1. What does delta band tell us about cognitive processes: A mental calculation study Stavros I. Dimitriadis,Nikolaos A. Laskaris, Vasso Tsirka, Michael Vourkas, Sifis Micheloyannis Electronics Laboratory, Department of Physics, University of Patras, Patras 26500, Greece Artificial Intelligence & Information Analysis Laboratory, Department of Informatics, Aristotle University, Thessaloniki, Greece Medical Division (Laboratory L.Widιn), University of Crete, 71409 Iraklion/Crete, Greece Technical High School of Crete, Estavromenos, Iraklion, Crete, Greece http://users.auth.gr/~stdimitr 1

2. Outline Introduction -Multichannels EEG recordings -math calculations (comparison and multiplication) -delta activity (cognition and relation to the difficulty of the task -DMN (default mode network) Methodology - four delta sub-bands (0.78 – 3.96 Hz) -Signal Power (SP) (derived via squaring and averaging the filtered EEG data) -network analysis (clustering coefficient (C) + path length (L)) -Small-World theory (γ,λ,σ) 2

3. Results Conclusions Outline 3

4. IntroMethodResultsConclusion s Mathematical thinking, as a cognitive process, activates local and spatially distributed cortical networks Exact calculations are correlated with language function activating language specific regions located in the left hemisphere During mental calculations different processes are necessary, such as the -recognition of the numbers in their Arabic form, -the comprehension of verbal representation of numbers, -the assignment of magnitudes to numerical quantities, -attention, memory, and other more specialized processes During difficult math calculations, additional cortical regions, particularly of the left hemisphere, show increased activation. These calculations demand retrieval of simple mathematical fact 4

5. IntroMethodResultsConclusion s Motivation Most widely studied bands are theta, alpha, beta and lower gamma Delta and higher gamma activity have been examined less due to artifact contamination We intended not only to replicate the previous findings but also to promote the understanding about the significance of this slow band in math calculation An increase of delta activity has been reported (Dolce & Waldeier,1974,Harmony et al., 1996) 5

6. IntroMethodResultsConclusion s Outline of our methodology The employment of narrow subbands gave us the opportunity to distinquish the actual brain activity from eye movement related activity, which is equally visible in all frequency range Based on EEG activity and the network of electrodes the notion of functional connectivity graph (FCG) topology, is utilized to identify different modes of brain’s self organization. Network analysis is performed for each subject/task and the inter- task comparison reveals significant differences between the two cognitive tasks Calculation of SP for each recording site 6

7. Data acquisition: Math Experiment IntroMethodResultsConclusion s 3 Conditions: Control Comparison Multiplication 18 subjects 30 EEG electrodes Horizontal and Vertical EOG Trial duration: 3 x 8 seconds Single trial analysis The recording was terminated when at least an EEG-trace without visible artifacts had been recorded for each condition 7

8. IntroMethodResultsConclusion s Using a zero-phase band-pass filter (3 rd order Butterworth filter), signals were extracted within four different narrow bands (0.78-3.9 Hz was divided into non-overlapping subbands, each of 0.78 Hz width) Filtering Artifact Correction Working individually for each subband and using EEGLAB (Delorme & Makeig,2004), artifact reduction was performed using ICA -Components related to eye movement were identified based on their scalp topography which included frontal sites and their temporal course which followed the EOG signals. -Components reflecting cardiac activity were recognized from the regular rythmic pattern in their time course widespread in the corresponding ICA component. 8

9. IntroMethodResultsConclusion s Signal Power (SP) Calculation of SP for each recording site The SP values corresponding to each single electrode were contrasted for every subband and additionally the whole delta-band. Significant changes were captured via one-tailed paired t-tests (p < 0.001). Τhe functional connectivity graph (FCG) describes coordinated brain activity In order to setup the FCG, we have to establish connections between the nodes (i.e. the 30 EEG electrodes). Phase synchronization, is a mode of neural synchronization, that can be easily quantified through EEG signals 9

