Robust retrospective motion correction of head motion using navigator-based and markerless motion tracking techniques.

PURPOSE: This study investigated the artifacts arising from different types of head motion in brain MR images and how well these artifacts can be compensated using retrospective correction based on two different motion-tracking techniques. METHODS: MPRAGE images were acquired using a 3 T MR scanner on a cohort of nine healthy participants. Subjects moved their head to generate circular motion (4 or 6 cycles/min), stepwise motion (small and large) and "simulated realistic" motion (nodding and slow diagonal motion), based on visual instructions. One MPRAGE scan without deliberate motion was always acquired as a "no motion" reference. Three dimensional fat-navigator (FatNavs) and a Tracoline markerless device (TracInnovations) were used to obtain motion estimates and images were separately reconstructed retrospectively from the raw data based on these different motion estimates. RESULTS: Image quality was recovered from both motion tracking techniques in our stepwise and slow diagonal motion scenarios in almost all cases, with the apparent visual image quality comparable to the no-motion case. FatNav-based motion correction was further improved in the case of stepwise motion using a skull masking procedure to exclude non-rigid motion of the neck from the co-registration step. In the case of circular motion, both methods struggled to correct for all motion artifacts. CONCLUSION: High image quality could be recovered in cases of stepwise and slow diagonal motion using both motion estimation techniques. The circular motion scenario led to more severe image artifacts that could not be fully compensated by the retrospective motion correction techniques used.

CG-SENSE revisited: Results from the first ISMRM reproducibility challenge.

PURPOSE: The aim of this work is to shed light on the issue of reproducibility in MR image reconstruction in the context of a challenge. Participants had to recreate the results of "Advances in sensitivity encoding with arbitrary k-space trajectories" by Pruessmann et al. METHODS: The task of the challenge was to reconstruct radially acquired multicoil k-space data (brain/heart) following the method in the original paper, reproducing its key figures. Results were compared to consolidated reference implementations created after the challenge, accounting for the two most common programming languages used in the submissions (Matlab/Python). RESULTS: Visually, differences between submissions were small. Pixel-wise differences originated from image orientation, assumed field-of-view, or resolution. The reference implementations were in good agreement, both visually and in terms of image similarity metrics. DISCUSSION AND CONCLUSION: While the description level of the published algorithm enabled participants to reproduce CG-SENSE in general, details of the implementation varied, for example, density compensation or Tikhonov regularization. Implicit assumptions about the data lead to further differences, emphasizing the importance of sufficient metadata accompanying open datasets. Defining reproducibility quantitatively turned out to be nontrivial for this image reconstruction challenge, in the absence of ground-truth results. Typical similarity measures like NMSE of SSIM were misled by image intensity scaling and outlier pixels. Thus, to facilitate reproducibility, researchers are encouraged to publish code and data alongside the original paper. Future methodological papers on MR image reconstruction might benefit from the consolidated reference implementations of CG-SENSE presented here, as a benchmark for methods comparison.

Sharpness in motion corrected quantitative imaging at 7T.

Sub-millimeter imaging at 7T has opened new possibilities for qualitatively and quantitatively studying brain structure as it evolves throughout the life span. However, subject motion introduces image blurring on the order of magnitude of the spatial resolution and is thus detrimental to image quality. Such motion can be corrected for, but widespread application has not yet been achieved and quantitative evaluation is lacking. This raises a need to quantitatively measure image sharpness throughout the brain. We propose a method to quantify sharpness of brain structures at sub-voxel resolution, and use it to assess to what extent limited motion is related to image sharpness. The method was evaluated in a cohort of 24 healthy volunteers with a wide and uniform age range, aiming to arrive at results that largely generalize to larger populations. Using 3D fat-excited motion navigators, quantitative R1, R2* and Quantitative Susceptibility Maps and T1-weighted images were retrospectively corrected for motion. Sharpness was quantified in all modalities for selected regions of interest (ROI) by fitting the sigmoidally shaped error function to data within locally homogeneous clusters. A strong, almost linear correlation between motion and sharpness improvement was observed, and motion correction significantly improved sharpness. Overall, the Full Width at Half Maximum reduced from 0.88 mm to 0.70 mm after motion correction, equivalent to a 2.0 times smaller voxel volume. Motion and sharpness were not found to correlate with the age of study participants. We conclude that in our data, motion correction using fat navigators is overall able to restore the measured sharpness to the imaging resolution, irrespective of the amount of motion observed during scanning.

