daily prefecture-level city data on air quality measured by the air quality index (AQI) in "2 + 26" cities of China in 2015 and 2018, this study first builds an air pollution transport network (APTN), i.e., the cities as the nodes and the association relationships between the nodes as the edges. Furthermore, this paper reveals the spatial association effect and the temporal lagged attribute of the APTN using the Social network analysis (SNA) and the Generalized impulse response function (GIRF). The results are summarized as follows. (1) Every city has significant spatial association effects of air pollution with at least another city in the APTN, and northern APTN affects most to the air pollution of other cities, while southern APTN is obviously always affected by air pollution in other cities. (2) Transport strength peaks on the second day of an air pollution transport process, and the transport process lasts for 7-12 days. (3) The APTN is divided into four subgroups: Sycophants, Primary, Bidirectional, and Brokers, with Baoding, Zhengzhou, Heze, and Hengshui as the central cities of each group, respectively. Overall, our study provides a networked, modular, and early-warning governance model for policymakers.

Characterization and correction of diffusion gradient-induced eddy currents in second-order motion-compensated echo-planar and spiral cardiac DTI.

PURPOSE: Very high gradient amplitudes played out over extended time intervals as required for second-order motion-compensated cardiac DTI may violate the assumption of a linear time-invariant gradient system model. The aim of this work was to characterize diffusion gradient-related system nonlinearity and propose a correction approach for echo-planar and spiral spin-echo motion-compensated cardiac DTI. METHODS: Diffusion gradient-induced eddy currents of 9 diffusion directions were characterized at b values of 150 s/mm2 and 450 s/mm2 for a 1.5 Tesla system and used to correct phantom, ex vivo, and in vivo motion-compensated cardiac DTI data acquired with echo-planar and spiral trajectories. Predicted trajectories were calculated using gradient impulse response function and diffusion gradient strength- and direction-dependent zeroth- and first-order eddy current responses. A reconstruction method was implemented using the predicted k $$ k $$ -space trajectories to additionally include off-resonances and concomitant fields. Resulting images were compared to a reference reconstruction omitting diffusion gradient-induced eddy current correction. RESULTS: Diffusion gradient-induced eddy currents exhibited nonlinear effects when scaling up the gradient amplitude and could not be described by a 3D basis alone. This indicates that a gradient impulse response function does not suffice to describe diffusion gradient-induced eddy currents. Zeroth- and first-order diffusion gradient-induced eddy current effects of up to -1.7 rad and -16 to +12 rad/m, respectively, were identified. Zeroth- and first-order diffusion gradient-induced eddy current correction yielded improved image quality upon image reconstruction. CONCLUSION: The proposed approach offers correction of diffusion gradient-induced zeroth- and first-order eddy currents, reducing image distortions to promote improvements of second-order motion-compensated spin-echo cardiac DTI.

Thermal variation in gradient response: measurement and modeling.

PURPOSE: Many aspects and imperfections of gradient dynamics in MRI have been successfully captured by linear time-invariant (LTI) models. Changes in gradient behavior due to heating, however, violate time invariance. The goal of this work is to study such changes at the level of transfer functions and model them by thermal extension of the LTI framework. METHODS: To study the impact of gradient heating on transfer functions, a clinical MR system was heated using a range of high-amplitude DC and AC waveforms, each followed by measuring transfer functions in rapid succession while the system cooled down. Simultaneously, gradient temperature was monitored with an array of temperature sensors positioned according to initial infrared recordings of the gradient tube. The relation between temperatures and transfer functions is cast into local and global linear models. The models are analysed in terms of self-consistency, conditioning, and prediction performance. RESULTS: Pronounced thermal effects are observed in the time resolved transfer functions, largely attributable to in-coil eddy currents and mechanical resonances. Thermal modeling is found to capture these effects well. The keys to good model performance are well-placed temperature sensors and suitable training data. CONCLUSION: Heating changes gradient response, violating time invariance. The utility of LTI modeling can nevertheless be recovered by a linear thermal extension, relying on temperature sensing and adequate one-time training.

Direct comparison of gradient Fidelity and acoustic noise of the same MRI system at 3 T and 0.75 T.

PURPOSE: To analyze the difference between gradient fidelity and acoustic noise of the same MRI scanner operated at product field strength (3 T) and lower field strength (0.75 T). METHODS: Gradient modulation transfer functions (GMTFs) were measured using a four-slice 2D phase-encoded chirp-based sequence on the same scanner operated at 3 T and, following ramp-down, at 0.75 T with identical gradient specifications (40 mT/m, 200 T/m/s). Calibrated audio measurements were performed at both field strengths to correlate audio spectra with GMTFs. RESULTS: While eddy currents were independent of field strength, mechanical resonances were substantially decreased at lower field, resulting in a reduction of GMTF distortions by up to 95% (88% on average) at the mechanical resonances of the gradient system. Audio spectra amplitudes were reduced by up to 87% when comparing 0.75 T versus 3 T. CONCLUSION: Lower static fields lead to reduced Lorentz forces on the gradient coil and, in turn, to reduced mechanical resonances, thereby improving gradient fidelity. Simultaneously, the reduction of acoustic noise may help to improve patient comfort.

