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Locally low-rank denoising preserves statistical confidence in task-based functional activation under scan duration reduction
Nolan Meyer1, Norbert G Campeau2, David F Black2, Kirk M Welker2, Erin Gray2, Daehun Kang2, MyungHo In2, John Huston2, Yunhong Shu2, Matt A Bernstein2, and Joshua D Trzasko2
1Mayo Clinic Graduate School of Biomedical Sciences, Rochester, MN, United States, 2Radiology, Mayo Clinic, Rochester, MN, United States

Synopsis

Functional MRI activation maps derived from locally low-rank (LLR) denoising of complex-valued time series echo planar imaging (EPI) data were compared to those obtained from conventional non-denoised data for a six-block verbal task-based fMRI exam obtained in five healthy subjects, as data were retrospectively truncated block-by-block. The LLR-denoised fMRI activation maps exhibited superior performance as timeframes were removed in sets of blocks, with acceptable statistical confidence overall in localizing verbal activation following retrospective truncation of scan data. LLR denoising significantly increases temporal signal to noise ratio of timecourse data, a performance advantage which remains stable as timeframes are removed.

Introduction

Blood oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI)1 permits non-invasive mapping of eloquent brain tissue, clinically useful for presurgical and pre-radiotherapy planning purposes.2-4 Acquisition time remains a limitation of clinical fMRI. We previously adapted locally low-rank (LLR)5-8 regularization for task-based fMRI, demonstrating increased statistical confidence in activation maps following LLR denoising of complex-valued echo planar imaging (EPI) time series.9 Here we demonstrate that LLR denoising improves signal integrity with significant increases in temporal signal to noise ratio (tSNR) remaining stable as timepoints are truncated.

Increases in tSNR reduce the number of timepoints required to achieve a certain effect size at a fixed $$$p$$$-value in fMRI data.10 At known tSNR and effect estimate $$$eff$$$, the number of timepoints required to achieve $$$p$$$ can be modeled as

$$N=8\bigg(\frac{erfc^{-1}(p)}{tSNR\cdot{eff}}\bigg)^2 \hspace{1cm}(1)$$
suggesting quadratic decreases in required timepoints as tSNR is increased, all other quantities held constant and under idealized conditions.10 Here we investigate this behavior by truncating fMRI time series data and applying LLR denoising, yielding significant boosts in tSNR, preceding analysis of activation map behavior.

Methods

Define $$$G=X+Z$$$ as a set of $$$T$$$ $$$N\times{N}$$$ complex-valued MR images spatiotemporally rearranged as a $$$N^2\times T$$$ Casorati matrix, with target signal $$$X$$$ and $$$Z\sim CN(0,\sigma^2)$$$ denoting zero-mean complex Gaussian noise. Then LLR denoising comprises singular value thresholding11 implemented blockwise:
$$\hat{X}=C^{-1}\sum_{b\in\Omega}R_b^*\big\{SVT_{\lambda/2}\{R_bG\}\big\}$$
where a binary operator $$$R_b$$$ selects a block $$$b$$$ of size $$$\beta$$$ from a set of overlapping blocks $$$\Omega$$$, with matrix $$$C=\sum_{b\in\Omega}R_b^*{R_b}$$$ and regularization parameter $$$\lambda$$$.

Five healthy volunteers were scanned on a compact 3T MRI scanner12 under an IRB-approved protocol. Imaging parameters were $$$N_x\times{N_y}\times{N_z}\times {N_t}=128\times{128}\times{75}\times{200}$$$ at a $$$24$$$cm FOV, i.e., $$$1.9$$$mm isotropic resolution, with $$$TR/TE=2000/30$$$ms and a $$$77^{\circ}$$$ flip angle. Simultaneous multi-slice acceleration13-17 ($$$R=3$$$) was used, enabling whole-brain acquisition at these spatial and temporal resolutions. In-plane acceleration was omitted. A $$$1.0$$$mm isotropic sagittal MPRAGE facilitated registration. A custom semantic decision language task fMRI exam2 was conducted with $$$6$$$ and $$$1/2$$$ blocks of $$$30$$$ second control and experimental prompts eliciting verbal activation, beginning and ending with control blocks. Full scan duration was $$$6$$$ minutes, $$$40$$$ seconds with $$$10$$$ initial task-free seconds.

Image reconstruction was performed in C++ yielding complex-valued image data. Data were denoised with LLR using $$$\beta=5,\lambda=4\sqrt{N_t}$$$ scaling singular value thresholds as timeframes varied. LLR denoising was completed before saving magnitude image data.

Five sets of timecourse image data were prepared by retrospectively removing $$$60$$$-second blocks from the end of each exam. Data were then either conventionally processed or LLR-denoised before identical processing of scanner DICOM (i.e., control) data and LLR-denoised data with Analysis of Functional Neuroimages (AFNI).18 Initial $$$8$$$ seconds of TRs were discarded before LLR denoising or functional processing depending on processing variant to suppress transient signal.19 Image data were spatially smoothed with a $$$4$$$mm full-width at half-maximum Gaussian blur in processing to mirror local clinical processing practices. Multiple comparisons correction and cluster simulations were omitted in this preliminary methodological analysis of robust clusters, thresholding cluster volumes to $$$40$$$ voxels. For each subject, a spherical region of interest (ROI) enveloping the visual word form area (VWFA) was manually located as a mask to track performance as blocks were truncated. Whole-brain and ROI-specific tSNRs were collected and compared.

