Using self-consistency for an iterative trajectory adjustment (SCITA)

A single oscillating waveform-based gradient delay estimation

PURPOSE

We present a time efficient method to estimate gradient delay using a single oscillating waveform.

METHODS

Single oscillating waveform-based gradient delay estimation algorithm (SODA) was proposed. It estimated gradient delays by measuring the relative shifts of echoes acquired at consecutive time points. An acceleration was achieved by a three spin-echo sequence acquiring measurements for all gradient channels within a single excitation. Simulations and phantom experiments were carried out to compare SODA with a reference method. In addition, we monitored the change of the gradient delay over time using an integrated sequence with high gradient amplitude on a 3 T scanner. High-resolution imaging was performed for phantom and in vivo studies to compare images quality with and without gradient delay correction (GDC).

RESULTS

Simulations showed no significant difference in gradient delay estimates when comparing SODA with the reference method for noise levels 1 to 5. The phantom results confirmed strong agreements on delay estimates between SODA with the three spin-echo sequence and the reference method with six pulse repetitions. The gradient delays were observed nearly consistent over time for the scanner. For high-resolution imaging, the reconstruction with GDC exhibit sharper and clearer depictions of images structures than reconstruction without GDC.

CONCLUSION

SODA can provide accurate gradient delay estimates with short calibration scan time. The three spin-echo sequence can be seamlessly integrated with any host sequence to measure the gradient delay and provide accurate spiral trajectory. It may be a valuable tool for gradient delay correction in spiral imaging.

Joint radial trajectory correction for accelerated T2 * mapping on an MR-Linac

BACKGROUND

T2 * mapping can characterize tumor hypoxia, which may be associated with resistance to therapy. Acquiring T2 * maps during MR-guided radiotherapy could inform treatment adaptation by, for example, escalating the dose to resistant sub-volumes.

PURPOSE

The purpose of this work is to demonstrate the feasibility of the accelerated T2 * mapping technique using model-based image reconstruction with integrated trajectory auto-correction (TrACR) for MR-guided radiotherapy on an MR-Linear accelerator (MR-Linac).

MATERIALS AND METHODS

The proposed method was validated in a numerical phantom, where two T2 * mapping approaches (sequential and joint) were compared for different noise levels (0,0.1,0.5,1) and gradient delays ([1, -1] and [1, -2] in units of dwell time for x- and y-axis, respectively). Fully sampled k-space was retrospectively undersampled using two different undersampling patterns. Root mean square errors (RMSEs) were calculated between reconstructed T2 * maps and ground truth. In vivo data was acquired twice weekly in one prostate and one head and neck cancer patient undergoing treatment on a 1.5 T MR-Linac. Data were retrospectively undersampled and T2 * maps reconstructed, with and without trajectory corrections were compared.

RESULTS

Numerical simulations demonstrated that, for all noise levels, T2 * maps reconstructed with a joint approach demonstrated less error compared to an uncorrected and sequential approach. For a noise level of 0.1, uniform undersampling and gradient delay [1, -1] (in units of dwell time for x- and y-axis, respectively), RMSEs for sequential and joint approaches were 13.01 and 9.32 ms, respectively, which reduced to 10.92 and 5.89 ms for a gradient delay of [1, 2]. Similarly, for alternate undersampling and gradient delay [1, -1], RMSEs for sequential and joint approaches were 9.80 and 8.90 ms, respectively, which reduced to 9.10 and 5.40 ms for gradient delay [1, 2]. For in vivo data, T2 * maps reconstructed with our proposed approach resulted in less artifacts and improved visual appearance compared to the uncorrected approach. For both prostate and head and neck cancer patients, T2 * maps reconstructed from different treatment fractions showed changes within the planning target volume (PTV).

CONCLUSION

Using the proposed approach, a retrospective data-driven gradient delay correction can be performed, which is particularly relevant for hybrid devices, where full information on the machine configuration is not available for image reconstruction. T2 * maps were acquired in under 5 min and can be integrated into MR-guided radiotherapy treatment workflows, which minimizes patient burden and leaves time for additional imaging for online adaptive radiotherapy on an MR-Linac.

Model-based determination of the synchronization delay between MRI and trajectory data

PURPOSE

Real-time monitoring of dynamic magnetic fields has recently become a commercially available option for measuring MRI k-space trajectories and magnetic fields induced by eddy currents in real time. However, for accurate image reconstructions, sub-microsecond synchronization between the MRI data and field dynamics (ie, k-space trajectory plus other spatially varying fields) is required. In this work, we introduce a new model-based algorithm to automatically perform this synchronization using only the MRI data and field dynamics.

