An inverse problem approach to the correction of distortion in EPI images

Water/fat separation for self-navigated diffusion-weighted multishot echo-planar imaging

The purpose of this study was to develop a self-navigation strategy to improve scan efficiency and image quality of water/fat-separated, diffusion-weighted multishot echo-planar imaging (ms-EPI). This is accomplished by acquiring chemical shift-encoded diffusion-weighted data and using an appropriate water-fat and diffusion-encoded signal model to enable reconstruction directly from k-space data. Multishot EPI provides reduced geometric distortion and improved signal-to-noise ratio in diffusion-weighted imaging compared with single-shot approaches. Multishot acquisitions require corrections for physiological motion-induced shot-to-shot phase errors using either extra navigators or self-navigation principles. In addition, proper fat suppression is important, especially in regions with large B₀ inhomogeneity. This makes the use of chemical shift encoding attractive. However, when combined with ms-EPI, shot-to-shot phase navigation can be challenging because of the spatial displacement of fat signals along the phase-encoding direction. In this work, a new model-based, self-navigated water/fat separation reconstruction algorithm is proposed. Experiments in legs and in the head-neck region of 10 subjects were performed to validate the algorithm. The results are compared with an image-based, two-dimensional (2D) navigated water/fat separation approach for ms-EPI and with a conventional fat saturation approach. Compared with the 2D navigated method, the use of self-navigation reduced the shot duration time by 30%-35%. The proposed algorithm provided improved diffusion-weighted water images in both leg and head-neck regions compared with the 2D navigator-based approach. The proposed algorithm also produced better fat suppression compared with the conventional fat saturation technique in the B₀ inhomogeneous regions. In conclusion, the proposed self-navigated reconstruction algorithm can produce superior water-only diffusion-weighted EPI images with less artefacts compared with the existing methods.

Phantom assessment of three-dimensional geometric distortion of a dedicated wide-bore MR-simulator for radiotherapy

This study evaluated the machine-dependent three-dimensional geometric distortion images acquired from a 1.5T 700mm-wide bore MR-simulator based on a large geometric accuracy phantom. With the consideration of radiation therapy (RT) application requirements, every sequence was examined in various combinations of acquisition-orientations and receiver-bandwidths with console-integrated distortion correction enabled. Distortion was repeatedly measured over a six-month period. The distortion measured from the images acquired at the beginning of this period was employed to retrospectively correct the distortion in the subsequent acquisitions. Geometric distortion was analyzed within the largest field-of-view allowed. Six sequences were examined for comprehensive distortion analysis - VIBE, SPACE, TSE, FLASH, BLADE and PETRA. Based on optimal acquisition parameters, their diameter-sphere-volumes (DSVs) of CT-comparable geometric fidelity (where 1mm distortion was allowed) were 333.6mm, 315.1mm, 316.0mm, 318.9mm, 306.2mm and 314.5mm respectively. This was a significant increase from 254.0mm, 245.5mm, 228.9mm, 256.6mm, 230.8mm and 254.2mm DSVs respectively, when images were acquired using un-optimized parameters. The longitudinal stability of geometric distortion and the efficacy of retrospective correction of console-corrected images, based on prior distortion measurements, were inspected using VIBE and SPACE. The retrospectively corrected images achieved over 500mm DSVs with 1mm distortion allowed. The median distortion was below 1mm after retrospective correction, proving that obtaining prior distortion map for subsequent retrospective distortion correction is beneficial. The systematic evaluation of distortion using various combinations of sequence-type, acquisition-orientation and receiver-bandwidth in a six-month time span would be a valuable guideline for optimizing sequence for various RT applications.

Functional Activities Detected in the Olfactory Bulb and Associated Olfactory Regions in the Human Brain Using T2-Prepared BOLD Functional MRI at 7T

Olfaction is a fundamental sense that plays a vital role in daily life in humans, and can be altered in neuropsychiatric and neurodegenerative diseases. Blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) using conventional echo-planar-imaging (EPI) based sequences can be challenging in brain regions important for olfactory processing, such as the olfactory bulb (OB) and orbitofrontal cortex, mainly due to the signal dropout and distortion artifacts caused by large susceptibility effects from the sinonasal cavity and temporal bone. To date, few studies have demonstrated successful fMRI in the OB in humans. T2-prepared (T2prep) BOLD fMRI is an alternative approach developed especially for performing fMRI in regions affected by large susceptibility artifacts. The purpose of this technical study is to evaluate T2prep BOLD fMRI for olfactory functional experiments in humans. Olfactory fMRI scans were performed on 7T in 14 healthy participants. T2prep BOLD showed greater sensitivity than GRE EPI BOLD in the OB, orbitofrontal cortex and the temporal pole. Functional activation was detected using T2prep BOLD in the OB and associated olfactory regions. Habituation effects and a bi-phasic pattern of fMRI signal changes during olfactory stimulation were observed in all regions. Both positively and negatively activated regions were observed during olfactory stimulation. These signal characteristics are generally consistent with literature and showed a good intra-subject reproducibility comparable to previous human BOLD fMRI studies. In conclusion, the methodology demonstrated in this study holds promise for future olfactory fMRI studies in the OB and other brain regions that suffer from large susceptibility artifacts.

Regularized joint water-fat separation with B0 map estimation in image space for 2D-navigated interleaved EPI based diffusion MRI

Purpose

To develop a new water–fat separation and B₀ estimation algorithm to effectively suppress the multiple resonances of fat signal in EPI. This is especially relevant for DWI where fat is often a confounding factor.

Methods

Water–fat separation based on chemical‐shift encoding enables robust fat suppression in routine MRI. However, for EPI the different chemical‐shift displacements of the multiple fat resonances along the phase‐encoding direction can be problematic for conventional separation algorithms. This work proposes a suitable model approximation for EPI under B₀ and fat off‐resonance effects, providing a feasible multi‐peak water–fat separation algorithm. Simulations were performed to validate the algorithm. In vivo validation was performed in 6 volunteers, acquiring spin‐echo EPI images in the leg (B₀ homogeneous) and head‐neck (B₀ inhomogeneous) regions, using a TE‐shifted interleaved EPI sequence with/without diffusion sensitization. The results are numerically and statistically compared with voxel‐independent water–fat separation and fat saturation techniques to demonstrate the performance of the proposed algorithm.