Results

LLR denoising yields an average $$$50\%$$$ increase in tSNR measured both whole-brain and within VWFA ROIs as shown in Figure 1, which also illustrates tSNR masked by the ROI used for cluster volume computations in Figure 2. This increase in tSNR remains stable as exam data are truncated in time.

Two sets of individual subject results are shown in Figure pairs 2-3 and 4-5, illustrating comparisons of activation maps for control and LLR-denoised data, for full-duration ($$$6$$$:$$$40$$$) and truncated ($$$4$$$:$$$40$$$; $$$2$$$ blocks subtracted$$$)$$$ exams. Figures 2 and 4 hold $$$p$$$-values fixed to $$$p=1\times{10}^{-6}$$$, while figures 3 and 5 show maps thresholded approximately replicating VWFA ROI active cluster volume of full-duration control data at $$$p=1\times{10}^{-6}$$$. With scan durations held fixed, LLR denoising produces statistical activation maps with either increased VWFA cluster volumes (at fixed $$$p$$$) or increased thresholded $$$t$$$-statistics (at fixed VWFA volumes).

Discussion

fMRI activation maps derived from LLR-denoised data demonstrate a substantial performance increase in cluster behavior and tSNR compared with control following retrospective temporal truncation of exam data. The $$$50\%$$$ increase in whole-brain and ROI-specific tSNR afforded by LLR denoising yields a theoretical reduction to $$$0.44N_t$$$ with removal of $$$3$$$ blocks predicted by Equation 1. We assessed LLR to most appropriately enable truncation by $$$2$$$ blocks, preserving thresholds with $$$p$$$-values held fixed to $$$1\times{10}^{-6}$$$, for subjects shown in Figures 2-5. Idealized results predicted by Equation 1 are difficult to achieve with in vivo data, which exhibits superimposed physiologic signals with biases introduced by functional processing pipelines.10 Nonetheless, removal of $$$2$$$ blocks with preservation of acceptable confidence is significant, with nearly a one third decrease in scan time achieved with acceptable confidence in this retrospective analysis.

Conclusion

Compared to conventional processing, fMRI activation maps derived from LLR-denoised data demonstrate preservation of statistical confidence in localizing active tissue as data are temporally truncated, suggesting potential for shortened exam durations with preservation of clinically acceptable statistical confidence in localizing activation.

Acknowledgements

This work was supported by NIH Grants U01 EB024450 and U01 EB026979 and the National Science Foundation (NSF) Graduate Research Fellowship Program (GRFP).

References

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8. Hu Y, Levine EG et al. Motion‐robust reconstruction of multishot diffusion‐weighted images without phase estimation through locally low‐rank regularization. Magn Reson Med. 2019; 81(2):1181-1190.

9. Meyer NK, Campeau NG et al. Locally low-rank denoising of complex-valued EPI reconstructions preceding task fMRI analysis. Proc Intl Soc Mag Reson Med. 2020; 3877.

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17. Mark IT, Black DF et al. Higher temporal resolution multiband fMRI provides improved presurgical language maps. Neuroradiology 2020.

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Figures

Figure 1. At left, plot in red of VWFA ROI-specific ratios of LLR to control group mean tSNR with error bars showing standard deviation, with overlain plot of whole-brain mean tSNR ratios in cyan. At right, an individual subject (from Figures 2-3) example of an ROI enveloping the visual word form area used for mean tSNR and for cluster volume tracking in Figure 2. LLR significantly increases mean tSNR both in the VWFA ROI and globally.

Figure 2. Single subject (1) maps for six and four task blocks, with $$$p$$$ held fixed at $$$1\times{10}^{-6}$$$ (full scans: $$$180$$$ degrees of freedom $$$[DOF]$$$, $$$t=5.07$$$; truncated scans: $$$120$$$ $$$DOF$$$,$$$t=5.16$$$). Maps are identically slice-locked to localize the visual word form area (VWFA; blue arrows, top left). At top left, full scan, control; top right, full scan, denoised; bottom left, truncated scan, control; bottom right, truncated scan, denoised. Volumes of active voxels within an ROI encompassing the VWFA are overlain (volROI).

Figure 3. Single subject (1) maps for six and four task blocks, thresholded targeting similar cluster behavior of the visual word form area (VWFA; blue arrows, top left). Maps are identically slice-locked to localize the VWFA. At top left, full scan, control; top right, full scan, denoised; bottom left, truncated scan, control; bottom right, truncated scan, denoised. LLR data show VWFA cluster performance increases at fixed scan duration compared with control. Cluster performance of LLR-denoised, temporally-truncated data is similar to that of full-duration control.

Figure 4. Single subject (2) maps for six and four task blocks, with $$$p$$$ held fixed at $$$1\times{10}^{-6}$$$ (full scans: $$$180$$$ degrees of freedom $$$[DOF]$$$, $$$t=5.07$$$; truncated scans: $$$120$$$ $$$DOF$$$,$$$t=5.16$$$). Maps are identically slice-locked to localize the visual word form area (VWFA; blue arrows, top left). At top left, full scan, control; top right, full scan, denoised; bottom left, truncated scan, control; bottom right, truncated scan, denoised. Volumes of active voxels within an ROI encompassing the VWFA are overlain (volROI).

Figure 5. Single subject (2) maps for six and four task blocks, thresholded targeting similar cluster behavior of the visual word form area (VWFA; blue arrows, top left). Maps are identically slice-locked to localize the VWFA. At top left, full scan, control; top right, full scan, denoised; bottom left, truncated scan, control; bottom right, truncated scan, denoised. LLR data show VWFA cluster performance increases at fixed scan duration compared with control. Cluster performance of LLR-denoised, temporally-truncated data is similar to that of full-duration control.

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