NORDIC denoising on VASO data

Abstract

The use of submillimeter resolution functional magnetic resonance imaging (fMRI) is increasing in popularity due to the prospect of studying human brain activation non-invasively at the scale of cortical layers and columns. This method, known as laminar fMRI, is inherently signal-to-noise ratio (SNR)-limited, especially at lower field strengths, with the dominant noise source being of thermal origin. Furthermore, laminar fMRI is challenged with signal displacements due to draining vein effects in conventional gradient-echo blood oxygen level-dependent (BOLD) imaging contrasts. fMRI contrasts such as cerebral blood volume (CBV)-sensitive vascular space occupancy (VASO) sequences have the potential to mitigate draining vein effects. However, VASO comes along with another reduction in detection sensitivity. NOise Reduction with DIstribution Corrected (NORDIC) PCA (principal component analysis) is a denoising technique specifically aimed at suppressing thermal noise, which has proven useful for increasing the SNR of high-resolution functional data. While NORDIC has been examined for BOLD acquisitions, its application to VASO data has been limited, which was the focus of the present study. We present a preliminary analysis to evaluate NORDIC's capability to suppress thermal noise while preserving the VASO signal across a wide parameter space at 3T. For the data presented here, with a proper set of parameters, NORDIC reduced thermal noise with minimal bias on the underlying signal and preserved spatial resolution. Denoising performance was found to vary with different implementation strategies and parameter choices, for which we provide recommendations. We conclude that when applied properly, NORDIC has the potential to overcome the sensitivity limitations of laminar-specific VASO fMRI. Since very few groups currently have 3T VASO data, by sharing our analysis and code, we can compile and compare the effects of NORDIC across a broader range of acquisition parameters and study designs. Such a communal effort will help develop robust recommendations that will increase the utility of laminar fMRI at lower field strengths.

Keywords: NORDIC; VASO; denoising; laminar fMRI; submillimeter resolution.

Figure 1

Example images of previous attempts to perform NORDIC with VASO. (A) NORDIC removed the activity of interest and introduced false-positive activity in patches outside the brain. It is suspected that this was due to the wrong application of noise estimates with overestimated variance of multiple contrasts as one time series. In this study, we want to explore the effect of noise floor estimates on NORDIC-VASO. (B–D) NORDIC boosts the sensitivity and tSNR by an order of magnitude. However, the layer profiles of beta scores are altered. It is suspected that the noise threshold estimation might have been overestimated by the different signal compositions of VASO (B) or by applying NORDIC with inappropriate coil-combined phase data (D). This study explored the advantages and disadvantages of applying NORDIC-VASO in the complex-valued or magnitude-only domain. (E) The first NORDIC-VASO data published as a peer-reviewed journal article (denoising was performed on complex-valued data, separately on nulled and not-nulled time series, and without an appended noise volume). However, the aim of this study was not focused on the validation of NORDIC, and it did not report on the signal responses with and without denoising. In this study, we aimed to provide such validation and to provide recommendations to the field on how to apply NORDIC on VASO data with a minimum risk of adverse effects. Figures adapted with permission from Akbari et al. (2023), de Oliveira et al. (2023), Huber et al. (2023, , and Pizzuti et al. (2022).

Figure 2

Methodological overview of the main experiment (3T). (A) The functional VASO imaging slab covered visual and sensorimotor cortices. (B) The paradigm consisted of resting blocks (fixation) alternating with concurrent visual and sensorimotor stimulation (Huber et al., 2023). (C) Illustration of the different NORDIC implementation strategies evaluated in the present study (see main text, Section 2.2). (D) The main ROI (upper panel) spanned multiple slices and contained more than 7,000 voxels in visual and sensorimotor areas. Responsive regions were roughly identified using BOLD activation maps, and the ROI was then coarsely drawn from there. The small-layered ROI (lower panel, within the blue circle), used for laminar analysis, spanned a single slice.

