Transfer Entropy and Information Flow Patterns in Functional Brain ...

Transfer Entropy and Information Flow Patterns in Functional Brain Networks during Cognitive Activity Md. Hedayetul Islam Shovon1, D (Nanda) Nandagopal1, Ramasamy Vijayalakshmi2, Jia Tina Du1, and Bernadine Cocks1 1

Cognitive Neuroengineering Laboratory, Division of IT, Engineering and the Environments, University of South Australia, Adelaide, Australia 2 Department of Applied Mathematics and Computational Science, PSG College of Technology, Coimbatore, Tamil Nadu, India [email protected]

Abstract. Most previous studies of functional brain networks have been conducted on undirected networks despite the direction of information flow able to provide additional information on how one brain region influences another. The current study explores the application of normalized transfer entropy to EEG data to detect and identify the patterns of information flow in the functional brain networks during cognitive activity. Using a mix of signal processing, information and graph-theoretic techniques, this study has identified and characterized the changing connectivity patterns of the directed functional brain networks during different cognitive tasks. The results demonstrate not only the value of transfer entropy in evaluating the directed functional brain networks but more importantly in determining the information flow patterns and thus providing more insights into the dynamics of the neuronal clusters underpinning cognitive function. Keywords: Transfer entropy, directed functional brain network, EEG, cognitive load, graph theory.

1

Introduction

The human brain is a complex and dense network of billions of interconnected neurons. To quantify the topological features of this network, graph theoretical analysis has been successfully employed by researchers in the recent past [1-3]. Most of this graph theoretical analysis has, however, been applied to undirected networks. Such analysis can, however, be applied to directed networks [2]. This is perhaps, surprising given that directed networks exhibit more prominent features by providing directional interactions between pairwise elements thereby enabling more detailed analysis. Although Granger causality is often used to identify causal relationship in electroencephalogram (EEG) data, it is limited to the linear model of interaction [4]. As a result, it fails to accurately identify causal relationships in highly nonlinear systems such as the human brain. By comparison, the information theoretical measure of transfer entropy (TE) determines the direction and quantifies the information transfer between two processes [5]. TE estimates the amount of activity of a system which is not C.K. Loo et al. (Eds.): ICONIP 2014, Part I, LNCS 8834, pp. 1–10, 2014. © Springer International Publishing Switzerland 2014

2

M.H.I. Shovon et al.

dependent on its own past activity but on the past activity of another system. It does not require a model of the interaction and inherently non-linear [4]. As a consequence, TE has been used in various applications such as identifying information transfer between auditory cortical neurons using spike train data, investigating the influence of heart rate on breath rate and vice versa, and for the localization of the epileptic focus of epileptic patients on EEG data [5-8]. TE has however not been applied in the construction and analysis of directed functional brain networks (FBN) during different cognitive states. The current study reported in this paper aims to investigate the application of normalized TE to construct a directed FBN. It further explores graph theoretic and statistical analysis to characterize this directed FBN and its patterns of information flow during cognitive tasks. Complex network metrics have also been used to delineate the cognitive tasks and the comparative results are presented. The research literature on TE and graph theoretical analysis are reviewed and described in the following sections.

2

Transfer Entropy

Given two processes

and , the TE from , ,

,

to

is shown in Equation 1 [9]: ,

log

,

,

.

, .

,

1

Here, denotes the status (value) of signal/system at time , denotes the status of signal at time and denotes the status of signal at time 1. The value of is calculated by summing over all possible combination of , , and . ∞. Here, . There is another similar TE is in the range 0 equation for . In practice, for the calculation of TE, two additional steps were included to improve the calculation accuracy [7, 10]. Due to the finite size and nonstationarity of data, TE matrices usually contain much noise. In the existing literature, noise/bias has been removed from the estimate of TE by subtracting the average transfer entropy from to using shuffled version of denoted by , over several shuffles [10]. contains the same symbol as in but those symbols are rearranged in a randomly shuffled order. Then, normalized transfer entropy is calculated from to with respect to the total information in sequence itself. This will represent the relative amount of information transferred by . The normalized transfer entropy (NTE) is shown in Equation 2 as follows [7]: 2

| In equation 2, | represents the conditional entropy of process 1 given its value at time as shown in equation 3. |

, ,

log

,

at time 3

Transfer Entropy and Information Flow Patterns in Functional Brain Networks

NTE is in the range 0 1 . NTE is 0 when , and is 1 when transfers maximal information to .

