  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.
