Simultaneous motion and distortion correction using dual-echo diffusion weighted MRI

Abstract

Background and Purpose:

Geometric distortions resulting from large pose changes reduce the accuracy of motion measurements and interfere with the ability to generate artifact free information. Our goal is to develop an algorithm and pulse sequence to enable motion-compensated, geometric distortion compensated diffusion-weighted MRI, and to evaluate its efficacy in correcting for the field inhomogeneity and position changes, induced by large and frequent head motions.

Methods:

Dual echo planar imaging (EPI) with a blip-reversed phase encoding distortion correction technique was evaluated in 5 volunteers in two separate experiments and compared with static field map distortion correction. In the first experiment, dual-echo EPI images were acquired in two head positions designed to induce a large field inhomogeneity change. A field map and a distortion-free structural image were acquired at each position to assess the ability of dual-echo EPI to generate reliable field maps and enable geometric distortion correction in both positions. In the second experiment, volunteers were asked to move to multiple random positions during a diffusion scan. Images were reconstructed using the dual-echo correction and a slice-to-volume (SVR) registration algorithm. The accuracy of SVR motion estimates were compared to externally measured ground truth motion parameters.

Results:

Our results show that dual-echo EPI can produce slice-level field maps with comparable quality to field maps generated by the reference gold standard method. We also show that slice-level distortion correction improves the accuracy of SVR algorithms as slices acquired at different orientations have different levels of distortion, which can create errors in the registration process.

Conclusions:

Dual-echo acquisitions with blip-reversed phase encoding can be used to generate slice-level distortion free images, which is critical for motion-robust slice to volume registration. The distortion corrected images not only result in better motion estimates, they also enable a more accurate final diffusion image reconstruction.

INTRODUCTION

Diffusion weighted MRI (DW-MRI)¹ is sensitive to the apparent diffusion coefficient of brain tissue, which has become an important contributor to the study of microstructure and neural circuits. It is commonly used in neuroscience research as it provides a unique perspective on tissue diffusivity² and white matter tracts³. DW-MRI is used clinically for the assessment of stroke⁴, and for planning a surgical trajectory to a target of resection⁵, in order to avoid critical neural circuits that may be at risk in neurosurgery. It has an emerging role in the assessment of neurological disorders such as epilepsy, multiple sclerosis, Parkinson's and Alzheimer's disease^6-8. DW-MRI has provided new insight in to the maturation of the brain during early development, including fetal studies^9-13 and newborn studies^14-15.

However, as DW-MRI relies on encoding the amount and direction of the movement of water molecules, it is highly sensitive to involuntary patient motion. In a cohort of young children, it has been shown that even small differences in the amount of head motion is enough to yield false positive findings of differences in anisotropy and diffusivity between groups¹⁶. This phenomenon is even more pronounced when imaging newborns and fetuses, as these populations usually exhibit large and frequent motion. The effect of motion can be mitigated using sedation or anesthesia; however, while sedation and anesthesia can be carried out safely, they both create a risk of adverse events including acute respiratory or cardiac dysfunction, and are associated with dramatically increased expense in providing imaging. Consequently, research subjects typically do not undergo sedation or anesthesia, and many patients undergoing clinical imaging participate in programs to minimize the use of sedation and anesthesia^17-21. The availability of additional motion robust imaging strategies would facilitate the further reduction in the use of sedation and anesthesia for MRI.

The field of motion correction for DW-MRI in these populations has evolved to motion detection, removal, and correction at the slice level through slice-to-volume registration^22-25. These techniques detect and remove slices that are affected by intra-slice (through-plane) motion, and use SVR to realign the remaining slices. As each slice is acquired in around 100 milliseconds using an echo planar imaging (EPI) sequence, often only a fraction of slices are degraded by intra-slice motion. Therefore, by estimating an initial volumetric image, registering each slice to this image, and repeating the procedure (if needed), these methods can generate DW-MRI parameters even in highly uncooperative subjects.