3

3

transfers no information to

Functional Brain Networks and Graph Theoretical Analysis

To capture the dynamic interactions between the neuronal elements of human brain, FBNs can be derived from time series observations of EEG signals [2]. As EEG is cheap non-invasive method with high temporal resolution, it has been used extensively in research, medical diagnosis and brain computer interaction [3, 11]. In the present study, the FBNs are constructed by computing the NTE between EEG channels. According to the graph theory, graph is a mathematical model that consists of vertices (nodes) where the connection between each pairs of vertices is called an edge (link) [1, 2]. In the case of FBNs, scalp electrodes are considered as vertices and the connections/links between electrodes are measured using correlation. The following graph (or complex network) metrics are also used in this study: connectivity density representing the actual number of edges as a proportion to the total number of possible edges [1]; reciprocity representing the ratio of the number of pairs with a reciprocated edges relative to the total number of edges [12]; clustering coefficient quantifying the fraction of triangles around a node [13]; average of shortest path length between all node pairs known as the characteristic path length [14]; small world representing both high clustering and short characteristics path length [14]; node eccentricity representing the maximal shortest path length between any two nodes [12]; and node strength representing the total of all incoming and outgoing link weights [15].

4

Methods

4.1

Participants and EEG Data Acquisition

Six healthy, right handed adults (4 males, 2 females) volunteered for EEG data collection (age range 19-59) at the Cognitive Neuroengineering Laboratory of University of South Australia. The participants were recruited from staff and students cohort of University of South Australia. All reported normal hearing, normal or corrected-tonormal vision, with none reporting any psychological, neurological or psychiatric disorder. EEG data were acquired at a sampling rate of 1000 Hz through a 40 channel Neuroscan Nuamps amplifier using Curry 7 software. The 30 electrode sites used in the current study were based on the international 10-20 convention: FP1, FP2, F7, F3, Fz, F4, F8, FT7, FC3, FCz, FC4, FT8, T3, C3, Cz, C4, T4, TP7, CP3, CPz, CP4, TP8, T5, P3, Pz, P4, T6, O1, Oz and O2. Continuous EEG data were collected as each participant undertook three tasks in a Simuride Driving Simulator. In Task 1 (baseline), data were collected for 2 minutes (each) in both eyes open and eyes closed conditions. In Task 2, participants were asked to drive normally on a virtual winding road for approximately 4 minutes. In Task 3, participants were asked to drive, as per Task 2, while also responding to auditory stimuli. All stimulus onsets and participant responses were time-marked on the EEG record using STIM 2 software.

4

4.2

M.H.I. Shovon et al.

EEG Signal Pre-processing

A band pass filter of 1-70 Hz and a notch filter of 50 Hz were applied to the EEG data. Eye blinks were removed using principal component analysis (PCA), with any residual. Bad blocks were removed manually. For Tasks 1 and 2, two seconds epoched averaged data were extracted by applying back-to-back epoching process of Curry software using epoch length of 2 seconds, and then averaging those epochs. For tasks 3, two seconds epochs were extracted by identifying all two seconds epochs from stimulus onsets, where reaction times were between 1.5 and 3 seconds, and then averaging those epochs. 4.3

Proposed Methodology for the Analysis of Directed Functional Brain Network

The pre-processed EEG data during eyes open (EOP), driving only (Drive), and driving with audio distraction (DriveAdo) were used for the construction of TE matrices, where each cell of the TE matrices represents the TE value from one electrode to another. For noise removal, an average shuffled TE matrix (noise matrix) was calculated and subtracted from the original matrix. The data, information processing and associated computational steps are illustrated in Figure 1. EEG Data Acquisition Participant

EEG Signal Pre-processing

Raw EEG Data

Pre-processed EEG Data

Raw EEG Data Pre-processing

 Filtering (Band Pass, Notch)  Eye Blink Removal (PCA)  Epoching and Averaging

 Baseline – Eyes Open/ Eyes Closed  Cognitive load – Driving, Driving Audio

Graph Database Construction

Pre-processed EEG Data

Transfer Entropy Matrix

Normalized Transfer Entropy matrix

Noise/ Bias Matrix

-

Normalization

(Subtraction)

Graph Database Weighted/Binary/ Binary (Influential edge)

