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Using centrality measures to extract core pattern of brain dynamics during the resting state
Computer Methods and Programs in Biomedicine 179 (2019) 104985
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Computer Methods and Programs in Biomedicine journal homepage: www.elsevier.com/locate/cmpb
Using centrality measures to extract core pattern of brain dynamics during the resting state Abir Hadriche a,b,c,∗, Nawel Jmail c,d, Jean-Luc Blanc e, Laurent Pezard e a
Université de Sfax, ENIS, REGIM Lab, Sfax, Tunisie Université de Gabes, ISIMG, Gabes, Tunisie c Université de Sfax, Centre de Recherche Numérique de Sfax, Sfax, Tunisie d Université de Sfax, MIRACL, Sfax, Tunisie e Aix-Marseille Université, CNRS, LNSC UMR 7260, 3 Place Victor Hugo, Marseille 13003, France b
a r t i c l e
i n f o
Article history: Received 30 December 2018 Revised 10 July 2019 Accepted 13 July 2019 Available online xxx Keywords: Brain dynamics Coarse-graining Discrete dynamics Macroscopic transition graph Centrality measures Entropy rate Resting state Multiple sclerosis kNN classifier
a b s t r a c t The patterns of brain dynamics were studied during resting state on a macroscopic scale for control subjects and multiple sclerosis patients. Macroscopic brain dynamics is defined after successive coarsegrainings and selection of significant patterns and transitions based on Markov representation of brain activity. The resulting networks show that control dynamics is merely organized according to a single principal pattern whereas patients dynamics depict more variable patterns. Centrality measures are used to extract core dynamical pattern in brain dynamics and classification technique allow to define MS dynamics with relevant error rate.
1. 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 [3–5]. 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
∗
Corresponding author. E-mail addresses: [email protected] (A. Hadriche), nawel.jmail@ institution.tn (N. Jmail), [email protected] (J.-L. Blanc), [email protected] (L. Pezard). https://doi.org/10.1016/j.cmpb.2019.104985 0169-2607/© 2019 Published by Elsevier B.V.
© 2019 Published by Elsevier B.V.
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 G := (V, E ) where vertices V correspond to macroscopic states and edges E correspond to effective
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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 G 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 coarsegraining 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 multidimensional 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. 2. Materials and methods 2.1. 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. Secondly, a discretization step based on a subdivision algorithm [21] is used to truncate the PCA expansion. The brain dynamics is then reduced to a sequence of discrete meso-states which can be described by a first-order Markov process M. The next step, which leads to the macroscopic representation, relies on the identification of regions in the state space with specific dynamical features related to clique structures in the graph representation. Each step of this procedure was statistically tested and validated against adapted surrogate data tests [22,23]. The remaining macroscopic representation is composed of non-random macrostates and transitions between them. It is related to a transition graph G := (V, E ) where the edges E represent significant transitions between macroscopic states. This graph will be studied through different centrality measures in order to extract the core pattern at the macro-scale of the brain resting state dynamics. Moreover, meso- and macro-scale dynamics will be compared between controls and MS patients on the basis of their dynamical properties.
2.2. Centrality measures Several centrality measures have been introduced and studied for real networks. They depend on different nodes features and could be ranked in order of importance within network [20]. We used common centrality measures to characterize the core pattern of the macroscopic and mesoscopic transition graph for each subject EEG recording. 2.2.1. Degree centrality The degree centrality (DC) reflects the number of links incident upon a node (i.e., the number of ties for a node), that would describe the networks’ topology [24]. DC defines the immediate influence of a node on the network long-term effect [20] since for example the risk of contamination, in a network describing disease spreading is high for nodes connected to many others i.e. with high degree. Thus the DC of a vertex v is defined as:
DC (v ) = deg(v )
(1)
2.2.2. Betweenness centrality The betweenness centrality (BC) defines the influence of a node in the communication between pairs of nodes [20,25]. In other terms, BC gives the number of times the shortest path between two nodes crosses node v whose centrality is then measured by:
BC (v ) =
s,t ∈V
σ (s, t |v ) σ (s, t )
(2)
where σ (s, t) is the number of shortest (s, t)-paths, and σ (s, t|v) is the number of paths going through node v different from s and t [26]. 2.2.3. Closeness centrality The closeness centrality (CC) defines the accurate duration to propagate an information from a node to all other nodes sequentially [13]. In a connected graph there is a natural metric distance between all pairs of nodes, constructed through the length of their shortest paths. The remoteness of a node v is defined as the sum of its distances to all other nodes, and its closeness is defined as the inverse of the remoteness [15,16]. Thus, the more central the node is, the lower the remoteness is. Closeness centrality is then defined as:
CC (v ) =
2−dG (v,t ) .
(3)
t∈V \v
where dG (v,t ) is the distance between the different vertices of the graph G (v, t ). This measure is only used for connected networks, since the distance between unconnected nodes is undefined. 2.2.4. Eigenvector centrality Eigenvector centrality (EC) or eigencentrality is a measure of the influence of a node in a network. For a given node, EC is determined by the centrality of the nodes to which it is connected. In a social network, Bonacich and his collaborators [27] calculated EC as a weighted sum of direct connections and indirect connections of any length. and thus take into account the entire network. To estimate this measure, we must consider the eigenvectors and eigenvalues of the adjacency matrix A = (av,t ) where av,t = 1 if vertex v is linked to vertex t, and av,t = 0 otherwise. An eigenvector of A is a nonzero vector which satisfies the following equation:
Ax = λx
(4)
λ is then the associated eigenvalue. The EC(v) of a node v is defined as the vth entry in the eigenvector belonging to the largest eigenvalue of A denoted λ1 [28].
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Fig. 1. Macro-states network for control EEG data. The nodes present non-random macro-states, bidirectional transitions accuracy with highest transition probability that define the preferred dynamics direction. The core pattern with highest centrality measures is shown in the left of each network.