Fat navigators and Moiré phase tracking comparison for motion estimation and retrospective correction.

PURPOSE: To compare motion tracking by two modern methods (fat navigators [FatNavs] and Moiré phase tracking [MPT]) as well as their performance for retrospective correction of very high resolution acquisitions. METHODS: A direct comparison of FatNavs and MPT motion parameters was performed for several deliberate motion patterns to estimate the agreement between methods. In addition, two different navigator resolution were applied. 0.5 mm isotropic MP2RAGE images with simultaneous MPT and FatNavs tracking were acquired in 9 cooperative subjects with no intentional motion. Retrospective motion corrections based on both tracking modalities were compared qualitatively and quantitatively. The FatNavs impact on quantitative T1 maps was also investigated. RESULTS: Both methods showed good agreement within a 0.3 mm/° margin in subjects that moved very little. Higher resolution FatNavs (2 mm) showed overall better agreement with MPT than 4 mm resolution ones, except for fast and large motion. The retrospective motion corrections based on MPT or FatNavs were at par in 33 cases out of 36, and visibly improved image quality compared to the uncorrected images. In separate fringe cases, both methods suffered from their respective potential shortcomings: unreliable marker attachment for MPT and poor temporal resolution for FatNavs. The magnetization transfer induced by the navigator RF pulses had a visible impact on the T1 values distribution, with a shift of the gray and white matter peaks of 12 ms at most. CONCLUSION: This work confirms both FatNavs and MPT as excellent retrospective motion correction methods for very high resolution imaging of cooperative subjects.

Improved susceptibility-weighted imaging for high contrast and resolution thalamic nuclei mapping at 7T.

PURPOSE: The thalamus is an important brain structure and neurosurgical target, but its constituting nuclei are challenging to image non-invasively. Recently, susceptibility-weighted imaging (SWI) at ultra-high field has shown promising capabilities for thalamic nuclei mapping. In this work, several methodological improvements were explored to enhance SWI quality and contrast, and specifically its ability for thalamic imaging. METHODS: High-resolution SWI was performed at 7T in healthy participants, and the following techniques were applied: (a) monitoring and retrospective correction of head motion and B0 perturbations using integrated MR navigators, (b) segmentation and removal of venous vessels on the SWI data using vessel enhancement filtering, and (c) contrast enhancement by tuning the parameters of the SWI phase-magnitude combination. The resulting improvements were evaluated with quantitative metrics of image quality, and by comparison to anatomo-histological thalamic atlases. RESULTS: Even with sub-millimeter motion and natural breathing, motion and field correction produced clear improvements in both magnitude and phase data quality (76% and 41%, respectively). The improvements were stronger in cases of larger motion/field deviations, mitigating the dependence of image quality on subject performance. Optimizing the SWI phase-magnitude combination yielded substantial improvements in image contrast, particularly in the thalamus, well beyond previously reported SWI results. The atlas comparisons provided compelling evidence of anatomical correspondence between SWI features and several thalamic nuclei, for example, the ventral intermediate nucleus. Vein detection performed favorably inside the thalamus, and vein removal further improved visualization. CONCLUSION: Altogether, the proposed developments substantially improve high-resolution SWI, particularly for thalamic nuclei imaging.

Improved off-resonance phase behavior using a phase-inverted adiabatic half-passage pulse for 13 C MRS in humans at 7 T.