Results/ Visualization / Graph Theoretical Analysis /Statistical Analysis FP 1

FP2

FP1

F7

F8 F3

FT7

FC3

T3

TP 7

CP3

CPz

P3

Pz

C4

CP4

P4

T4

TP8

T6

FT7

FC3

T3

Oz

(a)

Fz

C4

FT7

FC3

TP7

CPz

CP 4

C3

TP8

T5

P3

Pz

P4

T6

T5 Oz

FT8

FC4

C4

CPz

P3

CP4

Pz

P4

T4

TP8

T6

O2

O1

(b)

F4

Cz

CP3

TP7

O2

Fz

FCz

T4

T3 CP3

F8 F3

FT8

FC4

Cz

FP2

F7

F4

FCz

C3

O1

O1

FP1 F8

F3

FT8

FC4

Cz

FP2

F7

F4

FCz

C3

T5

Fz

Oz

O2

(c)

Fig. 1. Framework for transfer entropy and information flow patterns during cognition

Transfer Entropy and Information Flow Patterns in Functional Brain Networks

5

The Normalized TE (NTE) matrices were used for the construction of both binary and weighed directed FBNs. The objectives of the proposed methodology are twofold: 1. To quantify the topological features of binary and weighted directed FBNs during different cognitive states; and 2. To determine information flow patterns during different cognitive states. To investigate the topological features and information flow patterns from constructed FBNs, the following complex network metrics were used. Connectivity density is calculated by counting the actual number of edges in a graph and then diving by all possible number of edges in that graph. For a directed graph with nodes where there is no self-connections/loop, the total number of possible connections are 1 . Reciprocity of a graph is calculated by finding the ratio of the total number of bidirectional edges relative to the total number of any directional edges between the node pairs. Clustering coefficient has been calculated using the technique of directed variant of clustering coefficient developed by Fagiolo [13]. In a directed graph, 3 nodes can generate up to 8 triangles. The clustering coefficient for node represents the ratio between all directed triangles actually formed by and the number of all possible triangles that could form. The experimental results and analysis are presented in the following section.

5

Results and Discussion

The NTE matrices (each are 30 by 30 in size) during EOP, Drive and DriveAdo states are presented in Figure 2. The increased information flow during cognitive load condition is demonstrated by the appearance of more cluttered brighter pixels (see Figure 2b and 2c). From this experiment, it can be inferred that, during cognitive load, information flow generally increases between the electrodes than in baseline condition (EOP). 0.1

(a)

(b)

(c)

0.0

Fig. 2. Normalized transfer entropy matrix during a) EOP, b) Drive and c) DriveAdo

5.1

Analysis of Binary Directed Functional Brain Network

The binary directed FBNs constructed using NTE matrices with threshold=0.002 was utilized in this study and as shown in Figure 3 demonstrating increased connectivity between the electrodes during the cognitive load. Due to space limitations the result of graph metrics analysis is shown only for one participant. As indicated in Figure 4a connectivity density is higher in the cognitive load than the baseline condition, inferring more connections are established to facilitate more active information flow.

6

M.H.I. Shovon et al.

Figure 4b shows that reciprocity is higher in the cognitive load condition, which further suggests that most electrode pairs are trying to establish mutual connections to facilitate effective information transmission within the network. FP1

FP2

FP1

F7

F8 F3

FT7

FC3

T3

TP7

F4

FCz

C3

C4

CPz

P3

O1

CP4

Pz

P4

Oz

T4

TP8

T6

FT7

FC3

T3

TP7

CPz

P3

T5

O1

(a)

Pz

Oz

C4

CP4

P4

FT7

FT8

FC4

Cz

CP3

F8 F3

F4

FCz

C3

O2

Fz

FP2

F7

F8 F3

FT8

FC4

Cz

CP3

T5

Fz

FP1

FP2

F7

FC3

T3

T4

T5

T6

CPz

P3

O1

Pz

Oz

FT8

FC4

Cz

CP3

O2

F4

FCz

C3

TP7

TP8

Fz

C4

CP4

P4

T4

TP8

T6

O2

(c)

(b)

Fig. 3. Binary directed functional brain network during a) EOP, b) Drive and c) DriveAdo

Density

Reciprocity

0.4

0.6 0.4 0.2 0

0.2 EOP

Drive

DriveAdo

0 EOP

(a)

Drive

DriveAdo

(b)

Fig. 4. Comparison of a) Connectivity density, and b) Reciprocity of the brain network during EOP, Drive and DriveAdo

Clustering Coefficient

Clustering coefficient value increases in almost all of the electrodes during cognitive load (Figure 5). This indicates that each node’s nearest neighbors directly communicate and form clusters. This type of segregated neural processing of brain network during cognitive load would increases the local efficiency of the information transfer. The electrodes F3, F8, FT7, FT8 and TP8 are not showing that trend which need to explore in further research.