Table 1 Statistics of the entropy rate computed for the meso-scale Markov process representation of the dynamics for the two datasets. Subjects
hrmin
hrmax
hrmean
hrsd
Control MS
0.76 bit/ms 0.7 bit/ms
0.97 bit/ms 1.14 bit/ms
0.86 bit/ms 0.89 bit/ms
0.06 bit/ms 0.13 bit/ms
Alternatively, it is equivalent to the summed centrality of its neigh-
bors [27]:
EC (v ) = xv =
N 1
λ1
Av,t xt
(5)
t=1
2.3. Data The data sets have already been analyzed using an approach based on information theory [29] and are detailed in this previous article. Only the main characteristics are summarized here.
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Fig. 2. Macro-states network for MS EEG data. The nodes present non-random macro-states, bidirectional transitions accuracy with highest transition probability that define the preferred dynamics direction. The core pattern with highest centrality measures is shown in the left of each network.
The sample included 25 participants with clinically defined Relapsing Remitting Multiple Sclerosis. Neurological status and disability were assessed by Expanded Disability Status Scale [30] which ranges from 0 (i.e. normal) to 10 (i.e. death). Patients’ EDSS scores ranged from 1 to 5 (median: 3) which indicates a moderate mobility disability. Control data for EEG parameters were obtained by recording a sample of 12 healthy subjects.
EEG signals were recorded using 17 Ag/AgCl electrodes (C3, C4, Cz, F3, F4, F7, F8, Fz, O1, O2, P3, P4, T3, T4, T5, T6) placed on the scalp according to the 10/20 international electrode placement system. The reference electrode was placed on the nose. EEG signals were digitized on 16 bits of precision using a 256 Hz sampling frequency and filtered using a band-pass filter between 0.5 Hz and 70 Hz. Twenty minutes of EEG recordings were obtained from each participant in eyes closed and resting condition.
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Fig. 2. Continued
2.4. Dynamics entropy rate To support the comparison between healthy and pathological brain dynamics, the entropy rate of sequences of states h(M) was computed for mesoscale and macroscale levels for each control and
MS subjects. The entropy rate of a discrete Markov process with transition probabilities τ i,j and stationary distribution π i was computed using:
h (M ) = −
i, j
πi(k) τi,(kj ) log τi,(kj )
(6)
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where the π (k) and τ (k) are both maximum likelihood estimate of, respectively, the stationary distribution and probability of transition and log is taken as natural logarithm. 2.5. Classification Since most of the centrality measures define the same core pattern as the average measure (see Results) we defined the core patterns as the nodes with the highest average centrality measure. A classification step using the k-Nearest Neighbors Classifier (kNN) algorithm was performed to test whether core macroscopic patterns were sufficient for mapping resting state brain dynamic of MS patients. The kNN algorithm was used for several pattern recognition problems [31–33]. It is relatively simple and has a rapid convergence speed when compared with other classifiers. The kNN classifier is based on defining the K-nearest neighbors vote to classify input patterns. In order to determine the exact number of k-neighbors, we used a cross validation grid-search technique that computes the lowest test error rate and the highest accuracy. The classifier was applied to the most important patterns according to average centrality measure selected from entire non random macro patterns for each subject separately. The learning set consisted in a dataset of both MS patients and control macro patterns. The test set used the remaining non random macro patterns from MS patients (162). Since the number of MS patients core patterns was higher than that of control subjects (31 vs. 12), the learning sets consisted in a random sample of 12 MS patterns out of the 31 to avoid an over-representation of MS core patterns in the learning set. The number of core patterns was thus the same for MS and control condition and avoid biased classification. The classification step was repeated 100 times varying randomly the learning and test sets in order to ensure the robustness of the patterns obtained as the best match of rest state for MS brain’s macrodynamics. We computed different error rates and their standard deviation of MS patterns classification obtained for the 100 trials. 3. Results 3.1. Dynamics characterization We obtained an effective coarse-grained dynamical skeleton for 12 control subjects and 25 MS patients with a 17-dimensional measurement space E for T = 3.104 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 G 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 across subjects and between groups. Between subjects, the main difference is due to the fact that the number of significant patterns vary between 3 and 15. MS networks are moreover different from healthy ones since in the case of control subjects, networks have almost a constant number of significant patterns whereas this number is variable in MS patients. Moreover, the healthy dynamic is ruled by a unique main dominant macro pattern whereas in the MS dynamics the transitions seem organized according to multiple principal macro patterns. On this basis, the networks topology induced by non-random transitions differ between groups. The entropy rate of the Markov process representation was computed for the meso-scale (see Table 1) and macro-scale (see Table 2) dynamics. This index does not provide any indication of
Table 2 Statistics of the entropy rate computed for the macro-scale Markov process representation of the dynamics for the two datasets. Subjects
hrmin
hrmax
hrmean
hrsd
Control MS
0.45 bit/ms 0.52 bit/ms
0.55 bit/ms 0.91 bit/ms
0.5 bit/ms 0.7 bit/ms
0.02 bit/ms 0.1 bit/ms
difference between the two groups for the meso-scale (Welch twosample t-test: t = −0.96 df = 34.9 p-value= 0.17) whereas it depicts a significant lower value for control than for MS patients for the macro-scale (Welch two-sample t-test: t = −9.61 df = 27.7 pvalue < 0.001). In order to extract core macro patterns with central importance in cortical dynamic, we computed the entire set of centrality measurements: centrality degree (DC), betweenness centrality (BC), closeness centrality (CC) and eigenvalue centrality (EC) for each node V in graph G. For each subject, it characterizes its macro graph G and allows to extract the most accurate core macroscopic node or pattern. Most of the centrality measures define the same core pattern as the average measure: for 28 out of 37 cases (75.6%) the four centrality measures are in accordance with the average, for 8 out of 37 cases (21.6%) three centrality measures are in accordance with the average and for only one case two centrality measure are in accordance with the average. For control data, almost all core patterns depict an occipital activation (right or left) with high amplitude. This proves the existence of an alpha rhythm during the rest state for 10 subjects among 12. Only two subjects are different which is in concordance with the proposed archetypes in healthy rest state mode based on Affinity Propagation method [34]. For MS data, we notice that centrality measurements are quite close in comparison with healthy data (supplementary figures), that proves the absence of a dominant macro pattern (Fig. 3). 3.2. Classification results In the classification step, we evaluated the robustness of centrality measurements to extract typical core pattern able to represent the MS macroscopic dynamics. In fact, the selected core patterns from the learning data predict the MS rest state macroscopic behavior, with an error rates below 13% obtained from 100 repetitions (mean: 9.7%, sd: 0.83). The misclassification rate was low enough to provide reliable definition of MS brain dynamics during resting state. To complete the results obtained for average centrality measure, classification was also performed using each centrality measure (see Table 3). In each case, the learning set was slightly different from that obtained for average centrality measure and the mean error rate was lower for the closeness and degree centrality and higher for eigenvector and betweenness centrality than for average centrality. To check whether the centrality measures are able to describe the MS brain dynamics independently from the scale of the dynamics, we apply the same centrality selection to both the networks that include all the macroscopic patterns and the meso-scale networks. To ensure the consistency of the comparison, the same number of patterns as for the non-random macroscopic scale was used in the test set for both new test sets. Two other classification tests (repeated 100 times each) were performed. In each case, the learning set was defined as previously and the test set consisted in randomly chosen patterns (162) from all the remaining MS patterns. Classification results are given in Table 4 and depict a higher miss-classification rates than for the non-random macroscopic networks.
