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Robust motion- and $$$\delta B_0$$$ -correction for high-resolution QSM at 7T1Biomedical Engineering Department, School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom, 2Centre for the Developing Brain, School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom, 3London Collaborative Ultra high field System (LoCUS), London, United Kingdom, 4Department for Forensic and Neurodevelopmental Sciences, Institute of Psychiatry, Psychology and Neuroscience, King's College London, London, United Kingdom, 5Biomedical Image Technologies, Universidad Politécnica de Madrid and CIBER-BNN, Madrid, Spain, 6Siemens Healthcare Limited, Frimley, United Kingdom, 7Guys and St Thomas’ NHS Foundation Trust, King's College London, London, United Kingdom, 8Department of Radiology, Stanford University, Palo Alto, CA, United States, 9Department of Electrical Engineering, Stanford University, Palo Alto, CA, United States
Synopsis
Keywords: Signal Modeling, Susceptibility
Motivation: Quantitative susceptibility mapping (QSM) provides valuable clinical information and is widely used, especially at ultra-high field (7T). Due to long echo times, QSM acquisitions are extra sensitive to the changes in B0 ($$$\delta\textbf{B}_0$$$), such as those secondary to motion.
Goal(s): To provide purely data-driven motion and $$$\delta\textbf{B}_0$$$ correction for QSM.
Approach: We use the self-navigated DISORDER k-space re-ordering, originally proposed for motion correction, to additionally estimate $$$\delta\textbf{B}_0$$$. Within-scan motion and $$$\delta\textbf{B}_0$$$ are then retrospectively corrected during image reconstruction.
Results: We show improved reconstruction in all 5 scanned volunteers when additionally correcting $$$\delta\textbf{B}_0$$$. This directly improves QSM.
Impact: The proposed method can result in improved image quality when scanning in presence of motion and , e.g. due to heavy breathing. Combining this approach with an optimized QSM protocol will provide motion- and -robust QSM.
Introduction
Quantitative susceptibility mapping (QSM) estimates local magnetic susceptibility ($$$\chi$$$) using the MRI-signal phase1, with clinical applications studying imaging biomarkers, brain development, and neurological diseases2-5. For high-resolution QSM, of special interest at 7T, long scan times make the sequence sensitive to motion6. Additionally, due to the long echo times (TE), QSM acquisitions are very sensitive to changes in the polarizing magnetic field ($$$\delta\textbf{B}_0$$$), which becomes more problematic at higher field strength (7T)7,8. We recently proposed a method to estimate both motion and $$$\delta\textbf{B}_0$$$ from navigators by appropriately designing the k-space trajectory and by using a robust optimizer9. In this work, we deploy this method to the self-navigated DISORDER trajectory10 to obtain within-scan $$$\delta\textbf{B}_0$$$ estimates in addition to the usually obtained motion estimates. Both motion and $$$\delta\textbf{B}_0$$$ are then retrospectively corrected during image reconstruction.Methods
AlignedSENSE:The alignedSENSE11 performs motion correction by dividing the k-space acquisition into temporal groups (shots) of readouts (each acquired per repetition time TR), where each shot $$$n$$$ has a different motion state with rigid motion parameters $$$\textbf{z}_n$$$, which can be jointly optimized together with the image:$$(\hat{\mathbf{x}},\hat{\mathbf{z}}_n)=argmin_{\textbf{x},\textbf{z}_n }\sum_{n}{||\textbf{A}_n\textbf{F}\textbf{ST}(\textbf{z}_n))\textbf{x}-\textbf{y}_n||^2_2}\ \ \ \ \ \ \ \ \ \ \ \ (1)$$where $$$\textbf{T,S,F,A}_n$$$ and $$$\textbf{y}_n$$$ respectively represent rigid motion, coil sensitivities, Fourier operator, sampling structure, and measured multi-coil k-space data. Using the DISORDER phase encoding scheme, which samples uniformly across k-space per shot, allows robust motion estimation and image reconstruction.
