Time varying connectivity in large scale networks in the ... - Lirias

DOCTORAL SCHOOL OF BIOMEDICALSCIENCES

Faculty of Medicine

Time varying connectivity in largescale networks in the human brain

Eshwar Gorakhnath Ghumare

Dissertation presented in partialfulfillment of the requirements for the

degree of Doctor in BiomedicalSciences

December 2017

Supervisors:Prof. dr. Patrick DupontProf. dr. Rik Vandenberghe

Time varying connectivity in large scale networks inthe human brain

Eshwar Gorakhnath GHUMARE

Jury:Prof. dr. Peter Janssen, chairProf. dr. Patrick Dupont (Promoter)Prof. dr. Rik Vandenberghe (Co-promoter)Prof. dr. Frederik MaesProf. dr. Dante MantiniProf. dr. Pieter Van Mierlo (UGent)Prof. dr. Laura Astolfi (La Sapienza, Rome)

Dissertation presented in partialfulfillment of the requirements forthe degree of Doctor in BiomedicalSciences

December 2017

KU LeuvenBiomedical Sciences GroupFaculty of MedicineDepartment of Neurosciences

© 2017 KU Leuven – Faculty of MedicineUitgegeven in eigen beheer, Eshwar Gorakhnath Ghumare, Herestraat 49, ON-2, box 1027, 3000 Leuven,Belgium (Belgium)

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All rights reserved. No part of the publication may be reproduced in any form by print, photoprint, microfilm,electronic or any other means without written permission from the publisher.

This work is dedicated to my beloved parents and family!Their endless support, encouragement and sacrifices haveinspired me to do research in the field of computationalneurosciences. I hope my work will contribute to the fieldto improve the health and well being of the mankind.

Eshwar G. Ghumare,Leuven, Belgium

“If the human brain were so simple that we couldunderstand it, we would be so simple that we couldn’t.”

Emerson M. Pugh

Dedicated to ...

i

Abstract

It is well understood that the functioning of the human brain is based on aprecise communication between a large number of brain regions. The functionalcommunication also referred to as functional connectivity, is the result ofcoordination of spatially diverse and widely-distributed cortical brain regions.Moreover, the connectivity span over frequency and temporal dimensions andit is direction specific. Therefore, estimated functional connectivity should bedirected, time varying and frequency dependent to fully uncover the functioningof the brain.

Deriving time varying connectivity requires careful selection of the imagingmodalities and the consideration of several technical steps. Compared tofMRI, EEG data have an excellent time resolution. Throughout this work, wediscussed methods to calculate time varying connectivity from the sources ofEEG data either measured during visual spatial attention tasks or generatedwith simulations. We specifically focused on the directed connectivity amongareas. This allows understanding the influence of one brain area on the otherareas and vice versa.

We started with constructing a pipeline for source modelling from surface EEGdata and for the calculation of time-varying connectivity from the estimatedsources. This involved understanding and carefully selecting different sourcemodelling algorithms and methods. We constructed a realistic head modelusing subject-specific anatomy and EEG channel locations. Standardized low-resolution brain electromagnetic tomography (sLORETA) was used to estimatethe brain sources. For the connectivity analysis, we mainly focused on twoapproaches: (1) time-varying multivariate autoregressive modelling (TV-MVAR)of the data followed by calculation of partial directed coherence (PDC), aGranger Causality (GC) based multivariate spectral measure. (2) In a secondapproach, the phase lag index (PLI), a phase synchronisation based measure,was used. We also used PLI weighted with the cross-spectral power, referred toas weighted PLI (wPLI), to improve the noise performance.

iii

iv ABSTRACT

In the first study, we applied the weighted phase lag index based time varyingconnectivity framework to electrocorticography (ECoG) data acquired during avisual spatial attention task. We observed significant directed influences relatedto the invalidity and competition effects in the parietal cortex. We found thatin invalid trials, the superior parietal lobule (SPL) was driving the activity inthe intraparietal sulcus (IPS). Furthermore, when a competing distracter waspresent, a prolonged effect of anterior IPS to middle IPS regions was found.Overall, this suggests the origin of late selection in IPS at the postperceptualstage. The study provided for the first time the electrophysiological signature ofspatial shifting in response to an invalid cued spatial trial in SPL. Based on timevarying connectivity we were able to study the reversal of the directed influencessomething which is not possible with undirected time-invariant connectivity.

Then, we moved a step further by comparing methods to estimate the timevarying connectivity based on PDC. In these methods, the accurate estimationof the time varying MVAR model is an essential step. Kalman filtering basedapproaches such as the classical Kalman filter (CKF) and the General LinearKalman filter (GLKF) offer a robust framework. However, there are a few waysin which Kalman filtering based techniques can be implemented when data areacquired in the form of multiple trials as is usually the case. We used simulateddata with a predefined connectivity model and used a realistic approach togenerate EEG data from EEG sources. We studied the impact of the numberof trials and SNR on both approaches. Given the faster computation time,GLKF is the best choice in most cases except when the number of trials istoo low. Unfortunately, a lower limit of trials cannot be set for GLKF as itdepends on several other parameters like the number of channels. Furthermore,the extraction of time series in a region is an essential step before connectivityestimation. Due to the ill-posed nature of the source modelling problem, thesources are smooth. We showed that the dipole with time series showing thehighest correlation with the region average time series also indicated the highestcorrelation with the ground truth time series and this dipole had the lowestlocalisation error compared to other strategies.

Finally, we studied temporal networks related to a visual spatial attentionexperiment in the human brain. We used EEG data acquired in 14 healthysubjects. The role of the parietal lobe in visual spatial attention is wellestablished. However, there exist anatomically and functionally dissociableregions in the parietal lobe. To uncover the mechanisms of attention, theunderlying connectivity between parietal regions needs to be investigated.We applied EEG source modelling combined with time-varying connectivityestimation based on partial directed coherence. With this approach, we studieda directed network at high temporal resolution using pre-defined regions mainlyin the parietal lobe.

vi ABBREVIATIONS

Abbreviations

AAR automatic artifact removalAC anterior commissureAIC Akaike information criterionANOVA analysis of varianceAR autoregressiveBEM boundary element methodCKF classical Kalman filterCSD cross-spectral densityCSF cerebral spinal fluidCT computed tomographyCTF cross talk functiondPLI directed phase lag indexDC directed coherenceDCM dynamic causal modellingdDTF direct directed transfer functionDTF directed transfer functionECoG ElectrocorticographyEEG electroencephalographyEOG electrooculographyERP event related potentialsERSP event-related spectral perturbationFEF frontal eye fieldFEM finite element methodFG fusiform gyrusfMRI functional magnetic resonance imagingGC Granger causalityGLKF general linear Kalman filterGM grey matterIH interhemisphericIPL inferior parietal lobuleIPS intra parietal sulcusITC inter trial coherenceLAURA local autoregressive average

ABBREVIATIONS vii

LIP lateral intra parietalLORETA low-resolution brain electromagnetic tomographyLPA left pre-auricularMEG magneto encephalogramMFG middle frontal gyrusmIPS middle intraparietal sulcusMNE minimum norm estimatesMNI Montreal Neurological InstituteMRI magnetic resonance imagingMSE mean square errorMUSIC multiple signal classificationMVAR multi variate auto regressiveNAS nasionPC posterior commissurePDC partial directed coherencePET positron emission tomographypIPS posterior Intra parietal sulcusPLI phase lag indexREV relative error varianceROI region of interestRPA right pre-auricularSBC Swartz Bayesian criteriaSCS subject coordinate systemSD standard deviationSEM structural equation modellingSFG superior frontal gyrussLORETA standardised low-resolution brain electromagnetic tomographySNR signal-to-noise ratioSOBI second order blind identificationSPL superior parietal lobuleSVD singular value decompositionTPJ temporoparietal junctionTV time varyingVA visual areasVFC/AI ventral frontal cortex and anterior insulawPLI weighted phase lag index

Contents

Abstract iii

Abbreviations v

Contents ix

List of Figures xv

List of Tables xxi

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Electroencephalogram (EEG) . . . . . . . . . . . . . . . 2

1.1.2 Electrocorticography (ECoG) . . . . . . . . . . . . . . . 4

1.1.3 Inverse source modeling . . . . . . . . . . . . . . . . . . 4

1.1.4 Connectivity . . . . . . . . . . . . . . . . . . . . . . . . 6

1.1.5 Directed and Time-varying connectivity . . . . . . . . . 7

1.1.6 Visual spatial attention networks . . . . . . . . . . . . . 9

1.2 Aims of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . 11

ix

x CONTENTS

2 Methods and Modeling approaches 13

2.1 EEG source modeling . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1 The forward model . . . . . . . . . . . . . . . . . . . . . 13

2.1.2 The inverse model . . . . . . . . . . . . . . . . . . . . . 17

2.2 Connectivity methods . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Granger causality based connectivity . . . . . . . . . . . 20

2.2.2 Time-varying connectivity . . . . . . . . . . . . . . . . . 24

2.2.3 Phase synchronisation based connectivity . . . . . . . . 30

3 Electrocorticography of spatial shifting and attentional selection inhuman superior parietal cortex 33

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . 36

3.2.1 Subject . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2.2 Experimental paradigm . . . . . . . . . . . . . . . . . . 36

3.2.3 ECoG and EOG acquisition and preprocessing . . . . . 38

3.2.4 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.2.5 Behavioral analyses . . . . . . . . . . . . . . . . . . . . 40

3.2.6 ECoG analysis . . . . . . . . . . . . . . . . . . . . . . . 40

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.1 Behavioral analysis . . . . . . . . . . . . . . . . . . . . . 42

3.3.2 Effects of the direction of attentional cue . . . . . . . . 43

3.3.3 Invalidity effect . . . . . . . . . . . . . . . . . . . . . . . 43

3.3.4 Selection between competing stimuli . . . . . . . . . . . 45

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.4.1 ECoG effects of invalidity in SPL . . . . . . . . . . . . . 48

3.4.2 Relation to visual neglect and the clinical symptom ofextinction . . . . . . . . . . . . . . . . . . . . . . . . . . 53

CONTENTS xi

3.4.3 Effects of cue direction during the delay phase . . . . . 53

3.4.4 ECoG effects in IPS of a competing distracter . . . . . . 54

3.4.5 Study limitations . . . . . . . . . . . . . . . . . . . . . . 54

3.4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 55

4 Comparison of different Kalman filter approaches in deriving timevarying connectivity from EEG data 57

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2.1 Theoretical Background . . . . . . . . . . . . . . . . . . 59