Results

The reference separation algorithm without the proposed spatial shift correction caused water–fat ambiguities in simulations and in vivo experiments. Some spectrally selective fat saturation approaches also failed to suppress fat in regions with severe B₀ inhomogeneities. The proposed algorithm was able to achieve improved fat suppression for DWI data and ADC maps in the head–neck and leg regions.

Conclusion

The proposed algorithm shows improved suppression of the multi‐peak fat components in multi‐shot interleaved EPI applications compared to the conventional fat saturation approaches and separation algorithms.

Dual polarity encoded MRI using high bandwidth radiofrequency pulses for robust imaging with large field inhomogeneity

PURPOSE

The ability to use dual polarity encoded MRI with the missing pulse steady-state free precession (MP-SSFP) sequence is demonstrated to perform robust MRI with low radiofrequency (RF) amplitude, where the field is distorted by embedding metallic screws in an agar phantom. Image-based estimation of the 3D ΔB₀ map and image distortion correction is shown to require ~1 minute to perform.

THEORY AND METHODS

Dual polarity encoded MP-SSFP was implemented at 1.5T and used to image agar phantoms with one stainless steel and one titanium screw embedded inside. A multispectral fast spin-echo acquisition was performed for comparison. Self-consistent ΔB₀ estimation is performed iteratively using a 3D B-spline basis, which is compared to the ΔB₀ estimate generated by the multispectral sequence.

RESULTS

Dual polarity encoded MP-SSFP yields image quality similar to the multispectral sequence used with substantially less imaging time, provided the MP-SSFP experimental parameters are chosen well. The multispectral sequence appears to visualize modestly closer in proximity to the metallic screws used, despite the spectral bins covering the same bandwidth as the pulses used in MP-SSFP. However, MP-SSFP avoids ripple artifacts characteristic of the multispectral sequence. The ΔB₀ estimate generated by MP-SSFP is qualitatively similar to that generated by the multispectral sequence but larger in magnitude.

CONCLUSION

Despite longer processing time compared to multispectral imaging, MP-SSFP yields similar image quality with significantly lower acquisition times in the absence of parallel imaging. The work herein demonstrates the ability to perform 3D ΔB₀ estimation and image correction within a reasonable amount of time, ~1 minute.

Contemporary approaches to high-field magnetic resonance imaging with large field inhomogeneity

Despite its importance as a clinical imaging modality, magnetic resonance imaging remains inaccessible to most of the world's population due to its high cost and infrastructure requirements. Substantial effort is underway to develop portable, low-cost systems able to address MRI access inequality and to enable new uses of MRI such as bedside imaging. A key barrier to development of portable MRI systems is increased magnetic field inhomogeneity when using small polarizing magnets, which degrades image quality through distortions and signal dropout. Many approaches address field inhomogeneity by using a low polarizing field, approximately ten to hundreds of milli-Tesla. At low-field, even a large relative field inhomogeneity of several thousand parts-per-million (ppm) results in resonance frequency dispersion of only 1-2 kHz. Under these conditions, with necessarily wide pulse bandwidths, fast spin-echo sequences may be used at low field with negligible subject heating, and a broad range of other available imaging sequences can be implemented. However, high-field MRI, 1.5 T or greater, can provide substantially improved signal-to-noise ratio and image contrast, so that higher spatial resolution, clinical quality images may be acquired in significantly less time than is necessary at low-field. The challenge posed by small, high-field systems is that the relative field inhomogeneity, still thousands of ppm, becomes tens of kilohertz over the imaging volume. This article describes the physical consequences of field inhomogeneity on established gradient- and spin-echo MRI sequences, and suggests ways to reduce signal dropout and image distortion from field inhomogeneity. Finally, the practicality of currently available image contrasts is reviewed when imaging with a high magnetic field with large inhomogeneity.

Susceptibility artifact correction for sub-millimeter fMRI using inverse phase encoding registration and T1 weighted regularization

BACKGROUND

Functional magnetic resonance imaging (fMRI) enables non-invasive examination of both the structure and the function of the human brain. The prevalence of high spatial-resolution (sub-millimeter) fMRI has triggered new research on the intra-cortex, such as cortical columns and cortical layers. At present, echo-planar imaging (EPI) is used exclusively to acquire fMRI data; however, susceptibility artifacts are unavoidable. These distortions are especially severe in high spatial-resolution images and can lead to misrepresentation of brain function in fMRI experiments.

NEW METHOD

This paper presents a new method for correcting susceptibility artifacts by combining a T1-weighted (T_1w) image and inverse phase-encoding (PE) based registration. The latter uses two EPI images acquired using identical sequences but with inverse-PE directions. In the proposed method, the T_1w image is used to regularize the registration, and to select the regularization parameters automatically. The motivation is that the T_1w image is considered to reflect the anatomical structure of the brain.

RESULTS

Our proposed method is evaluated on two sub-millimeter EPI-fMRI datasets, acquired using 3T and 7T scanners. Experiments show that the proposed method provides improved corrections that are well-aligned to the T_1w image.

COMPARISON WITH EXISTING METHODS

The proposed method provides more robust and sharper corrections and runs faster compared with two other state-of-the-art inverse-PE based correction methods, i.e. HySCO and TOPUP.

CONCLUSIONS

The proposed correction method used the T_1w image as a reference in the inverse-PE registration. Results show its promising performance. Our proposed method is timely, as sub-millimeter fMRI has become increasingly popular.

Joint B0 and image estimation integrated with model based reconstruction for field map update and distortion correction in prostate diffusion MRI

In prostate Diffusion Weighted MRI, differences in susceptibility values exist at the interface between the prostate and rectal-air. This can result in off-resonance magnetic field leading to geometric distortions including signal stretching and signal pile-up in the reconstructed images. Using a set of EPI data acquired with blip-up and blip-down phase encoding gradient directions, model based reconstruction has recently been proposed that can correct these distortions by using a B0 field estimated from a separate B0 scan. However, change in the size of the rectal air region across time can occur that can result in a mismatch of the B0 field to the EPI scan. Also, the measured B0 field itself can be erroneous in regions of low Signal to Noise ratio around the prostate rectal air interface. In this work, using a set of single shot EPI data acquired with blip-up and blip-down phase encoding gradient directions, a novel joint model based reconstruction is proposed that can account for changes in the off resonance effects between the B0 and EPI scans. For ten prostate patients, using a measured B0 field as an initial B0 estimate, on a 5-point scale (1-5) image quality scores evaluated by an experienced radiologist, the proposed framework achieved scores of 3.50 ± 0.85 and 3.40 ± 0.51 for b-values of 0 and 500 s/mm2, respectively compared to 3.40 ± 0.70 and 3.30 ± 0.67 for model based reconstruction. The proposed framework is also capable of estimating a distortion corrected EPI image even without an initial B0 field estimate in situations where a separate B0 scan cannot be obtained due to time constraint.

