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Improved signal integrity in multi-echo fMRI through locally low-rank tensor regularization1Mayo Clinic Graduate School of Biomedical Sciences, Rochester, MN, United States, 2Radiology, Mayo Clinic, Rochester, MN, United States
Synopsis
Locally low-rank (LLR) regularization is extended to a multi-echo tensor framework for resting-state fMRI, building on previous generalizations of LLR frameworks. We demonstrate substantial increases in temporal SNR with improved robustness in mapping default mode, auditory, and sensorimotor resting-state connectivity networks in a preliminary seed-based analysis.
Introduction
Blood oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI)1 in the clinic enables task-based2-4 and resting-state (rs)5-9 physiologic imaging of the brain. Limitations of fast acquisitions (e.g., echo planar imaging [EPI]) enabling functional imaging are inherited by fMRI data, including relatively low signal to noise ratio (SNR) and spatial/temporal resolution along with artifacts, especially signal dropout in regions of susceptibility.10,11 These limitations yield uncertainty in derived activation maps, confounding interpretation and impeding widespread clinical adoption of rs-fMRI.12,13 Advances in system design and next-generation scanners such as the compact 3T14,15 used herein afford enhanced resolution, SNR, and robustness to artifacts, but acceleration techniques required to achieve ultramodern functional acquisitions introduce tradeoffs. Simultaneous multi-slice (SMS) imaging16-21 improves spatial and/or temporal resolution, but with decreased temporal SNR (tSNR) at higher acceleration factors, especially combined with in-plane techniques.22 Multi-echo (ME) fMRI improves performance in regions of susceptibility and boosts statistical power for detecting functional signals,10 but shares SNR limitations when combined with acceleration methods. EPI-based fMRI thus remains SNR limited.We previously adapted locally low-rank (LLR)23-26 regularization ("denoising") for single-echo task-based fMRI, demonstrating increased statistical confidence in derived activation maps following LLR denoising of complex-valued data.27 Here we extend LLR regularization to the multi-echo image time series tensor, adapting previous generalizations28-32 and yielding improved signal integrity and stronger correlation networks achieved at group level for ME-fMRI.
Methods
Define $$$\mathbf{G}=\mathbf{X}+\mathbf{Z}$$$ as an $$$N\times{T}\times{E}$$$ 3-way tensor of dimensions space, time, and echoes. The complete solution of estimating $$$\mathbf{X}$$$ must be determined iteratively. However, the first iteration result arising from a variable splitting approach typically yields sufficient performance and is reported herein. We estimate $$$\hat{\mathbf{X}}$$$ with singular value thresholding33 (SVT) of a specific matricization of $$$\mathbf{G}$$$, i.e.$$\hat{\mathbf{X}}=Q^{-1}C_{(2)}^{-1}\bigg\{\sum_b(I\otimes{R_b})^*SVT_\lambda\big\{(I\otimes{R_b})C_{(2)}\{\mathbf{G}\}\big\}\bigg\}$$
where $$$Q=\sum_b{R_b^*R_b}$$$, $$$R_bC_{(n)}\{\mathbf{U}\}$$$ denotes extraction by binary operator $$$R_b$$$ of a spatial submatrix $$$b$$$ from the $$$n$$$th matricization of tensor $$$\mathbf{U}$$$, $$$\Omega$$$ is the set of overlapping blocks of size $$$\beta$$$ tiling the tensor spatial dimension, $$$\otimes$$$ is the Kronecker product, and $$$\lambda$$$ is a regularization parameter. Here, $$$C_{(2)}\{\mathbf{G}\}$$$ is the $$$NE\times{T}$$$ matricization of $$$\mathbf{G}$$$, orthogonally separating space and echoes from time.
Seven healthy volunteers were scanned under an institutional review board protocol. Whole-brain ME-fMRI acquisition at $$$1810$$$ ms $$$TR$$$ was enabled by a high gradient performance compact 3T (C3T) scanner.14,15 Resting-state fMRI data were collected using a $$$32$$$-channel head coil with imaging parameters $$$N_x\times{N_y}\times{N_z}\times{N_t}=160\times{160}\times{51}\times{234}$$$, $$$22.4$$$ cm FOV, $$$74^{\circ}$$$ flip angle, $$$3\times{3}$$$ through-plane (SMS) and in-plane (ARC) acceleration, and $$$TE=12.10,34.29,$$$ and $$$56.57$$$ ms. A sagittal MPRAGE facilitated registration. Cardiac and respiratory data were collected during fMRI.
Multi-echo fMRI data were jointly denoised with LLR tensor regularization in Matlab on DICOM image data with $$$\beta=8,\lambda=25$$$. Two initial TRs were discarded preceding LLR denoising or functional processing for control.34 Control and LLR-denoised data were then equivalently processed using Analysis of Functional Neuroimages (AFNI), working from afni_proc.py.35 Processing steps included despiking, physiologic nuisance signal removal (RETROICOR),36 slice timing adjustment, alignment and volume registration, T2*-weighted echo combination,11,37 $$$4$$$ mm full-width at half-maximum (FWHM) Gaussian spatial smoothing, and motion- and hardware-related linear regression (ANATICOR).38 Resulting residual time series datasets were atlased to the TT_N27 template.
Functional connectivity analysis entailed computing seed-based correlation maps of the default mode, auditory, and sensorimotor networks. For each network, a $$$5$$$ mm radius ($$$515$$$ voxels) sphere was manually placed within the template and used as a standard mask of atlased individual residual time series for control and LLR-denoised data. Resulting mean time series seeds were used for each subject, processing variant, and network in correlation analysis. Correlation maps were converted to Fisher $$$z$$$-scores for group-level analysis with one-sided $$$t$$$-tests.
Results
LLR denoising provides a substantial quantified increase in temporal signal-to-noise ratio (tSNR). LLR-denoised echo-combined mean global tSNR, grey-matter masked tSNR, and default mode, auditory, and sensorimotor network seed tSNRs were $$$251\%$$$, $$$240\%$$$, $$$180\%$$$, $$$234\%$$$, and $$$210\%$$$ of respective control tSNRs. LLR-denoised data better preserves tSNR in regions of susceptibility, demonstrated in Figure 1. Static image SNR is reported for one subject visually in Figure 2, showing improvements in single-echo and combined-echo image quality through joint denoising. In group-level analysis, LLR denoising afforded robust mapping of default mode, auditory, and sensorimotor resting-state connectivity networks as shown in Figures 3, 4, and 5 with $$$93.3\%$$$, $$$49.9\%$$$, and $$$98.6\%$$$ increases in seed-containing cluster volumes at fixed $$$p=1\times{10}^{-3}$$$.Discussion
Locally low-rank tensor regularization of multi-echo fMRI data yields highly increased tSNR with robustly improved network connectivity maps compared with equivalently processed control data. Increases in tSNR are preserved in regions adjacent to susceptibility. LLR tensor regularization for multi-echo fMRI thus improves functional signal integrity, boosts connectivity detection and introduces potential to reduce scan time leveraging increased tSNR.39 A systematic comparison with existing smoothing methods, functional processing pipeline optimization, and extension to independent components analysis (ICA) is omitted in this preliminary work but will soon be pursued.Conclusion
Locally low-rank regularization extended to a multi-echo tensor framework for resting-state fMRI yields substantial increases in temporal SNR and improved robustness of mapping resting-state connectivity networks demonstrated in a preliminary seed-based analysis.Acknowledgements
This work was supported by NIH Grants U01 EB024450 and U01 EB026979 and the National Science Foundation Graduate Research Fellowship Program (GRFP).References
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