4.2.2 Simulated data . . . . . . . . . . . . . . . . . . . . . . . 60

4.2.3 Performance analysis . . . . . . . . . . . . . . . . . . . . 63

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5 A time-varying connectivity analysis from distributed EEG sources:a simulation study 67

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.2.1 Time-varying connectivity . . . . . . . . . . . . . . . . . 70

5.2.2 Time varying MVAR model estimation using Kalmanfiltering . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.2.3 Simulated ground truth data . . . . . . . . . . . . . . . 72

5.2.4 Simulated scalp EEG data . . . . . . . . . . . . . . . . . 74

5.2.5 Source modeling of simulated EEG data . . . . . . . . . 75

5.2.6 Regions of interest and dipole selection . . . . . . . . . 76

5.2.7 Evaluation of different Kalman filtering approaches . . . 78

5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

xii CONTENTS

5.3.1 Dipole selection to extract ROI time series . . . . . . . 79

5.3.2 Performance of Kalman filtering approaches . . . . . . . 81

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6 Time-varying connectivity in the parietal cortex during visuospatialattention 93

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6.2.1 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6.2.2 Stimulus presentation and paradigm . . . . . . . . . . . 96

6.2.3 MRI data acquisition . . . . . . . . . . . . . . . . . . . . 98

6.2.4 EEG recording and processing . . . . . . . . . . . . . . 98

6.2.5 Processing for source modeling . . . . . . . . . . . . . . 99

6.2.6 Regions of interest and time series extraction . . . . . . 100

6.2.7 Time varying connectivity estimation . . . . . . . . . . 102

6.2.8 Time frequency analysis . . . . . . . . . . . . . . . . . . 102

6.2.9 Statistical analysis . . . . . . . . . . . . . . . . . . . . . 102

6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.3.1 Cue related effects . . . . . . . . . . . . . . . . . . . . . 103

6.3.2 Grating related effects . . . . . . . . . . . . . . . . . . . 104

6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7 General discussion 109

7.1 General Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 109

7.2 Future research directions . . . . . . . . . . . . . . . . . . . . . 114

7.2.1 Partial directed coherence (PDC) . . . . . . . . . . . . . 114

7.2.2 Source modeling and dipole selection . . . . . . . . . . . 115

CONTENTS xiii

7.2.3 EEG-fMRI integration . . . . . . . . . . . . . . . . . . . 115

7.2.4 Structurally constrained functional connectivity . . . . . 116

7.2.5 Graph theoretical analysis of time varying directed networks116

A Conflict of interest statement, Acknowledgements and PersonalContribution 119

Bibliography 121

Curriculum vitae 145

Publications 149

Acknowledgements 151

List of Figures

1.1 Overview of an experimental setup for EEG recording during astimulus presentation, the analysis pipeline and computationalmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Overview of EEG source modeling . . . . . . . . . . . . . . . . 6

1.3 Different neuroimaging modalities and the types of network studies 7

1.4 Depiction of different network dimensions comprised of spatial,temporal and directional components provides insight intodifferent functional components of the brain network. Solidlines represent time-invariant or stationary connections, whereasdashed lines represent time-varying relationships. A) Anundirected network. B) Time-varying networks under differenttask conditions on the “fast” scale (associated with stimulus-evoked measurement; upper panel) and operating at the “slow”scale are associated with learning (lower panel) C) A directednetwork. The figure is adapted from (Mill et al., 2017b) withElsevier license to reuse in a thesis/dissertation, License Number-4204421036349. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5 After the presentation of a spatial attention cue, timings of theactivations in different regions and time intervals. LIP = lateralintraparietal area; IPSa = anterior intraparietal sulcus; IPL= inferior parietal lobe; SFG = superior frontal gyrus; MFG= middle frontal gyrus; IPSv = ventral intraparietal sulcus;FEF = frontal eye fields. Figure reused from (Simpson et al.,2011; Vossel et al., 2014) for non-commercial purposes underthe terms of the Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License (http: // creativecommons.org/ licenses/ by-nc-sa/ 3. 0 ). . . . . . . . . . . . . . . . . . 10

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http://creativecommons.org/licenses/by-nc-sa/3.0


xvi LIST OF FIGURES

1.6 Depiction of directed time-varying connectivity . . . . . . . . . . 11

3.1 (A) Distribution of the electrode positions on a surface renderingof the patient’s MRI. SPL and the postcentral sulcus areartificially dilated in order to better show the position of theelectrodes with respect to these sulci. (B) Hybrid spatial cueingparadigm (Gillebert et al., 2011). . . . . . . . . . . . . . . . . . 37

3.2 (A) Accuracy of the study participant in the different experimentalconditions. (B) Reaction times of the study participant in thedifferent experimental conditions (mean and S.D.). (C) Accuracyin the same paradigm in a group of 22 healthy controls. (D)Reaction times in the same paradigm in a group of healthy controls(mean and S.D.). Note that the Y axis differs between the patientand the controls given the overall slower reaction times in thepatient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.3 Leftward vs. rightward cueing trials: ERP analysis. Significanteffects that occur in the interval between cue onset and gratingonset are marked by a green bar. Time point 0 refers to theonset of the grating. The significance threshold is set at P <0.05 corrected for the number of electrodes during a minimumcontinuous period of 10 ms. The plots for the different electrodesare positioned in accordance with their position on the corticalsurface (Figure 3.1A). . . . . . . . . . . . . . . . . . . . . . . . 45

3.4 (A) ERP during validly cued trials and during invalidly cuedtrials. Significant deficits following target onset between validlycued and invalidly cued trials are marked by a green bar. Thesignificance threshold is set at P < 0.05 corrected for the numberof electrodes during a minimum continuous period of 10 ms. Theplots for the different electrodes are positioned in accordance withtheir position on the cortical surface. (B) ITC analysis withinthe theta band (4–7 Hz) during invalid vs. valid cueing trials.The significance threshold is set at P < 0.05 corrected for thenumber of electrodes (n = 9) using a nonparametric bootstrappingapproach with 1000 randomizations. . . . . . . . . . . . . . . . 46

LIST OF FIGURES xvii

3.5 (A) Time-frequency plots during invalidly minus validly cuedsingle-grating trials. The ERSP is thresholded at P < 0.05 cor-rected for the number of electrodes (n = 9) using a nonparametricbootstrapping approach with 1,000 randomizations. (B) wPLIanalysis for the frequency band from 15 to 20 Hz, indicating theeffect of invalidity on functional connection between IPS and SPL.A positive y value means that the phase lead is in the directionfrom A3 to A12, as mentioned in the title of the plot, a negativey value that it goes in the opposite direction. The significancethreshold was P < 0.05 corrected for the number of connectionstested (n = 36) using a nonparametric bootstrapping approachwith 2,000 randomizations. . . . . . . . . . . . . . . . . . . . . . 47

3.6 (A) ERP during competition trials compared to validly cued single-grating trials. Significant deficits following target onset betweenvalidly cued and invalidly cued trials are marked by a green bar.The significance threshold is set at P < 0.05 corrected for thenumber of electrodes during a minimum continuous period of 10ms. The plots for the different electrodes are placed in accordancewith their position on the cortical surface (Figure 3.1A). (B)Inter-trial coherence during competition trials compared to validlycued single-grating trials. The significance threshold is set at P< 0.05 corrected for the number of electrodes (n = 9) using anonparametric bootstrapping approach with 1,000 randomizations. 49

3.7 (A) Time-frequency plots during competition trials minus validlycued single-grating trials. The ERSP was thresholded at P <0.05 corrected for the number of electrodes (n = 9) using anonparametric bootstrapping approach with 1,000 randomizations.(B) wPLI analysis indicating the effect of competition trialscompared to valid single-grating trials on functional connectionbetween anterior and posterior IPS in the frequency band 15–20Hz. The significance threshold was P < 0.05 corrected for thenumber of connections tested (n = 36) using a nonparametricbootstrapping approach with 2,000 randomizations. (C) wPLIanalysis indicating the effect of competition trials compared tovalid single-grating trials on the functional connection betweenIPS and SPL in the frequency band 6–10 Hz. Same significancethreshold as in (B) . . . . . . . . . . . . . . . . . . . . . . . . . 50

xviii LIST OF FIGURES

4.1 Connectivity pattern imposed among 3 nodes. The value of thecausal connection from S1→ S3 and S3→ S2 are time dependent(dotted arrow) and constant for the rest (continuous arrow). Thetheoretical (simulated) values are represented by the blue plotsnear each connection for the time lag given by Tij (representingthe constant delay in the propagation from node j to node i). Forthe other time lags, aij = 0. A time lag (model order) of 1 and 2correspond to 4 and 8 ms, respectively. . . . . . . . . . . . . . . . 61

4.2 Figures of merit (MVARfom and PDCfom) for different Kalmanfilter approaches at various levels of trials, EEG channels andSNR for TV-MVAR and TV-PDC estimation. . . . . . . . . . . 64

5.1 The simulated visual spatial attention model consisting of aninput area (V1), two visual areas (VA), the intraparietal sulcus(IPS), the frontal eye fields (FEF), the temporoparietal junction(TPJ), the anterior insula in the ventral frontal cortex (VFC/AI)and the middle frontal gyrus (MFG). The model was takenfrom (Corbetta et al., 2008) with some minor modifications:connections between FEF, IPS, and MFG were slightly adapted,and the visual input region was added. The arrows indicatedirected interactions consisting of a stimulus-driven control(orange), top-down control (blue) and the visual input signal(black). Bidirectional interhemispheric connections were modeledas stationary with a strength of 0.5. The time-varying MVARconnectivity was imposed based on the timings of the significanteffects observed in different regions as described in (Simpson et al.,2011) and (Vossel et al., 2014) and are shown by the figures nextto each directed connection. These time-varying connections wereadded on top of the stationary connection in which the latterhad a strength of 0.2. The time lag for MVAR parameters forthe connection in blue and orange was chosen as 16 ms and forblack as 4ms. The exact onset of the directional time-varyinginteractions, its amplitudes and duration as well as the time lagwere chosen arbitrarily. . . . . . . . . . . . . . . . . . . . . . . 73

5.2 The performance parameters for the dipole selection strategies atdifferent levels of SNR. Box-and-Whisker plots across all regionsand 100 noise realizations are shown. (a) Euclidean distance inmm from the ground truth location (b) Surface distance from theground truth location along the cortex. . . . . . . . . . . . . . . 80