Although these methods have significantly improved the success rate of DW-MRI acquisitions in uncooperative populations, there are still remaining challenges to be addressed for these methods to be adopted extensively. One of the most important challenges is the susceptibility of EPI to distortions that arise from local magnetic field inhomogeneities. Several approaches have been described to correct for these distortions. The most common methods involve acquiring a separate multi-echo gradient echo (GRE) sequence to measure a static volumetric field inhomogeneity map²⁶ or acquiring a separate point spread function map²⁷, and using these maps to correct for the displacement of every voxel. In the presence of motion, these static maps no longer provide correct compensation for magnetic susceptibility induced geometric distortion. The more that slices are displaced by motion, the less accurate the geometric distortion correction becomes. For patient groups with a high frequency and magnitude of observed motion, such as young children, the elderly, newborns and fetuses, new strategies are needed to provide distortion compensation. Another approach is to acquire each diffusion direction twice with opposing phase encoding directions, i.e. one volume with positive k_y blips (typically Posterior->Anterior), the other with negative k_y blips (typically Anterior->posterior). As the voxel displacements from geometric distortions are expected to be of equal magnitude but in opposite directions in these two acquisitions, it is possible to use an image-based registration technique to find the underlying undistorted image²⁸. This method requires the subject to stay still between two volume acquisitions, which limits its utility in subjects that may move, such as children and adults who suffer from Parkinson's disease.

In this work, we implement and test an alternative approach that does not require the subject to stay still for long periods, by acquiring a blip-reversed EPI readout using multiple echoes for each slice. Gallichan et al.³⁰ previously demonstrated that blip-reversed EPI acquisitions have over 99% SNR efficiency, compared to single echo EPI acquisitions and that they can be used to refine an acquired field map by estimating the field that minimizes the difference between the distortion-corrected images. Gallichan et al.³⁰ assumed there is no motion during the whole scan and physically restrained the subjects during their experiments, allowing them to work on a whole brain field map acquired in the absence of motion. Gallichan et al. demonstrated that by combining a volume acquired with blip up and blip down dual echoes with a volume acquired with blip down and blip up echoes in the absence of any motion, an improved geometric distortion correction could be achieved by using the four echos at each slice position to update a conventional field map distortion estimate. However, the time required to acquire a field map and paired volumes with two (blip-up blip-down and blip-down blip-up) dual echoes exceeds the ability of many subjects to hold perfectly still. In this work, we use a dual echo sequence, with echoes separated by less than 50ms, to estimate a distortion map at each slice position. We then use the distortion corrected slice to improve the slice-to-volume registration, enabling the position of the distortion corrected slice to be established. Slice to volume registration (SVR) has been shown to enable the alignment of EPI slices to a reference volume, despite the presence of geometric distortion²⁹. We demonstrate in this work that dual echo acquisition and per-slice distortion compensation improves the accuracy and fidelity of slice-to-volume registration. The main contribution of our work is, therefore, the development of a motion robust distortion compensated diffusion-weighted image acquisition and processing pipeline using a dual-echo spin-echo EPI sequence, and the evaluation of its efficacy in large and frequent motion scenarios. We performed multiple experiments on adult volunteers, where an external head position tracking system (Endoscout, Robin Medical Inc. Baltimore USA) was available for making ground truth motion measurements, including discrete motion experiments where field measurements and structural anatomical scans were acquired at each position. The results show that: 1) the motion measurement accuracy of SVR registration methods improves when slice-level distortion correction is applied; 2) a dual-echo EPI acquisition with diffusion weighted gradients can generate geometric distortion maps equivalent to GRE based field inhomogeneity measurement; and 3) final quantitative diffusion parameter maps obtained from our approach match the structural scans better than single echo acquisitions, with or without static field inhomogeneity map correction.