10. IntroMethodResultsConclusion s Phase-locking Value (PLV) PLV quantifies the frequency-specific synchronization between two neuroelectric signals (Mormann et al., 2000 ; Lachaux et. al. 1999). We obtain the phase of each signal using the Hilbert transform.  (t, n) is the phase difference φ1(t, n) - φ2(t, n) between the signals. PLV measures the inter-trial variability of this phase difference at t. If the phase difference varies little across the trials, PLV is close to 1; otherwise is close to 0 10

11. PLV procedure for a pair of electrodes IntroMethodResultsConclusion s Adopted from Lachaux et al,1999 11

12. 0.9 0.6 Building the FCG The process is repeated for every electrode, creating a complete graph. Establishing links for a single electrode IntroMethodResultsConclusion s 12

13. Surrogate Analysis IntroMethodResultsConclusion s -To detect significant connections, we utilized surrogate data to form a distribution of PLI values, for each electrode-pair separately, that corresponds to the case in which there is no functional coupling - Functional connections that showed significant differences, with respect to the distribution of PLI values generated by a randomization procedure corresponding to each electrode pair,were only considered. -Since our analysis was based on a single sweep, we shuffled the time series of the second electrode for each pair (in contrast to the case of multiple trials where one shuffles the trials of the second electrode as described in Lachaux et al., 2000). 13

14. -Finally, the original PLI values were compared against the emerged baseline distribution (surrogate data) and this comparison was expressed via a p-value which was set at p < 0.001. IntroMethodResultsConclusion s Surrogate Analysis - Graph edges where the above criterion was not met, were assigned a zero-weighted link. 5% Nonparametric Null Distribution 14

15. IntroMethodResultsConclusion s Network Analysis The clustering coefficient C of network is defined as : in which k i is the degree of the current node The characteristic path length L is defined (through integration across all nodes) as: 15

16. IntroMethodResultsConclusion s Small – World network measures -We rewired each network 1000 times using the algorithm proposed in (Maslov & Sneppen, 2002) -Derived C r and L r as the averages corresponding to the ensemble of randomized graphs. The two (normalized) ratios γ= C/C r and λ= L/L r were used in the summarizing measure of “small-worldness”, defined as σ= γ/λ, which becomes greater than 1 in the case of networks with small-world topology -The above described computations were performed for each subject separately - Results were employed to detect systematic trends, via statistical comparison among different tasks (comparison–control, multiplication–control,comparison–multiplication), across subjects. 16

17. IntroMethodResultsConclusion s Small – World network measures The three graph metrics (γ,λ and σ ) were contrasted, for every subband, in a similar manner via paired t-test. Recording Montage -The selected data had been originally recorded based on a montage using a common reference electrode. -Since, this selection could influence significantly the subsequent computations of SP and phase-synchrony we additionally re- reference the data. -Using average-reference, we repeated the above described calculations. - We mention the observed differences and commonalities. 17

18. IntroMethodResultsConclusion s Signal Power (SP) Bi-color (black and grey) circles denote the sites where significant increase is observed before, but not after average re-referencing Αll subbands show widespread SP-increase during math Higher SP values of delta rhythm are seen over regions of the left hemisphere during multiplication in contrast to the number comparison 18

19. IntroMethodResultsConclusion s Network Analysis The (normalized) clustering coefficient and the (normalized) path length are higher during multiplication, for networks corresponding to those subbands which showed significant inter-task SP-differences. These findings could be considered as the result of increased nodal (local) activity and less efficient remote connections within the corresponding brain networks. Simultaneously, all subbands show small-world network characteristics i.e. optimum organization. 19

20. Conclusions We investigate brain activity in four sub-bands during math calculation. We characterize EEG recorded brain activity (Related to any particular cognitive task and the four sub-bands) Based on functional connectivity graphs Artifact contamination (occulographic and myographic activity) can be overcomed using sub-bands + ICA. Our methodology offers novel knowledge about delta activity during math calculation and the nodal organization of the related FCGs. The changes in SP and network organization related to delta rhythm could be possibly explained as the results of inhibitory mechanisms reflecting the deactivation of the default network. IntroMethodResultsConclusion s 20

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