LIST OF FIGURES xix

5.3 The correlation coefficient with corresponding ground truth timeseries for the dipole selection strategies at different levels ofSNR. Box-and-Whisker plots across all regions and 100 noiserealizations are shown. (a) ROIs with the correct sign of thedominant direction compared to the ground truth direction (b)ROIs with an incorrect sign of the dominant direction comparedto the ground truth direction (c) Overall results. . . . . . . . . . . 81

5.4 Mean square error (MSE) after linear fitting with ground truthtime series for the dipole selection strategies at different levelsof SNR. Box-and-Whisker plots across all regions and 100 noiserealizations are shown. (a) ROIs with the correct sign of thedominant direction compared to the ground truth direction (b)ROIs with an incorrect sign of the dominant direction comparedto the ground truth direction (c) Overall results. . . . . . . . . 82

5.5 MSEMVAR for different Kalman filtering approaches at variouslevels of SNR and number of trials for existing model connectionsand using the ground truth based dipole selection GT2 and thedata driven dipole selections DD1, DD2 and DD3. . . . . . . . 83

5.6 MSEPDC for different Kalman filtering approaches at variouslevels of SNR and number of trials for existing model connectionsand using the ground truth based dipole selection GT2 and thedata driven dipole selections DD1, DD2 and DD3. . . . . . . . 84

5.7 MSEMVAR for different Kalman filtering approaches at variouslevels of SNR and number of trials for non-existing connectionsof the model and using the ground truth based dipole selectionGT2 and the data driven dipole selections DD1, DD2 and DD3 85

5.8 MSEPDC for different Kalman filtering approaches at variouslevels of SNR and number of trials for non-existing connectionsof the model and using the ground truth based dipole selectionGT2 and the data driven dipole selections DD1, DD2 and DD3 86

6.1 Time varying PDC connectivity for the cue locked data for threedifferent contrasts of the type of cue . . . . . . . . . . . . . . . 104

6.2 The main effects of the number of gratings (singles vs double)for the substracted time varying squared PDC connectivity . . . 106

6.3 The interaction effects between the number of gratings (singlesvs double) and the direction of attention (left vs right) for thesubstracted time varying squared PDC connectivity . . . . . . . 107

List of Tables

3.1 MNI coordinates of the electrode positions. . . . . . . . . . . . 39

5.1 MNI coordinates of the cortical ground truth sources . . . . . . 74

6.1 List of conditions and corresponding control tasks . . . . . . . 97

6.2 Regions selected from (Eickhoff et al., 2005; Neyens et al., 2017) 101

xxi

Chapter 1

Introduction

In this chapter, we aim at introducing electroencephalogram (EEG) measure-ments and the connectivity approaches followed by the objectives and outline ofthe thesis. To provide the reader with some general background, in section 1.1,we give an overview of the origin of EEG and source modeling to estimate thesignals at the level of the brain. We describe the general idea of connectivity andthe need to focus on the direction and time-varying influences between brainregions. In this thesis, we applied our method to visual spatial attention datafrom healthy subjects, and therefore we touch upon the relevant background onthe visual attention system in the human brain. In addition to the background,the general objectives of this thesis are depicted in section 1.2 and the outlineof the thesis in section 1.3.

1.1 Background

We acknowledge the fact that the human brain is one of the most complexsystems in nature. Every part of it must work together not only to keep thebody functioning but also to generate our mental states and behavior. In spiteof ongoing investigations, understanding of the human brain is still one of thegreatest scientific challenges (Poldrack and Farah, 2015). To study the linkbetween mental processes and behavior, measurements of the brain are obtainedusing a variety of techniques. In the field of brain imaging, our understanding islimited by the capabilities of the imaging techniques applied. Imaging techniquescan be broadly classified into the neuroimaging modalities and the methodsused for processing and analyzing the data obtained from imaging modalities.

1

2 INTRODUCTION

The computational methods are based on different assumptions of the brainsignals and still do not capture the brain processes completely (Mahjooryet al., 2017; Smith and Escudero, 2017; Mill et al., 2017b; Bassett and Sporns,2017). Furthermore, neuroimaging modalities differ in sensitivity to the differentneurophysiological processes. By combining imaging techniques, we make useof the strengths of each technique (Calamante et al., 2017; Amico et al., 2017;Wiebel et al., 2014). In this thesis, we focused on data acquired from EEGand applied connectivity methods to explore the direction and time-varyingbehavior of the visuospatial attention networks in the human brain using thestructural MRI from each subject for source modeling.

1.1.1 Electroencephalogram (EEG)

Around a century back in 1924, Prof. Hans Berger obtained the first human EEGrecording. Berger also invented the name electroencephalogram for the device.Since then EEG is considered as one of the most remarkable developments in thehistory of clinical neurology and an excellent tool for studying neurophysiologicalprocesses (Mulert et al., 2010). EEG is noninvasive and recorded at the scalpsurface by placing electrodes in a standard configuration. EEG measuressynchronized electrical activities due to the extracellular currents in the humanbrain. The extracellular currents occur as a result of the flow of ionic currentsbetween thousands of cortical pyramidal neurons. This is related to the changesin the resting membrane potential inside the neurons against the extracellularspace (Buzsáki et al., 2012). The change in the potential is measured from thescalp and referred as EEG. Due to the orientation with long apical dendritesorthogonal to the cortical surface, large cortical pyramidal neurons in deepcortical layers play an important role in the generation of EEG. In the scalpEEG, the activity at a single electrode is measured in the same time frame itoccurs and spatially summed across different brain areas. The instant and directmeasurement of the neuronal activity allows the study of transient changes ofcognitive processes at a high temporal resolution. However due to the tissuelayers in the human head, like the brain, skull, and scalp, with different electricalproperties, the signals are attenuated. The exact origin of the activity cannotbe revealed directly from EEG (Cohen, 2017).

In patients, EEG is used to monitor or diagnose neurological problems ordiseases, e.g. monitoring seizure activity in epilepsy. Many brain disordersare diagnosed by visual inspection of EEG signals. To understand cognitiveprocessing in healthy subjects, EEG data are often acquired when a subject isasked to perform a series of tasks during an experiment. The stimulus events aresynchronized to the EEG recording to mark the event occurrences. An overviewof such an experimental setup is depicted in figure 1.1. The EEG electrode

BACKGROUND 3

cap used, comes in various sizes based on the number of electrodes arrangedin standard configurations. The unit of EEG measurement is volts (typicallymicrovolts or µV). Often EEG is measured along with electrooculography(EOG) signals to record eye movements. The potentials generated during theeye movements and blinks can be orders of magnitude higher than the EEGsignals and can conduct through the scalp to distort EEG measurements. Thiswill affect the interpretation of EEG, so it is thereby important to remove theEOG artifacts from the raw EEG recording before further analysis.

Figure 1.1: Overview of an experimental setup for EEG recording during astimulus presentation, the analysis pipeline and computational methods

EEG signals are multidimensional that comprise time and space and which arecharacterized by frequency, power, and phase. The multidimensional informationprovides unparalleled possibilities for understanding the cognitive processing ofinformation, representation, and transfer (Cohen, 2014). The computationalmethods used to analyze EEG data allow simultaneous study of one or moredimensions of the EEG data (figure 1.1) (Lopes da Silva, 2013). The event-related potential (ERP) offers a computationally efficient way to study time-locked EEG amplitudes at a high temporal resolution. ERPs are often derivedfrom the average of the EEG segments under the specific stimulus. Furthermore,

4 INTRODUCTION

the frequencies of the EEG signals are important. The frequencies changebetween brain conditions e.g. wakefulness versus sleep. The main frequencybands that are used in EEG studies are (from low to high) (Sanei and Chambers,2007; Sakkalis, 2015):

name abbreviation range (Hz)delta δ 1-3theta θ 4-7alpha α 8-13beta β 14-30gamma γ 31-100

1.1.2 Electrocorticography (ECoG)

ECoG is the measurement of EEG signals in which electrodes are placed on thebrain surface, and it is, therefore, an invasive procedure. The electrode arraygrid can be placed epidural or subdural. The size of the grid can vary from 4to 256 electrodes. To set the grid, a surgeon needs to perform a craniotomy,removing a part of the skull. Hence, ECoG is only used in special clinical caseslike pre surgical evaluation of refractory epilepsy patients. The grid placementis often assisted by computed tomography (CT) and MRI (Murugesan et al.,2017; Ding et al., 2007).

ECoG recordings offer an opportunity to understand the human brain functionwith superior spatial, temporal, and spectral resolution compared to EEG(Schrooten et al., 2017). In case of EEG, electrical signals from the cortex areattenuated while conducting through the low conductivity skull. In contrast,the recording at the cortical surface offers data with a higher signal-to-noiseratio (SNR). ECoG provides higher spatial resolution than EEG as ECoG ismuch less affected by the volume conduction problem. This an advantage forpre surgical planning. The conduction through the skull severely affects signalsin the higher frequency range. In contrast with ECoG, we can study informationin higher gamma bands more reliably (Daitch et al., 2013).

1.1.3 Inverse source modeling

The EEG data measured at a scalp surface are the result of summations ofelectrical activity coming from brain regions that are spatially distributedover the cortical surface. Due to the conductivity properties of the differenthead tissues, a single brain source can be measured at several electrodes.

BACKGROUND 5

This problem is referred to as volume conduction. Therefore, many differentsource configurations can generate the same EEG potentials on the scalp.Hence, the recorded scalp EEG cannot directly be related to active brainareas. Understanding the different brain areas underlying the experimental orpathological conditions are essential to study the brain (Michel et al., 2004).This requires the localization of the neuronal sources which generated themeasured EEG, and the only way is to solve the so-called inverse problem, alsoreferred to as EEG inverse source modeling (Pascual-Marqui, 1999).

In EEG source modeling, a small patch of the activated cortex, i.e. a setof neuronal populations is represented by an equivalent current dipole actingas a point source. To take into account the anatomical-functional variation,the cortical surface is divided into a large number of sources in the order of5000-15000. Given that the number of EEG measurement signals are in theorder of 10-256 and the number of unknowns to estimate, i.e. sources are in theorder of 15000, the problem is severely underdetermined or ill-posed, and severalsolutions are possible. There are two major ways to overcome this problem:1) Regularization to restrict the number of possible solutions. This results ina smoothed solution with a cost of increased cross talk or spillover effect. 2)Limit the solution space to a small number of dipoles compared to the numberof EEG sensors. This requires a priori knowledge about the number of sources.

