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

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.

Rapid fat-water separated T1 mapping using a single-shot radial inversion-recovery spoiled gradient recalled pulse sequence

T1 mapping is increasingly used in clinical practice and research studies. With limited scan time, existing techniques often have limited spatial resolution, contrast resolution and slice coverage. High fat concentrations yield complex errors in Look-Locker T1 methods. In this study, a dual-echo 2D radial inversion-recovery T1 (DEradIR-T1) technique was developed for fast fat-water separated T1 mapping. The DEradIR-T1 technique was tested in phantoms, 5 volunteers and 28 patients using a 3 T clinical MRI scanner. In our study, simulations were performed to analyze the composite (fat + water) and water-only T1 under different echo times (TE). In standardized phantoms, an inversion-recovery spin echo (IR-SE) sequence with and without fat saturation pulses served as a T1 reference. Parameter mapping with DEradIR-T1 was also assessed in vivo, and values were compared with modified Look-Locker inversion recovery (MOLLI). Bland-Altman analysis and two-tailed paired t-tests were used to compare the parameter maps from DEradIR-T1 with the references. Simulations of the composite and water-only T1 under different TE values and levels of fat matched the in vivo studies. T1 maps from DEradIR-T1 on a NIST phantom (Pcomp  = 0.97) and a Calimetrix fat-water phantom (Pwater  = 0.56) matched with the references. In vivo T1 was compared with that of MOLLI: R comp 2 = 0.77 ; R water 2 = 0.72 . In this work, intravoxel fat is found to have a variable, echo-time-dependent effect on measured T1 values, and this effect may be mitigated using the proposed DRradIR-T1.

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.

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.

Preclinical MRI to Quantify Pulmonary Disease Severity and Trajectories in Poorly Characterized Mouse Models: A Pedagogical Example Using Data from Novel Transgenic Models of Lung Fibrosis

Structural remodeling in lung disease is progressive and heterogeneous, making temporally and spatially explicit information necessary to understand disease initiation and progression. While mouse models are essential to elucidate mechanistic pathways underlying disease, the experimental tools commonly available to quantify lung disease burden are typically invasive (e.g., histology). This necessitates large cross-sectional studies with terminal endpoints, which increases experimental complexity and expense. Alternatively, magnetic resonance imaging (MRI) provides information noninvasively, thus permitting robust, repeated-measures statistics. Although lung MRI is challenging due to low tissue density and rapid apparent transverse relaxation (T₂* <1 ms), various imaging methods have been proposed to quantify disease burden. However, there are no widely accepted strategies for preclinical lung MRI. As such, it can be difficult for researchers who lack lung imaging expertise to design experimental protocols-particularly for novel mouse models. Here, we build upon prior work from several research groups to describe a widely applicable acquisition and analysis pipeline that can be implemented without prior preclinical pulmonary MRI experience. Our approach utilizes 3D radial ultrashort echo time (UTE) MRI with retrospective gating and lung segmentation is facilitated with a deep-learning algorithm. This pipeline was deployed to assess disease dynamics over 255 days in novel, transgenic mouse models of lung fibrosis based on disease-associated, loss-of-function mutations in Surfactant Protein-C. Previously identified imaging biomarkers (tidal volume, signal coefficient of variation, etc.) were calculated semi-automatically from these data, with an objectively-defined high signal volume identified as the most robust metric. Beyond quantifying disease dynamics, we discuss common pitfalls encountered in preclinical lung MRI and present systematic approaches to identify and mitigate these challenges. While the experimental results and specific pedagogical examples are confined to lung fibrosis, the tools and approaches presented should be broadly useful to quantify structural lung disease in a wide range of mouse models.

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.

Cardiac and Respiratory Self-Gating in Radial MRI Using an Adapted Singular Spectrum Analysis (SSA-FARY)

Cardiac Magnetic Resonance Imaging (MRI) is time-consuming and error-prone. To ease the patient's burden and to increase the efficiency and robustness of cardiac exams, interest in methods based on continuous steady-state acquisition and self-gating has been growing in recent years. Self-gating methods extract the cardiac and respiratory signals from the measurement data and then retrospectively sort the data into cardiac and respiratory phases. Repeated breathholds and synchronization with the heart beat using some external device as required in conventional MRI are then not necessary. In this work, we introduce a novel self-gating method for radially acquired data based on a dimensionality reduction technique for time-series analysis (SSA-FARY). Building on Singular Spectrum Analysis, a zero-padded, time-delayed embedding of the auto-calibration data is analyzed using Principle Component Analysis. We demonstrate the basic functionality of SSA-FARY using numerical simulations and apply it to in-vivo cardiac radial single-slice bSSFP and Simultaneous Multi-Slice radiofrequency-spoiled gradient-echo measurements, as well as to Stack-of-Stars bSSFP measurements. SSA-FARY reliably detects the cardiac and respiratory motion and separates it from noise. We utilize the generated signals for high-dimensional image reconstruction using parallel imaging and compressed sensing with in-plane wavelet and (spatio-)temporal total-variation regularization.