METHODS

The algorithm works by enforcing consistency among the MRI data, field dynamics, and receiver sensitivity profiles by iteratively alternating between convex optimizations for (a) the image and (b) the synchronization delay. A healthy human subject was scanned at 7 T using a transmit-receive coil with integrated field probes using both single-shot spiral and EPI, and reconstructions with various synchronization delays were compared with the result of the proposed algorithm. The accuracy of the algorithm was also investigated using simulations, in which the acquisition delays for simulated acquisitions were determined using the proposed algorithm and compared with the known ground truth.

RESULTS

In the in vivo scans, the proposed algorithm minimized artifacts related to synchronization delay for both spiral and EPI acquisitions, and the computation time required was less than 30 s. The simulations demonstrated accuracy to within tens of nanoseconds.

CONCLUSIONS

The proposed algorithm can automatically determine synchronization delays between MRI data and field dynamics measured using a field probe system.

CSR-PERT: Joint framework for MRI and HARDI data reconstruction using perturbed radial trajectory estimated from compressively sensed measurements

Radial sampling pattern is an important signal acquisition strategy in magnetic resonance imaging (MRI) owing to better immunity to motion-induced artifacts and less pronounced aliasing due to undersampling compared to the Cartesian sampling. These advantages of radial sampling can be exploited in acquisition of multidimensional signals such as High Angular Resolution Diffusion Imaging (HARDI), with tremendous scope of acceleration. Despite such benefits, gradient delays lead to samples being acquired from unknown miscentered radial trajectories, severely degrading the image reconstruction quality. In the present work, we propose Csr-Pert that is a joint framework, wherein these perturbed radial trajectories are estimated and utilized for image reconstruction from the compressively sensed measurements of (i) MRI data and (ii) HARDI data. The proposed Csr-Pert method is tested on one real MRI dataset with trajectory deviations and is observed to perform better than the existing state-of-the-art method at high acceleration factors up to 8. To the best of our knowledge, this is the first work to address the problem of estimating perturbed trajectories using the compressively sensed MRI and HARDI data. The method is also tested for varying combinations of trajectory deviations and sampling proportions. It is observed to yield very good quality HARDI reconstruction for a wide variety of scenarios. We have also demonstrated the robustness of the proposed method on real datasets in clinical settings assuming perturbed as well as noisy trajectories.

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.

Field camera versus phantom-based measurement of the gradient system transfer function (GSTF) with dwell time compensation

PURPOSE

The gradient system transfer function (GSTF) can be used to describe the dynamic gradient system and applied for trajectory correction in non-Cartesian MRI. This study compares the field camera and the phantom-based methods to measure the GSTF and implements a compensation for the difference in measurement dwell time.

METHODS

The self-term GSTFs of a MR system were determined with two approaches: 1) using a dynamic field camera and 2) using a spherical phantom-based measurement with standard MR hardware. The phantom-based GSTF was convolved with a box function to compensate for the dwell time dependence of the measurement. The field camera and phantom-based GSTFs were used for trajectory prediction during retrospective image reconstruction of 3D wave-CAIPI phantom images.

RESULTS

Differences in the GSTF magnitude response were observed between the two measurement methods. For the wave-CAIPI sequence, this led to deviations in the GSTF predicted trajectories of 4% compared to measured trajectories, and residual distortions in the reconstructed phantom images generated with the phantom-based GSTF. Following dwell-time compensation, deviations in the GSTF magnitudes, GSTF-predicted trajectories, and resulting image artifacts were eliminated (< 0.5% deviation in trajectories).

CONCLUSION

With dwell time compensation, both the field camera and the phantom-based GSTF self-terms show negligible deviations and lead to strong artifact reduction when they are used for trajectory correction in image reconstruction.

The temperature dependence of gradient system response characteristics

PURPOSE

The gradient system transfer function (GSTF) characterizes the frequency transfer behavior of a dynamic gradient system and can be used to correct non-Cartesian k-space trajectories. This study analyzes the impact of the gradient coil temperature of a 3T scanner on the GSTF.

METHODS

GSTF self- and B₀ -cross-terms were acquired for a 3T Siemens scanner (Siemens Healthcare, Erlangen, Germany) using a phantom-based measurement technique. The GSTF terms were measured for various temperature states up to 45°C. The gradient coil temperatures were measured continuously utilizing 12 temperature sensors which are integrated by the vendor. Different modeling approaches were applied and compared.

RESULTS

The self-terms depend linearly on temperature, whereas the B₀ -cross-term does not. Effects induced by thermal variation are negligible for the phase response. The self-terms are best represented by a linear model including the three gradient coil sensors that showed the maximum temperature dependence for the three axes. The use of time derivatives of the temperature did not lead to an improvement of the model. The B₀ -cross-terms can be modeled by a convolution model which considers coil-specific heat transportation.