An overview of a source modeling procedure is depicted in figure 1.2. Themodeling requires a head model which can be derived from the anatomicalscan, EEG electrode positions, and the data and noise covariances of the EEGdata. EEG source modeling consists of the estimation of a linear inversesolution/matrix which multiplied with sensor space EEG time series gives thetime series of the cortical sources. The cortical sources are modeled with currentdipoles that represent a set of neuronal populations. The computation of thelead field matrix is an essential step before the inverse solution can be estimated.The lead field matrix also referred to as the forward matrix, gives the linearrelation between the cortical sources and the scalp EEG data (Grech et al., 2008;Baillet et al., 2001). The computation of the forward matrix requires modelingof the conductivities of the different tissue classes which can be obtained bysegmentation of a template or the subject specific structural scan (Hallez et al.,2007). The forward matrix also requires alignment of EEG electrode positionswith the head surface. The vertices of the cortical surface mesh are modeledas current sources. Recently, source modeling has been widely studied, and anumber of methods have been developed using different assumptions (Beckeret al., 2015). However, each method offers some advantages and disadvantagesas discussed further in this manuscript.

6 INTRODUCTION

Figure 1.2: Overview of EEG source modeling

1.1.4 Connectivity

Neuronal populations in different areas of the brain are specialized in distinctfunctions. To process the information, the areas communicate and interactwith each other in a coordinated fashion. The interaction is through synapticconnections with the flow of ionic current. This results in increasing or decreasingactivity in the interacting areas. By measuring the changing levels of activityin the different areas, we can study the association between regions and theirrole in the cognitive processing. The associations are widely referred to asconnectivity, and together with the regions, they form a network.

The network, consist of a set of nodes and their links or connections. The nodesdefine the scale of the network and are often represented by a set of anatomicalregions. The human brain consists of large complex networks (Bullmore andSporns, 2008). Connections between nodes define the type of the network, i.e.structural (anatomical) or functional (change in the activity) and measure thestructural and functional association between nodes (Bullmore and Sporns,2008). In structural network studies, connections between cortical areas areestimated from diffusion imaging MRI data, and such connectivity is morestatic over a much longer time span. In functional network studies, connectionsbetween cortical areas are estimated from functional MRI (fMRI) or electro- ormagnetoencephalogram (EEG/MEG) signals (figure 1.3).

BACKGROUND 7

Figure 1.3: Different neuroimaging modalities and the types of network studies

Functional data are acquired during the performance of a task or under restingstate conditions (Park et al., 2013). Functional connectivity is dynamic andcan be different under different conditions or during a resting state. Theselarge-scale networks circulate information and determine how we think andact. One of the important ongoing questions in the field is finding out whichbrain regions are connected and how networks function. The analysis of brainnetworks forms the basis of understanding the organization and functioning ofthe human brain (Mill et al., 2017b; Fornito et al., 2016).

1.1.5 Directed and Time-varying connectivity

Furthermore, functional connectivity studies are based on connections that areundirected and give mere association and not the direction of the interaction.This way we loose valuable information about how information flows acrossdifferent regions. The pattern of directed relationships is known as “directedor effective connectivity” (Schmidt et al., 2016). In contrast to functionalconnectivity, only effective connectivity allows to identify the information flowand therefore to better understand the interaction mechanisms within the brainnetworks. Directed connections can be bi-directional like a feedforward andfeedback connection in response to cognitive demands at different time intervals(Cekic et al., 2017).

8 INTRODUCTION

The interactions within brain regions are highly non-stationary. The cognitiveevents occur on a temporal scale that spans hundreds of milliseconds to a fewseconds. Understanding the events requires not just the spatial distributionof activity in the brain but also the temporal information of the nodes andconnections of the brain network (Preti et al., 2016; Hari and Parkkonen, 2015).The study of temporal information of the connections is known as “Time-varying connectivity.” Brain areas are continually interacting with one or theother connectivity pattern. Time-varying interactions occur in addition to thetime-invariant connections. The time-varying connection can be a temporarychange in the functional strength of the connection (Leistritz et al., 2016).

Figure 1.4: Depiction of different network dimensions comprised of spatial,temporal and directional components provides insight into different functionalcomponents of the brain network. Solid lines represent time-invariant orstationary connections, whereas dashed lines represent time-varying relationships.A) An undirected network. B) Time-varying networks under different taskconditions on the “fast” scale (associated with stimulus-evoked measurement;upper panel) and operating at the “slow” scale are associated with learning(lower panel) C) A directed network. The figure is adapted from (Mill et al.,2017b) with Elsevier license to reuse in a thesis/dissertation, License Number-4204421036349.

The spatial, temporal and directional components of the network operatecollectively within a network to process information (figure 1.4). To understandall the functional connectivity components during a cognitive task or behaviour,more advanced functional connectivity estimation methods are required (Millet al., 2017b). The investigation of the timing of responses in the different brainareas requires methods offering a higher temporal resolution (Hutchison et al.,2013). In contrast to functional data from fMRI, the data measured with EEGand MEG offers a high temporal resolution so that the directions and timing ofthe functional connectivity within a network can be reliably studied.

BACKGROUND 9

1.1.6 Visual spatial attention networks

Our brain can process limited data from a vast amount of information in ourenvironment. Selecting the most relevant information from the surroundingenvironment for processing while neglecting less relevant information allowsus to respond quickly to accomplish behavioural goals efficiently (Katsukiand Constantinidis, 2014). Such cognitive processing of information selectionis referred to as attention. Among several forms of attention, visual spatialattention is a form of visual attention that involves directing or maintainingattention to a location in space. Visual spatial attention allows us to selectivelyprocess visual information with prioritization of an area or an important itemor a feature within the visual field (Corbetta and Shulman, 2002).

Two common spatial attentional processes are reorienting or shift of attentionand selective attention. Reorienting of attention occurs when we respondto stimuli that are outside of the current focus of attention. The processalso requires decreasing attention to unwanted or irrelevant inputs to improvedetection of the stimuli. The stimuli may differ in the appearance or locationand can attract our attention more effectively because they match our currentbehavioural goals or associate with our long term memory(Corbetta et al.,2008). Selective attention occurs when multiple stimuli are presented. It isdefined as the ability to respond to certain stimuli selectively when several occursimultaneously with one or more stimuli (Yantis, 2008). During the process,the brain reconfigures itself in a way that the response is determined by theselected or attended, task relevant stimuli.

There are commonly two distinct functions of attention. First bottom-up (orexogenous) attention which is induced to process the information automaticallyselected based on the features of stimuli. Another function is top-down (orendogenous) attention which is a process induced internally to attend stimuliof interest while neglecting or suppressing the irrelevant information (Katsukiand Constantinidis, 2014). The two attentional functions are often described toinvolve distinct neural processes and constantly influence each other to carryout reorientation and selective attention.

An example of a visual spatial attention task is the presentation of a cueindicating the direction of attention. After a short delay, stimuli are shown.During such a visual spatial attention task, a distributed set of brain areas inthe frontal and parietal cortex are activated. Using different task conditionsbrain areas specific to the orienting or shifting of attention in space can bestudied. Using a network approach based on different modalities, we cancharacterize directed time-varying connections among brain regions involved inspatial attention (Parks and Madden, 2013; Corbetta and Shulman, 2011). This

10 INTRODUCTION

will give us a better understanding of critical regions (hubs) and the topologicalorganization of the attention networks (Heinen et al., 2017; Meehan et al., 2017).

Figure 1.5: After the presentation of a spatial attention cue, timings of theactivations in different regions and time intervals. LIP = lateral intraparietalarea; IPSa = anterior intraparietal sulcus; IPL = inferior parietal lobe; SFG =superior frontal gyrus; MFG = middle frontal gyrus; IPSv = ventral intraparietalsulcus; FEF = frontal eye fields. Figure reused from (Simpson et al., 2011;Vossel et al., 2014) for non-commercial purposes under the terms of the CreativeCommons Attribution-Noncommercial-Share Alike 3.0 Unported License (http:// creativecommons. org/ licenses/ by-nc-sa/ 3. 0 ).

A MEG study by (Simpson et al., 2011) examined the time course in severalregions of interest after the onset of a centrally presented spatial cue thatoriented attention to the left or right hemifield (figure 1.5). The activity isthe result of information flow from visual areas to higher parietal and frontalareas. Starting from such high temporal resolution data, directed time-varyingconnectivity methods can lead to an understanding of the processing of spatialcue information and the role of the different regions at various time intervals.A sample demonstrative model of such directed time varying connectivity isdepicted in figure 1.6.

1.2 Aims of the thesis

The aims of the studies included in this Ph.D. are:(1) To develop a pipeline for calculation of the EEG sources using a subject-specific head model, to apply time-varying connectivity methods and to calculate



OUTLINE OF THE THESIS 11

Figure 1.6: Depiction of directed time-varying connectivity

various directed connectivity measures.(2) To study time-varying connectivity measures directly from electrocorticogra-phy (ECoG) data.(3) To compare different dipole selection strategies in which the time serieswill be extracted and to compare the performance of different approaches tocalculate time-varying connectivity from EEG cortical sources using partialdirected coherence.(4) To study (dynamic) functional connectivity in visual spatial attentionusing EEG data from a group of healthy controls to understand the dynamicinteractions of the areas in the parietal cortex.

1.3 Outline of the thesis

The contents of the chapters follow the different objectives of this thesis.

In Chapter 2, we describe the pipeline for source modeling and time-varyingconnectivity methods and measures. We explain the merits of the variousmethodological choices and validate the strategies used.

In Chapter 3, we apply the time-varying connectivity framework to Electro-corticography (ECoG) data acquired during a visual spatial attention task ina patient. The aim of the study was to understand the role of the superiorparietal cortex in spatial shifting and attentional selection.

In Chapter 4, we use a very simple connectivity model to compare differentKalman filter approaches of time-varying multivariate autoregressive modelestimates used to estimate time-varying partial directed coherence basedconnectivity.

In Chapter 5, we use a more realistic connectivity model derived from the

12 INTRODUCTION

visuospatial attention literature. Here we first compared several strategies fordipole selection to extract the time series used for the time-varying connectivityanalysis. Second, we compare different Kalman filter approaches of time-varyingmultivariate autoregressive model estimates used to estimate time-varyingpartial directed coherence using the outperforming dipole selection strategies.

In Chapter 6, we study the temporal network of visuospatial attention using EEGsource connectivity. We used data acquired at our lab in a visuospatial attentionexperiment using EEG and structural scanning in fourteen subjects. The pipelinedescribed earlier was applied to understand the dynamic interactions betweendifferent brain regions.