Figure 3

Evaluation of tSNR and t-value gains following denoising. (A) tSNR maps computed from nulled, motion-corrected, and detrended files. (B) t-values were computed across single-trial PSC estimates (N = 72). (C) Bar graphs representing ROI-averaged tSNR (upper) and t-values (lower) for all versions. For this plot, to illustrate the variability across runs, we computed absolute-valued t-scores across single-trial PSCs within each run (N = 12 per run). All versions had increased tSNR and t-values compared with noNORDIC (p < 0.05, denoted by dotted black horizontal lines and asterisks). The combined versions had higher tSNR on average than the separate versions (p < 0.05). This was reversed for t-values which were, higher on average for the separate versions than for the combined versions (p < 0.05). Error bars represent standard error across runs.

Figure 4

Effect of NORDIC on response amplitude. (A) Voxel- and run-averaged PSCs with and without denoising (represented with bars and horizontal red lines, respectively). Circles denote the PSC of individual runs. All versions had a reduced PSC compared with noNORDIC (p < 0.05, denoted by a dotted black horizontal line and asterisk). This effect was larger on average for the combined versus the separate versions (p < 0.05). (B) Colored circles depict the run-wise differences in PSC between noNORDIC and NORDIC (red circles minus black circles in A). Black horizontal lines represent the mean across runs. The “separate, with noise-vol, magnitude-only” version had significantly smaller PSC reduction than each of the other versions (p < 0.05, denoted by a dotted red horizontal line and asterisk). (C) Same as “combined-withNoiseVolume-magnitudeOnly” in A but using a smaller patch size.

Figure 5

Replication of Figure 4 using voxels (N = 1,463) within the ROI with t-values >2 based on noNORDIC trials from the first three runs. Red (noNORDIC) and black (NORDIC) circles in A represent PSCs of the last three runs. The corresponding run-wise PSC differences between noNORDIC and NORDIC are represented by colored circles in B.

Figure 6

Single-trial percent signal change as a function of trial number following thermal noise suppression through extensive voxel averaging. The remaining trial-by-trial variance, assumed to reflect “true” signal variability and physiological noise sources, appears to be contained after NORDIC as desired.

Figure 7

Did NORDIC spatially blur the data? (A) Mean images of NORDIC minus noNORDIC time series. For complex images, the difference was computed as the absolute value of the complex difference, and for magnitude-only images, it was computed as the absolute value of the magnitude difference. (B) g-factor maps estimated by two different NORDIC versions, shown here to illustrate that the mean of the difference time series in A appears as non-structured random noise scaled by the g-factor.

Figure 8

Layer-dependent signal preservation with NORDIC. (A) Laminar profiles for each version obtained from the layered ROI shown in Figure 2D. (B) Laminar profiles with different subsampling schemes for the “separate, with noise-vol, magnitude-only” version. For plot 1.1, trials 1:1:72 were averaged; for plot 1.2, one of the profiles was averaged across trials 1:2:72 (2:2:72 for the other), etc. Note that these layer-fMRI profiles represent a relatively small cortical patch (Figure 2D) that is manually selected to be (i) a sulcus inside the brain without noise transitions between tissue and skull and (ii) not affected by large pial vessels that might have residual intravascular BOLD fluctuations at 3T.

Figure 9

Illustrating the trade-off between noise removal and signal preservation. (A) Average VASO PSC across ROI voxels and trials for different scaling factors with corresponding t-value maps. The dashed line represents the mean PSC of noNORDIC. Error bars reflect standard error across trials. (B) Across-trial-averaged delta (mean of stimulation blocks minus mean of rest blocks) computed from the noNORDIC minus NORDIC difference time series with corresponding delta activation maps. Note that since difference time series cannot readily be BOLD-corrected, we used not-nulled (BOLD) time series for this plot. The dashed line represents a delta of 0 as expected if no signal is removed. Error bars reflect standard error across trials.

Figure 10

Effects of the g-factor estimate on denoising performance. Same types of plots as in Sections 3.1–3.5. Columns 2–3 depict results from the NIFTI_NORDIC.m versions (magnitude-only or complex-valued, respectively). Columns 4–5 depict results from the NORDIC.m versions (using the same g-factor map from the beginning of the session for all runs or run-specific maps, respectively). For all versions, denoising was performed with appended noise volumes and on separate nulled and not-nulled time series.

Figure 11

Brain-masked g-factor maps either estimated by NORDIC using MP-PCA (Veraart et al., 2016a, 2016b) or estimated using the vendor’s reconstruction in IcePat. Note that the motion-induced difference across runs only minimally affected the denoising based on Figure 10.