Enhanced clinical task-based fMRI metrics through locally low-rank denoising of complex-valued data

Abstract

Objective

This study investigates a locally low-rank (LLR) denoising algorithm applied to source images from a clinical task-based functional MRI (fMRI) exam before post-processing for improving statistical confidence of task-based activation maps.

Methods

Task-based motor and language fMRI was obtained in eleven healthy volunteers under an IRB approved protocol. LLR denoising was then applied to raw complex-valued image data before fMRI processing. Activation maps generated from conventional non-denoised (control) data were compared with maps derived from LLR-denoised image data. Four board-certified neuroradiologists completed consensus assessment of activation maps; region-specific and aggregate motor and language consensus thresholds were then compared with nonparametric statistical tests. Additional evaluation included retrospective truncation of exam data without and with LLR denoising; a ROI-based analysis tracked t-statistics and temporal SNR (tSNR) as scan durations decreased. A test-retest assessment was performed; retest data were matched with initial test data and compared for one subject.

Results

fMRI activation maps generated from LLR-denoised data predominantly exhibited statistically significant (p = 4.88×10^–4 to p = 0.042; one p = 0.062) increases in consensus t-statistic thresholds for motor and language activation maps. Following data truncation, LLR data showed task-specific increases in t-statistics and tSNR respectively exceeding 20 and 50% compared to control. LLR denoising enabled truncation of exam durations while preserving cluster volumes at fixed thresholds. Test-retest showed variable activation with LLR data thresholded higher in matching initial test data.

Conclusion

LLR denoising affords robust increases in t-statistics on fMRI activation maps compared to routine processing, and offers potential for reduced scan duration while preserving map quality.

Introduction

Task-based blood oxygenation level dependent (BOLD) ¹ functional magnetic resonance imaging (fMRI) is clinically useful for presurgical mapping of cortical brain activity and associations with cerebral pathology preceding interventional therapy for tumors or epilepsy,^2–5 with improved outcomes for patients receiving fMRI before surgical resection. ⁶

Brain activation maps in fMRI are derived from source image data inherently subject to limitations of fast acquisition methods necessitated in measurement. The requirement for temporal resolution enabling dynamic functional imaging introduces tradeoffs including noisy measurements with low signal-to-noise ratio (SNR), spatial resolution, and artifact vulnerability especially in echo planar imaging (EPI) readouts, which are most commonly used. Noise limitations present challenges in precisely and accurately localizing active eloquent cortices of interest, confound clinical interpretation, and necessitate prolonged scan times for sufficient statistical power in functional maps. Such lengthy scans—especially with multiple task paradigms—can be intolerable for ill patients, may conflict with available patient scan time, burden patients in maintaining concentration on task activity, and predispose to increased motion artifact. Uncertainty related to low SNR in fMRI data remains a clinical limitation and has contributed to delaying clinical adoption of resting-state fMRI.^7,8

In this study, we define “noise” specifically as truly random uncertainty within the fMRI signal, originating from stochastic thermal variations in the sample and measurement electronics. While advances in system design and pulse sequence development improve data quality, enhanced signal processing is also essential in refining clinical fMRI. The compact 3T (C3T) MR system ⁹ used in this study is equipped with an advanced gradient system providing reduced echo spacing, improving artifact robustness and enabling acceleration strategies yielding increased temporal and/or spatial resolution depending on the chosen imaging parameters.^10,11 However, dynamic imaging with high spatial resolution at 3T manifests SNR limitations and remains a challenge. Since SNR scales approximately linearly with field strength, performing fMRI at 7T is advantageous, ¹² but is not a practicable solution for all patients and institutions due to cost, siting, safety, and geometric fidelity challenges.^13,14 Through-plane multi-band (or simultaneous multi-slice) acceleration techniques improve temporal and spatial resolution characteristics,^15–19 introducing improvements in fMRI results, ²⁰ but with penalties in temporal SNR (tSNR) at higher acceleration factors, especially when combined with in-plane acceleration. ²¹

MRI data are acquired in quadrature, with complex-valued k-space data naturally reconstructing into complex-valued images. ²² However, complex-valued images are typically unused in clinical fMRI, as scanner-generated magnitude (modulus) DICOM images are typically saved as source data used to compute activation maps. Proceeding past a complex-valued reconstruction to magnitude images introduces cumbersome statistical properties, that is, non-central Chi bias for root-sum-of-squares (RSS) combined non-accelerated phased array data, ²³ of which Rician bias is a special case for single-channel data. ²⁴ By comparison, complex-valued MR image data are well-modeled as zero-mean and Gaussian, amenable to advanced statistical signal processing techniques.

In BOLD fMRI processing pipelines, random noise is conventionally suppressed primarily with spatial smoothing of EPI data for a modular tSNR increase preceding statistical computations. Commonly this entails Gaussian filters applied isotropically ²⁵ or with masking or surface methods to confine smoothing to active gray matter.^26,27 Spatial smoothing is fast and increases SNR and activation sensitivity, but degrades spatial resolution, omits signal properties known a priori, introduces local correlations, and can shift centers of maximal activity and/or merge functionally and anatomically separate tissue.^26,28,29 Adaptive spatial smoothing has been proposed, but requires substantial computation time and is formulated for 2D data. ³⁰ Temporal smoothing has also been pursued, but spatially varying autocorrelation and other fMRI data characteristics present challenges.^31–35