Finally, in Chapter 7, we briefly discuss the most important findings of thethesis and suggestions for future research.

Chapter 2

Methods and Modelingapproaches

In this chapter, we describe the methods for EEG source modeling andtime-varying connectivity measures. We explain the merits of the variousmethodological choices and the strategies used.

2.1 EEG source modeling

Though the EEG measurements have a high temporal resolution, it does notindicate the exact locations of the underlying active set of neurones at a giveninstance. This is due to the summation of electrical currents of active neuronalsources distributed across different brain areas. To observe the activity at thelevel of brain areas, EEG inverse source modeling is required. The fundamentalsteps for the modeling involve a computation of the head model also called asthe forward model and solving the inverse model. In this section, we provide anoverview of the forward and inverse models. We describe different methodologicalchoices and parameters used in this work.

2.1.1 The forward model

The forward model is essential for the solution of the inverse model. In theforward model computation, the scalp EEG measurements are estimated fora given electrical sources and a given head conductivity model (head model)

13

14 METHODS AND MODELING APPROACHES

(Mosher et al., 1999). The computation requires modeling of the flow of electricalcurrent through the geometry of the different brain tissues surfaces up to thescalp surface. Furthermore, it also requires the position of EEG recordingelectrodes and topology and restrictions of the source space. The end productis the forward matrix also referred to as the lead field matrix that gives therelationship between each source and the sensor space.

Overview

An accurate definition of head geometry and electrical conductivity values usedin the forward model are important for the accuracy of the inverse solution(Akalin Acar and Makeig, 2013). The most simple head model is the so-calledspherical head model, in which the head geometry is approximated by concentricspheres where each sphere corresponds to a certain tissue type. Other models areoften constructed using an MNI anatomy template. However, a spherical headmodel or MNI anatomy does not account for intersubject variability. This can becrucial in several clinical applications. To overcome this problem, more realistichead models constructed from subject specific anatomy are recommended (Hallezet al., 2007).

Boundary Element Models (BEM) and Finite Element Models (FEM) are thetwo most commonly used realistic and subject-specific head modeling methods(Huang et al., 2016; Wendel et al., 2009). They differ in the assumptions ofthe conductivity in the different tissues of the head geometry. In BEM, eachbrain tissue compartment is considered to have isotropic and homogeneousconductivities (Adde et al., 2003). Therefore, the boundaries between twocompartments, i.e. surface segmentations are required in the modeling. InFEM, the whole MRI is divided into elementary volumes with each labelled asa particular type of tissue. FEM allows considering anisotropic conductivities.FEM is considered more accurate but at the expense of computational efforts(Vorwerk, 2011). However, in realistically shaped head models up to 3-4layers, BEM and FEM perform very well (Vorwerk et al., 2012). Furthermore,Symmetric BEM is based on a combination of single as well as double layerpotentials, and it has been shown that symmetric BEM is much more accuratecompared to FEM as well as to classical BEM (Clerc et al., 2010; Vorwerk et al.,2012). However, FEM performance can be improved by including a highernumber of tissue classes and their conductivities (Liu et al., 2017) but in thatcase, we must take into account the segmentation quality which can drop if weinclude more tissue classes as well as the computational cost of FEM. In ourpipeline, we have limited the analysis to symmetric BEM and have includedthe most essential tissue classes, i.e, skin, skull and brain tissues (CSF, GM,WM) (Vorwerk et al., 2012).

EEG SOURCE MODELING 15

The computations for the head models depend on the number of brain tissuesor layers included. Theoretically, modeling different tissues and detailedsegmentation would lead to superior accuracy, but state-of-the-art methodsuse a limited number of tissue classes. This is often to simplify the modeland reduce the computational efforts. Furthermore, the accuracy of the headmodel also depends on the quality of the segmentations of the surfaces or tissueclasses (Montes-Restrepo et al., 2014; Akalin Acar and Makeig, 2013; Lanferet al., 2012). This can be an issue when the number of layers and tissue typesincreases. Usually, BEM is constructed with four layers, i.e. scalp, outer andinner skull and grey matter (pial) surface. This corresponds to 3 compartmentswith homogenous conductivity 1) scalp 2) skull and 3) Brain (CSF+GM).

Segmentation of the head surfaces

We obtained different head surfaces using BrainSuite (http://brainsuite.org/) which is an automated cortical surface identification tool (Shattuck andLeahy, 2002). Using the subject specific T1 MRI, a brain mask was extractedfor the segmentation process. The MRI was corrected for intensity bias andsegmented into grey and white matter tissues and cerebrospinal fluid. TheColin27 anatomy MNI template and tissue probability maps were used. Thepial surface, skin, inner and outer skull surfaces were extracted. The surfaceswere automatically corrected for topological irregularities and holes (Kazemiand Noorizadeh, 2014). The surfaces were registered with the MRI volume forfurther processing.

Registration of MRI and EEG

Further processing was done using Brainstorm software (http://neuroimage.usc.edu/brainstorm/) which is an open source toolbox for source modeling(Tadel et al., 2011). The MRI and different brain surfaces were imported inBrainstorm. The fiducials points of Nasion (NAS), left and right pre-auricular(LPA and RPA), Anterior commissure (AC), Posterior commissure (PC) andInterhemispheric point (IH) were marked manually on the MRI scan requiredfor the registration with EEG channel positions. A subject coordinate system(SCS) was defined based on NAS, LPA and RPA.

The subject specific EEG channel positions were recorded with a neuronavigationsystem during the same session as the EEG recording. The channel positioncoordinates were marked with reference to the NAS, LPA and RPA fiducialpoints. In addition to the EEG channel positions, more than 200 head points

http://brainsuite.org/

http://brainsuite.org/

http://neuroimage.usc.edu/brainstorm/

http://neuroimage.usc.edu/brainstorm/


were also recorded to achieve a more accurate registration with the MRI scan.EEG channel and head points coordinates were imported in Brainstorm.

Using a three-dimensional distance minimization algorithm, EEG channellocations were co-registered to the head/scalp surface with the help of therecorded head points. EEG channels were projected to onto the scalp surfaceto ensure non-floating EEG channels.

The forward matrix

Smoothed and uniform surfaces are required for symmetric BEM (Akalin Acarand Makeig, 2013; Cho et al., 2015). In spite of segmentations with Brainsuite,some irregularities can be present in inner and outer skull layers, and even asmall amount would lead to an error in head model estimation. Brainstorm cangenerate rough approximations of the inner skull and outer skull based on thesubject’s cortex and head surfaces and ICBM152’s inner and outer skull surfaces.The generated surfaces in Brainstorm are by construction non-intersecting. Wegenerated inner-skull and outer skull surfaces with a 4mm skull thickness usingthe ‘Generate BEM Surfaces’ function in Brainstorm (Giacometti et al., 2014).

The head model was based on the above segmentation with constant electricalconductivities within each compartment. The skull-to-brain/scalp ratio wasset to 1/80. The symmetric BEM was constructed with the following defaultparameters in Brainstorm for the conductivity values: scalp-1 S/m, skull-0.0125S/m, brain-1 S/m (Dmochowski et al., 2017; Despotovic et al., 2013). TheCSF/grey matter interface was chosen as the source space model, i.e., eachvertex point of the mesh was a source. The model included approximately15,000 sources (vertices) arranged along the cortical surface.

To calculate the forward matrix for each source to each scalp electrode, Brain-storm employed the OpenMEEG tool (Gramfort et al., 2010). OPENMEEGimplementation in Brainstorm was used to construct the forward matrix usingthe adaptive integration option. This generated the matrix G with 45000columns spanning the 3 Cartesian orientations of the 15000 cortical sourcesand with each row representing an electrode. Given the forward matrix G therelationship between the cortical sources S(n) and surface EEG (D(n)) at eachtime point n is defined as

D(n) = G · S(n) + e(n) (2.1)

where e(n) is the measurement noise.


2.1.2 The inverse model

The inverse model finds the estimates of the EEG source distribution S(n) giventhe forward matrix G and the EEG measurement D(n). The inverse matrix Tis defined as

S(n) = T(G, e) ·D(n) (2.2)

Where the estimated inverse matrix T is a function of the forward matrix Gand the measurement noise e defined in equation 2.1. EEG inverse sourcemodeling is mathematically ill-posed. The solution requires a regularisation toovercome such a highly undetermined problem (Michel et al., 2004; Baillet et al.,2001). The forward matrix, noise covariance of the EEG data, regularisationand assumptions about the source distribution are the essential input for theinverse matrix computation. There are several approaches to solve the inverseproblem. Depending on the algorithm used, the assumptions can be purelymathematical, based on physiological phenomena or knowledge derived fromother structural or functional imaging modalities (Becker et al., 2015).

To overcome the ill-posed problem, often a lower number of dipoles based on priorknowledge of the source locations are selected. The approach is widely referredto as dipole modeling. However, such an approach significantly limits the spatialextent at which sources can be estimated. Contrary, data-driven distributedsource modeling approaches make no assumption about the actual sourcelocation. Each solution point on the cortical surface is considered as a possiblelocation of the current source. The price we pay is the low spatial resolutiondue to the ill-posed nature. The distributed source modeling approaches areconsidered more genuine solutions of the sources and can estimate sources ateach time point in the EEG data. For an overview and the comparison betweenseveral inverse solution methods, we refer the reader to (Grech et al., 2008).In this thesis, we will focus on distributed linear inverse solutions, and this isdescribed further in detail.

Distributed source modeling

Distributed source modeling approaches are better suited to study theinvolvement of multiple brain regions at a given instance. The solution providesa linear relationship between sources and surface EEG. The approaches are non-parametric, defined in the Bayesian sense and do not make any prior assumptionon the location of active sources (Becker et al., 2016; Pascual-Marqui, 2007b).For each source or dipole position, the orientation and amplitude of the dipolemoment in each of three Cartesian directions are estimated. This is referred toas the unconstrained inverse solution. However, it is understood that sources are


intracellular currents in the dendritic trunks of the cortical pyramidal neurons,which are oriented orthogonal to the cortical surface (He and Ding, 2013; Liuet al., 2006). Hence, it makes sense to reduce the number of parameters estimatedby limiting the orientation of dipoles normal to the cortical surface. In case of afixed orientation, the source Cartesian orientations are reduced to the directionnormal to the cortical surface, i.e. a constrained forward matrix containing15000 columns in this case. Only the amplitudes of these dipole sources arethen determined with orientations and locations fixed based on the corticalmesh. Compared to the unconstrained case, a constrained approach benefitsfrom lower computational efforts and a higher spatial resolution. Throughoutthis work, constrained orientations of the dipole were used to estimate thedistributed source models.