METHODS

Implementation of dual-echo EPI

A product spin-echo EPI sequence was modified, as shown in Figure 1, to add a second readout matching the first readout in terms of resolution, field of view (FOV) and bandwidth, but with reversed order k-space traversal in the phase encoding direction³⁰. A 180° refocusing pulse and spoiler gradients were used to generate the second spin-echo. The frequency encoding direction was also reversed between the two echoes to maintain consistent temporal spacing between k-space points³¹. Parallel imaging with an acceleration factor of 2 was used to reduce the echo train length of each echo, as well as the overall imaging time. Partial Fourier of 6/8 was used for both echoes to reduce both the minimum echo time for the first echo and the time difference between the two echoes. A fat saturation pulse was used before the RF excitation pulse to eliminate the fat signal from the skull. We used monopolar diffusion gradients for all the experiments described below.

Figure 1:

Pulse sequence diagram of the sequence.

After each scan the raw data was exported and an in-house developed reconstruction algorithm was used to generate diffusion weighted images. Images were formed using a Dual-Polarity GRAPPA (DPG)³² implementation for both Nyquist ghost correction and in-plane data recovery. The same DPG kernel was employed for both echoes and all diffusion directions, and was derived from temporally encoded pre-scan EPI calibration data with no diffusion encoding gradients (a b0 image). Partial Fourier reconstruction was achieved using a homodyne reconstruction algorithm³³ with a ramp-envelope.

Ground truth motion measurements were acquired using an electromagnetic tracker with 4 sensors attached to the forehead of the subjects using a headband^34,35. In order to generate motion measurements, the custom dual-echo sequence was modified with additional gradient blips in 3 orthogonal directions (in x, y and z) prior to the excitation pulse, to ensure spin evolution between the RF excitation and readouts were consistent with the original diffusion sequence.

Imaging sequence parameters:

For all the volunteer studies, a standard 30-direction single shell diffusion weighting with a b-value of 1000 s/mm² (b1000) and five images (spread out during acquisition) without any diffusion encoding gradients (b0) were acquired. Sequence parameters were TE₁ = 72 ms, TE₂ = 108 ms, GRAPPA = 2, TR = 12000 ms, 2 mm isotropic resolution with 70 slices resulting in a scan time of 6 minutes. In comparison, a single echo acquisition would have a TR of 9300 ms with these settings, corresponding to an acquisition time penalty of 2700 ms (or 29%). FOV was set at 256 mm, resulting in an in-plane matrix size of 128x128. Slices were interleaved with a factor of 2 to reduce spin history artifacts. A T2-weighted fast spin echo sequence was also acquired to provide a structural reference image. Seventy slices were acquired with TE = 86 ms, TR = 12000 ms, 1mm in-plane resolution and 2 mm slice thickness resulting in a 2-minute scan time. A 2D GRE sequence was also acquired to generate field inhomogeneity maps with TE₁ = 4.92 ms, TE₂ = 7.32 ms, TR = 300 ms, FA = 25°, resolution = 2mm isotropic, in 48 seconds.

Motion Experiments:

All volunteer experiments were performed on a whole-body 3T MRI scanner (MAGNETOM Skyra; Siemens, Erlangen, Germany) equipped with quadrature transmit and a 64-channel phased array head coil. Five volunteers (3 female; aged 28–37 years) were scanned after providing written informed consent in accordance with an Institutional Review Board-approved protocol.

Two different sets of experiments were performed on each volunteer:

Experiment 1:

In the first set, volunteers were scanned with two identical diffusion acquisitions and they were instructed to move around 10 degrees between each scan. The two positions were selected as “nod up” and “nod down” as this kind of motion (rotation perpendicular to the main magnetic field direction) is expected to generate the largest field changes. A T2-weighted Fast Spin Echo (FSE) sequence (down-sampled to 2 mm isotropic) and a multi-echo 2D GRE sequence (2 mm isotropic) were acquired at each position to provide a reference structural image and field map at each position. Imaging FOV was matched between all the scans. We compared the distortion corrected images with the T2 FSE images, assuming FSE images have minimal geometric distortions. A canny edge detection filter was used to be able to compare the FSE images to the diffusion-weighted images. Field maps generated from distortion correction using dual echoes were also compared with the reference field maps created using the 2D GRE scan. These reference field maps were calculated from a weighted mean of the phase difference between the two GRE echoes via the sum over channels of the Hermitian inner product of the complex image data.