Low-rank matrix denoising methods which exploit inherent redundancy in acquired data have received much recent attention in signal processing and image reconstruction literature, with techniques recently applied to iterative reconstructions of fMRI data.^36–40 Spatial and temporal correlations in fMRI data reduce the rank of its Casorati matrix, ⁴¹ a vectorization of space and time separating orthogonal temporal and spatial dimensions: that is, spatial data (voxels) along rows and temporal data (time series) along columns. This property can be exploited to accelerate fMRI acquisitions or preserve image quality in reconstructing images from undersampled data. Further extending low-rank methods to local spatiotemporal regions of MRI time series data enables effective signal recovery when a fully model-based reconstruction approach would be complicated or intractable, and balances degrees of freedom between the spatial and temporal domains since MRI data typically have spatial dimensionality far exceeding temporal extent. These locally low-rank (LLR) methods and extensions thereof have demonstrated advantages in dynamic, quantitative, and parallel MRI.^42–52

LLR promotes local spatiotemporal coherence and structure over random fluctuation, in this work isolating task-elicited responses of interest. Structured signal components preserved by LLR may include physiologic processes including respiration, pulsation, cardiac motion, and other temporally smooth and low-order processes. ⁴⁴

Various strategies are available for estimating clean BOLD signals from noisy fMRI data. ⁵³ Ideally, noise suppression in an fMRI pipeline should improve statistical and diagnostic confidence in derived activation maps, introduce potential for reduced scan time, incur no penalties in resolution, be parallelizable and amenable to clinical workflow, and derive from first principles leveraging advantageous statistical properties. We will demonstrate all the above with a post-reconstruction, single-iteration process applied to complex-valued EPI data preceding task fMRI analysis using standard pipelines. Preliminary versions of the material in this work were presented.^54–56

Methods

A broad overview of study design with functional acquisitions, LLR denoising, processing, and analyses is given schematically in Supplementary Figure 1. Detailed descriptions follow in respective sections.

Data Acquisition

Eleven healthy volunteers (9 females, 2 males, 1 left-handed), with ages ranging from 21 to 46 years, were scanned under a Mayo Clinic institutional review board (IRB)-approved protocol (number 14-001036) after obtaining written informed consent. Acquisitions were completed on a compact 3T MR scanner ⁹ running a General Electric (GE) DV26 software platform. The C3T is not CE cleared in the European Union or 510(k) cleared by the United States Food and Drug Administration (FDA), but has been in continuous service for research since March 2016. The C3T scanner has a high-performance gradient system capable of achieving simultaneous 80 mT/m maximal gradient amplitude with 700 T/m/s slew rate with peripheral nerve stimulation rarely observed and readily managed when observed. ⁵⁷ Scans were acquired with a 32 channel coil (Nova Medical, Wilmington, MA, USA) and included a standard 1.0 mm isotropic T1-weighted MPRAGE ⁵⁸ for anatomic reference followed by task-based functional acquisitions with motor and language paradigms currently used in our clinical practice for presurgical functional mapping.^4,5 Task paradigms were (in order) rhyming, alternating bilateral finger tapping, sentence completion, and semantic decision. Functional MRI stimuli were presented using Prism Acquire^® (RRID:SCR_016977; Elm Grove, WI; https://www.prismclinical.com). ⁵⁹

All fMRI acquisitions were echo-planar based with common imaging parameters of 24 cm FOV, TR/TE = 2000/30 ms, and flip angle 77°. Multi-band through-plane acceleration ¹⁹ was utilized enabling whole-brain acquisition at respective spatial and temporal resolutions of functional series. Rhyming and sentence completion acquisitions were completed at 2.5 mm isotropic spatial resolution (96×96×66 matrix), with multi-band acceleration factor R = 2; finger tapping and semantic decision acquisitions, 1.9 mm isotropic resolution (128×128×75) with multi-band R = 3. In-plane acceleration was not used.

In the rhyming task paradigm, subjects viewed word pairs in the 20 seconds experimental block and tasked with a button press if words rhymed; control blocks displayed sets of vertical and diagonal bars eliciting button presses for matching bar sets. In sentence completion, subjects subvocally completed legible incomplete sentences with blanks in 20 seconds experimental blocks; they passively viewed nonsensical sentences with blanks in control blocks. The finger tapping task included alternating 20 seconds periods of rest, tapping fingers of the right hand, then of the left hand in four cycles. In the semantic decision task, subjects evaluated word pairs which were possibly related by categories (e.g., fruit; pear) and pressed buttons for related words; similarly to rhyming, subjects pressed buttons for matching bar pairs during control blocks. All functional acquisitions were executed for 120 time points (4:00 minutes duration) with alternating control and experimental blocks of equal duration and number except for the semantic decision task, which had 10 initial task-free seconds preceding six full pairs of 30 seconds control and experimental blocks, ending with an additional control block for a 6:40 duration.