In vivo 13 C MRS at high field benefits from an improved SNR and spectral resolution especially when using surface coils in combination with adiabatic pulses, such as the adiabatic half-passage (AHP) pulse for 13 C excitation. However, the excitation profile of the AHP pulse is asymmetric relative to the carrier frequency, which could lead to asymmetric excitation of the spectral lines relative to the center of the spectrum. In this study, a pulse-acquire sequence was designed for adiabatic 13 C excitation with a symmetric bandwidth, utilizing a combination of two AHP pulses with inverted phases in alternate scans. Magnetization and phase behavior as a function of frequency offset and RF amplitude of the B1 field, as well as the steady-state transverse magnetization response to off-resonance, were simulated. Excitation properties of the combined pulse sequence were studied by 23 Na imaging and 13 C spectroscopy in vitro on a phantom and in vivo on the human calf at 7 T. Simulations demonstrated symmetric transverse magnetization and phase with respect to positive and negative frequency offsets when using two AHP pulses with inverted phases in alternate scans, thereby minimizing baseline distortion and achieving symmetric T1 weighting, as confirmed by in vitro measurements. The intensities of the lipid peaks at 15, 30, 62, 73, and 130 ppm were in agreement with those theoretically predicted using two AHP pulses with inverted phases in alternate scans. We conclude that using two phase-inverted AHP pulses improves the symmetry of the 13 C excitation profile and phase response to off-resonance effects at 7 T in comparison with using a single AHP pulse.

Evaluation of 3D fat-navigator based retrospective motion correction in the clinical setting of patients with brain tumors.

PURPOSE: A 3D fat-navigator (3D FatNavs)-based retrospective motion correction is an elegant approach to correct for motion as it requires no additional hardware and can be acquired during existing 'dead-time' within common 3D protocols. The purpose of this study was to clinically evaluate 3D FatNavs in the work-up of brain tumors. METHODS: An MRI-based fat-excitation motion navigator incorporated into a standard MPRAGE sequence was acquired in 40 consecutive patients with (or with suspected) brain tumors, pre and post-Gadolinium injection. Each case was categorized into key anatomical landmarks, the temporal lobes, the infra-tentorial region, the basal ganglia, the bifurcations of the middle cerebral artery, and the A2 segment of the anterior cerebral artery. First, the severity of motion in the non-corrected MPRAGE was assessed for each landmark, using a 5-point score from 0 (no artifacts) to 4 (non-diagnostic). Second, the improvement in image quality in each pair and for each landmark was assessed blindly using a 4-point score from 0 (identical) to 3 (strong correction). RESULTS: The mean image improvement score throughout the datasets was 0.54. Uncorrected cases with light and no artifacts displayed scores of 0.50 and 0.13, respectively, while cases with moderate artifacts, severe artifacts, and non-diagnostic image quality revealed a mean score of 1.17, 2.25, and 1.38, respectively. CONCLUSION: Fat-navigator-based retrospective motion correction significantly improved MPRAGE image quality in restless patients during MRI acquisition. There was no loss of image quality in patients with little or no motion, and improvements were consistent in patients who moved more.

Diffusion MRI of the human brain at ultra-high field (UHF): A review.

The continued drive towards MRI scanners operating at increasingly higher main magnetic fields is primarily motivated by the maxim that more teslas mean more signal and lead to better images. This promise of increased signal, which cannot easily be achieved in other ways, encourages efforts to overcome the inextricable technical challenges which accompany this endeavor. Unlike for many applications, however, diffusion imaging is not currently able to directly reap these potential signal gains - at the time of writing it seems fair to say that, for matched gradient and RF hardware, the majority of diffusion images acquired at 7T, while comparable in quality to those achievable at 3T, do not demonstrate a clear advantage over what can be obtained at lower field. This does not mean that diffusion imaging at UHF is not a worthwhile pursuit - but more a reflection of the fact that the associated challenges are manifold - and converting the potential of higher field strengths into 'better' diffusion imaging is by no means a straightforward task. This article attempts to summarize the specific reasons that make diffusion imaging at UHF more complicated than one might expect, and to highlight the range of developments that have already been made which have enabled diffusion images of excellent quality to be acquired at 7T.

Investigating the accuracy of FatNav-derived estimates of temporal B0 changes and their application to retrospective correction of high-resolution 3D GRE of the human brain at 7T.

