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Rapid calibration scan for estimating temporally-varying eddy currents in diffusion imaging using a time-resolved PEPTIDE imaging approach
Merlin J Fair1 and Kawin Setsompop1,2
1Radiological Sciences Laboratory, Stanford University, Stanford, CA, United States, 2Electrical Engineering, Stanford University, Stanford, CA, United States

Synopsis

A rapid calibration scan for estimating eddy-currents in diffusion acquisitions was developed using the time-resolved PEPTIDE imaging approach. This calibration scan estimates temporally-varying eddy-current fields across three principal diffusion-directions in <30s, with estimates of eddy-fields across other directions derived through a linear model. The accuracy of this method was validated in simulation, phantom and in-vivo experiments. In a high-SNR diffusion phantom, estimated eddy-fields closely match that of “FSL-eddy” on a large blip-up and blip-down 64-direction EPI dataset. For in-vivo data at b=5000s/mm2, estimates from PEPTIDE-based calibration was able to maintain high-accuracy estimation of the eddy-current field despite low SNR.

Introduction

Diffusion imaging is well known to suffer from eddy-currents, manifesting as distortions in EPI1. Many methods for correcting such distortion effects have been proposed2,3,4, with commonly applied techniques relying on estimating the eddy-current fields from a series of distorted images across diffusion-directions5. As an alternative, field-probes6,7 have shown excellent promise for direct eddy-current field measurements, with capability to capture both spatial and temporal variations8,9, but this is specialized hardware and not yet widely accessible.

Recently, a distortion- and blurring-free multi-shot EPI technique, termed echo-planar time-resolved imaging (EPTI)10, has been developed, that additionally provides a time-resolved multi-contrast imaging capability. Moreover, EPTI has been combined with a PROPELLER-like readout in the PEPTIDE approach11,12 for self-navigated diffusion-relaxometry imaging (method overview in Figure 1a). These time-resolved imaging approaches avoid the typical image-distortion artifacts from B0 and eddy-current fields, with the phase evolution effects from these fields instead captured in the reconstructed time-series images.

In this work, we exploit this phase evolution information in the PEPTIDE imaging-series to create a rapid eddy-current calibration scan (Figure 1b). Realistic simulations were performed to demonstrate the capability of such an approach to accurately capture both spatial and temporal eddy-current field variations, with an iterative PEPTIDE-reconstruction also developed to ensure robust estimation, even in the presence of strong eddy-currents. This was then further validated through phantom and in-vivo experiments.

Methods

Eddy-field estimation: Estimations can be performed using data from a single PEPTIDE-blade across three principal diffusion directions, with estimates of eddy-fields across other diffusion-directions calculated through a linear model. Estimation for each principal diffusion-direction is performed using the time-series images from that direction and the b=0 reference, which contain the following phase components (Figure 1b):


$$\phi_{DWI}(t)=\phi_{background,DWI}+\phi_{B0}(t)+\phi_{EC}(t)$$
$$\phi_{b=0}(t)=\phi_{background,b=0}+\phi_{B0}(t)$$

Across the time-series, the background phase is removed from both datasets and the difference between the two resultant image phases found, to yield the eddy current induced phase. A weighted quadratic fit is then applied per time-point to determine the time-varying phase spatial components. For the case where is assumed to vary linearly with time, a temporal-fit to a constant eddy-field is performed. Assuming a TR of 3.5s, the proposed 3-direction, single-PEPTIDE-blade acquisition requires 3.5s x 4 = 13.5s (including a reference b=0), with an additional PEPTIDE reconstruction reference scan of ~15s13, resulting in a total eddy-current calibration acquisition time of <30s. More blades/directions can be added as needed to improve eddy-field estimation.

Simulation validation: Simulated PEPTIDE-data for the proposed calibration scan were generated using previously-acquired fully-sampled in-vivo k-t dataset, as previously described11. Here, realistic eddy-current phase changes were also added to the data, using eddy-current fields estimated with FSL eddy5 from EPI-acquisitions with matched parameters. Two cases were simulated: static eddy-field and eddy-field with an exponential temporal decay.

Phantom & in-vivo validation: Phantom and in-vivo datasets were acquired on a Siemens Prisma 3T with a 32-channel coil. A high-SNR diffusion phantom was used for optimal eddy-current estimation and in-vivo data were acquired in a healthy subject. Diffusion-PEPTIDE and diffusion-EPI were both acquired with ESP/TE/TR=1.1ms/128ms/3.5s, 1.5x1.5x3.0mm3, 18-slices, 64 diffusion-directions, b=5000s/mm2. The EPI acquisitions were repeated with reverse phase-encode directions to enable accurate eddy-field estimation with FSL eddy5,14 for use as comparison. PEPTIDE was acquired with 10-blades (with a single blade used for field-estimation) and other parameters as previously reported12.

Results

With the simulated PEPTIDE-data, eddy-current phases were accurately estimated for both static and temporally-varying eddy-current fields cases (Figure 2). The use of a second iteration of the PEPTIDE reconstruction was also investigated, where the estimated eddy-current is incorporated into the B0-GRAPPA PEPTIDE-reconstruction, which is shown to reduce the already low reconstruction errors and further improve the eddy-field estimates (Figure 3). The relatively low errors seen at both b=1000s/mm2 and b=5000s/mm2, supported the resilience of the technique.