Image reconstruction and denoising

We define the set of noisy measured MRI signals $G=X+W$ as an $N^2\mathrm{\times }T$ Casorati matrix^42,44 rearranged from a length T time series of complex-valued $N\mathrm{\times }N$ MR images, with $W\sim CN\left(0,{\sigma }^2\right)$ representing zero-mean independent and identically distributed (i.i.d.) complex Gaussian noise with variance ${\sigma }^2$ . Denoising comprises the estimation of the clean latent MR images X from the set of noisy images G. This is herein done through a Bayesian maximum a posteriori (MAP) estimation process comprising regularized least squares estimation. Specifically, locally low-rank (LLR) denoising^42,44 is used to promote estimation of results favoring local spatiotemporal coherence over noise-induced random fluctuations. This is achieved by solving the following cost function-based optimization problem:

$$\widehat{X}=\underset{X}{{\displaystyle \arg \min }}\left\{\lambda {\displaystyle \sum _{b\mathrm{\in }\mathrm{\Omega }}{\Vert R_{b}X\Vert }_{\ast }+{\Vert X-G\Vert }_F^2}\right\}$$ (1)

where R _b is a block extraction operator that selects a subset of rows from the target X, representing a bth $\beta \mathrm{\times }\beta \mathrm{\times {\rm T}}$ spatiotemporal region of image data from a set $\mathrm{\Omega }$ of overlapping regions; ${\Vert \hspace{0.17em}.\hspace{0.17em}\Vert }_{\ast }$ and ${\Vert \hspace{0.17em}.\hspace{0.17em}\Vert }_F$ respectively denote nuclear and Frobenius norms; and $\lambda$ is a user-selected denoising parameter dictating the filtering level. While exactly determining $\widehat{X}$ requires computationally expensive iterative numerical methods, we demonstrate sufficient performance from a single pass of a standard variable splitting routine for solving this problem. The LLR denoising task estimates X as

$$\widehat{X}=C^{-1}{\displaystyle \sum _{b\mathrm{\in }\mathrm{\Omega }}{R}_b^{\ast }\left\{SV{T}_{\tau }\left\{R_{b}G\right\}\right\}}$$ (2)

for diagonal matrix $C={\displaystyle {\sum }_{b\mathrm{\in }\mathrm{\Omega }}{R}_b^{\ast }{R}_b}$ and where SVT is the conventional singular value thresholding operator^44,60 with threshold $\tau$ (proportional to $\lambda$ ).

Image reconstruction was completed in C++ using the General Electric Orchestra (GE Healthcare, Waukesha, WI; version 1.7–1) and Eigen ⁶¹ software libraries to obtain complex-valued reconstructions. Coil channel data were combined with the method of Roemer ⁶² after multi-band unfolding. LLR denoising was completed with β = 8, λ = 5β² (320) for rhyming, sentence completion, and finger-tapping image data to be assessed by radiologists; and $\lambda =1.5{\beta }^2\sqrt{N_t}\left(96\sqrt{N_t}\right)$ for data undergoing retrospective truncation of exam duration. Values of λ were manually tuned as multiples of β² and for data processed under scan duration truncation, scaled by $\sqrt{N_t}$ to balance fidelity and denoising as timeframes varied. First singular values were unaltered to preserve contrast. EPI time series volumes were denoised with LLR, then saved as magnitude DICOMs for functional processing.

Functional processing

Functional processing was completed enabling three analyses comparing control (vendor-generated DICOM) and LLR-denoised images: (1) analysis of rhyming, sentence completion, and finger tapping fMRI activation maps by clinical neuroradiologists; (2) examination of performance characteristics under scan duration reduction for all paradigms; and (3) test-retest evaluation for one volunteer. fMRI processing was completed using AFNI, with a general linear model approach. All experiments were block-design in presentation of task stimuli and analysis. Hemodynamic responses of interest were modeled as predetermined waveforms tailored to block-design experiments, obtained by convolving a binary function indicating stimulus timing with an assumed response function, for example, a gamma-like function for the scan truncation analysis.

In the radiologist-led analysis, routine non-denoised DICOM data (i.e., control) and LLR-denoised data from task-based fMRI acquisitions were equivalently processed with Prism Process^®, ⁵⁹ the FDA-cleared fMRI software tool used in clinical practice at our institution, employing Analysis of Functional Neuroimages (AFNI) as a processing engine. ²⁵ Processing matched that used in routine clinical fMRI as closely as possible. The first four TRs were discarded to suppress transient signal before LLR denoising or conventional processing depending on processing variant in all analyses. ⁵³ Pre-processing steps included slice timing correction, volume registration and motion correction with 6-degree rigid body transformations, and spatial smoothing of EPI data with a 4 mm full-width at half-maximum (FWHM) Gaussian kernel. Computation of effect coefficients was completed with ordinary least squares regression (3dDeconvolve in AFNI) using predetermined waveforms modeling expected task-inherent responses; significance testing on effect coefficients yielded t-statistic activation maps. Resulting t-statistic maps were filtered to a specified 4 mm FWHM for reader thresholding of activation maps overlain on anatomic images. Clusters were thresholded to 210 μL in volume.

Analysis of LLR as a mechanism for scan time truncation was completed using data from all task paradigms. The scan time truncation analysis required high-throughput processing of more than 30 relatively high-resolution data sets from all subjects, paradigms, processing variants, and durations. Hence, rather than burdening our clinical system, this analysis was completed on a Linux server. Activation maps were generated from non-denoised and denoised image data at sets of durations respective to the task paradigm. Image data were retrospectively truncated from the end of the exam preceding either ordinary processing or LLR denoising followed by processing. For the semantic decision paradigm, beginning with full duration exam data, 60 seconds block pairs were retrospectively truncated from the end of each exam, from durations of 6:40 to 2:40 minutes. For all other paradigms (rhyming, finger tapping, sentence completion), data were truncated from 4 minutes to 2 minutes in 40 seconds (20-TR) increments for four distinct processing durations each. For rhyming and sentence completion, this corresponded to truncation by one block pair per increment. For finger tapping data, which utilized three sets of alternating blocks (control, tap right, and tap left), this corresponded to arbitrary retrospective truncation of data. Functional analyses of truncated data were completed using AFNI, which serves as the functional engine of Prism, again imitating local clinical preferences. Pre-processing steps included slice timing correction; alignment to anatomic images with 12-degree affine transformations combined with EPI volume registration and motion correction using 6-degree rigid body transformations, and spatial smoothing with a 4 mm FWHM Gaussian kernel. Alignment and motion parameters of full-duration data were stored and re-used for truncated data. Regression was completed with ordinary least squares (3dDeconvolve in AFNI) yielding t-statistic maps. Mean and derivative motion parameters were used as regressors of no interest.