Noncontrast MR angiography: An update

Both computed tomography (CT) angiography (CTA) and contrast-enhanced MR angiography (CEMRA) have proven to be useful and accurate cross-sectional imaging modalities over a wide range of vascular territories and vascular disorders. A key advantage of MRA is that, unlike CTA, it can be performed without the administration of a contrast agent. In this review article we consider the motivations for using noncontrast MRA, potential contrast mechanisms, imaging techniques, advantages, and drawbacks with respect to CTA and CEMRA, and the level of evidence for using the various MRA techniques. In addition, we explore new developments that promise to expand the reliability and range of clinical applications for noncontrast MRA, along with functional MRA capabilities not available with CTA or CEMRA. Level of Evidence: 1 Technical Efficacy: Stage 1 J. Magn. Reson. Imaging 2019;49:355-373.

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.

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.

Volumetric MRI thermometry using a three-dimensional stack-of-stars echo-planar imaging pulse sequence

PURPOSE

To measure temperature over a large brain volume with fine spatiotemporal resolution.

METHODS

A three-dimensional stack-of-stars echo-planar imaging sequence combining echo-planar imaging and radial sampling with golden angle spacing was implemented at 3T for proton resonance frequency-shift temperature imaging. The sequence acquires a 188x188x43 image matrix with 1.5x1.5x2.75 mm3 spatial resolution. Temperature maps were reconstructed using sensitivity encoding (SENSE) image reconstruction followed by the image domain hybrid method, and using the k-space hybrid method. In vivo temperature maps were acquired without heating to measure temperature precision in the brain, and in a phantom during high-intensity focused ultrasound sonication.

RESULTS

In vivo temperature standard deviation was less than 1°C at dynamic scan times down to 0.75 s. For a given frame rate, scanning at a minimum repetition time (TR) with minimum acceleration yielded the lowest standard deviation. With frame rates around 3 s, the scan was tolerant to a small number of receive coils, and temperature standard deviation was 48% higher than a standard two-dimensional Fourier transform temperature mapping scan, but provided whole-brain coverage. Phantom temperature maps with no visible aliasing were produced for dynamic scan times as short as 0.38 s. k-Space hybrid reconstructions were more tolerant to acceleration.

CONCLUSION

Three-dimensional stack-of-stars echo-planar imaging temperature mapping provides volumetric brain coverage and fine spatiotemporal resolution. Magn Reson Med 79:2003-2013, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

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.

Autocalibrated wave-CAIPI reconstruction; Joint optimization of k-space trajectory and parallel imaging reconstruction

PURPOSE

Fast MRI acquisitions often rely on efficient traversal of k-space and hardware limitations, or other physical effects can cause the k-space trajectory to deviate from a theoretical path in a manner dependent on the image prescription and protocol parameters. Additional measurements or generalized calibrations are typically needed to characterize the discrepancies. We propose an autocalibrated technique to determine these discrepancies.

METHODS

A joint optimization is used to estimate the trajectory simultaneously with the parallel imaging reconstruction, without the need for additional measurements. Model reduction is introduced to make this optimization computationally efficient, and to ensure final image quality.

RESULTS

We demonstrate our approach for the wave-CAIPI fast acquisition method that uses a corkscrew k-space path to efficiently encode k-space and spread the voxel aliasing. Model reduction allows for the 3D trajectory to be automatically calculated in fewer than 30 s on standard vendor hardware. The method achieves equivalent accuracy to full-gradient calibration scans.

CONCLUSIONS

The proposed method allows for high-quality wave-CAIPI reconstruction across wide ranges of protocol parameters, such as field of view (FOV) location/orientation, bandwidth, echo time (TE), resolution, and sinusoidal amplitude/frequency. Our framework should allow for the autocalibration of gradient trajectories from many other fast MRI techniques in clinically relevant time. Magn Reson Med 78:1093-1099, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

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.