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Table 3 Classification results for each centrality measure and differences between learning set for average centrality measure and each other centrality measure. Centrality measure
Mean error rate (sd)
Difference between learning sets
Betweenness (BC) Degree (DC) Closeness (CC) Eigenvector (EC)
11.03% (sd: 0.79) 8.6% (sd: 0.9) 7.9% (sd: 1.12) 12.8% (sd: 1.55)
2 2 1 3
MS MS MS MS
patterns patterns pattern and 2 control patterns patterns
Fig. 3. Non random macro-states for MS real EEG data set performed in the space of their graph centrality measures such as betweenness centrality (blue circle), degree centrality (red star), closeness centrality (green plus) and eigenvector centrality (black triangle). Black curve depicts the average of the measurements. Only the node of G which has the largest average centrality measures values will be considered as the core macroscopic pattern of the cerebral macro-scopic dynamic. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 3. Continued
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Table 4 Classification results for meso-scale and complete macro-scale networks. Patterns
Learning data
Test data
Mean error rate (sd)
All macro patterns Meso patterns
12 control + 12 MS 12 control + 12 MS
162 MS patterns 162 MS patterns
20.72% (sd: 1.7) 23.12% (sd: 2.97)
4. 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 representation of brain dynamics. Moreover, at the macroscopic scale, the brain dynamics of MS patients depicts a higher entropy rate than controls dynamics. These indices reinforce the previous results on the disorganisation of MS brain dynamics [29,35]. We introduced different centrality measures to extract core patterns from a graph composed of non-random macro-states and significant transitions related to the macroscopic dynamic directory of brain activity. We selected for all the subjects the most dominant macroscopic pattern by maximizing the centrality measures. In fact, this pattern was able to describe electrical brain activity at resting state for most of the subjects. This activity was exhibited through occipital oscillations either on the right or the left side characterized by a high amplitude. This pattern could be considered as a macroscopic meta-stable state which appears as a hub in a macro-scale network. All the centrality measures are dealing with slightly different characteristics about the nodes properties, e.g. nodes with high degree are nodes very well connected in the networks, while nodes with high betweenness centrality are nodes that facilitate communication in the network. Although most of these measures extract the same core pattern as the average measure, classification results are somewhat better for degree and closeness centrality. These measure should thus be studied on their own to provide physiological interpretation related to their dynamical meaning. The dynamic repertoire of brain electrical activity was defined in MS patients using the same procedure. A kNN classifier proved that core macroscopic MS patterns defined using average centrality measure are sufficient to define MS dynamics with only an average of error rate of 9.7%. However evaluating the dynamics at the macroscopic level could be completed by the study at lower level dynamics. So, we have re-applied the centrality measures to the lower level dynamic networks (all macroscopic and mesoscopic scales). Indeed for each level, we have extracted the most significant patterns using the average centrality measure and computed the MS patterns classification technique. As a result, we obtained higher error rates than those obtained with macroscpic selected level. These rates exceed 20% at the mesoscopic scale after classifying 6873 MS patterns. This increase of the error rate can be explained by the large number of patterns in the training data in relation to those in the learning data. Enriching the learning data can be a solution to further characterize MS mesoscopic brain dynamics at the rest state. This will lead to a better correlation between learning and training patterns. Our results show a change in both the dynamical organisation of brain dynamics and core patterns of cortical activity in MS patients. Since it has been demonstrated recently that the thalamus is involved in the global oscillatory slowing within the MEG α -
band in MS and that there is an association with thalamic atrophy [36], our result also suggest that this disturbance could also be revealed at the macroscopic scale of core patterns. If this hypothesis could be verified it would reinforce the role of the thalamus as a critical hub region involved in actively maintaining the modular structure of cortical functional networks [37]. The consequences of the dynamical interplay between thalamus and cortical activity in macroscopic brain dynamics for both healthy and MS brain activity deserve further studies. 5. 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 complexity and core patterns could serve as a potential marker of brain state in relapsing-remitting MS. 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. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cmpb.2019.104985.