In a test-retest reliability assessment, one volunteer was rescanned several months after their initial session. Re-test data were processed using Prism.

Reader assessment

Four board-certified neuroradiologists (DB, NC, KW, JH), respectively, with 10, 22, 23, and 32 years of experience practicing radiology and 10, 3, 14, and 14 years of experience in clinical fMRI assessed activation maps of control and LLR data by visually optimizing filtered t-statistic thresholds for all paradigms and subjects. Thresholds were set by consensus of the neuroradiologists, all present for each analysis, and adjusted to provide the most informative map for neurosurgical navigation, balancing the needs to clearly demonstrate eloquent cortical activations while minimizing noise in the statistical map. This custom thresholding step is needed because of intra-subject variability in the strength of the BOLD response and mirrors the method in which fMRI statistical maps are clinically prepared for neurosurgical guidance. Assessments were completed in consensus to reduce impacts of operator dependence, inter-observer variability, and subjectivity in functional map interpretation.

For motor and language task paradigms, region-specific thresholding was completed before thresholding aggregate activation maps as if reading clinically. Motor map assessment entailed specifically thresholding the supplementary motor area (SMA), primary non-dominant and dominant motor clusters, cerebellum, and finally aggregate maps. Language map assessment encompassed thresholding of Broca’s and Wernicke’s areas, then aggregate maps, for rhyming and sentence completion. For aggregate maps, care was taken by the neuroradiologist team to assign thresholds which produced LLR-denoised maps which were as close as possible to those generated from non-denoised data. For instance, if an aggregate motor map was set to preserve SMA activation along with the nondominant and dominant motor clusters for non-denoised image data, then an LLR-denoised map was accordingly thresholded to preserve approximately the same activation patterns. For specific task paradigms and threshold targets (e.g., rhyming/Wernicke’s), if data showed insufficient BOLD signal with poor activation or motion artifact unacceptably confounding thresholding, or t < 1 for either control or LLR data, then both control and LLR data were discarded from subsequent analyses.

Consensus statistical thresholds for each region and aggregate map were recorded and statistically assessed with nonparametric right-tailed Wilcoxon signed rank tests, hypothesizing that LLR t-statistics exceeded those of control. Matched-pairs rank-biserial correlations were computed as nonparametric analogs of effect size. ⁶³ Resultant p-values for rhyming and sentence completion data were combined with Fisher’s method, yielding fused p-values reflecting both language paradigms respective to each threshold target. 11 subjects were scanned and evaluated to exceed nine subjects required to demonstrate statistically significant improvements assuming a 10% expected score difference, 10% standard deviation within scores, 80% power adjusted to 84% for nonparametric tests, and 5% significance level. During initial testing, score differences exceeding increases of 10% were consistently observed and we conservatively opted for hypothesized 10% differences and standard deviations.

Scan truncation analysis

A region of interest (ROI) analysis tracked evolution of tSNR and t-statistics as data were progressively truncated. Using 1.0 mm isotropic MPRAGE image data, ROIs were selected as a manually placed 6 mm radius (925 voxels) spherical mask enveloping active cortex respective to task paradigms. ROIs were selected using full-duration control data for each subject. Data specific to subject and task paradigm which were omitted in the radiologists’ analysis due to motion artifact were also not assessed in the scan truncation analysis. For semantic decision data, ROIs were placed in occipitotemporal cortex along the left fusiform gyrus at the visual word form area (VWFA). The VWFA was selected as a site of clinically significant BOLD activation that is typically less robust than Broca’s or Wernicke’s area, therefore providing a sensitive site for monitoring effects of exam length truncation. However, the VWFA showed variable activation between language paradigms and subjects. Thus, for rhyming data, ROIs were placed within Broca’s area; and for sentence completion, within Wernicke’s area accordant with clinical recommendations of task paradigms to visualize activation of these areas. ⁴ For finger tapping data, two separate ROIs were placed within dominant and non-dominant primary motor cortical areas and each were assessed.

A single-subject set of activation maps was additionally selected for comparison with assessment of activation maps from all task paradigms, at full and reduced durations, with and without application of LLR denoising. A 15 mm radius sphere enveloping the VWFA was placed in a subject whose maps exhibited concordant VWFA activation among all language paradigms. Additionally, two 15 mm radius spherical ROIs were placed enveloping dominant and non-dominant motor cortex and used to assess map metrics. For this subject, maps were first thresholded setting t-statistics such that p = 1×10⁻⁹, and for all paradigms, resulting volumes of surviving clusters within each ROI were recorded; second, maps were thresholded to match ROI volumes of full-duration control data and resulting t-statistics were recorded, for all paradigms. Clusters were thresholded to 40 voxels in volume and maps recorded for comparison.