Experiment 2:

In the second set, subjects were instructed to move to a different position using audio commands every minute during the diffusion scan. Motion amplitudes were selected to be similar to levels reported for younger children³⁵. Motion measurements from the EM tracker were recorded at each slice.

Distortion Correction

The most common method of distortion correction using two acquisitions with opposing phase encoding directions was suggested by Andersson et al.²⁸. They suggested estimating the voxel displacement that minimizes the sum-of-squares difference between the two unwarped volumes, generated from applying the field to the distorted images acquired with opposing phase encoding directions. We use a similar strategy here, but, to account for large and frequent motion, we calculated a distortion map on a slice level instead of a volume level. Since our images come from two different echo times resulting in different contrast, we were able to achieve a good slice level distortion map by optimization of two important parameters:

1). Contrast matching

As both echoes are acquired with the exact same diffusion encoding gradient, they have the same diffusion weighting; however, since they are acquired at different echo times, the T2 weighting will be different between echoes. As each voxel has a different T2 weighting, voxelwise contrast matching is not possible as the two echoes have different distortions. We found that scaling the second echo in a brain mask region gives good results and used this approach for this study. By assuming a linearized model of R2 relaxation⁴⁹ based on the small echo time difference, we scaled the second echo by the ratio of the mean signal difference between the two magnitude images in a brain mask region.

2). Mask region

Selecting a good brain mask is crucial for two reasons. First, as explained above, the masked region can be used to correctly scale the two images. Second, we found that although the region of interest is the brain, and most tissues in the brain (i.e. gray and white matter) have similar T2’s and therefore similar contrast, there are regions with very high or low T2’s that create artifacts in the images if not excluded. This includes regions like dura matter and ventricles. Figure 2 shows an example of applying an improper mask to the two echoes. Several reliable and fast brain extraction tools are available^36,37. For simplicity and wide applicability in its study, we used the FSL brain extraction tool (BET)³⁸ to exclude dura matter to create a brain region mask separately for both echoes.

Figure 2:

Example dual-echo distortion corrected image without a brain mask applied to the data. This results in artifacts in the regions near dura matter in the frontal lobe as shown by a red arrow.

We used the masked and scaled echo images with the FSL topup program²⁸ to generate a field map, and applied it to both echoes. We then used a sum-of-squares approach to combine the echoes into a single slice image. This image was then registered to a target volume, which was reconstructed through an iterative process by running inter-slice motion tracking method for all b=0 volumes. The SVR algorithm registers each diffusion-weighted image slice sequentially in acquisition order²⁹, exploiting robust state estimation (based on Kalman filtering) for SVR-based motion tracking. After the motion parameters are estimated, diffusion gradient directions are corrected according to these estimates and diffusion tensor parameters are calculated for every voxel in a 3D volume using weighted linear least squares.

RESULTS

Experiment 1:

Figure 3 and 4 show examples from the first set of experiments where the volunteer moved from position 1 (nod up) to position 2 (nod down). As expected, in both positions the first and second echoes show different distortions since they have opposing phase encoding directions. For example, near the sinuses, the first echo has signal pile up whereas the second echo shows dispersion of voxels in that region. Echoes 1 and 2 show slightly different contrast, mostly between ventricles and gray/white matter. Figures 3.c and 3.g show distortion corrected images using the proposed algorithm, and Figures 3.d and 3.h show distortion corrected images using the field map acquired at position 1. For both positions, the distortion correction algorithm based on dual echoes acquired at each slice successfully eliminated the effects of local field inhomogeneities, whereas the static field map correction was only successful in position 1, where the field map was acquired. In position 2, the static field map correction introduced artifacts mostly in the frontal region bilaterally involving the frontal cortex.