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References [1] A. Hadriche, L. Pezard, J. Nandrino, H. Ghariani, A. Kachouri, K. Jirsa, Mapping the dynamic repertoire of the resting brain., NeuroImage J. 78 (2013). 448–62 [2] G. Deco, V.K. Jirsa, Ongoing cortical activity at rest: criticality, multistability, and ghost attractors., J. Neurosci. 32 (2012) 3366–3375. [3] N. Jmail, M. Gavaret, F. Wendling, A. Kachouri, G. Hamadi, J.-M. Badier, C.-G. Bénar, A comparison of methods for separation of transient and oscillatory signals in EEG, J. Neurosci. Methods 199 (2) (2011) 273–289. [4] N. Jmail, M. Gavaret, F. Bartolomei, C.-G. Bénar, Despikifying SEEG signals using a temporal basis set, in: Intelligent Systems Design and Applications (ISDA), 2015 15th International Conference on, IEEE, 2015, pp. 580–584. [5] N. Jmail, M. Gavaret, F. Bartolomei, C.-G. Bénar, Despiking SEEG signals reveals dynamics of gamma band preictal activity, Physiol. Measur. 38 (2017) N42–N56. [6] C. Stam, Nonlinear dynamical analysis of eeg and meg: review of an emerging field., Clin. Neurophysiol. 116 (2005) 2266–2301. [7] J.-P. Lachaux, L. Pezard, L. Garnero, C. Pelte, B. Renault, F. Varela, J. Martinerie, The spatial extension of brain activity fools the single-channel reconstruction of eeg dynamics, Hum. Brain Mapping 5 (1997) 26–47. [8] C. Allefeld, H. Atmanspacher, J. Wackermann, Mental states as macrostates emerging from brain electrical dynamics, Chaos 19:015102 (2009) 281–297. [9] P. Foteini, M. Dimitris, N. Smyrnis, C. Siettos, A coarse-grained analysis of the functional brain connectivity from EEG recordings of a visuo-perceptual discrimination task., Front. Comput. Neurosci. 8 (2014) 1–12, doi:10.1063/1. 4825658. [10] C. Quan L.and Yi-Feng, F. Shou-Zen, M.F. Abbod, J.-S. S., EEG artifacts reduction by multivariate empirical mode decomposition and multiscale entropy for monitoring depth of anaesthesia during surgery., Med. Biol. Eng. Comput. (2015) 16pages, doi:10.1155/2015/232381. [11] A. Hadriche, N. Jmail, R. Elleuch, L. Pezard, Different methods for partitioning the phase space of a dynamic system, Int. J. Comput. Appl. 93 (15) (2014). [12] R. Jarray, N. Jmail, A. Hadriche, T. Frikha, A comparison between modeling a normal and an epileptic state using FHN and the epileptor model, in: Proceedings of the International Conference on Innovations in Bio-inspired Computing and Applications, Springer, 2017, pp. 245–254. [13] S. Wasserman, K. Faust, Social Network Analysis, Cambridge University Press (1994). [14] A. Schneeberger, C. Mercer, S. Gregson, N. Ferguson, C. Nyamukapa, R. Anderson, A. Johnson, G. Garnett, Scale-free networks and sexually transmitted diseases - a description of observed patterns of sexual contacts in britain and zimbabwe., Sex. Transm. Dis 31 (6) (2004) 380–387. [15] M. Faloutsos, P. Faloutsos, C. Faloutsos, On power-law relationships of the internet topology, ACM SIGCOMM Comput. Commun. Rev. 29, 4 (1999) 251–262. [16] R. Albert, H. Jeong, A.-L. Barabasi (Eds.), Diameter of the world wide web, Nature, London, 1999. [17] H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, A.L. Barabasi, The large-scale organization of metabolic networks., Nature 407 (20 0 0) 651–654.
[18] S. Wuchty, Scale-free behavior in protein domain networks., Mol. Biol. Evol. 18 (2001) 1694–1702. [19] A.-L. Barabasi, R. Albert, Emergence of scaling in random networks, Science 286 (5439) (1999) 509–512. [20] L.C. Freeman, Centrality in social networks. conceptual clarification, Social Netw. 1 (1979) 215–239. 1 [21] M. Dellnitz, A. Hohmann, A subdivision algorithm for the computation of unstable manifolds and global attractors, Numerische Mathematik 75 (1997) 293–317. [22] J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, J. Farmer, Testing for nonlinearity in time series: the method of surrogate data., Physica D 58 (1992) 77–94. [23] T. Schreiber, A. Schmitz, Surrogate time series., Physica D 142 (20 0 0) 346–382. [24] D.J. Watts, Small World: The Dynamics of Networks Between Order and Randomness, Princeton University Press, Princeton University, 1999. [25] U. Brandes, A faster algorithm for betweenness centrality., J. Math. Sociol. 25(2) (2001) 163–177. [26] U. Brandes, On variants of shortest-path betweenness centrality and their generic computation., Social Netw. 30(2) (2008) 136–145. [27] P. Bonacich, P. Lloyd, Eigenvector like measures of centrality for asymmetric relations., Social Netw. (2001) 191–201. [28] A.Z.A. Fornito, B. E., Fundamentals of Brain Networks Analysis., Elsevier, 2016. [29] B. Lenne, J.-L. Blanc, J.-L. Nandrino, P. Gallois, P. Hautecur, L. Pezard, Decrease of mutual information in brain electrical activity of patients with relapsing-remitting multiple sclerosis, Behav. Neurol. 27 (2013) 201–212. [30] F.J. Kurtzke, Rating neurologic impairment in multiple sclerosis, Neurology 33 (11) (1983). 1444–1444 doi: 10.1212/WNL.33.11.1444. [31] F. Moreno-Seco, L. Mico, J.A. Oncina, Modification of the laesa algorithm for approximated kNN classification., Pattern Recognit. Lett. 24 (2003) 47–53. [32] T. Abidin, W. Perrizo (Eds.), SMART-TV: a fast and scalable nearest neighbor based classifier for data mining., Proceedings of ACM SAC-06, Dijon, France, 2006. [33] A.H. Ullah, M. Wajid, S.A. Rauf, S.M.N. Mohamad, M.A. Saeed, Classification of eeg signals based on pattern recognition approach, Front. Comput. Neurosci. 11 (2017) 103–121. [34] B.J. Frey, D. Dueck, Clustering by passing messages between data points, Science 315 (2007) 972-949. [35] M. Gschwind, D. Van De Ville, M. Hardmeier, P. Fuhr, C. Michel, M. Seeck, Id 249 corrupted fractal organization of EEG topographical fluctuations predict disease state in minimally disabled multiple sclerosis patients., Clin. Neurophysiol. 127 (3) (2016) e72. [36] D. Schoonhoven, M. Fraschini, P. Tewarie, B. Uitdehaag, A. Eijlers, J. Geurts, A. Hillebrand, M. Schoonheim, C. Stam, E. Strijbis, Resting-state MEG measurement of functional activation as a biomarker for cognitive decline in MS., Multiple Sclerosis J. (2018) 1–11. [37] H. K., B. MA., L. WB., D. M., The human thalamus is an integrative hub for functional brain networks., J. Neurosci. 37 (23) (2017) 5594–5607.