Test-Retest analysis

In analyzing retest data, filtered t-statistical maps were exported and analyzed using AFNI alongside initial test data set to consensus thresholds. Test-retest characteristics were assessed using Dice coefficients.^64,65 Retest data cluster masks were computed through a range of t-statistic values equispaced by 0.05. Thresholds maximizing Dice coefficients between initial and retest cluster masks were selected matching control and LLR test and retest data. Retest data were thresholded accordingly in Prism and activation maps recorded.

Results

Absolute runtime for LLR denoising, parallelized in-plane, on a 2.9 GHz Intel Core i9 6-core machine with 32 GB of 2400 MHz DDR4 memory required approximately 9 s per slice for N _x ×N _y ×N _z ×N _t = 96×96×66×116 matrix data (rhyming, sentence completion; initial 4 TRs discarded), 20 s per slice for 128×128×75×116 matrix data (finger tapping), and 25 s per slice for 128×128×75×196 matrix data (semantic decision).

Two subjects were discovered during radiologists’ assessment to have insufficient BOLD signal for at least one language task series. One subject’s sentence completion task data showed severe motion artifact preventing the reader team from assigning suitable thresholds for each thresholded region (t < 1 for each threshold target). Another subject’s rhyming task data exhibited minimal activation in Wernicke’s area only, whereas suitable thresholds were obtained for Broca’s area and in aggregate. These data were considered by the assessing radiologists to be too poor for analysis and were discarded. ⁶⁶ Following this, there remained at least 10 threshold pairs for each subject, task paradigm, and threshold target.

In consensus neuroradiologist assessment, LLR enabled setting of t-statistical maps to higher thresholds. Reducing LLR thresholds to those of control inflated activation patterns. Conversely, setting control thresholds to those of LLR extinguished active clusters. Examples of both characteristics are shown for language and motor single-subject activation maps in Figure 1 and Figure 2, showing motor data as filled clusters and superimposed language data as overlapping rings.

Figure 1.

Full set of single-subject motor and language activation maps at neuroradiologists’ consensus thresholds. Left quadrant set (a) shows motor (finger tapping) data; right quadrant set (b), language (rhyming and sentence completion) data. Each quadrant set shows, at top left, control data at respective threshold; at top right, LLR data at control threshold; at bottom left, control data at LLR threshold; at bottom right, LLR data at respective threshold. LLR data exhibit higher thresholds for all paradigms, with increased activation at control thresholds. Control data set at LLR thresholds show diminished activation patterns, with near complete loss for nondominant motor (white arrows, (a), at bottom left) and substantial loss in Broca’s and Wernicke’s areas for both language paradigms (white arrows, (b), bottom left).

Figure 2.

Second example of a full set of single-subject motor and language activation maps at neuroradiologists’ consensus thresholds. Quadrant sets (a) and (b) are shown as in Figure 1. LLR data exhibit higher t-statistical thresholds set in consensus for all task paradigms, with inflation of activation at control thresholds. Control data set at LLR thresholds show weakened activation, with complete loss for nondominant motor (white arrow, (a), at bottom left) and sentence completion signal in Broca’s area (white arrow, (b), bottom left).

LLR denoising resulted in increased region-specific thresholds. We report results as significant or not with respect to p-values resulting from Wilcoxon signed-rank tests, relative to α = 0.05. In all cases but one (the cerebellum), LLR thresholds exceeded control with statistical significance. Additionally, we supplement our results with nonparametric effect estimates computed as matched-pairs rank-biserial correlations (r-values), that is, differences in rank sum proportions ⁶³ consistent or inconsistent with hypothesized increases in LLR thresholds. In all cases these were positive and exceeded 0.5. This indicates rank sum proportions favoring LLR thresholds over control, and thereby nontrivial increases in effect through LLR. These results are tabulated with means and standard deviations alongside corresponding matched-pairs rank-biserial correlations r and p-values in Table 1, with quotients visualized in Figure 3. LLR denoising yielded statistically significant improvements in consensus thresholds, with nontrivial increases reflected in r, for all motor thresholds except the cerebellum (r = 0.546, p = 0.062), and all language thresholds. Language p-values fused between rhyming and sentence completion variants were significant for Broca’s area (p = 1.40×10⁻⁵), Wernicke’s area (p = 4.55×10⁻⁴), and in aggregate (p = 2.78×10⁻⁴). While LLR did not outperform control data for certain paradigms and subjects, it preserved diagnostically relevant information in activation maps lost at control thresholds; examples of the two threshold target cases where control most strongly outperformed LLR are shown in Figure 4.

Table 1.

Consensus t-statistical thresholds (t) for control and LLR by region with mean and standard deviation (µ ± σ) by task (FT: finger tapping; R: rhyming; SC: sentence completion), with respective matched-pairs rank-biserial correlations r and p-values. Also shown are mean and standard deviation LLR to control threshold ratios corresponding to error bars in Figure 3.