PURPOSE: To investigate the precision of estimates of temporal variations of magnetic field achievable by double-echo fat image navigators (FatNavs), and their potential application to retrospective correction of 3-dimensional gradient echo-based sequences. METHODS: Both head motion and temporal changes of B0 were tracked using double-echo highly accelerated 3-dimensional FatNavs as navigators, allowing estimation of the temporal changes in low spatial-order field coefficients. The accuracy of the method was determined by direct comparison to controlled offsets in the linear imaging gradients. Double-echo FatNavs were also incorporated into a high-resolution, 3-dimensional gradient echo-based sequence to retrospectively correct for both motion and temporal changes in B0 during natural and deep breathing. The additional scan time was 5 min (a 40% increase). Correction was also investigated using only the first echo of the FatNav to explore the trade-off in accuracy versus scan time. RESULTS: Excellent accuracy (0.27 Hz, 1.57-2.75 Hz/m) was achieved for tracking field changes, and no significant bias could be observed. Artifacts in the 3-dimensional gradient echo-based images induced by temporal field changes, if present, were effectively reduced using either the field estimates from the double echo or the first echo only from the FatNavs. CONCLUSION: The FatNavs were shown to be an excellent candidate for accurate, fast, and precise estimation of global field variations for the tested patterns of respiration. Future work will investigate ways to increase the temporal sampling to increase robustness to variations in breathing patterns. Magn Reson Med 80:585-597, 2018. © 2018 International Society for Magnetic Resonance in Medicine.

Tracking discrete off-resonance markers with three spokes (trackDOTS) for compensation of head motion and B0 perturbations: Accuracy and performance in anatomical imaging.

PURPOSE: To develop a novel approach for head motion and B0 field monitoring based on tracking discrete off-resonance markers with three spokes (trackDOTS). METHODS: Small markers filled with acetic acid were built and attached to a head cap. Marker positions and phase were tracked with fast MR navigators (DotNavs) consisting of three off-resonance, double-echo, orthogonal one-dimensional projections. Individual marker signals were extracted using optimized coil combinations, and used to estimate head motion and field perturbations. To evaluate the approach, DotNavs were integrated in submillimeter MP2RAGE and long-echo time gradient-echo sequences at 7 Tesla, and tested on six healthy volunteers. RESULTS: The DotNav-based motion estimates differed by less than 0.11 ± 0.09 mm and 0.19 ± 0.17 ° from reference estimates obtained with an existing navigator approach (FatNavs). Retrospective motion correction brought clear improvements to MP2RAGE image quality, even in cases with submillimeter involuntary motion. The DotNav-based field estimates could track deep breathing-induced oscillations, and in cases with small head motion, field correction visibly improved the gradient-echo data quality. Conversely, field estimates were less robust when strong motion was present. CONCLUSIONS: The trackDOTS approach is suitable for head-motion tracking and correction, with significant benefits for high-spatial-resolution MRI. With small head motion, DotNav-based field estimates also allow correcting for deep-breathing artifacts in T2 *-weighted acquisitions. Magn Reson Med 79:160-171, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

High spatio-temporal resolution in functional MRI with 3D echo planar imaging using cylindrical excitation and a CAIPIRINHA undersampling pattern.

PURPOSE: The combination of 3D echo planar imaging (3D-EPI) with a 2D-CAIPIRINHA undersampling scheme provides high flexibility in the optimization for spatial or temporal resolution. This flexibility can be increased further with the addition of a cylindrical excitation pulse, which exclusively excites the brain regions of interest. Here, 3D-EPI was combined with a 2D radiofrequency pulse to reduce the brain area from which signal is generated, and hence, allowing either reduction of the field of view or reduction of parallel imaging noise amplification. METHODS: 3D-EPI with cylindrical excitation and 4 × 3-fold undersampling in a 2D-CAIPIRINHA sampling scheme was used to generate functional MRI (fMRI) data with either 2-mm or 0.9-mm in-plane resolution and 1.1-s temporal resolution over a 5-cm diameter cylinder placed over both temporal lobes for an auditory fMRI experiment. RESULTS: Significant increases in image signal-to-noise ratio (SNR) and temporal SNR (tSNR) were found for both 2-mm isotropic data and the high-resolution protocol when using the cylindrical excitation pulse. Both protocols yielded highly significant blood oxygenation level-dependent responses for the presentation of natural sounds. CONCLUSION: The higher tSNR of the cylindrical excitation 3D-EPI data makes this sequence an ideal choice for high spatiotemporal resolution fMRI acquisitions. Magn Reson Med 79:2589-2596, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Optimizing the acceleration and resolution of three-dimensional fat image navigators for high-resolution motion correction at 7T.