Reducing motion sensitivity in 3D high-resolution T2*-weighted MRI by navigator-based motion and nonlinear magnetic field correction

T₂*-weighted gradient echo (GRE) MRI at high field is uniquely sensitive to the magnetic properties of tissue and allows the study of brain and vascular anatomy at high spatial resolution. However, it is also sensitive to B₀ field changes induced by head motion and physiological processes such as the respiratory cycle. Conventional motion correction techniques do not take these field changes into account, and consequently do not fully recover image quality in T₂*-weighted MRI. Here, a novel approach was developed to address this by monitoring the B₀ field with a volumetric EPI phase navigator. The navigator was acquired at a shorter echo time than that of the (higher resolution) T₂*-weighted GRE imaging data and accelerated with parallel imaging for high temporal resolution. At 4 ​mm isotropic spatial resolution and 0.54 ​s temporal resolution, the accuracy for estimation of rotation and translation was better than 0.2° and 0.1 ​mm, respectively. The 10% and 90% percentiles of B₀ measurement error using the navigator were -1.8 and 1.5 Hz  at 7 T, respectively. A fast retrospective reconstruction algorithm correcting for both motion and nonlinear B₀ changes was also developed. The navigator and reconstruction algorithm were evaluated in correcting motion-corrupted high-resolution T₂*-weighted GRE MRI on healthy human subjects at 7 ​T. Excellent image quality was demonstrated with the proposed correction method.

Calibration-Free B0 Correction of EPI Data Using Structured Low Rank Matrix Recovery

We introduce a structured low rank algorithm for the calibration-free compensation of field inhomogeneity artifacts in echo planar imaging (EPI) MRI data. We acquire the data using two EPI readouts that differ in echo-time. Using time segmentation, we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled Fourier measurements. The temporal profile at each pixel is modeled as a single exponential, which is exploited to fill in the missing entries. We show that the exponential behavior at each pixel, along with the spatial smoothness of the exponential parameters, can be exploited to derive a 3-D annihilation relation in the Fourier domain. This relation translates to a low rank property on a structured multi-fold Toeplitz matrix, whose entries correspond to the measured k-space samples. We introduce a fast two-step algorithm for the completion of the Toeplitz matrix from the available samples. In the first step, we estimate the null space vectors of the Toeplitz matrix using only its fully sampled rows. The null space is then used to estimate the signal subspace, which facilitates the efficient recovery of the time series of images. We finally demonstrate the proposed approach on spherical MR phantom data and human data and show that the artifacts are significantly reduced.

Model-based reconstruction framework for correction of signal pile-up and geometric distortions in prostate diffusion MRI

PURPOSE

Prostate diffusion-weighted MRI scans can suffer from geometric distortions, signal pileup, and signal dropout attributed to differences in tissue susceptibility values at the interface between the prostate and rectal air. The aim of this work is to present and validate a novel model based reconstruction method that can correct for these distortions.

METHODS

In regions of severe signal pileup, standard techniques for distortion correction have difficulty recovering the underlying true signal. Furthermore, because of drifts and inaccuracies in the determination of center frequency, echo planar imaging (EPI) scans can be shifted in the phase-encoding direction. In this work, using a B0 field map and a set of EPI data acquired with blip-up and blip-down phase encoding gradients, we model the distortion correction problem linking the distortion-free image to the acquired raw corrupted k-space data and solve it in a manner analogous to the sensitivity encoding method. Both a quantitative and qualitative assessment of the proposed method is performed in vivo in 10 patients.

RESULTS

Without distortion correction, mean Dice similarity scores between a reference T2W and the uncorrected EPI images were 0.64 and 0.60 for b-values of 0 and 500 s/mm2 , respectively. Compared to the Topup (distortion correction method commonly used for neuro imaging), the proposed method achieved Dice scores (0.87 and 0.85 versus 0.82 and 0.80) and better qualitative results in patients where signal pileup was present because of high rectal gas residue.

CONCLUSION

Model-based reconstruction can be used for distortion correction in prostate diffusion MRI.

Reducing distortions in echo-planar breast imaging at ultrahigh field with high-resolution off-resonance maps

PURPOSE

DWI is a promising modality in breast MRI, but its clinical acceptance is slow. Analysis of DWI is hampered by geometric distortion artifacts, which are caused by off-resonant spins in combination with the low phase-encoding bandwidth of the EPI sequence used. Existing correction methods assume smooth off-resonance fields, which we show to be invalid in the human breast, where high discontinuities arise at tissue interfaces.

METHODS

We developed a distortion correction method that incorporates high-resolution off-resonance maps to better solve for severe distortions at tissue interfaces. The method was evaluated quantitatively both ex vivo in a porcine tissue phantom and in vivo in 5 healthy volunteers. The added value of high-resolution off-resonance maps was tested using a Wilcoxon signed rank test comparing the quantitative results obtained with a low-resolution off-resonance map with those obtained with a high-resolution map.

RESULTS

Distortion correction using low-resolution off-resonance maps corrected most of the distortions, as expected. Still, all quantitative comparison metrics showed increased conformity between the corrected EPI images and a high-bandwidth reference scan for both the ex vivo and in vivo experiments. All metrics showed a significant improvement when a high-resolution off-resonance map was used (P < 0.05), in particular at tissue boundaries.

CONCLUSION

The use of off-resonance maps of a resolution higher than EPI scans significantly improves upon existing distortion correction techniques, specifically by superior correction at glandular tissue boundaries.

Susceptibility-induced distortion that varies due to motion: Correction in diffusion MR without acquiring additional data

Because of their low bandwidth in the phase-encode (PE) direction, the susceptibility-induced off-resonance field causes distortions in echo planar imaging (EPI) images. It is therefore crucial to correct for susceptibility-induced distortions when performing diffusion studies using EPI. The susceptibility-induced field is caused by the object (head) disrupting the field and it is typically assumed that it remains constant within a framework defined by the object, (i.e. it follows the object as it moves in the scanner).

However, this is only approximately true. When a non-spherical object rotates around an axis other than that parallel with the magnetic flux (the z-axis) it changes the way it disrupts the field, leading to different distortions. Hence, if using a single field to correct for distortions there will be residual distortions in the volumes where the object orientation is substantially different to that when the field was measured.