Electrodes

Fig. 5. Clustering coefficient across electrodes during EOP, Drive and DriveAdo

Transfer Entropy and Information Flow Patterns in Functional Brain Networks

7

Between the regular lattice and completely random networks there is a class of networks which has the properties of high clustering and short path length. That means, most of the nodes are not neighbors but most of the nodes can traverse each other’s by small number of edges. This class of network is called as “small world network” [14]. Small world network can be also characterized as a set of network with both high local and global efficiency [16]. Efficiency estimates how well the information propagates over the network. The small world properties of the directed FBNs during different cognitive tasks are illustrated in Table 1. Table 1. Small-worldness of directed FBNs during EOP, Drive and DriveAdo Cognitive Tasks EOP Drive DriveAdo

0.4735 0.5736 0.7930

0.4708 0.4882 0.4905

1.5345 1.4356 1.2425

1.5264 1.5126 1.5011

/

/

1.0056 1.1749 1.6167

1.0053 0.9491 0.8277

/ 1.0003 1.2680 1.9532

Here, and are the clustering coefficient of a tested and random network respectively; and are the characteristic path length of a tested and random network respectively. The results reveal that characteristics path length decreases during cognitive load which would suggest a high global efficiency of information transfer in the FBN. The directed FBNs during EOP, Drive and DriveAdo all exhibit smallworldness ( 1 , however, the FBN constructed during cognitive load exhibits more small world properties than that of the baseline condition suggesting that the FBN facilitates both high local and global efficiency of information transfer. 5.2

Analysis of Binary Directed Functional Brain Network (Influential Edges Only)

Eccentricity

Binary FBNs were constructed by keeping only the influential edges between each electrode pair during different cognitive states; namely, two electrodes and , may have two possible edges: and . In the current study, the maximum weight value’s edge or was chosen.

Electrodes

Fig. 6. Comparison of node eccentricity across electrodes during EOP, Drive and DriveAdo

8

M.H.I. Shovon et al.

Eccentricity was then calculated for different cognitive states (See Figure 6). The maximum number of edges traversed to reach one node from another during EOP, Drive and DriveAdo are 6, 5 and 4 edges, respectively. It may be concluded that, during cognitive load, information may travel pretty quickly in FBN than in baseline condition. 5.3

Analysis of Weighted Directed Functional Brain Network

Strength

NTE matrices without applying any threshold were also used to construct weighted FBN. Figure 7 represents the comparison of the node strengths during different cognitive states computed using the weighted network. As shown, almost all the electrodes have higher strength values during cognitive load, which indicates that each electrode sends and receives more information during cognitive load.

Electrodes

Fig. 7. Comparison of strength across electrodes during EOP, Drive and DriveAdo

5.4

Statistical Analysis

1 2 3

0.02

0.04

0.06

0.08

0.1

1 2 3

0.12 0.1 .1 12 00.06 12

Mean of Total Information Flow

(a)

Cognitive States

Cognitive States

Cognitive States

The following experiments were conducted to demonstrate the statistical significance of information flow during various cognitive states. For the three cognitive states, the total information flow of each electrode to all other electrodes was calculated. Oneway analysis of variance (ANOVA) was applied to compare the mean information flow of each group and the multi-comparison results are shown in Figure 8.

0.08

0.1

0.12

0.14

2 3

00.16 .16 00.02

Mean of Total Information Flow

(b)

1

0.03

0.04

0.05

0.06

0.07

0.08

Mean of Total Information Flow

(c)

Fig. 8. Multi-comparison of mean total information flow of each electrode to all other electrodes during different cognitive states for 3 participants (a) DP1, (b) DP2 and (c) DP3 (YAxis: Cognitive States 1 for EOP, 2 for Drive, and 3 for DriveAdo)

Transfer Entropy and Information Flow Patterns in Functional Brain Networks

9

The statistical significance of the differences between means is calculated using t-test at 0.05 (two-tailed) and the results are shown in Table 2. The results demonstrate that mean of total information flow is significantly different in EOP and DriveAdo experiments for all participants. Table 2. Statistical validation of mean information flow difference in different cognitive states States Drive DriveAdo DriveAdo