PURPOSE: To investigate the effect of spatial resolution and parallel imaging acceleration factor on the quality of the motion estimates derived from image navigators with a three-dimensional (3D) gradient-recalled echo (GRE) acquisition with fat excitation (3D FatNavs) for neuroimaging at 7T. METHODS: Six healthy subjects were scanned for 10 min, during which time repeated GRE volumes were acquired during small movements-alternating between fat and water excitations (WaterNavs)-allowing retrospective decimation of the data to simulate a variety of combinations of image resolution and acceleration factor. Bias and error in the motion estimates were then compared across navigator parameters. RESULTS: The 2-mm, 4 × 4 accelerated data (TRvolume = 1.2 s) provided motion estimates that were almost indistinguishable from those from the full original acquisition (2 mm, 2 × 2, TRvolume = 5.2 s). For faster navigators, it was found that good accuracy and precision were achievable with TRvolume = 144 ms, using a lower spatial resolution (4 mm, 6 × 6 acceleration) to avoid the bias observed at exceptionally high acceleration factors (8 × 8 or higher). Parameter estimates from WaterNavs and FatNavs showed close agreement with FatNavs, with better performance at exceptionally high acceleration factors. CONCLUSION: Our data help to guide the parameter choice for 3D FatNavs when a compromise must be reached between the quality of the motion estimates and the available scan time. Magn Reson Med 77:547-558, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Retrospective correction of involuntary microscopic head movement using highly accelerated fat image navigators (3D FatNavs) at 7T.

PURPOSE: The goal of the present study was to use a three-dimensional (3D) gradient echo volume in combination with a fat-selective excitation as a 3D motion navigator (3D FatNav) for retrospective correction of microscopic head motion during high-resolution 3D structural scans of extended duration. The fat excitation leads to a 3D image that is itself sparse, allowing high parallel imaging acceleration factors--with the additional advantage of a minimal disturbance of the water signal used for the host sequence. METHODS: A 3D FatNav was inserted into two structural protocols: an inversion-prepared gradient echo at 0.33 × 0.33 × 1.00 mm resolution and a turbo spin echo at 600 µm isotropic resolution. RESULTS: Motion estimation was possible with high precision, allowing retrospective motion correction to yield clear improvements in image quality, especially in the conspicuity of very small blood vessels. CONCLUSION: The highly accelerated 3D FatNav allowed motion correction with noticeable improvements in image quality, even for head motion which was small compared with the voxel dimensions of the host sequence.

Three-dimensional echo planar imaging with controlled aliasing: A sequence for high temporal resolution functional MRI.

PURPOSE: In this work, we combine three-dimensional echo planar imaging (3D-EPI) with controlled aliasing to substantially increase temporal resolution in whole-brain functional MRI (fMRI) while minimizing geometry-factor (g-factor) losses. THEORY AND METHODS: The study was performed on a 7 Tesla scanner equipped with a 32-channel receive coil. The proposed 3D-EPI-CAIPI sequence was evaluated for: (i) image quality, compared with a conventionally undersampled parallel imaging acquisition; (ii) temporal resolution, the ability to sample and remove physiological signal fluctuations from the fMRI signal of interest and (iii) the ability to distinguish small changes in hemodynamic responses in an event-related fMRI experiment. RESULTS: Whole-brain fMRI data with a voxel size of 2 × 2 × 2 mm(3) and temporal resolution of 371 ms could be acquired with acceptable image quality. Ten-fold parallel imaging accelerated 3D-EPI-CAIPI data were shown to lower the maximum g-factor losses up to 62% with respect to a 10-fold accelerated 3D-EPI dataset. FMRI with 400 ms temporal resolution allowed the detection of time-to-peak variations in functional responses due to multisensory facilitation in temporal, occipital and frontal cortices. CONCLUSION: 3D-EPI-CAIPI allows increased temporal resolution that enables better characterization of physiological noise, thus improving sensitivity to signal changes of interest. Furthermore, subtle changes in hemodynamic response dynamics can be studied in shorter scan times by avoiding the need for jittering. Magn Reson Med 75:2350-2361, 2016. © 2015 Wiley Periodicals, Inc.