In this paper we present a post-processing method for estimating the field as it changes with motion during the course of an experiment. It only requires a single measured field and knowledge of the orientation of the subject when that field was acquired. The volume-to-volume changes of the field as a consequence of subject movement are estimated directly from the diffusion data without the need for any additional or special acquisitions. It uses a generative model that predicts how each volume would look predicated on field change and inverts that model to yield an estimate of the field changes. It has been validated on both simulations and experimental data. The results show that we are able to track the field with high accuracy and that we are able to correct the data for the adverse effects of the changing field.

Generalized image deconvolution by exploiting the transmission matrix of an optical imaging system

Intact optical information of an object delivered through an imaging system is deteriorated by imperfect optical elements and unwanted defects. Image deconvolution has been widely exploited as a recovery technique due to its practical feasibility, and operates by assuming linear shift-invariant property of the imaging system. However, shift invariance does not rigorously hold in all imaging situations and is not a necessary condition for solving an inverse problem of light propagation. Several improved deconvolution techniques exploiting spatially variant point spread functions have been proposed in previous studies. However, the full characterization of an optical imaging system for compensating aberrations has not been considered. Here, we present a generalized method to solve the linear inverse problem of coherent light propagations without any regularization method or constraint on shift invariance by fully measuring the transmission matrix of the imaging system. Our results show that severe aberrations produced by a tilted lens or an inserted disordered layer can be corrected properly only by the proposed generalized image deconvolution. This work generalizes the theory of image deconvolution, and enables distortion-free imaging under general imaging condition.

Susceptibility-induced distortion correction in hyperpolarized echo planar imaging

Purpose

Echo planar imaging is an attractive rapid imaging readout that can image hyperpolarized compounds in vivo. By alternating the sign of the phase encoding gradient waveform, spatial offsets arising from uncertain frequency shifts can be determined. We show here that blip‐reversed echo planar imaging can also be used to correct for susceptibility and B₀ inhomogeneity effects that would otherwise produce image‐domain distortion in the heart.

Methods

Previously acquired blip‐reversed cardiac 3D‐Spectral‐Spatial echo planar imaging volumetric timecourses of hyperpolarized [1‐¹³C]pyruvate were distortion corrected by a deformation field estimated by reconstructing signal‐to‐noise ratio (SNR)‐weighted progressively subsampled temporally summed images of each metabolite.

Results

Reconstructing blip‐reversed data as proposed produced volumetric timecourses that overlaid with proton reference images more consistently than without such corrections.

Conclusion

The method proposed may form an attractive method to correct for image‐domain distortions in hyperpolarized echo planar imaging experiments. Magn Reson Med 79:2135–2141, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

High slew-rate head-only gradient for improving distortion in echo planar imaging: Preliminary experience

PURPOSE

To investigate the effects on echo planar imaging (EPI) distortion of using high gradient slew rates (SR) of up to 700 T/m/s for in vivo human brain imaging, with a dedicated, head-only gradient coil.

MATERIALS AND METHODS

Simulation studies were first performed to determine the expected echo spacing and distortion reduction in EPI. A head gradient of 42-cm inner diameter and with asymmetric transverse coils was then installed in a whole-body, conventional 3T magnetic resonance imaging (MRI) system. Human subject imaging was performed on five subjects to determine the effects of EPI on echo spacing and signal dropout at various gradient slew rates. The feasibility of whole-brain imaging at 1.5 mm-isotropic spatial resolution was demonstrated with gradient-echo and spin-echo diffusion-weighted EPI.

RESULTS

As compared to a whole-body gradient coil, the EPI echo spacing in the head-only gradient coil was reduced by 48%. Simulation and in vivo results, respectively, showed up to 25-26% and 19% improvement in signal dropout. Whole-brain imaging with EPI at 1.5 mm spatial resolution provided good whole-brain coverage, spatial linearity, and low spatial distortion effects.

CONCLUSION

Our results of human brain imaging with EPI using the compact head gradient coil at slew rates higher than in conventional whole-body MR systems demonstrate substantially improved image distortion, and point to a potential for benefits to non-EPI pulse sequences. J. Magn. Reson. Imaging 2016;44:653-664.

Co-registration and distortion correction of diffusion and anatomical images based on inverse contrast normalization

Diffusion MRI provides quantitative information about microstructural properties which can be useful in neuroimaging studies of the human brain. Echo planar imaging (EPI) sequences, which are frequently used for acquisition of diffusion images, are sensitive to inhomogeneities in the primary magnetic (B0) field that cause localized distortions in the reconstructed images. We describe and evaluate a new method for correction of susceptibility-induced distortion in diffusion images in the absence of an accurate B0 fieldmap. In our method, the distortion field is estimated using a constrained non-rigid registration between an undistorted T1-weighted anatomical image and one of the distorted EPI images from diffusion acquisition. Our registration framework is based on a new approach, INVERSION (Inverse contrast Normalization for VERy Simple registratION), which exploits the inverted contrast relationship between T1- and T2-weighted brain images to define a simple and robust similarity measure. We also describe how INVERSION can be used for rigid alignment of diffusion images and T1-weighted anatomical images. Our approach is evaluated with multiple in vivo datasets acquired with different acquisition parameters. Compared to other methods, INVERSION shows robust and consistent performance in rigid registration and shows improved alignment of diffusion and anatomical images relative to normalized mutual information for non-rigid distortion correction.

Distortion correction in EPI using an extended PSF method with a reversed phase gradient approach

In echo-planar imaging (EPI), such as commonly used for functional MRI (fMRI) and diffusion-tensor imaging (DTI), compressed distortion is a more difficult challenge than local stretching as spatial information can be lost in strongly compressed areas. In addition, the effects are more severe at ultra-high field (UHF) such as 7T due to increased field inhomogeneity. To resolve this problem, two EPIs with opposite phase-encoding (PE) polarity were acquired and combined after distortion correction. For distortion correction, a point spread function (PSF) mapping method was chosen due to its high correction accuracy and extended to perform distortion correction of both EPIs with opposite PE polarity thus reducing the PSF reference scan time. Because the amount of spatial information differs between the opposite PE datasets, the method was further extended to incorporate a weighted combination of the two distortion-corrected images to maximize the spatial information content of a final corrected image. The correction accuracy of the proposed method was evaluated in distortion-corrected data using both forward and reverse phase-encoded PSF reference data and compared with the reversed gradient approaches suggested previously. Further we demonstrate that the extended PSF method with an improved weighted combination can recover local distortions and spatial information loss and be applied successfully not only to spin-echo EPI, but also to gradient-echo EPIs acquired with both PE directions to perform geometrically accurate image reconstruction.