Minimum norm estimates (MNE)

Among several distributed source modeling approaches the minimum normestimates (MNE) method is widely applied. MNE gives a unique solution forthe combination of sources that have both the lowest power (minimum norm)with the best fit to the data (Gramfort et al., 2014). However, MNE suffers tolocalize deeper cortical sources by favouring the weak and superficial sourceswith respect to the position of the electrode array. MNE assumes a Gaussianprior distribution for sources and measurement noise with a known covariancematrix. For the measured data D(n) with M channels with noise covariancematrix C, to estimate the activity S(n) of P sources with source covariancematrix R, the regularised linear MNE inverse operator (T ) as described in(Hämäläinen and Ilmoniemi, 1994; Gramfort et al., 2014) is given by the MxPmatrix and calculated as follows:

T = RGT (GRGT + λ2C)−1 (2.3)

where G is the forward matrix and λ2 a regularisation parameter. The calculatedinverse operator (T ) is applied to the measured data D(n) to estimate the sourceactivity S(n) as in the equation 2.2. The unknown current amplitudes dependon the regularisation parameter λ2. The parameter corresponds to the amountof regularisation applied, and large λ2 leads to more smoothing of the currentestimates. It is important to note that MNE employs whitening. The whiteningoperator is derived from the noise covariance matrix of the data. The operatoris applied to the forward matrix in the process of source estimation.


Regularisation and Noise covariances

There are two different types of regularisations required in the MNE solutions:1) regularisation of the noise covariance matrix and 2) regularisation of theinverse matrix (T ). The first regularisation is required to estimate the whiteningoperator. To estimate the whitening operator an eigenvalue decomposition ofthe noise covariance matrix is performed. The noise covariance is calculatedusing a baseline of the measurements (i.e. pre-stimulus interval). Often avery small amount of data is available for the noise covariance calculation dueto shorter baseline intervals. This can lead to an unreliable estimate of theeigenvalues and the whitening operator. In this work, we used multi-trial data,and noise covariance was estimated using the baseline of the all the trials in thedata. Due to a high number of trials used in the noise covariance calculation,we did not apply any regularisation for the noise covariance matrix (Engemannand Gramfort, 2015).

The second, regularisation (λ2) applied for the inverse operator is necessaryand crucial for the accuracy of the inverse model (Hincapié et al., 2016). Thisconsists of an approximation of an ill-posed problem by a family of neighbouringwell-posed problems. The λ2 is related to the residual deviation between themeasurements and the measurements predicted by the MNE solution, i.e. noisein the measurements. Based on the mathematical formulation of MNE, thisparameter can be obtained as λ2 = 1

SNR2 , where SNR is the signal-to-noiseratio (amplitude) of the whitened measurements (Gramfort et al., 2014; Bradleyet al., 2016).

In this work, we estimated λ2 for each subject based on the estimated SNRin that subject. This way we can best capture the variability among themeasurements across the subjects. For the details of the regularisation, werefer the readers to (Gramfort, 2009; Hincapié et al., 2016). In this work, weestimated SNR from the whitened data or used a fixed value of SNR.

The inverse matrix

A popular MNE based approach is sLORETA (standardised low-resolution brainelectromagnetic tomography) (Pascual-Marqui, 2002). sLORETA is robustagainst noise, is less biased towards superficial sources and the solutions arevery smooth. Based on the source variance, sLORETA applies a standardisationof the MNE estimates to reduce the error in depth localisation. sLORETA is apromising method and performs well as compared to other linear approachesfor source localisation (Saha et al., 2015; Jatoi et al., 2014).


Using sLORETA implemented in Brainstorm, we computed a shared inversionkernel (T ) for all the trials in the data. The estimated shared kernel was appliedto each trial of EEG data to obtain the corresponding cortical signal in eachdipole position.

2.2 Connectivity methods

Understanding the relationships between different brain areas is essential toour understanding of the human brain. The relationship we are interested inis so-called functional connectivity between brain regions and these functionalconnections are derived from EEG and fMRI modalities. Functional connectivityis usually represented by correlations between the activity of different brainareas. However, other more accurate forms of connectivity measures can bederived. These are usually broadly classified based on which features of thetime series, e.g. amplitude, phase or information criteria are used to calculatethe connectivity measure. For an overview of advantages and disadvantagesof several connectivity measures, we refer the reader to (Cekic et al., 2017;Colclough et al., 2016; Kida et al., 2016; Bastos and Schoffelen, 2015; vanDiessen et al., 2015; Wang et al., 2014; Greenblatt et al., 2012). In this work,we focussed on Granger causality and Phase synchronisation based measures.

2.2.1 Granger causality based connectivity

Functional connectivity should ideally give information about the direction ofthe interaction between a pair of brain regions. Directed functional connectivityis widely referred to as effective connectivity. Compared to the model basedapproaches for effective connectivity analysis such as Dynamic Causal Modeling(DCM) and Structural Equation Modeling (SEM), data-driven MultivariateAutoregressive modeling (MVAR) based on the concept of Granger Causality(GC) is widely applied due to its simplicity (Astolfi et al., 2008). GC basedMVAR modeling is data driven and not model based like DCM and SEM. GCbased MVAR measures give the directed flow by estimating a linear causalrelationship among brain regions. This linear causal relationship can be studiedwith both time and frequency domain measures. Among the GC based measures,we focused on partial direct coherence (PDC), one of the commonly appliedfrequency domain measures. PDC is a full multivariate spectral measure, usedto determine the directed influences between a pair of time series with theinfluence of the remaining time series removed (Baccalá and Sameshima, 2001;Baccala et al., 2007).

CONNECTIVITY METHODS 21

MVAR modeling

Multivariate autoregressive (MVAR) modeling is applied to a multivariatedata set, that is an ensemble of simultaneously recorded time series, and itmodels each time series and the relationships between them. The MVAR modelestimation requires no a priori knowledge about the relationships. The modelstructure allows the identification of directed connections between each pair ofvariables. MVAR model estimation is based on the assumption that the timeseries to be studied are stationary and stochastic. The MVAR model representseach time series as a linear function of both its previous values and those ofall other time series. Thus, the model estimation divides each time series intotwo additive components, the predictable time series and the prediction errorsequence. The latter is also called the noise source of the corresponding timeseries and modelled with white noise (Koichi Sameshima et al., 2014) .

For the discrete time series y(n) ∈ R m×N measured in m signals with N timesamples, obtained from noninvasive EEG recordings or from the reconstructionof neuroelectrical cortical activities based on scalp measures:

y(n) =[y1(n) y2(n) · · · ym(n)

]T (2.4)

where n refers to time and m is the number of electrodes or cortical areasconsidered.

MVAR modeling implies that the value of the current sample in a data sequenceof length N can be predicted by a linearly weighted sum of the p most recentsample values of all signals included in MVAR modeling, with p being the modelorder. An adequate description of the dataset y(n) by the MVAR process isrepresented as

y(n) =p∑k=1

Aky(n− k) + e(n) (2.5)

Equation 2.5 can be re-written in a matrix form:

y1(n)y2(n)

· · ·ym(n)

m×N

=p∑k=1

Ak

y1(n − k)y2(n − k)

· · ·ym(n − k)

+

e1(n)e2(n)

· · ·em(n)

(2.6)

where y(n) is the set of time series , e(n) = [e1(n), e2(n),..., em(n)] is a vector ofmultivariate zero-mean uncorrelated white noise playing the role of predictionerror and A1, A2, ...Ap are the p matrices of size m×m containing the MVARmodel parameters. The bidirectional connections are described by the separateoff-diagonal elements of the matrices , i.e. aijk and ajik for each i 6= j. The


coefficient aijk describes the contribution of yj(n-k) to predict yi(n) (Hytti et al.,2006).

MVAR model order (p)

The model order p indicates the number of previous data points used for MVARmodeling. The choice of the MVAR model order is an important parameterfor the correctness of the connectivity of a real network. If the model orderis too high, the model overfits unwanted components, and if it is too low, itdoes not capture the essential dynamics of the data (Porcaro et al., 2009).There are a few considerations in the literature to select and apply the modelorder to MVAR modeling: (1) The model order p must be high enough todescribe all relevant delays in interaction among the brain areas included inthe modeling and low enough to ensure reliable model estimation (Hytti et al.,2006); (2) The autocorrelation function of the residual time series should alsobe studied, and if p is correct, the residuals should be uncorrelated white noise(Schlögl, 2000); (3) The model order affects the frequency resolution of theMVAR parameters (Schlögl and Supp, 2006). Low-order MVAR models cannotcapture low-frequency components due to their short window size. On the otherhand, high-order MVAR models can lead to overparameterization, and a reliableestimation requires more data points (Omidvarnia et al., 2014).

The model order can be selected based on information criteria. We apply SwartzBayesian criteria (SBC) implemented in the arfit.m function in the ARFITsoftware package (Schneider and Neumaier, 2001). This criterion was found themost accurate in the presence of noise and leads to a model order close to theground truth (Porcaro et al., 2009). SBC is calculated for a range of values forp starting from 1 to pmax. The value of pmax is limited by the number of timepoints. The value of pmax is usually set to 30 when EEG data sampling rate is256 Hz i.e 120 ms.

To ensure that the estimated model can describe the signal, the model orderwas further validated based on the comparison of the power spectrum of thesignal using a non-parametric Welch and parametric Burg method (van Mierloet al., 2013). We calculated the power spectrum of the data from the Welchalgorithm with a 500ms moving Hanning window. In parametric approach,Burg algorithm was used with the model order determined by SBC. The twospectra were compared by visual inspection to judge the quality of the modelorder found.


Prediction error and its covariance

The optimal MVAR parameters are found when the mean squared predictionerror (E(e(n)2)) is minimised. The estimation of MVAR parameters is basedon the assumption of uncorrelated noise sources, i.e. white noise (Hytti et al.,2006). If the noise can be completely separated from the signal, then theprediction error covariance matrix W is diagonal, and the optimal set of MVARparameters can be found. However, the MVAR model only captures linearcausal relationships, and if there are any non-linear, zero lag interactions, thenthe off-diagonal values of W tend to differ from zero. The covariance matrix Wof prediction error e(n) can be represented (Foxe and Simpson, 2002) as:

W =

σ2

11 σ12 · · · σ1mσ21 σ2

22 · · · σ2m...