3D T 2-weighted imaging at 7T using dynamic kT-points on single-transmit MRI systems.

OBJECTIVES: For turbo spin echo (TSE) sequences to be useful at ultra-high field, they should ideally employ an RF pulse train compensated for the B 1 (+) inhomogeneity. Previously, it was shown that a single kT-point pulse designed in the small tip-angle regime can replace all the pulses of the sequence (static kT-points). This work demonstrates that the B 1 (+) dependence of T 2-weighted imaging can be further mitigated by designing a specific kT-point pulse for each pulse of a 3D TSE sequence (dynamic kT-points) even on single-channel transmit systems MATERIALS AND METHODS: By combining the spatially resolved extended phase graph formalism (which calculates the echo signals throughout the sequence) with a gradient descent algorithm, dynamic kT-points were optimized such that the difference between the simulated signal and a target was minimized at each echo. Dynamic kT-points were inserted into the TSE sequence to acquire in vivo images at 7T. RESULTS: The improvement provided by the dynamic kT-points over the static kT-point design and conventional hard pulses was demonstrated via simulations. Images acquired with dynamic kT-points showed systematic improvement of signal and contrast at 7T over regular TSE-especially in cerebellar and temporal lobe regions without the need of parallel transmission. CONCLUSION: Designing dynamic kT-points for a 3D TSE sequence allows the acquisition of T 2-weighted brain images on a single-transmit system at ultra-high field with reduced dropout and only mild residual effects due to the B 1 (+) inhomogeneity.

Parallel imaging with phase scrambling.

PURPOSE: Most existing methods for accelerated parallel imaging in MRI require additional data, which are used to derive information about the sensitivity profile of each radiofrequency (RF) channel. In this work, a method is presented to avoid the acquisition of separate coil calibration data for accelerated Cartesian trajectories. METHODS: Quadratic phase is imparted to the image to spread the signals in k-space (aka phase scrambling). By rewriting the Fourier transform as a convolution operation, a window can be introduced to the convolved chirp function, allowing a low-resolution image to be reconstructed from phase-scrambled data without prominent aliasing. This image (for each RF channel) can be used to derive coil sensitivities to drive existing parallel imaging techniques. As a proof of concept, the quadratic phase was applied by introducing an offset to the x(2) - y(2) shim and the data were reconstructed using adapted versions of the image space-based sensitivity encoding and GeneRalized Autocalibrating Partially Parallel Acquisitions algorithms. RESULTS: The method is demonstrated in a phantom (1 × 2, 1 × 3, and 2 × 2 acceleration) and in vivo (2 × 2 acceleration) using a 3D gradient echo acquisition. CONCLUSION: Phase scrambling can be used to perform parallel imaging acceleration without acquisition of separate coil calibration data, demonstrated here for a 3D-Cartesian trajectory. Further research is required to prove the applicability to other 2D and 3D sampling schemes.

Fast low-specific absorption rate B0 -mapping along projections at high field using two-dimensional radiofrequency pulses.

PURPOSE: At 7 Tesla (T), conventional static field (B0 ) projection mapping techniques, e.g., FASTMAP, FASTESTMAP, lead to elevated specific absorption rates (SAR), requiring longer total acquisition times (TA). In this work, the series of adiabatic pulses needed for slab selection in FASTMAP is replaced by a single two-dimensional radiofrequency (2D-RF) pulse to minimize TA while ensuring equal shimming performance. METHODS: Spiral gradients and 2D-RF pulses were designed to excite thin slabs in the small tip angle regime. The corresponding selection profile was characterized in phantoms and in vivo. After optimization of the shimming protocol, the spectral linewidths obtained after 2D localized shimming were compared with conventional techniques and published values from (Emir et al NMR Biomed 2012;25:152-160) in six different brain regions. RESULTS: Results on healthy volunteers show no significant difference (P > 0.5) between the spectroscopic linewidths obtained with the adiabatic (TA = 4 min) and the new low-SAR and time-efficient FASTMAP sequence (TA = 42 s). The SAR can be reduced by three orders of magnitude and TA accelerated six times without impact on the shimming performances or quality of the resulting spectra. CONCLUSION: Multidimensional pulses can be used to minimize the RF energy and time spent for automated shimming using projection mapping at high field.