$$$\delta\textbf{B}_0$$$-informed alignedSENSE:
Assuming small or moderate motion levels, lower order $$$\delta\textbf{B}_0$$$ explains most of the B0 variations7,8. Therefore, we model $$$\delta\textbf{B}_0$$$ using 2nd-order solid harmonics with basis $$$\textbf{L}$$$ and coefficients $$$\textbf{c}$$$:$$$\delta\textbf{B}_0=\textbf{L}\textbf{c}$$$. For spoiled sequences, this model can be included in the alignedSENSE forward model12:$$\textbf{y}_n=\textbf{A}_n\textbf{F}\textbf{ST}(\textbf{z}_n)\textbf{P}( \textbf{c}_n)\textbf{x}\ \ \ \ \ \ \ \ \ \ \ \ (2)$$where $$$\textbf{P}(\textbf{c}_n)$$$ is the induced phase $$$e^{i2\pi\textbf{Lc}_nTE}$$$ for shot $$$n$$$. Image, motion, and $$$\textbf{c}_n$$$ are jointly estimated by performing an alternating optimization:$$(\hat{\mathbf{x}},\hat{\mathbf{z}}_n,\hat{\mathbf{c}}_n)=argmin_{\textbf{x},\textbf{z}_n,\textbf{c}_n}\sum_{n}{||\textbf{A}_n\textbf{F}\textbf{ST}(\textbf{z}_n)\textbf{P}( \textbf{c}_n)\textbf{x}-\textbf{y}_n||^2_2}\ \ \ \ \ \ \ \ \ \ \ \ (3)$$where $$$\textbf{z}_n$$$ and $$$\textbf{c}_n$$$ are estimated using the Levenberg-Marquardt algorithm9,11.
In-vivo data acquisition:
We used a single-echo GRE ($$$\Delta$$$=0.85x0.85x0.85mm3,TE/TR=20/31ms,FA=15°,FOV=224×224×157mm3,Head-Foot frequency encoding, acquisition time (TA)=11min) modified to allow for robust motion and $$$\delta\textbf{B}_0$$$ estimation: First, the DISORDER trajectory was used. Next, a high bandwidth (800Hz/voxel) was set to suppress differential distortion from varying $$$\delta\textbf{B}_0$$$. A moderate acceleration R=1.5x1.4 was used following previous recommendations10. 5 healthy volunteers (HV) were scanned at 7T (MAGNETOM Terra, Siemens Healthcare, Erlangen, Germany), where the HV was instructed to either be relaxed or to perform heavy breathing to induce temporal $$$\delta\textbf{B}_0$$$. Coil sensitivities were estimated from a reference scan (TA=18sec) using ESPIRiT13.
Image reconstruction:
Acquired data was reconstructed without correction (SENSE14), with only motion correction (alignedSENSE), and with the proposed motion+$$$\delta\textbf{B}_0$$$ correction. Since no ground truth (GT) is available, image quality is quantified using the normalized gradient squared (NGS)15.
QSM processing:
Susceptibility maps were generated from the reconstructed image phase using the SEPIA toolbox16 with the following options: SEGUE phase unwrapping17, PDF background field removal18, and the threshold-based k-space division for $$$\chi$$$-computing19.
Results and discussion
Figure 1 shows the motion traces for all 5 HVs when estimating motion only (A) and motion+$$$\delta\textbf{B}_0$$$ (B). The estimated motion traces became much more orderly when additionally modeling and estimating $$$\delta\textbf{B}_0$$$. The corresponding reconstructed images are shown in Figure 2 for all correction methods (rows) and HV (columns). Incremental improvements in image quality compared to the uncorrected case (A) are observed by estimating motion (B) and motion+$$$\delta\textbf{B}_0$$$ (C) (yellow arrows indicate areas of notable improved quality). Figure 3 shows the same figure for the “heavy breathing” experiment, where the same observations hold. A case of substantial improvement with the proposed method is indicated in red. A quantitative evaluation of the image quality is presented in Figure 4. In all cases, the proposed method results in higher quality scores. Finally, Figure 5 shows a pilot QSM reconstruction, performed on the “heavy breathing” acquisition in HV1. Consistent with the reconstructed image, substantial improvements are obtained by using the proposed reconstruction. Note that the acquisition was suboptimal for QSM processing and better QSM maps are expected with protocol parameters that balance the ability to correct motion/$$$\delta\textbf{B}_0$$$ as well as to perform QSM20.Conclusion
We have integrated a method to estimate motion and $$$\delta\textbf{B}_0$$$ into a retrospective motion+$$$\delta\textbf{B}_0$$$ corrected reconstruction, especially of interest in acquisitions with long TE. Robust performance was achieved using the self-navigated DISORDER trajectory. We show improved motion traces and image reconstruction in all in-vivo acquisitions, both qualitatively and quantitatively. A pilot QSM reconstruction shows the potential to use this method for QSM at 7T.Acknowledgements
This work was funded by the King’s College London & Imperial College London EPSRC Centre for Doctoral Training in Medical Imaging [EP/S022104/1], by core funding from the Wellcome/EPSRC Centre for Medical Engineering [WT203148/Z/16/Z], the Wellcome Trust Collaboration in Science grant [WT201526/Z/16/Z] and by the National Institute for Health Research (NIHR) Biomedical Research Centre based at Guy’s and St Thomas’ NHS Foundation Trust and King’s College London and/or the NIHR Clinical Research Facility. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health and Social Care.References
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