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Scale-Free and Multifractal Time Dynamics of fMRI Signals During Rest and Task

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Scale-Free and Multifractal Time Dynamics of fMRI Signals During Rest and Task

P Ciuciu et al. Front Physiol.

Abstract

Scaling temporal dynamics in functional MRI (fMRI) signals have been evidenced for a decade as intrinsic characteristics of ongoing brain activity (Zarahn et al., 1997). Recently, scaling properties were shown to fluctuate across brain networks and to be modulated between rest and task (He, 2011): notably, Hurst exponent, quantifying long memory, decreases under task in activating and deactivating brain regions. In most cases, such results were obtained: First, from univariate (voxelwise or regionwise) analysis, hence focusing on specific cognitive systems such as Resting-State Networks (RSNs) and raising the issue of the specificity of this scale-free dynamics modulation in RSNs. Second, using analysis tools designed to measure a single scaling exponent related to the second order statistics of the data, thus relying on models that either implicitly or explicitly assume Gaussianity and (asymptotic) self-similarity, while fMRI signals may significantly depart from those either of those two assumptions (Ciuciu et al., 2008; Wink et al., 2008). To address these issues, the present contribution elaborates on the analysis of the scaling properties of fMRI temporal dynamics by proposing two significant variations. First, scaling properties are technically investigated using the recently introduced Wavelet Leader-based Multifractal formalism (WLMF; Wendt et al., 2007). This measures a collection of scaling exponents, thus enables a richer and more versatile description of scale invariance (beyond correlation and Gaussianity), referred to as multifractality. Also, it benefits from improved estimation performance compared to tools previously used in the literature. Second, scaling properties are investigated in both RSN and non-RSN structures (e.g., artifacts), at a broader spatial scale than the voxel one, using a multivariate approach, namely the Multi-Subject Dictionary Learning (MSDL) algorithm (Varoquaux et al., 2011) that produces a set of spatial components that appear more sparse than their Independent Component Analysis (ICA) counterpart. These tools are combined and applied to a fMRI dataset comprising 12 subjects with resting-state and activation runs (Sadaghiani et al., 2009). Results stemming from those analysis confirm the already reported task-related decrease of long memory in functional networks, but also show that it occurs in artifacts, thus making this feature not specific to functional networks. Further, results indicate that most fMRI signals appear multifractal at rest except in non-cortical regions. Task-related modulation of multifractality appears only significant in functional networks and thus can be considered as the key property disentangling functional networks from artifacts. These finding are discussed in the light of the recent literature reporting scaling dynamics of EEG microstate sequences at rest and addressing non-stationarity issues in temporally independent fMRI modes.

Keywords: brain dynamics; fMRI; multifractality; rest; scale invariance; self-similarity; task; wavelet Leader.

Figures

Figure 1
Figure 1
From left to right and top to bottom, group-level MSDL maps V = |v1|…|v42| inferred from the multi-subject (S = 12) resting-state fMRI dataset (Neurological convention: left is left). Functional (F), Artifactual (A), and Undefined (U) maps appear color-coded boxes in red, blue, and green, respectively. Let us denote ℱ, 𝒜, and 𝒰 the index sets of F/A/U-maps, respectively and Card (ℱ) = 25, Card (𝒜) = 13, and Card (𝒰) = 4 their respective size. Each map vk consists of loading parameters within the (−1, 1) range where positive and negative values are depicted by the hot and cold parts of the color bar.
Figure 2
Figure 2
(A) Welch (blue curves) vs. Wavelet (black curves) spectra associated with a F-map (f18). Solid and dashed lines correspond to rest and task, respectively. (B) Corresponding multifractal spectra 𝒟(h).
Figure 3
Figure 3
From left to right: Group-averaged map-dependent MF parameters μ1,kj (top), μ2,kj (bottom) specific to F/A/U-maps defined in Table 1. Black and red curves code for j = {R} (Rest) and j = {T} (Task).
Figure 4
Figure 4
Group-level grand-mean self-similarity parameter μ¯1,kj averaged over the F/A/U-maps, i.e., k∈ℱ/𝒜/𝒰 (A), the functional networks, k∈𝒩 (B) and the artifact types, k∈𝒯, (C). Group-level grand-mean multifractality parameter μ¯2,kj averaged over the F/A/U-maps, i.e., k∈𝒻/𝒜/𝒰 (D), the functional networks, k∈𝒩 (E) and the artifact types, k∈𝒯, (F). Black and red curves code for j = R (Rest) and j = T (Task).
Figure 5
Figure 5
Corrected p-values associated with one-sample Student-t (formula image) and WSR (formula image) tests performed on resting-state ([A,C,E]) and task-related multifractal parameters ([B,D,F]) for assessing H0,j(1,) (blue curves) and H0,j(2,) (red curves) on the functional ([A-B]), artifactual ([C-D]) and undefined maps ([E-F]), respectively. Significance level (α = 0.05) is shown in formula image.
Figure 6
Figure 6
Corrected p-values associated with one-sample Student-t (formula image) and WSR (formula image) tests performed on resting-state ([A,C,E]) and task-related multifractal parameters ([B,D,F]) for assessing H0,j(1,) (blue curves) and H0,j(2,) (red curves) on the the averaged map types ([A-B]), networks 𝒩 ([C-D]) and artifact types 𝒯 ([E-F]), respectively. Significance level (α = 0.05) is shown in formula image.
Figure 7
Figure 7
Uncorrected p-values associated with two-samples Student-t test performed between resting-state and task-related multifractal parameters for assessing H˜0(1,) (blue curves) and H˜0(2,) (red curves) on the on the functional (A), artifactual (C) and undefined maps (E), respectively. Similar tests were computed at a broader spatial scale on the functional networks (B), the artifacts (D) and the averaged map types (F), respectively. Significance levels (α1 = 0.01 and α2 = 0.05) are shown in - - and formula image, respectively.

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