Feasibility of spiral fMRI based on an LTI gradient model.

Spiral imaging is very well suited for functional MRI, however its use has been limited by the fact that artifacts caused by gradient imperfections and B0 inhomogeneity are more difficult to correct compared to EPI. Effective correction requires accurate knowledge of the traversed k-space trajectory. With the goal of making spiral fMRI more accessible, we have evaluated image reconstruction using trajectories predicted by the gradient impulse response function (GIRF), which can be determined in a one-time calibration step. GIRF-predicted reconstruction was tested for high-resolution (0.8 mm) fMRI at 7T. Image quality and functional results of the reconstructions using GIRF-prediction were compared to reconstructions using the nominal trajectory and concurrent field monitoring. The reconstructions using nominal spiral trajectories contain substantial artifacts and the activation maps contain misplaced activation. Image artifacts are substantially reduced when using the GIRF-predicted reconstruction, and the activation maps for the GIRF-predicted and monitored reconstructions largely overlap. The GIRF reconstruction provides a large increase in the spatial specificity of the activation compared to the nominal reconstruction. The GIRF-reconstruction generates image quality and fMRI results similar to using a concurrently monitored trajectory. The presented approach does not prolong or complicate the fMRI acquisition. Using GIRF-predicted trajectories has the potential to enable high-quality spiral fMRI in situations where concurrent trajectory monitoring is not available.

Prospective GIRF-based RF phase cycling to reduce eddy current-induced steady-state disruption in bSSFP imaging.

PURPOSE: To propose an explicit Balanced steady-state free precession (bSSFP) signal model that predicts eddy current-induced steady-state disruptions and to provide a prospective, practical, and general eddy current compensation method. THEORY AND METHODS: Gradient impulse response functions (GIRF) were used to simulate trajectory-specific eddy current-induced phase errors at the end of a repetition block. These phase errors were included in bloch simulations to establish a bSSFP signal model to predict steady-state disruptions and their corresponding image artifacts. The signal model was embedded in the MR system and used to compensate the phase errors by prospectively modifying the phase cycling scheme of the RF pulse. The signal model and eddy current compensation method were validated in phantom and in vivo experiments. In addition, the signal model was used to analyze pre-existing eddy current mitigation methods, such as 2D tiny golden angle radial and 3D paired phase encoded Cartesian acquisitions. RESULTS: The signal model predicted eddy current-induced image artifacts, with the zeroth-order GIRF being the primary factor to predict the steady-state disruption. Prospective RF phase cycling schemes were automatically computed online and considerably reduced eddy current-induced image artifacts. The signal model provides a direct relationship for the smoothness of k-space trajectories, which explains the effectiveness of phase encode pairing and tiny golden angle trajectory. CONCLUSIONS: The proposed signal model can accurately predict eddy current-induced steady-state disruptions for bSSFP imaging. The signal model can be used to derive the eddy current-induced phase errors required for trajectory-specific RF phase cycling schemes, which considerably reduce eddy current-induced image artifacts.

Rapid acquisition of the 3D MRI gradient impulse response function using a simple phantom measurement.

PURPOSE: To provide a simple tool for rapid measurement of the 3D gradient modulation transfer function (GMTF) of clinical MRI systems using a phantom. Knowledge of the transfer function is useful for gradient chain characterization, system calibration, and improvement of image reconstruction results. METHODS: Starting from the well-established thin slice method used for phantom-based measurement of the 1D GMTF, we add phase encoding to partition the thin slices into voxels that act as localized field probes. From the signal phase evolution measured at the 3D voxel positions, the GMTF can be derived for cross and higher order spatial terms represented by spherical harmonics up to 3rd order. RESULTS: Using spherical phantoms, 16 GMTFs representing all terms up to 3rd order harmonics can be determined in a scan time of <2 min. A large voxel volume of >1 mL yields high SNR, enabling signal acquisition using the system's body coil. The method is applied for improving system calibration and for characterizing the effect of additional hardware in the bore. CONCLUSION: The presented method seems well-suited for rapid measurement of the GMTF of a clinical system, as it delivers high-quality results in a short scan time.

Gradient waveform pre-emphasis based on the gradient system transfer function.