DP 1 EOP Drive EOP

Mean Diff 0.0244 -0.0108 0.0339*

95% CI [0.0244,0.0651] [-0.0329,0.0113] [0.0191,0.0487]

DP 2 Mean Diff 0.0218 0.0239 0.0457*

95% CI [-0.0033,0.0469] [-0.0071,0.0550] [0.0200,0.0715]

DP 3 Mean Diff 0.0155* 0.0235* 0.039*

95% CI [ 0.0053, 0.0258] [ 0.0110, 0.0360] [0.0285, 0.0495]

*Mean difference is significant at p< .05 level.

6

Conclusion

In this study the information theoretical NTE measure has been applied to construct EEG based directed FBNs in baseline and cognitive load conditions. Using the techniques of signal processing, information and graph theoretic measures, and inferential statistics, information flow patterns during cognition have been detected and identified. The overall results demonstrate that the directed FBNs constructed using NTE are sensitive to cognitive load. This sensitivity of NTE based FBN has the potential to assist the development of quantitative metrics to measure cognition. The NTE approach may have likely application in the clinical diagnosis of cognitive impairments in future. Future research should address the application of various graph mining algorithms on the constructed directed functional brain networks to detect and track possible patterns as well as quantum of information flow during cognitive activity. This may lead to deeper understanding of cognitive function. Acknowledgement. The authors wish to acknowledge partial support provided by the Defence Science and Technology Organisation (DSTO), Australia. The assistance and technical support provided by fellow researchers Mr Nabaraj Dahal and Mr Naga Dasari are greatly appreciated.

References 1. Rubinov, M., Sporns, O.: Complex network measures of brain connectivity: Uses and interpretations. Neuroimage 52, 1059–1069 (2010) 2. Bullmore, E., Sporns, O.: Complex brain networks: Graph theoretical analysis of structural and functional systems. Nature Reviews Neuroscience 10, 186–198 (2009) 3. Nandagopal, N.D., Vijayalakshmi, R., Cocks, B., Dahal, N., Dasari, N., Thilaga, M., Dharwez, S.: Computational Techniques for Characterizing Cognition Using EEG Data – New Approaches. Procedia Computer Science 22, 699–708 (2013) 4. Vicente, R., Wibral, M., Lindner, M., Pipa, G.: Transfer entropy—a model-free measure of effective connectivity for the neurosciences. Journal of Computational Neuroscience 30, 45–67 (2011) 5. Schreiber, T.: Measuring information transfer. Physical Review Letters 85, 461 (2000)

10

M.H.I. Shovon et al.

6. Chávez, M., Martinerie, J., Le Van Quyen, M.: Statistical assessment of nonlinear causality: Application to epileptic EEG signals. Journal of Neuroscience Methods 124, 113–128 (2003) 7. Gourévitch, B., Eggermont, J.J.: Evaluating information transfer between auditory cortical neurons. Journal of Neurophysiology 97, 2533–2543 (2007) 8. Sabesan, S., Narayanan, K., Prasad, A., Iasemidis, L., Spanias, A., Tsakalis, K.: Information flow in coupled nonlinear systems: Application to the epileptic human brain. In: Data Mining in Biomedicine, pp. 483–503. Springer (2007) 9. Kaiser, A., Schreiber, T.: Information transfer in continuous processes. Physica D: Nonlinear Phenomena 166, 43–62 (2002) 10. Neymotin, S.A., Jacobs, K.M., Fenton, A.A., Lytton, W.W.: Synaptic information transfer in computer models of neocortical columns. Journal of Computational Neuroscience 30, 69–84 (2011) 11. Kim, S.P.: A review on the computational methods for emotional state estimation from the human EEG. Computational and Mathematical Methods in Medicine 2013 (2013) 12. Hanneman, R.A., Riddle, M.: Introduction to social network methods. University of California Riverside (2005), published in digital form at http://faculty.ucr.edu/ ~hanneman/ 13. Fagiolo, G.: Clustering in complex directed networks. Physical Review E 76, 026107 (2007) 14. Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998) 15. Brain Connectivity Toolbox, https://sites.google.com/site/bctnet/ measures/list 16. Latora, V., Marchiori, M.: Economic small-world behavior in weighted networks. The European Physical Journal B-Condensed Matter and Complex Systems 32, 249–263 (2003)