CONCLUSION

The temperature dependency of the GSTF was analyzed for a 3T Siemens scanner. The self- and B₀ -cross-terms can be modeled using a linear and convolution modeling approach based on the three main temperature sensor elements.

Simultaneous auto-calibration and gradient delays estimation (SAGE) in non-Cartesian parallel MRI using low-rank constraints

PURPOSE

To correct gradient timing delays in non-Cartesian MRI while simultaneously recovering corruption-free auto-calibration data for parallel imaging, without additional calibration scans.

METHODS

The calibration matrix constructed from multi-channel k-space data should be inherently low-rank. This property is used to construct reconstruction kernels or sensitivity maps. Delays between the gradient hardware across different axes and RF receive chain, which are relatively benign in Cartesian MRI (excluding EPI), lead to trajectory deviations and hence data inconsistencies for non-Cartesian trajectories. These in turn lead to higher rank and corrupted calibration information which hampers the reconstruction. Here, a method named Simultaneous Auto-calibration and Gradient delays Estimation (SAGE) is proposed that estimates the actual k-space trajectory while simultaneously recovering the uncorrupted auto-calibration data. This is done by estimating the gradient delays that result in the lowest rank of the calibration matrix. The Gauss-Newton method is used to solve the non-linear problem. The method is validated in simulations using center-out radial, projection reconstruction and spiral trajectories. Feasibility is demonstrated on phantom and in vivo scans with center-out radial and projection reconstruction trajectories.

RESULTS

SAGE is able to estimate gradient timing delays with high accuracy at a signal to noise ratio level as low as 5. The method is able to effectively remove artifacts resulting from gradient timing delays and restore image quality in center-out radial, projection reconstruction, and spiral trajectories.

CONCLUSION

The low-rank based method introduced simultaneously estimates gradient timing delays and provides accurate auto-calibration data for improved image quality, without any additional calibration scans.

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.

A general algorithm for compensation of trajectory errors: Application to radial imaging

PURPOSE

To reconstruct artifact-free images from measured k-space data, when the actual k-space trajectory deviates from the nominal trajectory due to gradient imperfections.

METHODS

Trajectory errors arising from eddy currents and gradient delays introduce phase inconsistencies in several fast scanning MR pulse sequences, resulting in image artifacts. The proposed algorithm provides a novel framework to compensate for this phase distortion. The algorithm relies on the construction of a multi-block Hankel matrix, where each block is constructed from k-space segments with the same phase distortion. In the presence of spatially smooth phase distortions between the segments, the complete block-Hankel matrix is known to be highly low-rank. Since each k-space segment is only acquiring part of the k-space data, the reconstruction of the phase compensated image from their partially parallel measurements is posed as a structured low-rank matrix optimization problem, assuming the coil sensitivities to be known.

RESULTS

The proposed formulation is tested on radial acquisitions in several settings including partial Fourier and golden-angle acquisitions. The experiments demonstrate the ability of the algorithm to successfully remove the artifacts arising from the trajectory errors, without the need for trajectory or phase calibration. The quality of the reconstruction was comparable to corrections achieved using the Trajectory Auto-Corrected Image Reconstruction (TrACR) for radial acquisitions.

CONCLUSION

The proposed method provides a general framework for the recovery of artifact-free images from radial trajectories without the need for trajectory calibration.

Accelerated mapping of magnetic susceptibility using 3D planes-on-a-paddlewheel (POP) EPI at ultra-high field strength

With the advent of ultra-high field MRI scanners in clinical research, susceptibility based MRI has recently gained increasing interest because of its potential to assess subtle tissue changes underlying neurological pathologies/disorders. Conventional, but rather slow, three-dimensional (3D) spoiled gradient-echo (GRE) sequences are typically employed to assess the susceptibility of tissue. 3D echo-planar imaging (EPI) represents a fast alternative but generally comes with echo-time restrictions, geometrical distortions and signal dropouts that can become severe at ultra-high fields. In this work we assess quantitative susceptibility mapping (QSM) at 7 T using non-Cartesian 3D EPI with a planes-on-a-paddlewheel (POP) trajectory, which is created by rotating a standard EPI readout train around its own phase encoding axis. We show that the threefold accelerated non-Cartesian 3D POP EPI sequence enables very fast, whole brain susceptibility mapping at an isotropic resolution of 1 mm and that the high image quality has sufficient signal-to-noise ratio in the phase data for reliable QSM processing. The susceptibility maps obtained were comparable with regard to QSM values and geometric distortions to those calculated from a conventional 4 min 3D GRE scan using the same QSM processing pipeline. Copyright © 2016 John Wiley & Sons, Ltd.