Sparse-representation-based direct minimum L (p) -norm algorithm for MRI phase unwrapping

A sparse-representation-based direct minimum L^p-norm algorithm is proposed for a two-dimensional MRI phase unwrapping. First, the algorithm converts the weighted-L^p-norm-minimization-based phase unwrapping problem into a linear system problem whose system (coefficient) matrix is a large, symmetric one. Then, the coefficient-matrix is represented in the sparse structure. Finally, standard direct solvers are employed to solve this linear system. Several wrapped phase datasets, including simulated and MR data, were used to evaluate this algorithm's performance. The results demonstrated that the proposed algorithm for unwrapping MRI phase data is reliable and robust.

Improved B0 -distortion correction in diffusion MRI using interlaced q-space sampling and constrained reconstruction

PURPOSE

To enable high-quality correction of susceptibility-induced geometric distortion artifacts in diffusion magnetic resonance imaging (MRI) images without increasing scan time.

THEORY AND METHODS

A new method for distortion correction is proposed based on subsampling a generalized version of the state-of-the-art reversed-gradient distortion correction method. Rather than acquire each q-space sample multiple times with different distortions (as in the conventional reversed-gradient method), we sample each q-space point once with an interlaced sampling scheme that measures different distortions at different q-space locations. Distortion correction is achieved using a novel constrained reconstruction formulation that leverages the smoothness of diffusion data in q-space.

RESULTS

The effectiveness of the proposed method is demonstrated with simulated and in vivo diffusion MRI data. The proposed method is substantially faster than the reversed-gradient method, and can also provide smaller intensity errors in the corrected images and smaller errors in derived quantitative diffusion parameters.

CONCLUSION

The proposed method enables state-of-the-art distortion correction performance without increasing data acquisition time.

Phase stability in fMRI time series: effect of noise regression, off-resonance correction and spatial filtering techniques

Although the majority of fMRI studies exploit magnitude changes only, there is an increasing interest regarding the potential additive information conveyed by the phase signal. This integrated part of the complex number furnished by the MR scanners can also be used for exploring direct detection of neuronal activity and for thermography. Few studies have explicitly addressed the issue of the available signal stability in the context of phase time-series, and therefore we explored the spatial pattern of frequency specific phase fluctuations, and evaluated the effect of physiological noise components (heart beat and respiration) on the phase signal. Three categories of retrospective noise reduction techniques were explored and the temporal signal stability was evaluated in terms of a physiologic noise model, for seven fMRI measurement protocols in eight healthy subjects at 3T, for segmented CSF, gray and white matter voxels. We confirmed that for most processing methods, an efficient use of the phase information is hampered by the fact that noise from physiological and instrumental sources contributes significantly more to the phase than to the magnitude instability. Noise regression based on the phase evolution of the central k-space point, RETROICOR, or an orthonormalized combination of these were able to reduce their impact, but without bringing phase stability down to levels expected from the magnitude signal. Similar results were obtained after targeted removal of scan-to-scan variations in the bulk magnetic field by the dynamic off-resonance in k-space (DORK) method and by the temporal off-resonance alignment of single-echo time series technique (TOAST). We found that spatial high-pass filtering was necessary, and in vivo a Gaussian filter width of 20mm was sufficient to suppress physiological noise and bring the phase fluctuations to magnitude levels. Stronger filters brought the fluctuations down to levels dictated by thermal noise contributions, and for 62.5mm(3) voxels the phase stability was as low as 5 mrad (0.27°). In conditions of low SNR(o) and high temporal sampling rate (short TR); we achieved an upper bound for the phase instabilities at 0.0017 ppm, which is close to the dHb contribution to the GM/WM phase contrast.

A joint acquisition-reconstruction paradigm for correcting inhomogeneity artifacts in MR echo planar imaging

One of the main sources of signal degradation in rapid MR acquisitions, such as Echo Planar Imaging (EPI), is magnetic field variations caused by field inhomogeneities and susceptibility gradients. If unaccounted for during the reconstruction process, this spatially-varying field can cause severe image artifacts. In this paper, we show that correcting for the resulting degradations can be formulated as a blind image deconvolution problem. We propose a novel joint acquisition-processing paradigm to solve this problem. We describe a practical implementation of this paradigm using a multi-image acquisition strategy and a corresponding joint estimation-reconstruction algorithm. The estimation step computes the spatial distribution of the field maps, while the reconstruction step yields a Minimum Mean Squared Error (MMSE) estimate of the imaged slice. Our simulations show that this proposed joint acquisition-reconstruction method is robust and efficient, offering factors of improvement in the quality of the reconstructed image as compared to other traditional methods.

Removal of olefinic fat chemical shift artifact in diffusion MRI

Diffusion-weighted (DW) MRI has emerged as a key tool for assessing the microstructure of tissues in healthy and diseased states. Because of its rapid acquisition speed and insensitivity to motion, single-shot echo-planar imaging is the most common DW imaging technique. However, the presence of fat signal can severely affect DW-echo planar imaging acquisitions because of the chemical shift artifact. Fat suppression is usually achieved through some form of chemical shift-based fat saturation. Such methods effectively suppress the signal originating from aliphatic fat protons, but fail to suppress the signal from olefinic protons. Olefinic fat signal may result in significant distortions in the DW images, which bias the subsequently estimated diffusion parameters. This article introduces a method for removing olefinic fat signal from DW images, based on an echo time-shifted acquisition. The method is developed and analyzed specifically in the context of single-shot DW-echo-planar imaging, where image phase is generally unreliable. The proposed method is tested with phantom and in vivo datasets, and compared with a standard acquisition to demonstrate its performance.

Correction for susceptibility-induced distortion in echo-planar imaging using field maps and model-based point spread function

Susceptibility-induced distortion is one of the major artifacts in echo-planar imaging (EPI), and many solutions have been proposed for the problem, including the Fourier method and the point spread function (PSF) method. In this paper, a framework unifying both methods is presented. Under this framework, a model-based PSF method is proposed in which the PSF of the source object is modeled along with a single field map measured by TE-offset reference scans. EPI images of a phantom and a healthy human subject were acquired, and the results of distortion correction by the Fourier method, linear interpolation method, and the model-based PSF method were compared. The results showed that the model-based PSF method could correct for geometric distortion and signal intensity distortion satisfactorily, avoiding the rippling artifact shown in the Fourier method. In conclusion, the proposed framework gave us an overall picture of how different correction methods work. The model-based PSF method, which required fewer reference scans and less computational load, was more clinically feasible than other methods.

