Using centrality measures to extract core pattern of brain dynamics during the resting state
Introduction
Spontaneous brain electrical activity during wakeful rest displays specific spatio-temporal patterns which induce the dynamical activity observed at different scales [1]. Such patterns emerge from the dynamical interactions within the resting state networks [2]. The electroencephalogram (EEG) records this activity at a macro-scale level and is one of the major techniques for studying the human brain dynamics. It is a complex signal characterized by a mixture of transient and oscillatory activities independent or overleaped in the time and frequency domains [3], [4], [5]. These activities are translated into large scale information on the brain dynamics and have been investigated using manifold techniques [6]. These approaches have mainly examined the properties of continuous trajectories in brain’s phase space. The dilemma between high dimension of brain activity and low dimension of the recording setup, makes the discrimination of trajectories from stochastic process extremely difficult [7]. Thus statistical approaches would provide solution to study the dynamical system underlying brain activity [8].
Most of these alternative approaches of brain dynamics are based on a coarse-graining procedure. For example, EEG macrostates have been related to mental states [8] and an information flow between macro and micro scale in the β- and γ-bands have been associated with visuo-perceptual discrimination [9], but, no clear coupling was observed in the α-band between micro and macro scale. Coarse-graining techniques have also been used to remove EOG artifacts from EEG signal in order to define the depth of anesthesia. In fact, using multiple scales through coarse-graining decreased EOG effects [10].
In this paper we will proceed on the basis of a dynamical skeleton obtained using a coarse-graining procedure [1] applied to electrical activity [11], [12]. This procedure is based on successive steps which allow to obtain an effective macro-scale dynamical skeleton of brain electrical activity. The brain dynamics represented at this macro-scale can be described as a Markov process with a limited set of states. This Markov representation is also associated with a graph or network representation where vertices V correspond to macroscopic states and edges E correspond to effective transitions. Graph properties are then related to dynamical properties.
Several centrality indices have been introduced in network studies to evaluate the role played by the vertices in a network according to specific properties [13]. These indices are valuable to characterize the impact of each node in social networks [13], [14], as well as other types of networks, including internet networks [15], [16], and biological networks [17], [18]. These analysis have shown that the most important roles are related to a combination of a high number of nodes with low degree and a few nodes with high degree, the so-called “hubs” [19].
Hence, we will apply several centrality measures [13], [20] to extract the vertex of characterized by the largest centrality. In fact, this node represents the most important macroscopic pattern where dynamic recurs and defines a macroscopic meta-stable state [1] or a dynamical hub. Our main aim is to identify core patterns within the network representation of the Markov process at the macroscopic scale. We will extract the macroscopic dynamical skeleton for two sets of data of brain electrical activity during resting state: one for control subjects and one for patients suffering from multiple sclerosis (MS). The same centrality measures are also used to extract the most important patterns at lower scale to study the description of brain dynamics for healthy subjects and patients suffering from MS at several scales.
This paper is organized as follows. First, we describe an overview of the coarse graining approach [1] and present the centrality measures on which the selection of the core pattern is based. The data sets are described in the remainder of the material and methods section. Second, the results of the coarse-graining procedure and centrality selection for both data sets are presented together with the comparison of statistical characterization for control subjects and MS patients. Last, the results of multi-dimensional classification applied to core patterns are described. The last section is devoted to the conclusion of this study which follows the discussion of the results.
Section snippets
Coarse-graining procedure
A successive coarse-graining procedure [1] allows to obtain macroscopic qualitative properties of brain electrical dynamics on the sole basis of the time series. Only the main steps are summarized here. The procedure starts in the measurement space i.e. the voltage recorded by the EEG electrodes as a micro-scale level. Then a principal component analysis (PCA) is applied as a preprocessing step for rotating axis. The dimensions are reordered according to a decreasing variance defined by PCA.
Dynamics characterization
We obtained an effective coarse-grained dynamical skeleton for 12 control subjects and 25 MS patients with a 17-dimensional measurement space for data points using the successive coarse-graining methods described in the previous sections. In Figs. 1 and 2 we depict a set of macroscopic transition graphs obtained from non-random macro-states with their significant macro transitions for a sample of control subjects and MS patients respectively.
The obtained networks are different
Discussion
Our study of the brain dynamics at the macroscopic scale shows that brain dynamics can be ruled by different organisation between control subjects and MS patients. First, the topology of the networks is different since one macro pattern organises the dynamics for healthy subject whereas multiple macro patterns occur for MS patients. This might be related to the deficit in connectivity in brain dynamics observed using mutual information [29] which may lead to a disorganization of the network
Conclusion
This study provides several arguments for the ability to characterize brain dynamics at a macroscale level. It shows that non-random macroscale dynamical skeleton differs between control and MS brain activity leading to different dynamics with higher complexity in the pathological case. Moreover, the non-random patterns selected as dynamical hub using centrality measure ensure a reliable classification of macroscopic patterns from MS networks. These results suggest that features of dynamical
Conflict of interest
The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript.
Funding
This work was supported by 18 PJEC 12–21, 2018: Hatem Ben Taher project, Minister of Higher Education and Scientific Research in Tunisia.
CRediT authorship contribution statement
Abir Hadriche: Conceptualization, Data curation, Formal analysis, Funding acquisition, Writing - original draft, Writing - review & editing. Nawel Jmail: Formal analysis, Methodology, Writing - original draft, Writing - review & editing. Jean-Luc Blanc: Conceptualization, Data curation, Formal analysis, Investigation, Methodology. Laurent Pezard: Conceptualization, Methodology, Supervision, Validation, Writing - review & editing.
Acknowledgment
We wish to thank members of the team “Dynamique Émotionnelle et Pathologies” from the SCALAB UMR CNRS 9193 (CNRS, Université de Lille) for sharing data with us. We also thank two anonymous reviewers for their comments that allow to complete and improve this article.
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