Figure 3:

Axial views of the acquired diffusion data in two different positions (top row: nod up; bottom row: nod down) are shown for the two echoes with opposing phase encoding directions, the dual-echo corrected image, and the field map corrected image using the field map calculated from position 1. The field inhomogeneity map based on dual-echo data successfully corrected for geometric distortions at both positions whereas the field map calculated from position 1 introduced large artifacts bilaterally in the frontal cortex in position 2, as shown by arrows.

Figure 4:

Sample b1000 images corresponding to the positions shown in Figure 3. Similar artifacts (shown by red arrows) are visible bilaterally in the frontal cortex.

Figure 5 shows the results from the same experiment in the sagittal plane. This figure demonstrates that although the distortion correction was applied slice by slice in the axial plane, there are no visible discontinuities in the distortion corrected images.

Figure 5:

Sagittal views of the images acquired in two different positions (top row: nod up; bottom row: nod down) are shown for the two echoes with opposing phase encoding directions, the dual-echo corrected image, and the field map corrected image using the field map calculated from position 1. As can be seen in the bottom right image, field map correction also generated artifacts near the ventricles, and also overcorrected the geometric distortions in frontal lobe.

The effects of distortion correction are more evident in Figure 6, which shows the brain edges calculated using the first echo image (Figure 6.a), the dual-echo distortion corrected image (Figure 6.b) and the field map corrected image (Figure 6.c) overlaid on the distortion free axial T2 FSE image. The distortion corrected image using dual echoes shows an almost identical match in edges, whereas the first echo shows distinct mismatches especially around the sinuses.

Figure 6:

Edges of the diffusion weighted data from echo 1 (a), dual echo corrected data (b) and field map corrected data (c) from position 2 are overlaid on a T2 weighted structural image acquired in position 2. As expected, due to the signal pile up in echo 1, the edge features do not match the structural image. The dual echo corrected image shows a much better match with the structural data whereas the static field map correction introduced artificial edges in the frontal lobe.

Figure 7 shows a comparison between representative field maps calculated using the standard multi-echo GRE sequence and the dual-echo EPI sequence in positions 1 and 2, using a b=0 image and a b=1000 image. The DC component of the field is matched between these two maps, to account for any global frequency shift between these two acquisitions. Dual-echo field maps show a similar pattern to the reference field map, especially in the brain mask region in both positions. The Root Mean Square Error (RMSE) between the ground truth field maps and dual echo maps at position 2, averaged over all volunteer scans, were 12.6% ± 3.1%, showing an improvement compared to the field map at position 1 which had an RMSE of 21.6% ± 3.8%. The difference was statistically significant with P < 0.001.

Figure 7:

Representative field maps from a volunteer study, calculated using the dual-echo images (b0 and sample b1000) are compared to ground truth GRE-based multi-echo acquisitions (left) in position 1 (nod up) and position 2 (nod down). At both positions, dual-echo field maps show high correspondence compared to the GRE field map. This figure also shows why the field map corrections using position 1 create artifacts in position 2 as the field inhomogeneities completely change near the sinuses going from ~100Hz to ~−100Hz.

Experiment 2:

Figure 8 shows motion parameters reported by the EM motion tracking system compared to the SVR motion measurement results before and after distortion correction, using the reference field map and our estimated dual echo field map at each slice. Table 1 summarizes the errors of each algorithm compared to the ground truth EM tracking results. As expected the largest errors in the motion measurements were found in the anterior-posterior direction (y-axis) as this axis was selected as the phase encoding direction, resulting in the largest voxel displacements. Dual-echo distortion correction reduced the registration errors, mainly in this direction. Errors in all the axes were on the order of a quarter of a voxel for the dual echo corrected scans, whereas they were on the order of a voxel in the y direction in both the uncorrected and field map corrected scans.