A new distortion model for strong inhomogeneity problems in echo-planar MRI

This paper proposes a new distortion model for strong inhomogeneity problems in echo planar imaging (EPI). Fast imaging sequences in magnetic resonance imaging (MRI), such as EPI, are very important in applications where temporal resolution or short total acquisition time is essential. Unfortunately, fast imaging sequences are very sensitive to variations in the homogeneity of the main magnetic field. The inhomogeneity leads to geometrical distortions and intensity changes in the image reconstructed via fast Fourier transform. Also, under strong inhomogeneity, the accelerated intravoxel dephase may overly attenuate signals coming from regions with higher inhomogeneity variations. Moreover, coarse discretization schemes for the inhomogeneity are not able to cope with this problem, producing discretization artifacts when large inhomogeneity variations occur. Most of the existing models do not attempt to solve this problem. In this paper, we propose a modification of the discrete distortion model to incorporate the effects of the intravoxel inhomogeneity and to minimize the discretization artifacts. As a result, these problems are significantly reduced. Extensive experiments are shown to demonstrate the achieved improvements. Also, the performance of the new model is evaluated for conjugate phase, least squares method (minimized iteratively using conjugated gradients), and regularized methods (using a total variation penalty).

Improving robustness and reliability of phase-sensitive fMRI analysis using temporal off-resonance alignment of single-echo timeseries (TOAST)

Echo Planar Imaging (EPI), often utilized in functional MRI (fMRI) experiments, is well known for its vulnerability to inconsistencies in the static magnetic field (B(0)). Correction for these field inhomogeneities usually involves measuring the magnetic field at a single time point, and using this static information to correct a series of images collected over the course of one or multiple experiments. However, common phenomena, such as respiration and motion, change the characteristics of the B(0) field homogeneity in a time-dependent and often unpredictable manner, rendering previous field measurements invalid. The effects of these changes are particularly large in the image phase, due to its direct and sensitive relationship to the magnetic field, and methods utilizing complex information can suffer enormously. This dependence can be exploited to estimate the temporal dynamics of the B(0) field. Use of this information to correct fMRI data can provide more effective motion correction, reduce temporal "noise," and can substantially restore statistically significant power to complex fMRI data analysis. All of the necessary information is embedded in complex EPI images, and results indicate this is a robust way to improve the quality of fMRI data, especially when used with complex analysis.

Spin saturation artifact correction using slice-to-volume registration motion estimates for fMRI time series

Evaluation of functional magnetic resonance imaging (fMRI) as a reliable clinical imaging tool requires accurate assessment and correction of head motion artifacts. As the correction of bulk head motion is vital, the loss of signal strength from the confounding effect of head motion on spin magnetization may be an additional factor in activation analysis error. This study focuses on the evaluation and correction of the spin saturation artifact that occurs when parts of adjacent slices are selected due to changing head positions in single-shot multislice acquisitions. As a consequence of head movement, the acquired slices constituting a fMRI volume are no longer parallel to each other and the spin magnetization in fMRI voxels becomes dependent on head motion history. Motion corrections applying the same rigid motion estimates to all the slices in a volume may not be a reasonable approximation in cases where the magnitude of head motion exceeds a subvoxel range. For realistic ranges of motion in fMRI, an accurate estimate of rigid motion parameters for each echo planar imaging (EPI) slice is essential to correctly register voxel intensities. Previously we have implemented the map-slice-to-volume (MSV) motion correction method that maps each slice in a time series onto a reference anatomical volume, which proved to be effective in improving activation detection. To correctly evaluate the motion dependence of spin magnetization, each voxel is tracked with movement history that is available from MSV motion estimates. Relatively low in resolution, EPI voxels are composed of varying mixtures of white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF) and variations in the tissue composition give rise to voxel intensities that are functions of tissue T1 properties. We have developed a weighted-average spin saturation (WASS) correction method that can handle full rigid motion and account for the melange of different brain tissue isochromats at each EPI voxel location. We evaluated the effect of spin saturation artifacts and the performance of the WASS correction using simulated fMRI time series synthesized with known true activation, motion, and the associated spin saturation artifact. Two different ranges of head rotations, [-5,5] and [-2,2] deg, were introduced and the effect of the spin saturation artifact was quantified to show 18% and 13% reduction in activation detection rate, respectively. Following the MSV motion and WASS correction, results indicate that WASS correction can improve activation detection by 17% relative to MSV only correction.

Hybrid two-dimensional navigator correction: a new technique to suppress respiratory-induced physiological noise in multi-shot echo-planar functional MRI

A troublesome source of physiological noise in functional magnetic resonance imaging (fMRI) is due to the spatio-temporal modulation of the magnetic field in the brain caused by normal subject respiration. fMRI data acquired using echo-planar imaging are very sensitive to these respiratory-induced frequency offsets, which cause significant geometric distortions in images. Because these effects increase with main magnetic field, they can nullify the gains in statistical power expected by the use of higher magnetic fields. As a study of existing navigator correction techniques for echo-planar fMRI has shown that further improvements can be made in the suppression of respiratory-induced physiological noise, a new hybrid two-dimensional (2D) navigator is proposed. Using a priori knowledge of the slow spatial variations of these induced frequency offsets, 2D field maps are constructed for each shot using spatial frequencies between +/-0.5 cm(-1) in k-space. For multi-shot fMRI experiments, we estimate that the improvement of hybrid 2D navigator correction over the best performance of one-dimensional navigator echo correction translates into a 15% increase in the volume of activation, 6% and 10% increases in the maximum and average t-statistics, respectively, for regions with high t-statistics, and 71% and 56% increases in the maximum and average t-statistics, respectively, in regions with low t-statistics due to contamination by residual physiological noise.