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Computer Methods and Programs in Biomedicine journal homepage: www.elsevier.com/locate/cmpb
Using centrality measures to extract core pattern of brain dynamics during the resting state Abir Hadriche a,b,c,∗, Nawel Jmail c,d, Jean-Luc Blanc e, Laurent Pezard e a
Université de Sfax, ENIS, REGIM Lab, Sfax, Tunisie Université de Gabes, ISIMG, Gabes, Tunisie c Université de Sfax, Centre de Recherche Numérique de Sfax, Sfax, Tunisie d Université de Sfax, MIRACL, Sfax, Tunisie e Aix-Marseille Université, CNRS, LNSC UMR 7260, 3 Place Victor Hugo, Marseille 13003, France b
a r t i c l e
i n f o
Article history: Received 30 December 2018 Revised 10 July 2019 Accepted 13 July 2019 Available online xxx Keywords: Brain dynamics Coarse-graining Discrete dynamics Macroscopic transition graph Centrality measures Entropy rate Resting state Multiple sclerosis kNN classifier
a b s t r a c t The patterns of brain dynamics were studied during resting state on a macroscopic scale for control subjects and multiple sclerosis patients. Macroscopic brain dynamics is defined after successive coarsegrainings and selection of significant patterns and transitions based on Markov representation of brain activity. The resulting networks show that control dynamics is merely organized according to a single principal pattern whereas patients dynamics depict more variable patterns. Centrality measures are used to extract core dynamical pattern in brain dynamics and classification technique allow to define MS dynamics with relevant error rate.
1. 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 [3–5]. 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
∗
Corresponding author. E-mail addresses: [email protected] (A. Hadriche), nawel.jmail@ institution.tn (N. Jmail), [email protected] (J.-L. Blanc), [email protected] (L. Pezard). https://doi.org/10.1016/j.cmpb.2019.104985 0169-2607/© 2019 Published by Elsevier B.V.
© 2019 Published by Elsevier B.V.
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 G := (V, E ) where vertices V correspond to macroscopic states and edges E correspond to effective
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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 G 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 coarsegraining 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 multidimensional 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. 2. Materials and methods 2.1. 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. Secondly, a discretization step based on a subdivision algorithm [21] is used to truncate the PCA expansion. The brain dynamics is then reduced to a sequence of discrete meso-states which can be described by a first-order Markov process M. The next step, which leads to the macroscopic representation, relies on the identification of regions in the state space with specific dynamical features related to clique structures in the graph representation. Each step of this procedure was statistically tested and validated against adapted surrogate data tests [22,23]. The remaining macroscopic representation is composed of non-random macrostates and transitions between them. It is related to a transition graph G := (V, E ) where the edges E represent significant transitions between macroscopic states. This graph will be studied through different centrality measures in order to extract the core pattern at the macro-scale of the brain resting state dynamics. Moreover, meso- and macro-scale dynamics will be compared between controls and MS patients on the basis of their dynamical properties.
2.2. Centrality measures Several centrality measures have been introduced and studied for real networks. They depend on different nodes features and could be ranked in order of importance within network [20]. We used common centrality measures to characterize the core pattern of the macroscopic and mesoscopic transition graph for each subject EEG recording. 2.2.1. Degree centrality The degree centrality (DC) reflects the number of links incident upon a node (i.e., the number of ties for a node), that would describe the networks’ topology [24]. DC defines the immediate influence of a node on the network long-term effect [20] since for example the risk of contamination, in a network describing disease spreading is high for nodes connected to many others i.e. with high degree. Thus the DC of a vertex v is defined as:
DC (v ) = deg(v )
(1)
2.2.2. Betweenness centrality The betweenness centrality (BC) defines the influence of a node in the communication between pairs of nodes [20,25]. In other terms, BC gives the number of times the shortest path between two nodes crosses node v whose centrality is then measured by:
BC (v ) =
s,t ∈V
σ (s, t |v ) σ (s, t )
(2)
where σ (s, t) is the number of shortest (s, t)-paths, and σ (s, t|v) is the number of paths going through node v different from s and t [26]. 2.2.3. Closeness centrality The closeness centrality (CC) defines the accurate duration to propagate an information from a node to all other nodes sequentially [13]. In a connected graph there is a natural metric distance between all pairs of nodes, constructed through the length of their shortest paths. The remoteness of a node v is defined as the sum of its distances to all other nodes, and its closeness is defined as the inverse of the remoteness [15,16]. Thus, the more central the node is, the lower the remoteness is. Closeness centrality is then defined as:
CC (v ) =
2−dG (v,t ) .
(3)
t∈V \v
where dG (v,t ) is the distance between the different vertices of the graph G (v, t ). This measure is only used for connected networks, since the distance between unconnected nodes is undefined. 2.2.4. Eigenvector centrality Eigenvector centrality (EC) or eigencentrality is a measure of the influence of a node in a network. For a given node, EC is determined by the centrality of the nodes to which it is connected. In a social network, Bonacich and his collaborators [27] calculated EC as a weighted sum of direct connections and indirect connections of any length. and thus take into account the entire network. To estimate this measure, we must consider the eigenvectors and eigenvalues of the adjacency matrix A = (av,t ) where av,t = 1 if vertex v is linked to vertex t, and av,t = 0 otherwise. An eigenvector of A is a nonzero vector which satisfies the following equation:
Ax = λx
(4)
λ is then the associated eigenvalue. The EC(v) of a node v is defined as the vth entry in the eigenvector belonging to the largest eigenvalue of A denoted λ1 [28].
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Fig. 1. Macro-states network for control EEG data. The nodes present non-random macro-states, bidirectional transitions accuracy with highest transition probability that define the preferred dynamics direction. The core pattern with highest centrality measures is shown in the left of each network.