Region (task)	Control t: µ ± σ	LLR t: µ ± σ	Ratio: µ ± σ	r	p
SMA (FT)	2.90 ± 0.84	3.15 ± 0.95	1.09 ± 0.13	0.606	0.042
Cerebellum (FT)	4.54 ± 1.45	4.93 ± 1.52	1.10 ± 0.16	0.546	0.062
Nondominant motor (FT)	6.24 ± 1.97	7.23 ± 2.35	1.17 ± 0.16	0.879	3.42×10−3
Dominant motor (FT)	7.21 ± 2.82	8.31 ± 3.29	1.16 ± 0.07	1	4.88×10−4
Aggregate (FT)	6.14 ± 2.13	7.12 ± 2.54	1.17 ± 0.14	0.849	4.88×10−3
Wernicke’s area (R)	3.27 ± 0.55	3.85 ± 0.99	1.19 ± 0.30	0.636	0.042
Broca’s area (R)	3.54 ± 0.98	4.26 ± 1.36	1.20 ± 0.12	1	4.88×10−4
Aggregate (R)	3.24 ± 0.68	3.68 ± 0.95	1.13 ± 0.12	0.849	4.88×10−3
Wernicke’s area (SC)	3.87 ± 1.22	4.94 ± 1.64	1.28 ± 0.12	1	9.77×10−4
Broca’s area (SC)	3.46 ± 1.18	4.20 ± 1.52	1.21 ± 0.13	0.964	1.95×10−3
Aggregate (SC)	3.66 ± 1.20	4.24 ± 1.52	1.17 ± 0.14	0.891	4.88×10−3

Figure 3.

Ratios of LLR to control consensus threshold data for motor (left) and language (right) paradigms. Individual points show subject-level ratios of threshold targets. Horizontal bars and vertical error bars show mean and standard deviation, respectively. Dashed horizontal line indicates unity. Mean ratios for all regions and tasks favor LLR over control.

Figure 4.

Two examples from different subjects for which specific regions were thresholded with control most strongly outperforming LLR. Top row shows finger tapping thresholds of the SMA (white arrows) for one subject (S1). At LLR threshold, the SMA has similar size of control but with additional prefrontal and cerebellar activation reflected in the aggregate map threshold where control (t = 5.42) underperformed LLR (t = 5.92). Bottom row shows, for another subject (S2), rhyming thresholds for Wernicke’s area (white arrows) again with additional prefrontal and Broca’s area activation for LLR represented in aggregate maps where control threshold (t = 3.12) modestly exceeded LLR (t = 2.91).

LLR data showed increased t-statistics and tSNR over control in analyzing evolution of performance metrics under scan duration truncation. Advantages at a single-subject level are shown in Figure 5 and Figure 6, demonstrating activation map quality of reduced-duration LLR data rivaling that of full-duration control. This corresponded with truncation by 2 minutes of scan duration for semantic decision data (of 6:40 full duration) and by 1 minutes and 20 seconds for the 4-minutes paradigms. Increasing t-statistics to match region of interest volumes of full-duration control data tended to show affinity for increased thresholds to isolate activation in these areas for full-duration LLR data, although with some loss of subtle activation for certain paradigms, for example, as seen for sentence completion. Conversely, activation maps computed from data which had been truncated, but LLR-denoised, tended to show map quality comparable to full-duration control. Not all ROIs exhibited strong benefits from LLR denoising, for example, with strong boosts in activation for non-dominant motor cortex but modest enhancement for dominant motor. Nonetheless, quantifying on a region of interest basis, on average, LLR data exhibited increases in ROI t-statistics and tSNR exceeding 20% and 50%, respectively. These performance advantages remained stable under scan duration truncation, albeit with more variability when truncated to 2 minutes. These characteristics are shown with individual, group level, and LLR to control quotient plots for all paradigms in Figure 7.

Figure 5.

Scan truncation analysis for a single subject. Lettered quadrants show maps for all paradigms according to duration (full or reduced) and processing variant (control or LLR). (a), full-duration control maps; (b), full-duration LLR maps; (c), reduced-duration control maps; (d), reduced-duration LLR maps. Each map is in radiological convention, and labeled with respective task paradigm (Sem. Dec: semantic decision; Sent. Comp: sentence completion) and absolute scan time. Activation maps are thresholded such that p = 1×10⁻⁹ with corresponding t-statistics also shown. V_ROI for language paradigms indicates volume in voxels of a 15 mm radius spherical ROI encompassing the visual word form area (white arrows). V_D-ROI and V_ND-ROI for finger tapping indicates volume of 15 mm radius spherical ROIs enveloping the dominant and non-dominant primary clusters (red and blue, respectively). LLR increases activation at fixed duration, and at reduced duration, produces activation patterns similar to full duration control for most paradigms.

Figure 6.

Scan truncation analysis for a single subject. Lettered quadrants show maps accordant with Figure 5. Activation maps are thresholded to match volumes within ROIs for full-duration control data as closely as possible. For motor data, two distinct maps thresholded to match both the dominant and non-dominant ROIs are shown as spliced maps, indicated by white dashed lines. LLR enables more aggressive thresholding at full duration or matching of V_ROI at reduced duration depending on paradigm and ROI.

Figure 7.

Evolution of t-statistics and tSNR with varying durations for all task paradigms. Each panel is labeled on the independent axis with scan duration, from truncated to full. Plots show group mean and standard deviation of t-statistics and tSNR plotted as lines with error bars, and single-subject data as individual shapes aligned vertically with horizontal offsets for visualization. Data are shown for regions of interest specific to task paradigm: the visual word form area (VWFA) for semantic decision; Wernicke’s area for sentence completion; Broca’s area for rhyming; and dominant and non-dominant primary motor cortex for alternating bilateral finger tapping. LLR data exceed control in both performance metrics under truncated duration, with mean increases in ROI t-statistics and tSNR respectively exceeding 20 and 50% for most durations and paradigms.

Test-retest assessment of one subject yielded decreased magnitude and topological shifts of BOLD signal for rhyming and finger tapping scans for control and LLR data. In maximizing Dice coefficients between test and retest data, LLR maps achieved higher t-statistical thresholds. Figure 8 shows respective test and retest activation maps.