Image reconstruction in k-space from MR data encoded with ambiguous gradient fields.

PURPOSE: In this work, the limits of image reconstruction in k-space are explored when non-bijective gradient fields are used for spatial encoding. THEORY: The image space analogy between parallel imaging and imaging with non-bijective encoding fields is partially broken in k-space. As a consequence, it is hypothesized and proven that ambiguities can only be resolved partially in k-space, and not completely as is the case in image space. METHODS: Image-space and k-space based reconstruction algorithms for multi-channel radiofrequency data acquisitions are programmed and tested using numerical simulations as well as in vivo measurement data. RESULTS: The hypothesis is verified based on an analysis of reconstructed images. It is found that non-bijective gradient fields have the effect that densely sampled autocalibration data, used for k-space reconstruction, provide less information than a separate scan of the receiver coil sensitivity maps, used for image space reconstruction. Consequently, in k-space only the undersampling artifact can be unfolded, whereas in image space, it is also possible to resolve aliasing that is caused by the non-bijectivity of the gradient fields. CONCLUSION: For standard imaging, reconstruction in image space and in k-space is nearly equivalent, whereas there is a fundamental difference with practical consequences for the selection of image reconstruction algorithms when non-bijective encoding fields are involved.

Single-shot imaging with higher-dimensional encoding using magnetic field monitoring and concomitant field correction.

PURPOSE: PatLoc (Parallel Imaging Technique using Localized Gradients) accelerates imaging and introduces a resolution variation across the field-of-view. Higher-dimensional encoding employs more spatial encoding magnetic fields (SEMs) than the corresponding image dimensionality requires, e.g. by applying two quadratic and two linear spatial encoding magnetic fields to reconstruct a 2D image. Images acquired with higher-dimensional single-shot trajectories can exhibit strong artifacts and geometric distortions. In this work, the source of these artifacts is analyzed and a reliable correction strategy is derived. METHODS: A dynamic field camera was built for encoding field calibration. Concomitant fields of linear and nonlinear spatial encoding magnetic fields were analyzed. A combined basis consisting of spherical harmonics and concomitant terms was proposed and used for encoding field calibration and image reconstruction. RESULTS: A good agreement between the analytical solution for the concomitant fields and the magnetic field simulations of the custom-built PatLoc SEM coil was observed. Substantial image quality improvements were obtained using a dynamic field camera for encoding field calibration combined with the proposed combined basis. CONCLUSION: The importance of trajectory calibration for single-shot higher-dimensional encoding is demonstrated using the combined basis including spherical harmonics and concomitant terms, which treats the concomitant fields as an integral part of the encoding.

Monoplanar gradient system for imaging with nonlinear gradients.

OBJECT: In this paper we present a monoplanar gradient system capable of imaging a volume comparable with that covered by linear gradient systems. Such a system has been designed and implemented. MATERIALS AND METHODS: Building such a system was made possible by relaxing the constraint of global linearity and replacing it with a requirement for local orthogonality. A framework was derived for optimization of local orthogonality within the physical boundaries and geometric constraints. Spatial encoding of magnetic fields was optimized for their local orthogonality over a large field of view. RESULTS: A coil design consisting of straight wire segments was optimized, implemented, and integrated into a 3T human scanner to show the feasibility of this approach. Initial MR images are shown and further applications of the derived optimization method and the nonlinear planar gradient system are discussed. CONCLUSION: Encoding fields generated by the prototype encoding system were shown to be locally orthogonal and able to encode a cylindrical volume sufficient for some abdomen imaging applications for humans.