Figure 8:

Slice level motion measurements from one of the volunteer experiments, where the subject was instructed to move to a random position 6 times during a 5-minute diffusion weighted image acquisition. Ground truth motion (black) was measured using an external motion tracker. Motion measurements from slice-to-volume registration were more accurate when dual-echo correction was used (blue) compared to no correction (green) or field map correction acquired at the start of the scan (red). The largest errors where observed in y-translation, corresponding to the phase-encoding direction.

Table 1:

Summary of the accuracy of the volunteer scans

	Translation (mm)				Rotation (°)
	x	y	z	Mean	Ψx	θy	ϕz	Mean
No correction	0.59	1.89	0.32	0.93	0.46	0.68	0.59	0.57
Field map correction	0.55	2.48	0.29	1.12	0.36	0.58	0.64	0.53
Dual-echo correction	0.44	0.64	0.24	0.44	0.36	0.51	0.51	0.46
Maximum Motion	9.85	3.09	4.83		6.88	3.84	7.76

Summary of the accuracy (absolute error) of slice-to-volume registration compared to the ground truth external motion tracking measurements, averaged over 5 volunteer scans. Dual-echo correction resulted in the lowest errors. Since the phase encoding direction was selected as anterior-posterior, most errors were observed in the y-translation, which were reduced significantly using dual-echo corrections.

Figure 9 shows final b0 and mean diffusion images (b1000) before and after distortion correction in the sagittal plane. Even with the large and frequent motions reported here, SVR generated robust reconstructions. The uncorrected field inhomogeneities resulted in artifacts in the reconstructed images, as shown by arrows. Both b0 and b1000 images show artificial high signal in the frontal cortex in both the non-corrected images and static field map corrected images.

Figure 9:

Mean b0 (top row) and b1000 (bottom row) images are shown from a volunteer study for echo 1 (a), dual-echo correction (b) and field map correction (c) during an abrupt motion study. b1000 images show artificial high signal in the frontal cortex in the non-corrected images and field map corrected images (shown by arrows) due to the distortion differences between different diffusion-weighted volumes.

Figure 10 shows fractional anisotropy (FA) maps of the non-corrected images, dual-echo corrected images and field map corrected images. Similar to Figure 9, artifacts are seen in the non-corrected and field map corrected images, especially in regions where local field inhomogeneities differ between different head positions, whereas distortions have been effectively compensated using the proposed dual-echo simultaneous motion and distortion correction approach.

Figure 10:

Fractional anisotropy maps are shown from a volunteer study for echo 1 (a), dual-echo correction (b) and field map correction (c) during an abrupt motion study. Red arrows show the regions where the non-corrected images and field map corrected images exhibit artifacts due the distortion differences between different diffusion-weighted volumes.

DISCUSSION

In this work, we implemented and evaluated the use of dual-echo spin echo EPI with reversed phase encoding directions for simultaneous motion and distortion correction in DW-MRI of moving subjects. Slice-level distortion correction is crucial when the subject motion is large and frequent, as an initially acquired field map is no longer valid due to large changes in field inhomogeneity, and volume-level field corrections are inaccurate due to their latency in modeling distortions that change with fast and large slice-level motion. Our results show that slice-level corrections produce field maps equivalent to field maps generated by the reference gold standard. We also show that slice-level distortion correction improves the accuracy of SVR algorithms as the slices at different orientations have different levels of distortions, which can create errors in the registration process.

The eddy currents resulting from phase and frequency encoding gradients are inherently corrected in our approach since both gradients are reversed between the echoes. However, the eddy currents resulting from the diffusion gradients are not corrected. As our distortion corrected images show a good match with the distortion-free FSE image, we used monopolar gradients for all the experiments. In case the eddy currents from diffusion gradients cause large artifacts, employing a bipolar gradient scheme^39,40 or acquiring images with opposing gradient directions⁴¹ can be used to reduce these effects. Modern scanners also use actively shielded gradients and gradient pre-emphasis to reduce the effects of eddy currents.