... . . . ...σm1 σm2 · · · σ2

mm

m×m

e(n) being zero mean Gaussian-noise (white noise) with N0, σ2.

The mean square value of e(n) across all channels and time bins is defined asthe mean square error (MSE) of the MVAR estimation. For comparing theresults of different data sets, the MSE is normalised by the variance of thesignal (y(n)) to obtain the relative error variance (REV) (Schlögl, 2000).

REV = E(e(n)2)/E(y(n)2) (2.7)

Because E(y(n)2) is constant for a given data series; REV can be used (insteadof MSE) as a measure for the goodness-of-fit. REV=1 means that the modelparameters are zero and the signal is white noise; REV = 0 means that thesignal can be explained completely by the model (a theoretical considerationonly). The smaller the MSE (and REV) is, the larger is the part of the signalvariance that is explained by the estimated MVAR model parameters. In thissense, 1-REV is a measure for the goodness-of-fit and describes how well theMVAR estimates explain the measured signal y(n).

Partial Directed Coherence (PDC)

PDC (partial directed coherence) was proposed as a measure in the frequencydomain showing a direct causal relation between pairs of signals in a multivariatedata set (Baccalá and Sameshima, 2001). PDC from node j to node i is defined


using the frequency domain transformed MVAR model parameters:

πij(f) = Aij(f)√m∑r=1

Arj(f) AHrj(f),∑i

|πij(f)|2 = 1 (2.8)

where the superscript H stands for the Hermitian transpose, f is the normalisedfrequency in the interval [-.5,.5], and the matrix A(f) defined as:

A(f) = I −p∑k=1

Ake−i2πfk (2.9)

We used the squared value of PDC in this work. The squared PDC |πij(f)|2can be interpreted as the fraction of the power contributing to the total powerin i that originates in j at given frequency f. The better performance of squaredmethods compared to simple PDC has been demonstrated in a simulation study(Astolfi et al., 2006). Squared PDC values are in the interval [0,1] and thecolumn or outflow normalisation condition is given as

m∑i=1|πij(f)|2 = 1 (2.10)

2.2.2 Time-varying connectivity

Among all MVAR estimation approaches, a Kalman filter based MVAR modelinggained wider applications due to its accurate estimation of non-stationary andhigh-dimensional EEG data. Kalman filter based approaches can best followtransient changes in spectra of EEG data and give estimates of the MVAR modelat each time point. Hence time varying PDC (TV-PDC) can be calculated. Inthis section, we describe the concept and details to construct a TV-PDC basednetwork.

State-space representation for time-varying MVAR (TV-MVAR)

A Kalman Filter is an adaptive least square error filter that provides anefficient computational recursive solution for estimating a signal in the presenceof Gaussian noise. It makes optimal use of data described as a linear (ornearly linear) system with Gaussian errors to continuously update the MVARparameters hence time-dependent parameters can be determined.


For the discrete time series y ∈ R m×N measured in m channels with N samplesand based on equation 2.5, the time varying MVAR (TV-MVAR) process isdescribed as:

y(n) =p∑k=1

Ak(n) y(n− k) + e(n) (2.11)

where n being the n-th time bin of the N samples, p is the model order,Ak(n) ∈ R m×m is the matrix of TV-MVAR model parameters at time bin nfor delay k, k = 1, 2..., p and e(n) ∼ N (0,W (n)) is a vector of multivariatezero-mean uncorrelated white noise.

The application of the Kalman filtering algorithm to MVAR modeling is basedon a linear state-space representation of the signal. A linear state-space modelconsists of two joined linear equations: the state equation

Ap(n+ 1) = Ap(n) + v(n) (2.12)and a measurement equation

y(n) = Hp(n)Ap(n) + e(n) (2.13)

The state equation relates state Ap(n) of MVAR parameters at time bin n tothe state or MVAR estimates at time bin n+ 1 with v(n) ∼ N (0, V (n)), thestate white noise process and Hp(n) is a matrix with the p past data points ofthe measurement (equation 2.5). The TV-MVAR parameters Ap(n) are relatedto the TV-MVAR parameters Ak(n) (equation 2.5). The MVAR parametersAp(n) are estimated using Kalman filtering recursion equations.

Kalman filtering recursion

The algorithm works in a two-step process: first to predict and second to corrector update the MVAR estimates. In the prediction step, the Kalman filterproduces estimates of the current state variables Ap(n) from the previouslycalculated state Ap(n− 1), along with their uncertainties here modelled by theposterior error covariance matrix P (n).

In the correction step, with predicted estimates Ap(n) an outcome of themeasurement (i.e. the amount of error, including random noise) is observed.The observed error is weighted using the Kalman gain matrix and used to corrector update estimates Ap(n). Hence, more weight being given to estimates withhigher error or uncertainty. In the next recursion Ap(n+ 1) will be predictedfrom Ap(n) followed by a correction and the process continues at each value ofn. Because of the algorithm’s recursive nature, it can run in real time usingonly the present input measurements and the previously calculated state andits error matrix.


Posteriori error covariance matrix (P)

We define Ap(n) to be our a priori estimate (prediction) at n from the previousstate Ap(n− 1), and the corrected Ap(n) to be the posteriori state estimate atn given the measurement y(n). Note that the predicted Ap(n) is a predictionwhich is based on the previous values and not on the current observation attime n. The corrected Ap(n) on the other hand, uses the information in thecurrent observation. The Kalman gain matrix which weights the measurementerror to correct Ap(n) is estimated from the posteriori error covariance matrixP (n). Evolution of P (n) is estimated by the state error covariance matrix V (n).

Update coefficient (UC)

The update coefficient is also referred to as the forgetting factor and controlsthe adaption speed of the Kalman filter i.e. it controls the amount of correctionto minimise the error. There are 2 update coefficients c1 and c2 for the Kalmanfilter implementation. c1 controls the adaptation of the measurement errorcovariance matrix, where low values provide smoother estimates but a slowerreaction to transient changes of interactions among signals. c2 defines thestep-width of the random walk that is used to update the AR parameters. Thechoice of c2 leads to the same behaviour as the choice of c1. It gives a smoothertemporal course of AR parameters at the expense of an increased adaptationtime to rapid changes in process characteristics when c2 is decreased (Leistritzet al., 2013). Usually, c1 is equal to c2 and referred to as UC in this document.The range of values of UC applied in the literature varies from 0.5 to 0.001(Leistritz et al., 2013; Petti et al., 2013; Wacker et al., 2011; Milde et al., 2010).However based on a methodological study we fixed c1 = c2 = UC = 0.02(Leistritz et al., 2013).

TV-MVAR Implementations

There are mainly two different implementations of the Kalman filtering toperform TV-MVAR modeling: the Classical Kalman filter (CKF) (Arnold et al.,1998) or the General Linear Kalman filter (GLKF) (Milde et al., 2010). Theformer is implemented for single trial data while the latter has an implementationwhich takes into account multi-trial data and which is not a straightforwardextension of the classical Kalman filter, i.e. it does not reduce to the classicalKalman filter if one would consider single trial data as a special case of multi-trialdata.


Classical Kalman filter (CKF) The Classical Kalman filter (CKF) can beestimated using a single trial of the data. The algorithm is outlined below(Arnold et al., 1998):

Let Ap(n) and Hp(n) be given as:

Ap(n) =

vec[AT1 (n)]T...

vec[ATp (n)]T

∈ R mmp×1 (2.14)

in which vec means the vectorization of the matrix Ak(n) by selecting row byrow.

and

Hp(n) = I m×m ⊗

yT(n− 1)

...yT(n− p)

∈ R m×mmp (2.15)

where ⊗ denotes the Kronecker product of matrices. Form channel measurementof N samples, y ∈ R m×N , CKF is defined as follows:

For n=[1,...,p], initialize the TV-MVAR parameters Ap(n) = 0, the a-posteriorierror covariance matrix P (n) = I and the measurement error covarianceW (n) =I.


For each time bin n, apply the Kalman filtering recursion equations:

Find the measurement error (m × 1) :

e(n) = y(n) − Hp(n) Ap(n − 1)

Update the measurement error covariance (m × m) :

W (n) = (1 − UC) W (n − 1) + UC (e(n) e(n)T)

Calculate the residual covariance (m × m) :

X(n) = [Hp(n) P (n − 1) Hp(n)T + W (n)]−1

Calculate the Kalman gain (mmp × m) :

KG(n) = P (n − 1) Hp(n)T X(n)

Update the MVAR estimates (mmp × 1) :

Ap(n) = Ap(n − 1) + KG(n) e(n)

Calculate the state error covariance (mmp × mmp) :

V (n) = UC trace([I − KG(n) Hp(n)]P (n − 1))mmp

I

Update the a-posteriori error covariance (mmp × mmp) :

P (n) = [I − KG(n) Hp(n)] P (n − 1) + V (n)

(2.16)

The Update coefficient UC (0 < UC < 1) controls the adaptation speed of TV-MVAR parameters Ap(n). CKF was implemented using the mvaar.m functionavailable from the time series analysis toolbox (Schlögl, 2002).

General linear Kalman filter (GLKF) GLKF can estimate the TV-MVARmodel for multi-trial data. The algorithm is outlined below (Milde et al., 2010):Let Hp(n) be

Hp(n) = [O(n− 1)O(n− 2)....O(n− p)] where


O(n) =

y(1, n, 1) y(2, n, 1) · · · y(m,n, 1)y(1, n, 2) y(2, n, 2) · · · y(m,n, 2)

... . . . ......

y(1, n,K) y(2, n,K) · · · y(m,n,K)

∈ R K×m.

For m channel measurements with number of trials K, y ∈ R m×N×K , GLKFis defined as follows:

For n=[1,...,p], initialize the TV-MVAR parameters Ap(n) = 0 ∈ R mp×m, thea-posteriori error covariance matrix P (n) = I ∈ R mp×mp and the measurementerror covariance W (n) = I ∈ R m×m.

For each time bin n, apply the Kalman filtering recursion equations (Mildeet al., 2010):

Find the measurement error (K × m) :

e(n) = y(n)T − Hp(n) Ap(n − 1)

Update the measurement error covariance (m × m) :

W (n) = (1 − UC) W (n − 1) + UC e(n)T e(n)K − 1

Calculate the residual covariance (K × K) :

X(n) = [Hp(n) P (n − 1) Hp(n)T + trace(W (n))I]−1

Calculate the Kalman gain (mp × K) :

KG(n) = P (n − 1) Hp(n)T X(n)

Update the MVAR estimates (mp × m) :

Ap(n) = Ap(n − 1) + KG(n) e(n)

Calculate the state error covariance (mp × mp) :

V (n) = UC trace([I − KG(n) Hp(n)] P (n − 1))mmp

I

Update the a-posteriori error covariance (mp × mp) :

P (n) = [I − KG(n) Hp(n)]P (n − 1) + V (n)

(2.17)


The General Linear Kalman filter was implemented in MATLAB using custom-written scripts.