Zero and first-order phase shift correction for field map estimation with dual-echo GRE using bipolar gradients

A simple phase error correction technique used for field map estimation with a generally available dual-echo gradient-echo (GRE) sequence is presented. Magnetic field inhomogeneity maps estimated using two separate GRE volume acquisitions at different echo times are prone to dynamic motion errors between acquisitions. By using the dual-echo sequence, the data are collected during two back-to-back readout gradients in opposite polarity after a single radio frequency pulse, and interecho motion artifacts and alignment errors in field map estimation can be factored out. Residual phase error from the asymmetric readout pulses is modeled as an affine term in the readout direction. Results from phantom and human data suggest that the first-order phase correction term stays constant over time and, hence, can be applied to different data acquired with the same protocol over time. The zero-order phase correction term may change with time and is estimated empirically for different scans.

Quantitative investigation of connections of the prefrontal cortex in the human and macaque using probabilistic diffusion tractography

The functions of prefrontal cortex (PFC) areas are constrained by their anatomical connections. There is little quantitative information about human PFC connections, and, instead, our knowledge of primate PFC connections is derived from tracing studies in macaques. The connections of subcortical areas, in which white matter penetration and hence diffusion anisotropy are greatest, can be studied with diffusion-weighted imaging (DWI) tractography. We therefore used DWI tractography in four macaque and 10 human hemispheres to compare the connections of PFC regions with nine subcortical regions, including several fascicles and several subcortical nuclei. A distinct connection pattern was identified for each PFC and each subcortical region. Because some of the fascicles contained connections with posterior cortical areas, it was also possible to draw inferences about PFC connection patterns with posterior cortical areas. Notably, it was possible to identify similar circuits centered on comparable PFC regions in both species; PFC regions probably engage in similar patterns of regionally specific functional interaction with other brain areas in both species. In the case of one area traditionally assigned to the human PFC, the pars opercularis, the distribution of connections was not reminiscent of any macaque PFC region but, instead, resembled the pattern for macaque ventral premotor area. Some limitations to the DWI approach were apparent; the high diffusion anisotropy in the corpus callosum made it difficult to compare connection probability values in the adjacent cingulate region.

76-space analysis of grey matter diffusivity: methods and applications

Diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI) allow in vivo investigation of molecular motion of tissue water at a microscopic level in cerebral gray matter (GM) and white matter (WM). DWI/DTI measure of water diffusion has been proven to be invaluable for the study of many neurodegenerative diseases (e.g., Alzheimer's disease and Creutzfeldt-Jakob disease) that predominantly involve GM. Thus, quantitative analysis of GM diffusivity is of scientific interest and is promised to have a clinical impact on the investigation of normal brain aging and neuropathology. In this paper, we propose an automated framework for analysis of GM diffusivity in 76 standard anatomic subdivisions of gray matter to facilitate studies of neurodegenerative and other gray matter neurological diseases. The computational framework includes three enabling technologies: (1) automatic parcellation of structural MRI GM into 76 precisely defined neuroanatomic subregions ("76-space"), (2) automated segmentation of GM, WM and CSF based on DTI data, and (3) automatic measurement of the average apparent diffusion coefficient (ADC) in each segmented GM subregion. We evaluate and validate this computational framework for 76-space GM diffusivity analysis using data from normal volunteers and from patients with Creutzfeldt-Jakob disease.

The evolution of prefrontal inputs to the cortico-pontine system: diffusion imaging evidence from Macaque monkeys and humans

The cortico-ponto-cerebellar system is one of the largest projection systems in the primate brain, but in the human brain the nature of the information processing in this system remains elusive. Determining the areas of the cerebral cortex which contribute projections to this system will allow us to better understand information processing within it. Information from the cerebral cortex is conveyed to the cerebellum by topographically arranged fibres in the cerebral peduncle - an important fibre system in which all cortical outputs spatially converge on their way to the cerebellum via the pontine nuclei. Little is known of their anatomical organization in the human brain. New in vivo diffusion imaging and probabilistic tractography methods now offer a way in which input tracts in the cerebral peduncle can be characterized in detail. Here we use these methods to contrast their organization in humans and macaque monkeys. We confirm the dominant contribution of the cortical motor areas to the macaque monkey cerebral peduncle. However, we also present novel anatomical evidence for a relatively large prefrontal contribution to the human cortico-ponto-cerebellar system in the cerebral peduncle. These findings suggest the selective evolution of prefrontal inputs to the human cortico-ponto-cerebellar system.

Single-shot compensation of image distortions and BOLD contrast optimization using multi-echo EPI for real-time fMRI

Functional magnetic resonance imaging (fMRI) is most commonly based on echo-planar imaging (EPI). With higher field strengths, gradient performance, and computational power, real-time fMRI has become feasible; that is, brain activation can be monitored during the ongoing scan. However, EPI suffers from geometric distortions due to inhomogeneities of the magnetic field, especially close to air-tissue interfaces. Thus, functional activations might be mislocalized and assigned to the wrong anatomical structures. Several techniques have been reported which reduce geometric distortions, for example, mapping of the static magnetic field B(0) or the point spread function for all voxels. Yet these techniques require additional reference scans and in some cases extensive computational time. Moreover, only static field inhomogeneities can be corrected, because the correction is based on a static reference scan. We present an approach which allows for simultaneous acquisition and distortion correction of a functional image without a reference scan. The technique is based on a modified multi-echo EPI data acquisition scheme using a phase-encoding (PE) gradient with alternating polarity. The images exhibit opposite distortions due to the inverted PE gradient. After adjusting the contrast of the images acquired at different echo times, this information is used for the distortion correction. We present the theory, implementation, and applications of this single-shot distortion correction. Significant reduction in geometric distortion is shown both for phantom images and human fMRI data. Moreover, sensitivity to the blood oxygen level-dependent (BOLD) effect is increased by weighted summation of the undistorted images.

Iterative RF pulse design for multidimensional, small-tip-angle selective excitation

The excitation k-space perspective on small-tip-angle selective excitation has facilitated RF pulse designs in a range of MR applications. In this paper, k-space-based design of multidimensional RF pulses is formulated as a quadratic optimization problem, and solved efficiently by the iterative conjugate-gradient (CG) algorithm. Compared to conventional design approaches, such as the conjugate-phase (CP) method, the new design approach is beneficial in several regards. It generally produces more accurate excitation patterns. The improvement is particularly significant when k-space is undersampled, and it can potentially shorten pulse lengths. A prominent improvement in accuracy is also observed when large off-resonance gradients are present. A further boost in excitation accuracy can be accomplished in regions of interest (ROIs) if they are specified together with "don't-care" regions. The density compensation function (DCF) is no longer required. In addition, regularization techniques allow control over integrated and peak pulse power.