Figure 8.

Retest results for the subject shown in Figure 2. Activation strength and location varied on retest especially for rhyming. On maximizing Dice coefficients (D_max) in thresholding retest data to reader-thresholded initial test data, LLR data achieve higher thresholds.

Figure 9 shows static echo planar images with and without application of LLR denoising. Visual differences are apparent, especially for the 1.9 mm isotropic image, with difference images showing no visually discernible brain structure.

Figure 9.

Example static images without (“Control”) and with LLR denoising for 1.9 mm isotropic (used in finger tapping and semantic decision task paradigms) and 2.5 mm isotropic (rhyming and sentence completion) acquisitions. Images are matched by slice location and in time. Images are identically windowed; insets are additionally shown, identically windowed for effect. Difference images show noise only with no visually discernible structure within the brain.

Discussion

Three distinct analyses demonstrate advantages of LLR denoising over conventional processing. With LLR, fMRI activation maps could be thresholded to higher t-statistics compared to maps derived from non-denoised image data, increasing diagnostic confidence. Alternatively, in evaluating LLR maps, setting thresholds to those of control tended to reveal areas of activation suppressed in standard analysis. When thresholds of control data exceeded those of LLR, map quality of LLR data showed advantages, preserving activation lost by control at respective thresholds. Examination of data from the sole subject for whom LLR was consistently outperformed by control showed signs of over-filtering, that is, selection of a $\lambda$ effective for all but this subject. In general, $\lambda$ is tunable to fixed imaging protocols providing good results for most subjects; practitioners may vary $\lambda$ if unexpectedly poor results are encountered.

Random noise directly affects performance metrics commonly used to assess fMRI data. Noise suppression enhances SNR, and thereby tSNR and t-statistics in functional maps. These advantages should enable scan time reduction while preserving acceptable statistical confidence in inferring and localizing activation. Increases in tSNR introduce a possibility to reduce the number of timepoints required to achieve a certain effect size. ⁶⁷ LLR data exhibited substantial advantages in tSNR and t-statistical data on average, for most subjects and task paradigms, as scan duration was reduced. In analyzing single-subject activation maps, we assessed LLR to enable truncation to 70% of full duration while outperforming control, preserving cluster volumes at fixed p-values, demonstrating potential for accelerated scans preserving diagnostic characteristics. Variable enhancement of activation at low durations reflects reliance of activation inference on scan duration in general, and differential enhancement of specific regions via LLR denoising may reflect region-specific BOLD response variability.

Our test-retest reliability assessment yielded BOLD signal changes on retest. Decreases in activation magnitude and changes in location, especially for rhyming, were common to both control and LLR, reflecting test-retest reliability limitations of fMRI in general. ⁶⁸ Consistent with other analyses, LLR data showed higher thresholds than control on initial test data thresholded by radiologists, and on retest using Dice coefficients.

In this work, LLR was applied specifically on complex-valued image data, leveraging respective advantages upstream of any post-processing. Investigating LLR applied at different stages of an image reconstruction and post-processing pipeline would require applying LLR to magnitude data and was not pursued given associated suboptimalities. Additionally, interpolations in (e.g.) volume registration impart local noise correlations, possibly resembling structure and precluding mitigation by statistical algorithms. More broadly, LLR is fully compatible with signals containing structured spatiotemporal processes including periodic physiologic fluctuations and motion. ⁴⁴

This work is clinical in emphasis. In fundamental contrast to fMRI in neurocognitive research, which often serves as a tool to understand brain function through differences hypothesized and analyzed at group level, clinical fMRI is solely focused on functional diagnostics for individual subjects whose neuroanatomic dynamics may be suppressed in group-level analysis. ⁶⁹ The goal in clinical fMRI is identification of eloquent cortex and its location relative to a surgical target through neuroradiologists’ interpretation of single-subject results, for the benefit of a surgical team and ultimately the patient’s postsurgical function. Activation thresholds need to be assessed on a per-subject and possibly per-region basis due to interindividual variability in BOLD responses, obviating use of predefined thresholds and necessitating case-specific evaluation. This work emulated presurgical fMRI for which individual neuroanatomic and functional diagnostics are of sole interest, ⁵ with clinician-generated maps.^66,70

This study emphasized differences in t-statistics, which are a useful metric in clinically-focused fMRI studies.^20,71–73 In further single-subject studies, fMRI activity peaks derived from t-statistics have been used to predict peak of activity in ECoG measurements in prefrontal cortex, with utility in functional localization for brain-computer interfacing; ⁷⁴ and t-statistic peaks from fMRI at 7T have been shown to match activity peaks measured with ECoG. ⁷⁵ While t-statistics are influenced by variance and differ across and within subjects, they nonetheless facilitate functional localization of activity in single subjects. If study design accounts for these characteristics, t-statistics are a suitable metric for performance evaluation of a denoising algorithm under consideration for clinical use. Acknowledging inter-subject and intra-subject variability of t-statistics, in this work multiple specific neuroanatomic regions in addition to aggregate maps were thresholded for all subjects. This resulted in pairs of thresholds for maps generated from non-denoised and denoised image data. For targeted regions (e.g., SMA; Broca’s area), differences among threshold pairs were attributable not to subject or region, but to application of LLR denoising. For aggregate maps, region-specific variability exerted influence on assigned thresholds. However, since aggregate maps were thresholded to produce denoised and non-denoised maps which were as similar as possible, the increased thresholds assigned to aggregate maps are primarily attributable to LLR. Additionally, to augment t-statistics, we have supplemented our results with additional measures of temporal SNR in the scan truncation analysis.