Table 1 Statistics of the entropy rate computed for the meso-scale Markov process representation of the dynamics for the two datasets. Subjects
hrmin
hrmax
hrmean
hrsd
Control MS
0.76 bit/ms 0.7 bit/ms
0.97 bit/ms 1.14 bit/ms
0.86 bit/ms 0.89 bit/ms
0.06 bit/ms 0.13 bit/ms
Alternatively, it is equivalent to the summed centrality of its neigh-
bors [27]:
EC (v ) = xv =
N 1
λ1
Av,t xt
(5)
t=1
2.3. Data The data sets have already been analyzed using an approach based on information theory [29] and are detailed in this previous article. Only the main characteristics are summarized here.
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Fig. 2. Macro-states network for MS EEG data. The nodes present non-random macro-states, bidirectional transitions accuracy with highest transition probability that define the preferred dynamics direction. The core pattern with highest centrality measures is shown in the left of each network.
The sample included 25 participants with clinically defined Relapsing Remitting Multiple Sclerosis. Neurological status and disability were assessed by Expanded Disability Status Scale [30] which ranges from 0 (i.e. normal) to 10 (i.e. death). Patients’ EDSS scores ranged from 1 to 5 (median: 3) which indicates a moderate mobility disability. Control data for EEG parameters were obtained by recording a sample of 12 healthy subjects.
EEG signals were recorded using 17 Ag/AgCl electrodes (C3, C4, Cz, F3, F4, F7, F8, Fz, O1, O2, P3, P4, T3, T4, T5, T6) placed on the scalp according to the 10/20 international electrode placement system. The reference electrode was placed on the nose. EEG signals were digitized on 16 bits of precision using a 256 Hz sampling frequency and filtered using a band-pass filter between 0.5 Hz and 70 Hz. Twenty minutes of EEG recordings were obtained from each participant in eyes closed and resting condition.
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Fig. 2. Continued
2.4. Dynamics entropy rate To support the comparison between healthy and pathological brain dynamics, the entropy rate of sequences of states h(M) was computed for mesoscale and macroscale levels for each control and
MS subjects. The entropy rate of a discrete Markov process with transition probabilities τ i,j and stationary distribution π i was computed using:
h (M ) = −
i, j
πi(k) τi,(kj ) log τi,(kj )
(6)
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where the π (k) and τ (k) are both maximum likelihood estimate of, respectively, the stationary distribution and probability of transition and log is taken as natural logarithm. 2.5. Classification Since most of the centrality measures define the same core pattern as the average measure (see Results) we defined the core patterns as the nodes with the highest average centrality measure. A classification step using the k-Nearest Neighbors Classifier (kNN) algorithm was performed to test whether core macroscopic patterns were sufficient for mapping resting state brain dynamic of MS patients. The kNN algorithm was used for several pattern recognition problems [31–33]. It is relatively simple and has a rapid convergence speed when compared with other classifiers. The kNN classifier is based on defining the K-nearest neighbors vote to classify input patterns. In order to determine the exact number of k-neighbors, we used a cross validation grid-search technique that computes the lowest test error rate and the highest accuracy. The classifier was applied to the most important patterns according to average centrality measure selected from entire non random macro patterns for each subject separately. The learning set consisted in a dataset of both MS patients and control macro patterns. The test set used the remaining non random macro patterns from MS patients (162). Since the number of MS patients core patterns was higher than that of control subjects (31 vs. 12), the learning sets consisted in a random sample of 12 MS patterns out of the 31 to avoid an over-representation of MS core patterns in the learning set. The number of core patterns was thus the same for MS and control condition and avoid biased classification. The classification step was repeated 100 times varying randomly the learning and test sets in order to ensure the robustness of the patterns obtained as the best match of rest state for MS brain’s macrodynamics. We computed different error rates and their standard deviation of MS patterns classification obtained for the 100 trials. 3. Results 3.1. Dynamics characterization We obtained an effective coarse-grained dynamical skeleton for 12 control subjects and 25 MS patients with a 17-dimensional measurement space E for T = 3.104 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 G 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 across subjects and between groups. Between subjects, the main difference is due to the fact that the number of significant patterns vary between 3 and 15. MS networks are moreover different from healthy ones since in the case of control subjects, networks have almost a constant number of significant patterns whereas this number is variable in MS patients. Moreover, the healthy dynamic is ruled by a unique main dominant macro pattern whereas in the MS dynamics the transitions seem organized according to multiple principal macro patterns. On this basis, the networks topology induced by non-random transitions differ between groups. The entropy rate of the Markov process representation was computed for the meso-scale (see Table 1) and macro-scale (see Table 2) dynamics. This index does not provide any indication of
Table 2 Statistics of the entropy rate computed for the macro-scale Markov process representation of the dynamics for the two datasets. Subjects
hrmin
hrmax
hrmean
hrsd
Control MS
0.45 bit/ms 0.52 bit/ms
0.55 bit/ms 0.91 bit/ms
0.5 bit/ms 0.7 bit/ms
0.02 bit/ms 0.1 bit/ms
difference between the two groups for the meso-scale (Welch twosample t-test: t = −0.96 df = 34.9 p-value= 0.17) whereas it depicts a significant lower value for control than for MS patients for the macro-scale (Welch two-sample t-test: t = −9.61 df = 27.7 pvalue < 0.001). In order to extract core macro patterns with central importance in cortical dynamic, we computed the entire set of centrality measurements: centrality degree (DC), betweenness centrality (BC), closeness centrality (CC) and eigenvalue centrality (EC) for each node V in graph G. For each subject, it characterizes its macro graph G and allows to extract the most accurate core macroscopic node or pattern. Most of the centrality measures define the same core pattern as the average measure: for 28 out of 37 cases (75.6%) the four centrality measures are in accordance with the average, for 8 out of 37 cases (21.6%) three centrality measures are in accordance with the average and for only one case two centrality measure are in accordance with the average. For control data, almost all core patterns depict an occipital activation (right or left) with high amplitude. This proves the existence of an alpha rhythm during the rest state for 10 subjects among 12. Only two subjects are different which is in concordance with the proposed archetypes in healthy rest state mode based on Affinity Propagation method [34]. For MS data, we notice that centrality measurements are quite close in comparison with healthy data (supplementary figures), that proves the absence of a dominant macro pattern (Fig. 3). 3.2. Classification results In the classification step, we evaluated the robustness of centrality measurements to extract typical core pattern able to represent the MS macroscopic dynamics. In fact, the selected core patterns from the learning data predict the MS rest state macroscopic behavior, with an error rates below 13% obtained from 100 repetitions (mean: 9.7%, sd: 0.83). The misclassification rate was low enough to provide reliable definition of MS brain dynamics during resting state. To complete the results obtained for average centrality measure, classification was also performed using each centrality measure (see Table 3). In each case, the learning set was slightly different from that obtained for average centrality measure and the mean error rate was lower for the closeness and degree centrality and higher for eigenvector and betweenness centrality than for average centrality. To check whether the centrality measures are able to describe the MS brain dynamics independently from the scale of the dynamics, we apply the same centrality selection to both the networks that include all the macroscopic patterns and the meso-scale networks. To ensure the consistency of the comparison, the same number of patterns as for the non-random macroscopic scale was used in the test set for both new test sets. Two other classification tests (repeated 100 times each) were performed. In each case, the learning set was defined as previously and the test set consisted in randomly chosen patterns (162) from all the remaining MS patterns. Classification results are given in Table 4 and depict a higher miss-classification rates than for the non-random macroscopic networks.