Figure 4 demonstrates phantom acquisitions at b=5000s/m2. Even at this high b-value, artifacts in the uncorrected PEPTIDE acquisitions are subtle, with some small signal variations mitigated through the second-iteration reconstruction, suggesting successful estimation and correction of the eddy-currents. The estimated eddy-current phase appears approximately linear, and the associated field agrees closely with the FSL-EPI estimate obtained from 64 pairs of blipped-up and -down acquisitions.

While in-vivo data at b=5000s/mm2 has substantially lower-SNR than the phantom (Figure 5a), by using image phase in PEPTIDE rather than relying on small distortions in the magnitude images as in FSL-EPI, accurate eddy-field estimate is still feasible from a 3-direction dataset. Phantom (Figure 5b) and in-vivo (Figure 5c) PEPTIDE field estimates show good agreement with each other as well as with the FSL-EPI phantom estimates, while the in-vivo-FSL estimates contain significant deviation for this low-SNR, high-b-value acquisition.

Discussion/Conclusion

The time-resolved PEPTIDE technique has been demonstrated capable of accurately detecting eddy-current induced phase changes. Agreement is seen with the well-established FSL eddy technique in a high-SNR phantom, with PEPTIDE able to determine eddy-fields for arbitrary directions from as little as 3 diffusion-directions in-vivo at b=5000s/mm2. While the scanner data examined here appeared to have linear temporal field variations, based on simulations, this technique should also be able to detect higher-order temporal components, as well as higher-order spatial components, as needed. Future work would involve confirmation of the temporal field variations against field-probe measurements.

Acknowledgements

This work was supported in part by the NIH R01EB020613, R01EB019437, R01MH116173, R01EB016695, P41EB030006, and U01-EB025162.

References

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8. Chan, R.W., von Deuster, C., Giese, D., et al., Characterization and correction of eddy-current artifacts in unipolar and bipolar diffusion sequences using magnetic field monitoring, Journal of Magnetic Resonance, 2014; 244:74-84.

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10. Wang, F., Dong, Z., Reese, T.G., et al. Echo planar time‐resolved imaging (EPTI). Magn Reson Med. 2019; 81: 3599– 3615.

11. Fair, M.J., Wang, F., Dong., Z., Reese, T.G., Setsompop, K. Propeller echo‐planar time‐resolved imaging with dynamic encoding (PEPTIDE). Magn Reson Med. 2020; 83: 2124– 2137.

12. Fair, M.J., Liao, C., Manhard, MK., Setsompop, K. Diffusion‐PEPTIDE: Distortion‐ and blurring‐free diffusion imaging with self‐navigated motion‐correction and relaxometry capabilities. Magn Reson Med. 2020; 00: 1–17.

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Figures

Figure 1 - a) EPTI/PEPTIDE uses a zig-zag sampling trajectory to cover a large ky-t section per acquisition shot, with B0-informed-GRAPPA used to fill-in the missing data. PEPTIDE acquires rotated EPTI shots (blades) to cover the full k-t space. With full k-t data, each time-point has consistent phase and signal decay, so the images in the resolved time-series are free from typical-EPI distortion and blurring. b) The phase of the time-series images for a DWI acquisition can be compared with that of a diffusion-free (b=0) acquisition, to estimate eddy current induced phase changes.

Figure 2 – Eddy current estimation simulations. (top) A constant eddy current field causes a linear phase progression across time and the temporal and spatial components of this can be estimated accurately compared to the known ground truth in the simulated data. A linear temporal fit of the phase can be performed to create a static eddy field estimate. (bottom) The eddy field is simulated as varying with time, undergoing an exponential decay. This effect can be measured in the temporal phase estimates, which again match well with the ground truth.

Figure 3 - PEPTIDE simulated data with an eddy field from a single diffusion direction at b=1000 & 5000s/mm2. Recon error due to the eddy field (difference between with and without applied eddy field) is significantly lower in PEPTIDE than EPI, where stronger artifacts are seen due to image distortion. PEPTIDE errors are caused by phase mismatches between the GRAPPA kernel (eddy current free) and the data. After correction through a 2nd recon iteration, incorporating the estimated eddy field into the GRAPPA reference data, lower recon errors occur which helps improve the field estimate.

Figure 4 – b=5000 phantom. (top) A DWI for EPI, pre- and post-correction, and a full PEPTIDE recon for the 1st and 2nd recon iteration, as well as an MPRAGE structural reference. The distortion-free nature of PEPTIDE is visible and some small artifacts in the 1st iteration are mitigated on the 2nd iteration, suggesting successful correction using the self-estimated eddy current phase. (bottom, left) The eddy current phase evolution appears to be ~linear and so a temporal fit to the field was applied. (bottom, right) This PEPTIDE eddy field estimate matches well with the FSL-EPI estimate.

Figure 5 – (a) Single-shot data: phantom & in-vivo. The low SNR of b=5000 in-vivo data is apparent in both EPI and PEPTIDE (PEP), but image phase across time is still measurable. (b) Estimated phantom eddy fields, measured by FSL and PEPTIDE. First 3 directions for PEPTIDE are direct estimates (red square), while others are calculated using a linear model. (c) Estimated in-vivo eddy fields (with same diffusion-directions and acq. params as in phantom). “Phantom PEP-ref”: PEPTIDE-estimated field in the phantom, masked by the in-vivo brain FOV, for reference with the in-vivo results.

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)
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