Our primary analysis encompassed direct comparisons by clinicians between maps generated from LLR-denoised data versus conventional data, where removal of LLR from the pipeline would yield the control result. Radiologists experienced in clinical fMRI compared maps generated in all cases following local processing preferences, focused in scope to assessment of a novel denoising method compared with current practice. As utility to practicing clinicians was the primary motivating factor, and to make assignment of t-statistic thresholds specific to subjects, brain regions, and processing variants as controlled as possible, we utilized consensus evaluation of experienced readers. Some subjectivity is inherent to this analysis, but the experience and number of radiologists involved reduce potential for misclassification of results. Due to the time-intensive nature of interactive radiologist assessment of the results presented in this work, in this study LLR denoising performance was compared only against the standard clinical workflow of our institution. Use of automated thresholding techniques such as AMPLE ⁷⁶ could reduce subjectivity in assessment of results; however, interpretation of map character with and without application of LLR denoising with automated thresholding may itself require consultation with clinical readers. Thus, for this work, we elected direct assessment by clinicians. Adaptation of other image denoising algorithms for task fMRI and comparative assessment of their performance against LLR denoising will be the subject of a separate, future work. While objective quantitative measures were utilized in the ROI-based exam truncation analysis, further assessment pursuing strictly numeric metrics could be pursued in separate future work—although identifying quantitative metrics strongly correlating with clinical preference is nontrivial, hence our selection of t-statistics and tSNR. Also tangential to this work is expansion of test-retest assessments with additional subjects. Analysis of LLR for functional connectivity analysis will be pursued in separate future work.

Limitations of this work include a small sample size consisting of healthy subjects, which nonetheless exceeded the predicted sample required to demonstrate hypothesized results. Acquisitions were completed with spatial resolutions relatively high for clinical fMRI at 3T to explore the possibility of localizing activation with improved spatial fidelity through LLR. While functional processing was performed exclusively with general linear model analysis enabled by AFNI, this approach has been clinically vetted at our institution.

This work proceeded from initial development of LLR denoising of cardiac image data,^42,44 with subsequent application of LLR to clinical fMRI. There are several recently published studies which are appropriate to recognize and distinguish, including the independent development and publication of NORDIC. ⁷⁷ While NORDIC also uses locally low-rank modeling to suppress noise in complex-valued fMRI image time series, it differs from our approach in by utilizing scaling to adjust for geometric factor noise effects, employing hard rather than soft thresholding of singular values using empirically determined numeric thresholds, and application to 3D in addition to 2D volumes. In contrast, this work did not utilize in-plane parallel imaging, avoiding a need for g-factor corrections; uses soft thresholding with manually tuned thresholds; and has parallelized processing of 2D volumes for speed. We intend to study resulting performance differences in future work. In the later stages of this study, the publication of another study employing a similar analysis of presurgical task paradigms and scan duration reduction came to our attention. ⁷⁸ In contrast, LLR denoising implemented in this study makes no assumptions of a Gaussian distribution of noise in magnitude MRI data—in particular, EPI time-course images—staying within the complex domain as noise suppression is applied given aforementioned characteristics of these data types. Our study additionally entailed a further exploration into consensus assessment by multiple clinical readers in consensus, tracking group-level tSNR and single-subject ROI cluster characteristics under scan duration truncation, while following local clinical processing preferences including smoothing. We also acknowledge recent work extending the LLR methods underlying this work^42,79 to model-based iterative reconstruction (MBIR) for a custom fMRI sequence. ⁸⁰ While MBIR methods will generally outperform non-iterative post-reconstruction implementations, they require significantly higher computational expense and were not considered in this study.

LLR denoising as presented herein operates on complex-valued MRI data, representing a method upstream of and amenable to various functional processing strategies. It is thus compatible with both magnitude and phase-based fMRI techniques, as phase fMRI signals contain valuable functional information^81–87 as BOLD contrast originates from susceptibility effects and techniques utilizing complex-valued data have demonstrated advantages.^88–94 The signal model is agnostic to motion and physiologic effects, and amenable to subsequent correction strategies. It is compatible with functional analysis via both general linear model and independent components analysis. LLR is parallelizable, has reasonable processing time, is straightforward to tune, and can integrate seamlessly into clinical workflows.

Conclusion

LLR denoising of complex-valued time-course EPI data preceding functional analyses introduces significant advantages. Assessment by neuroradiologists demonstrates that activation maps derived from LLR-denoised data can be thresholded to higher t-statistics compared to routine non-denoised fMRI maps, increasing diagnostic confidence. Alternatively, LLR maps held at thresholds of control data tend to reveal additional areas of activation which may be suppressed in standard analyses. LLR data have distinct advantages additionally quantified in tSNR and t-statistics shown in a ROI-based analysis under scan duration reduction. These improvements yield potential for reduced scan times. LLR is implemented on complex-valued time series data, representing a versatile strategy amenably interfacing with a variety of subsequent processing techniques.

Appendix.

Abbreviations

blood oxygenation level dependent

(BOLD)

functional magnetic resonance imaging

(fMRI)

echo planar imaging

(EPI)

compact 3T

(C3T)

locally low-rank

(LLR)

temporal SNR

(tSNR)

ORCID iD

Nolan K Meyer https://orcid.org/0000-0003-3566-896X