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Table 3 Classification results for each centrality measure and differences between learning set for average centrality measure and each other centrality measure. Centrality measure
Mean error rate (sd)
Difference between learning sets
Betweenness (BC) Degree (DC) Closeness (CC) Eigenvector (EC)
11.03% (sd: 0.79) 8.6% (sd: 0.9) 7.9% (sd: 1.12) 12.8% (sd: 1.55)
2 2 1 3
MS MS MS MS
patterns patterns pattern and 2 control patterns patterns
Fig. 3. Non random macro-states for MS real EEG data set performed in the space of their graph centrality measures such as betweenness centrality (blue circle), degree centrality (red star), closeness centrality (green plus) and eigenvector centrality (black triangle). Black curve depicts the average of the measurements. Only the node of G which has the largest average centrality measures values will be considered as the core macroscopic pattern of the cerebral macro-scopic dynamic. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 3. Continued
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Table 4 Classification results for meso-scale and complete macro-scale networks. Patterns
Learning data
Test data
Mean error rate (sd)
All macro patterns Meso patterns
12 control + 12 MS 12 control + 12 MS
162 MS patterns 162 MS patterns
20.72% (sd: 1.7) 23.12% (sd: 2.97)
4. 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 representation of brain dynamics. Moreover, at the macroscopic scale, the brain dynamics of MS patients depicts a higher entropy rate than controls dynamics. These indices reinforce the previous results on the disorganisation of MS brain dynamics [29,35]. We introduced different centrality measures to extract core patterns from a graph composed of non-random macro-states and significant transitions related to the macroscopic dynamic directory of brain activity. We selected for all the subjects the most dominant macroscopic pattern by maximizing the centrality measures. In fact, this pattern was able to describe electrical brain activity at resting state for most of the subjects. This activity was exhibited through occipital oscillations either on the right or the left side characterized by a high amplitude. This pattern could be considered as a macroscopic meta-stable state which appears as a hub in a macro-scale network. All the centrality measures are dealing with slightly different characteristics about the nodes properties, e.g. nodes with high degree are nodes very well connected in the networks, while nodes with high betweenness centrality are nodes that facilitate communication in the network. Although most of these measures extract the same core pattern as the average measure, classification results are somewhat better for degree and closeness centrality. These measure should thus be studied on their own to provide physiological interpretation related to their dynamical meaning. The dynamic repertoire of brain electrical activity was defined in MS patients using the same procedure. A kNN classifier proved that core macroscopic MS patterns defined using average centrality measure are sufficient to define MS dynamics with only an average of error rate of 9.7%. However evaluating the dynamics at the macroscopic level could be completed by the study at lower level dynamics. So, we have re-applied the centrality measures to the lower level dynamic networks (all macroscopic and mesoscopic scales). Indeed for each level, we have extracted the most significant patterns using the average centrality measure and computed the MS patterns classification technique. As a result, we obtained higher error rates than those obtained with macroscpic selected level. These rates exceed 20% at the mesoscopic scale after classifying 6873 MS patterns. This increase of the error rate can be explained by the large number of patterns in the training data in relation to those in the learning data. Enriching the learning data can be a solution to further characterize MS mesoscopic brain dynamics at the rest state. This will lead to a better correlation between learning and training patterns. Our results show a change in both the dynamical organisation of brain dynamics and core patterns of cortical activity in MS patients. Since it has been demonstrated recently that the thalamus is involved in the global oscillatory slowing within the MEG α -
band in MS and that there is an association with thalamic atrophy [36], our result also suggest that this disturbance could also be revealed at the macroscopic scale of core patterns. If this hypothesis could be verified it would reinforce the role of the thalamus as a critical hub region involved in actively maintaining the modular structure of cortical functional networks [37]. The consequences of the dynamical interplay between thalamus and cortical activity in macroscopic brain dynamics for both healthy and MS brain activity deserve further studies. 5. 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 complexity and core patterns could serve as a potential marker of brain state in relapsing-remitting MS. 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. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cmpb.2019.104985.