The effects of geometric distortion correction on motion realignment in fMRI

RATIONALE AND OBJECTIVES

Subject motion is well recognized as a significant impediment to resolution and sensitivity in functional magnetic resonance imaging (fMRI). A parallel confounder to fMRI data quality is geometric image distortion, particularly at high field strengths, due to susceptibility-induced magnetic field inhomogeneity. Consequently, many high-field echo-planar imaging methods incorporate a post-processing distortion correction by acquiring a field map of the sample prior to the fMRI measurement. However, field mapping methods impose a spatial mask on the data, since field information is only obtainable from regions with adequate signal-to-noise ratio (SNR). This masking, when applied to subsequent images in the fMRI time series, can clip the effects of motion, resulting in inaccurate estimation and correction of motion-based changes in the images.

MATERIALS AND METHODS

The effects of geometric distortion correction on automated realignment (motion correction) of fMRI data are investigated from data acquired at 4 T. The results of image realignment with and without prior application of distortion correction are compared, using the estimated motion parameters and overall image realignment as metrics.

RESULTS

The application of field-map-based distortion correction prior to image realignment reduces the amount of motion detected by a standard motion correction algorithm. Moreover, motion correction applied before distortion correction is shown to result in superior realignment of motion-correction images.

CONCLUSION

It is preferable to perform motion realignment prior to correcting for geometric distortion.

How to correct susceptibility distortions in spin-echo echo-planar images: application to diffusion tensor imaging

Diffusion tensor imaging is often performed by acquiring a series of diffusion-weighted spin-echo echo-planar images with different direction diffusion gradients. A problem of echo-planar images is the geometrical distortions that obtain near junctions between tissues of differing magnetic susceptibility. This results in distorted diffusion-tensor maps. To resolve this we suggest acquiring two images for each diffusion gradient; one with bottom-up and one with top-down traversal of k-space in the phase-encode direction. This achieves the simultaneous goals of providing information on the underlying displacement field and intensity maps with adequate spatial sampling density even in distorted areas. The resulting DT maps exhibit considerably higher geometric fidelity, as assessed by comparison to an image volume acquired using a conventional 3D MR technique.

Fast, iterative image reconstruction for MRI in the presence of field inhomogeneities

In magnetic resonance imaging, magnetic field inhomogeneities cause distortions in images that are reconstructed by conventional fast Fourier trasform (FFT) methods. Several noniterative image reconstruction methods are used currently to compensate for field inhomogeneities, but these methods assume that the field map that characterizes the off-resonance frequencies is spatially smooth. Recently, iterative methods have been proposed that can circumvent this assumption and provide improved compensation for off-resonance effects. However, straightforward implementations of such iterative methods suffer from inconveniently long computation times. This paper describes a tool for accelerating iterative reconstruction of field-corrected MR images: a novel time-segmented approximation to the MR signal equation. We use a min-max formulation to derive the temporal interpolator. Speedups of around 60 were achieved by combining this temporal interpolator with a nonuniform fast Fourier transform with normalized root mean squared approximation errors of 0.07%. The proposed method provides fast, accurate, field-corrected image reconstruction even when the field map is not smooth.

An evaluation of the use of magnetic field maps to undistort echo-planar images

When a head is placed in an MRI scanner, differences between the magnetic susceptibility of tissue, bone, and air distort the magnetic field. While some of the resulting inhomogeneity can be corrected by the shimming process, much of it cannot, and this causes distortion (sometimes referred to as geometric distortion) of echo-planar images (EPIs). One strategy for the correction of distortion is to acquire a map of the magnetic field achieved in each subject and then to use this to undistort their EPIs after reconstruction (). Here, we present five experiments to evaluate the application of such a strategy on data from a 3-T scanner. We show that after undistortion, the shape of EPIs is more similar to the true shape of the brain, and we investigate the effect of head movement on the efficacy of undistortion. If undistortion was applied first, it was found that less nonlinear warping was required to transform EPIs into a standard space, particularly in the phase-encode direction. We show that if SPM 99 normalization is used to perform a nonlinear warp to standard space, the prior application of undistortion increases the statistical power of group studies with motor and auditory tasks. We show that this increase in power is due to an increase in the overlap of activation of different subjects. Finally, we evaluate where in the brain undistorting EPIs might be expected to have the greatesteffect, in terms both of mislocalization of activationand of a reduction in power. Overall, undistorting EPIs using field maps has proved extremely successful, improving the anatomical localization of activation and increasing statistical power.

Fast, automated, N-dimensional phase-unwrapping algorithm

This work investigates the general problem of phase unwrapping for arbitrary N-dimensional phase maps. A cost function-based approach is outlined that leads to an integer programming problem. To solve this problem, a best-pair-first region merging approach is adopted as the optimization method. The algorithm was implemented and tested with 3D MRI medical data for venogram studies, as well as for fMRI applications in EPI unwarping and rapid, automated shimming.

New robust 3-D phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images

The phase, as well as the magnitude, of MRI images can carry useful information. It may be used to encode flow or temperature, or to map the magnetic field for the undistorting of EPIs and automated shimming. In all cases, we measure the extra spin given to nuclei. Unfortunately, we can only measure the final phase of the spins: the rotation is wrapped into the range [-pi, +pi], and to obtain a measure of the parameter of interest the missing multiples of 2pi must be replaced--a process known as phase unwrapping. While simple in principle, standard phase unwrapping algorithms fail catastrophically in the presence of even small amounts of noise. Here we present a new algorithm for robust three-dimensional phase unwrapping, in which unwrapping is guided, so that it initially works on less noisy regions. We test the algorithm on simulated phase data, and on maps of magnetic field, which were then used to successfully undistort EPI images. The unwrapping algorithm could be directly applied to other kinds of phase data.

Current awareness in NMR in biomedicine

In order to keep subscribers up-to-date with the latest developments in their field, John Wiley & Sons are providing a current awareness service in each issue of the journal. The bibliography contains newly published material in the field of NMR in biomedicine. Each bibliography is divided into 9 sections: 1 Books, Reviews ' Symposia; 2 General; 3 Technology; 4 Brain and Nerves; 5 Neuropathology; 6 Cancer; 7 Cardiac, Vascular and Respiratory Systems; 8 Liver, Kidney and Other Organs; 9 Muscle and Orthopaedic. Within each section, articles are listed in alphabetical order with respect to author. If, in the preceding period, no publications are located relevant to any one of these headings, that section will be omitted.