Motion-insensitive carotid intraplaque hemorrhage imaging using 3D inversion recovery preparation stack of stars (IR-prep SOS) technique

PURPOSE

Carotid artery imaging is important in the clinical management of patients at risk for stroke. Carotid intraplaque hemorrhage (IPH) presents an important diagnostic challenge. 3D magnetization prepared rapid acquisition gradient echo (MPRAGE) has been shown to accurately image carotid IPH; however, this sequence can be limited due to motion- and flow-related artifact. The purpose of this work was to develop and evaluate an improved 3D carotid MPRAGE sequence for IPH detection. We hypothesized that a radial-based k-space trajectory sequence such as "Stack of Stars" (SOS) incorporated with inversion recovery preparation would offer reduced motion sensitivity and more robust flow suppression by oversampling of central k-space.

MATERIALS AND METHODS

A total of 31 patients with carotid disease (62 carotid arteries) were imaged at 3T magnetic resonance imaging (MRI) with 3D IR-prep Cartesian and SOS sequences. Image quality was determined between SOS and Cartesian MPRAGE in 62 carotid arteries using t-tests and multivariable linear regression. Kappa analysis was used to determine interrater reliability.

RESULTS

In all, 25 among 62 carotid plaques had carotid IPH by consensus from the reviewers on SOS compared to 24 on Cartesian sequence. Image quality was significantly higher with SOS compared to Cartesian (mean 3.74 vs. 3.11, P < 0.001). SOS acquisition yielded sharper image features with less motion (19.4% vs. 45.2%, P < 0.002) and flow artifact (27.4% vs. 41.9%, P < 0.089). There was also excellent interrater reliability with SOS (kappa = 0.89), higher than that of Cartesian (kappa = 0.84).

CONCLUSION

By minimizing flow and motion artifacts and retaining high interrater reliability, the SOS MPRAGE has important advantages over Cartesian MPRAGE in carotid IPH detection.

LEVEL OF EVIDENCE

1 J. Magn. Reson. Imaging 2017;45:410-417.

Trajectory Auto-Corrected image reconstruction

PURPOSE

To estimate k-space trajectory errors in non-Cartesian acquisitions and reconstruct distortion-free images, without trajectory measurements or gradient calibrations.

THEORY AND METHODS

The Trajectory Auto-Corrected image Reconstruction method jointly estimates k-space trajectory errors and images, based on SENSE and SPIRiT parallel imaging reconstruction. The underlying idea is that parallel imaging and oversampling in the center of k-space provides data redundancy that can be exploited to simultaneously reconstruct images and correct trajectory errors. Trajectory errors are represented as weighted sums of trajectory-dependent error basis functions, the coefficients of which are estimated using gradient-based optimization.

RESULTS

Trajectory Auto-Corrected image Reconstruction was applied to reconstruct images and errors in golden angle radial, center-out radial, and spiral in vivo 7 Tesla brain acquisitions in five subjects. Compared to reconstructions using nominal trajectories, Trajectory auto-corrected image reconstructions contained considerably less blurring and streaking and were of similar quality to images reconstructed using measured k-space trajectories in the center-out radial and spiral cases. Reconstruction cost function reductions and improvements in normalized image gradient squared were also similar to those for images reconstructed using measured trajectories.

CONCLUSION

Trajectory Auto-Corrected image Reconstruction enables non-Cartesian image reconstructions free from trajectory errors without the need for separate gradient calibrations or trajectory measurements. Magn Reson Med 76:757-768, 2016. © 2015 Wiley Periodicals, Inc.

Self-calibrated trajectory estimation and signal correction method for robust radial imaging using GRAPPA operator gridding

PURPOSE

In radial imaging, projections may become "miscentered" due to gradient errors such as delays and eddy currents. These errors may result in image artifacts and can disrupt the reliability of direct current (DC) navigation. The proposed parallel imaging-based technique retrospectively estimates trajectory error from miscentered radial data without extra acquisitions, hardware, or sequence modification.

THEORY AND METHODS

After phase correction, self-calibrated GRAPPA operator gridding (GROG) weights are iteratively applied to shift-miscentered projections toward the center of k-space. A search algorithm identifies the shift that aligns the peak k-space signals by maximizing the sum-of-squares DC signal estimate of each projection. The algorithm returns a trajectory estimate and a corrected radial k-space signal.

RESULTS

Data from a spherical phantom, the head, and the heart demonstrate that image reconstruction with the estimated trajectory restores image quality and reduces artifacts such as streaks and signal voids. The DC signal level is increased and variability is reduced.

CONCLUSION

Retrospective phase correction and iterative application of GROG can be used to successfully estimate the trajectory error in two-dimensional radial acquisitions for improved image reconstruction without requiring extra data acquisition or sequence modification.