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References [1] A. Hadriche, L. Pezard, J. Nandrino, H. Ghariani, A. Kachouri, K. Jirsa, Mapping the dynamic repertoire of the resting brain., NeuroImage J. 78 (2013). 448–62 [2] G. Deco, V.K. Jirsa, Ongoing cortical activity at rest: criticality, multistability, and ghost attractors., J. Neurosci. 32 (2012) 3366–3375. [3] N. Jmail, M. Gavaret, F. Wendling, A. Kachouri, G. Hamadi, J.-M. Badier, C.-G. Bénar, A comparison of methods for separation of transient and oscillatory signals in EEG, J. Neurosci. Methods 199 (2) (2011) 273–289. [4] N. Jmail, M. Gavaret, F. Bartolomei, C.-G. Bénar, Despikifying SEEG signals using a temporal basis set, in: Intelligent Systems Design and Applications (ISDA), 2015 15th International Conference on, IEEE, 2015, pp. 580–584. [5] N. Jmail, M. Gavaret, F. Bartolomei, C.-G. Bénar, Despiking SEEG signals reveals dynamics of gamma band preictal activity, Physiol. Measur. 38 (2017) N42–N56. [6] C. Stam, Nonlinear dynamical analysis of eeg and meg: review of an emerging field., Clin. Neurophysiol. 116 (2005) 2266–2301. [7] J.-P. Lachaux, L. Pezard, L. Garnero, C. Pelte, B. Renault, F. Varela, J. Martinerie, The spatial extension of brain activity fools the single-channel reconstruction of eeg dynamics, Hum. Brain Mapping 5 (1997) 26–47. [8] C. Allefeld, H. Atmanspacher, J. Wackermann, Mental states as macrostates emerging from brain electrical dynamics, Chaos 19:015102 (2009) 281–297. [9] P. Foteini, M. Dimitris, N. Smyrnis, C. Siettos, A coarse-grained analysis of the functional brain connectivity from EEG recordings of a visuo-perceptual discrimination task., Front. Comput. Neurosci. 8 (2014) 1–12, doi:10.1063/1. 4825658. [10] C. Quan L.and Yi-Feng, F. Shou-Zen, M.F. Abbod, J.-S. S., EEG artifacts reduction by multivariate empirical mode decomposition and multiscale entropy for monitoring depth of anaesthesia during surgery., Med. Biol. Eng. Comput. (2015) 16pages, doi:10.1155/2015/232381. [11] A. Hadriche, N. Jmail, R. Elleuch, L. Pezard, Different methods for partitioning the phase space of a dynamic system, Int. J. Comput. Appl. 93 (15) (2014). [12] R. Jarray, N. Jmail, A. Hadriche, T. Frikha, A comparison between modeling a normal and an epileptic state using FHN and the epileptor model, in: Proceedings of the International Conference on Innovations in Bio-inspired Computing and Applications, Springer, 2017, pp. 245–254. [13] S. Wasserman, K. Faust, Social Network Analysis, Cambridge University Press (1994). [14] A. Schneeberger, C. Mercer, S. Gregson, N. Ferguson, C. Nyamukapa, R. Anderson, A. Johnson, G. Garnett, Scale-free networks and sexually transmitted diseases - a description of observed patterns of sexual contacts in britain and zimbabwe., Sex. Transm. Dis 31 (6) (2004) 380–387. [15] M. Faloutsos, P. Faloutsos, C. Faloutsos, On power-law relationships of the internet topology, ACM SIGCOMM Comput. Commun. Rev. 29, 4 (1999) 251–262. [16] R. Albert, H. Jeong, A.-L. Barabasi (Eds.), Diameter of the world wide web, Nature, London, 1999. [17] H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, A.L. Barabasi, The large-scale organization of metabolic networks., Nature 407 (20 0 0) 651–654.
[18] S. Wuchty, Scale-free behavior in protein domain networks., Mol. Biol. Evol. 18 (2001) 1694–1702. [19] A.-L. Barabasi, R. Albert, Emergence of scaling in random networks, Science 286 (5439) (1999) 509–512. [20] L.C. Freeman, Centrality in social networks. conceptual clarification, Social Netw. 1 (1979) 215–239. 1 [21] M. Dellnitz, A. Hohmann, A subdivision algorithm for the computation of unstable manifolds and global attractors, Numerische Mathematik 75 (1997) 293–317. [22] J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, J. Farmer, Testing for nonlinearity in time series: the method of surrogate data., Physica D 58 (1992) 77–94. [23] T. Schreiber, A. Schmitz, Surrogate time series., Physica D 142 (20 0 0) 346–382. [24] D.J. Watts, Small World: The Dynamics of Networks Between Order and Randomness, Princeton University Press, Princeton University, 1999. [25] U. Brandes, A faster algorithm for betweenness centrality., J. Math. Sociol. 25(2) (2001) 163–177. [26] U. Brandes, On variants of shortest-path betweenness centrality and their generic computation., Social Netw. 30(2) (2008) 136–145. [27] P. Bonacich, P. Lloyd, Eigenvector like measures of centrality for asymmetric relations., Social Netw. (2001) 191–201. [28] A.Z.A. Fornito, B. E., Fundamentals of Brain Networks Analysis., Elsevier, 2016. [29] B. Lenne, J.-L. Blanc, J.-L. Nandrino, P. Gallois, P. Hautecur, L. Pezard, Decrease of mutual information in brain electrical activity of patients with relapsing-remitting multiple sclerosis, Behav. Neurol. 27 (2013) 201–212. [30] F.J. Kurtzke, Rating neurologic impairment in multiple sclerosis, Neurology 33 (11) (1983). 1444–1444 doi: 10.1212/WNL.33.11.1444. [31] F. Moreno-Seco, L. Mico, J.A. Oncina, Modification of the laesa algorithm for approximated kNN classification., Pattern Recognit. Lett. 24 (2003) 47–53. [32] T. Abidin, W. Perrizo (Eds.), SMART-TV: a fast and scalable nearest neighbor based classifier for data mining., Proceedings of ACM SAC-06, Dijon, France, 2006. [33] A.H. Ullah, M. Wajid, S.A. Rauf, S.M.N. Mohamad, M.A. Saeed, Classification of eeg signals based on pattern recognition approach, Front. Comput. Neurosci. 11 (2017) 103–121. [34] B.J. Frey, D. Dueck, Clustering by passing messages between data points, Science 315 (2007) 972-949. [35] M. Gschwind, D. Van De Ville, M. Hardmeier, P. Fuhr, C. Michel, M. Seeck, Id 249 corrupted fractal organization of EEG topographical fluctuations predict disease state in minimally disabled multiple sclerosis patients., Clin. Neurophysiol. 127 (3) (2016) e72. [36] D. Schoonhoven, M. Fraschini, P. Tewarie, B. Uitdehaag, A. Eijlers, J. Geurts, A. Hillebrand, M. Schoonheim, C. Stam, E. Strijbis, Resting-state MEG measurement of functional activation as a biomarker for cognitive decline in MS., Multiple Sclerosis J. (2018) 1–11. [37] H. K., B. MA., L. WB., D. M., The human thalamus is an integrative hub for functional brain networks., J. Neurosci. 37 (23) (2017) 5594–5607.