PURPOSE: The gradient system transfer function (GSTF) has been used to describe the distorted k-space trajectory for image reconstruction. The purpose of this work was to use the GSTF to determine the pre-emphasis for an undistorted gradient output and intended k-space trajectory. METHODS: The GSTF of the MR system was determined using only standard MR hardware without special equipment such as field probes or a field camera. The GSTF was used for trajectory prediction in image reconstruction and for a gradient waveform pre-emphasis. As test sequences, a gradient-echo sequence with phase-encoding gradient modulation and a gradient-echo sequence with a spiral read-out trajectory were implemented and subsequently applied on a structural phantom and in vivo head measurements. RESULTS: Image artifacts were successfully suppressed by applying the GSTF-based pre-emphasis. Equivalent results are achieved with images acquired using GSTF-based post-correction of the trajectory as a part of image reconstruction. In contrast, the pre-emphasis approach allows reconstruction using the initially intended trajectory. CONCLUSION: The artifact suppression shown for two sequences demonstrates that the GSTF can serve for a novel pre-emphasis. A pre-emphasis based on the GSTF information can be applied to any arbitrary sequence type.

A rapid and robust gradient measurement technique using dynamic single-point imaging.

PURPOSE: We propose a new gradient measurement technique based on dynamic single-point imaging (SPI), which allows simple, rapid, and robust measurement of k-space trajectory. METHODS: To enable gradient measurement, we utilize the variable field-of-view (FOV) property of dynamic SPI, which is dependent on gradient shape. First, one-dimensional (1D) dynamic SPI data are acquired from a targeted gradient axis, and then relative FOV scaling factors between 1D images or k-spaces at varying encoding times are found. These relative scaling factors are the relative k-space position that can be used for image reconstruction. The gradient measurement technique also can be used to estimate the gradient impulse response function for reproducible gradient estimation as a linear time invariant system. RESULTS: The proposed measurement technique was used to improve reconstructed image quality in 3D ultrashort echo, 2D spiral, and multi-echo bipolar gradient-echo imaging. In multi-echo bipolar gradient-echo imaging, measurement of the k-space trajectory allowed the use of a ramp-sampled trajectory for improved acquisition speed (approximately 30%) and more accurate quantitative fat and water separation in a phantom. CONCLUSION: The proposed dynamic SPI-based method allows fast k-space trajectory measurement with a simple implementation and no additional hardware for improved image quality. Magn Reson Med 78:950-962, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Gradient and shim pre-emphasis by inversion of a linear time-invariant system model.

PURPOSE: The goal of this contribution is to enhance the fidelity and switching speed of gradient and shim fields by advancing pre-emphasis toward broadband and full cross-term correction. THEORY AND METHODS: The proposed approach is based on viewing gradient and shim chains as linear, time-invariant (LTI) systems. Pre-emphasis is accomplished by inversion of a broadband digital system model. In the multiple-channel case, it amounts to a matrix of broadband filters that perform concerted self- and cross-term correction. This approach is demonstrated with gradients and shims up to the third order in a 7 Tesla whole-body MR system. RESULTS: Pre-emphasis by LTI model inversion is first verified by studying settling speeds and response behavior without and with the correction. It is then demonstrated for rapid shim updating, achieving substantially enhanced fidelity of field dynamics and shim settling within approximately 1 ms. In single-shot echo-planar imaging (EPI) acquisitions in vivo, this benefit is shown to translate into enhanced geometric fidelity. CONCLUSIONS: The fidelity of gradient and shim dynamics can be greatly enhanced by pre-emphasis based on inverting a general LTI system model. Permitting shim settling on the millisecond scale, broadband multiple-channel pre-emphasis promises to render higher-order shimming fully versatile at the level of MRI sequence design. Magn Reson Med 78:1607-1622, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Image reconstruction using a gradient impulse response model for trajectory prediction.

PURPOSE: Gradient imperfections remain a challenge in MRI, especially for sequences relying on long imaging readouts. This work aims to explore image reconstruction based on k-space trajectories predicted by an impulse response model of the gradient system. THEORY AND METHODS: Gradient characterization was performed twice with 3 years interval on a commercial 3 Tesla (T) system. The measured gradient impulse response functions were used to predict actual k-space trajectories for single-shot echo-planar imaging (EPI), spiral and variable-speed EPI sequences. Image reconstruction based on the predicted trajectories was performed for phantom and in vivo data. Resulting images were compared with reconstructions based on concurrent field monitoring, separate trajectory measurements, and nominal trajectories. RESULTS: Image reconstruction using model-based trajectories yielded high-quality images, comparable to using separate trajectory measurements. Compared with using nominal trajectories, it strongly reduced ghosting, blurring, and geometric distortion. Equivalent image quality was obtained with the recent characterization and that performed 3 years prior. CONCLUSION: Model-based trajectory prediction enables high-quality image reconstruction for technically challenging sequences such as single-shot EPI and spiral imaging. It thus holds great promise for fast structural imaging and advanced neuroimaging techniques, including functional MRI, diffusion tensor imaging, and arterial spin labeling. The method can be based on a one-time system characterization as demonstrated by successful use of 3-year-old calibration data. Magn Reson Med 76:45-58, 2016. © 2015 Wiley Periodicals, Inc.