In order to reduce the echo time of both echoes and the overall readout time, we used GRAPPA with an acceleration factor of 2. Since the goal of the study was to evaluate the dual-echo EPI sequence in the presence of large and frequent motions, one concern was the resilience of the GRAPPA reconstruction to large motions. We did not observe any motion-induced parallel imaging artifacts in any of the data sets that we acquired and reconstructed, with motions on the order of 10 mm/°. GRAPPA calibration employed temporal encoding of the calibration data, with GESTE (Ghost Elimination via Spatial and Temporal Encoding) processing to minimize artifacts⁴². In case of large motions during acquisition of the calibration data, reacquisition of these lines might be needed to get high quality reconstructions. It is also possible to reduce the echo times and the overall readout time by increasing the acceleration factor, but this would result in increased g-factor artifacts and reduced SNR for each echo.

Another alternative to reduce the effect of field inhomogeneities is to use a multi-shot approach^43,44. It is possible to correct for small motion by assuming that the phase variation changes linearly with rigid body motion. However, as shown in Figure 7, this assumption breaks down in the presence of large amplitude motion, which results in non-linear phase differences between shots, making any multi-shot approach ineffective.

A potential limitation of this approach is the requirement to have enough SNR in the second echo to reliably estimate a field map. For typical clinical protocols, i.e. b = 1000 and 2 mm isotropic resolution, this did not create a problem, as can be seen in the raw images and field maps generated from the raw images. We also did not observe any problems with diffusion images acquired with b=1000 and lower in terms of the amount of distortion the algorithm can reliably correct. Also as was shown by Gallichan et al³⁰, SNR efficiency of the dual-echo sequence is nearly the same as a single echo acquisition sequence, although the acquisition of the second echo results in an increased TR. If higher resolutions or larger b-values are required, better gradients resulting in lower TEs would be helpful. Such gradients have been used in the human connectome project⁴⁵. Another approach would be to interleave b = 0 volumes or slices⁴⁶ to generate a less frequently updated field maps, but using non-diffusion weighted images only.

One drawback of the dual-echo acquisition, compared to acquiring each echo separately is the different contrast between the echoes. This can potentially be solved using a triple-echo sequence, as suggested by Weiskopf et al in an fMRI sequence⁴⁷. With this method, the first and the third echo, which have the same encoding directions, can be used to simulate an image that is acquired at the second echo time but with reversed gradients. Then these two images, that have the same contrast but opposite k-space traversal, can be used to generate a field map. However, with the gradient strengths used in this paper, the third echo will be around 150 ms and therefore, depending on the protocol, it may not have enough signal to be effectively used in this approach. In the case of gradient echo EPI acquisitions, high acceleration rates can be used reduce the time between echoes to be able to reconstruct field maps from multiple echoes⁴⁸. The difference in contrast can also be used as an advantage, as it may provide different diagnostic information⁴⁹.

There is a need for motion compensated diffusion weighted MRI acquisitions. Geometric distortions resulting from large motions reduce the accuracy of motion measurements and interfere with the ability to generate artifact free information. Our method eliminates the effects of motion and distortions simultaneously to solve this problem. Our experiments are the first to demonstrate that dual-echo acquisitions with blip-reversed phase encoding can be used to generate slice-level distortion free images, which is critical for robust slice to volume registration for motion correction. The distortion corrected images not only result in better motion estimates, they also generate more accurate final diffusion image reconstructions. Our method will improve DW-MRI of regions with higher magnetic field inhomogeneity such as the anterior skull base, middle cranial fossa and lateral posterior fossa. This method can be used in studies where subject motion is inevitable such as body diffusion^50,51 and fetal brain^22-25 and lung⁵² diffusion studies, and can also be used to reduce the rate of sedation and anesthesia in imaging infants, young children and uncooperative patients. In addition, it can significantly simplify and enhance imaging, and reduce the costs of DW-MRI research studies on infants and toddlers where sedation and anesthesia cannot be justified for research.