Time varying Partial directed coherence (TV-PDC)

Using TV-MVAR parameters defined in equation 2.11 and PDC in equation2.8, we can obtain time varying PDC (TV-PDC) values. TV-PDC from node jto node i is calculated as a function of frequency and time as:

πij(f, n) = Aij(f, n)√m∑r=1

Arj(f, n) AHrj(f, n),∑i

|πij(f, n)|2 = 1 (2.18)

in which the superscript H stands for the Hermitian transpose and

A(f, n) = I −p∑k=1

Ak(n)e−i2πfk (2.19)

where f is the normalized frequency in the interval [-.5,.5]. We used the squaredvalues of PDC i.e. |πij(f, n)|2 as measure of connectivity.

2.2.3 Phase synchronisation based connectivity

Phase lag index (PLI)

The Phase Lag Index (PLI) is a measure of the asymmetry of the distributionof phase differences between two-time series. Different from other phasesynchronisation measures, PLI is robust in the presence of the influence ofcommon sources (volume conduction) and active reference electrodes. PLI isa consistent, non-zero phase lag between two times series. Such consistent,nonzero phase lags can be determined from the asymmetry of the distributionof instantaneous phase differences between two signals (Stam et al., 2007). It isimportant to note that PLI is a bivariate measure, and hence indirect links canbe present.

For two given signals yi(n) and yj(n) in region/electrode i and j, respectively,from dataset y(n) with M channel and K trials, PLI can be calculated asdescribed further (Stam et al., 2007). To obtain the analytical signal, weapplied the Hilbert transform. The Hilbert transform is the primary step in theestimation of the instantaneous phases φ of the signals. We narrow band pass(width of 5 Hz) filtered the data around the frequency peak of interest. The


frequency bands were selected based on the spectral power of the data estimatedusing the periodogram based Welch algorithm with a moving Hanning windowof 500 ms with 50% overlap. The instantaneous phase is computed in eachchannel in each frequency band of interest. The Hilbert transform is basedon an integral taken from –∞ to +∞. Its application over a finite length canresults in distortions at the beginning and end of each analyzed data segment.To overcome this, the Hilbert transform can be applied to the data segment thatextends at both ends beyond the segment of interest and discard values nearthe beginning and end of each segment. The threshold of 10% of the calculatedinstantaneous phase values to discard is based on the standard values usedin the literature (Mormann et al., 2000). For the epoched data y(m,n,k) theinstantaneous phase values are given as φ(m,f,n,k) . Where m is the channelsor electrodes of the recording, f is the frequency band, n is the time and k isepoch number.

Stationary PLI (time-invariant PLI) can be calculated across all time points(N) as

PLI(i,j,f,k) =| (1/N)N∑n=1

sign(sin(φ(i,f,n,k) − φ(j,f,n,k))) | (2.20)

and finally the results can be averaged across trials (Kaplan et al., 2014; Moonet al., 2015; van Straaten et al., 2015; Van Der Molen and Stam, 2014). Time-varying PLI can be calculated across all trials/epochs as (Aydore et al., 2013;Gordon et al., 2013; Ortiz et al., 2012; Pascual-Marqui, 2007a).

PLI(i,j,f,n) =| (1/K)K∑k=1

sign(sin(φ(i,f,n,k) − φ(j,f,n,k))) | (2.21)

where i and j are channels or electrodes. If we drop the absolute sign in equation2.20 and 2.21 we get directed information and denote it as directed PLI (dPLI).Positive values of dPLI indicates influence from yi → yj and negative valuesindicates influence from yj → yi. The estimated dPLI is in the range of -1 to1. It is important to note that equation 2.20 can be applied over a short timewindow, and dPLI can be estimated in a moving window (Ioannides et al., 2012;Lau et al., 2012; Hardmeier et al., 2014).

Weighted phase lag index (wPLI)

PLI estimates to what extent the phase leads and lags between signals. However,PLI can have serious problems when small perturbations turn phase lags into


leads and vice versa. This problem can be solved by weighted PLI where thecontribution of the observed phase leads and lags are weighted by the magnitudeof the imaginary component of the cross-spectrum. Weighted PLI has anadvantage over PLI, regarding reduced sensitivity to additional, uncorrelatednoise sources and increased statistical power to detect changes in the phase-synchronization.

After a Hilbert transform, the cross-spectral density (CSD) between two signalsor channels i and j for each frequency band was calculated for each time pointn and each trial k as:

CSDi,j,n,k = (y(i,n,k) + jy(i,n,k)) (y(j,n,k) + jy(j,n,k))∗ (2.22)

where * is the complex conjugate. wPLI was calculated across trials at eachtime point according to:

wPLI(i,j,n) =(1/K)

∑Kk=1 Im(CSDi,j,n,k))

(1/K)∑Kk=1 | Im(CSDi,j,n,k)) |

(2.23)

where Im indicates the imaginary part of CSD and K equals the number oftrials. Studies based on wPLI/dwPLI can be found in (Gordon et al., 2013;Ortiz et al., 2012; Phillips et al., 2014; Rana and Vaina, 2014; Sun et al., 2012;Vindiola et al., 2014).

In this chapter, we constructed the pipeline for source modeling based on asymmetric BEM head model and using sLORETA for the inverse modelling.For the time-varying connectivity methods, we used Kalman filtering basedapproaches to estimate partial directed coherence (PDC) based networks. Inaddition to PDC, we also introduced the weighted phase lag index (wPLI) basedon phase synchronisation.

Chapter 3

Electrocorticography ofspatial shifting andattentional selection inhuman superior parietalcortex

Spatial-attentional reorienting and selection between competing stimuli are twodistinct attentional processes of clinical and fundamental relevance. In thepast, reorienting has been mainly associated with inferior parietal cortex. Ina patient with a subdural grid covering the upper and lower bank of the leftanterior and middle intraparietal sulcus (IPS) and the superior parietal lobule(SPL), we examined the involvement of superior parietal cortex using a hybridspatial cueing paradigm identical to that previously applied in stroke and inhealthy controls. In SPL, as early as 164 ms following target onset, an invalidlycompared to a validly cued target elicited a positive event-related potential(ERP) and an increase in intertrial coherence in the theta band, regardless of

This chapter has been published as shared first author: Schrooten, M., Ghumare,E., Seynaeve, L., Theys, T., Dupont, P., Van Paesschen, W., and Vandenberghe, R.,Electrocorticography of Spatial Shifting and Attentional Selection in Human Superior ParietalCortex, Frontiers in Human Neuroscience, 2017. DOI: 10.3389/fnhum.2017.00240

33

34 ELECTROCORTICOGRAPHY OF SPATIAL SHIFTING AND ATTENTIONAL SELECTION IN HUMANSUPERIOR PARIETAL CORTEX

the direction of attention. From around 400 to 650 ms, functional connectivity(weighted phase lag index analysis) between SPL and IPS briefly inverted suchthat SPL activity was driving IPS activity. In contrast, the presence of acompeting distracter elicited a robust change mainly in IPS from 300 to 600ms. Within superior parietal cortex reorienting of attention is associated with adistinct and early electrophysiological response in the superior parietal lobulewhile attentional selection is indexed by a relatively late electrophysiologicalresponse in the intraparietal sulcus. The long latency suggests a role of IPS inworking memory or cognitive control rather than early selection.

3.1 Introduction

The distribution of spatial attention is characterized by periods of spatiallysustained attention alternating with transient spatial shifts. For several decades,based on patient lesion studies, models of spatial attention in the humanbrain have associated spatial shifting with the inferior parietal lobule, the righttemporoparietal junction (TPJ) in particular (Friedrich et al., 1998; Corbettaand Shulman, 2002); for review see (Vandenberghe et al., 2012). A role of TPJhas been confirmed by functional imaging studies in the intact human brain(Corbetta et al., 2000; Gillebert et al., 2013; Geng and Vossel, 2013). Contraryto what one would have predicted from lesion studies, recent functional imagingevidence in humans and nonhuman primates revealed that the medial and lateralwall of the superior parietal lobule are robustly and consistently activated duringspatial shifts (Vandenberghe et al., 2001; Yantis et al., 2002; Molenberghs et al.,2007; Caspari et al., 2015). Both in humans (Vandenberghe et al., 2001; Yantiset al., 2002) and in the nonhuman primate brain (Caspari et al., 2015), thecontribution of SPL to spatial shifts is independent of the direction of the shift,leftward or rightward. Furthermore, response amplitudes do not differ betweenleft and right SPL. The role of SPL in spatial shifting in the healthy braindoes not directly relate to the severely lateralized spatial-attentional problemsseen in clinical neglect. Clinical neglect commonly occurs following an ischemiclesion in the middle cerebral artery territory and SPL lies outside this territory.In nonhuman primates, the lack of an effect of the direction of attention in SPLstands in clear contrast with the attentional effects in IPS which are stronglysensitive to the direction of attention (Caspari et al., 2015), in line with thetopographical organisation described in IPS (Silver, 2005).

While a classical neglect syndrome is more severe and longer-lasting followingright- compared to left-hemispheric lesions, a contralesional spatial shiftingdeficit can occur both with left- and with right-sided parietal lesions (Posneret al., 1984; Gillebert et al., 2011). Recent patient lesion studies of spatial shifting

INTRODUCTION 35

and contingent reorienting have confirmed the contribution of superior parietalcortex to spatial attention deficits, both the intraparietal sulcus (Molenberghset al., 2008; Ptak and Schnider, 2010; Gillebert et al., 2011) and the superiorparietal lobule (Vandenberghe et al., 2012).

Electrocorticographic (ECoG) recordings offer an opportunity to investigatehuman brain function with unparallelled spatial, temporal, and spectralresolution. We report the results of a recording of the upper and lower bankof the left anterior and middle intraparietal sulcus (IPS) and the lateral andsuperiomedial side of the SPL during a hybrid spatial cueing paradigm in apatient under presurgical evaluation for refractory partial epilepsy (Figure 3.1A).The hybrid spatial cueing paradigm was identical to that used by (Gillebert et al.,2011) in patients with parietal lesions (Gillebert et al., 2011; Vandenbergheet al., 2012) and in healthy controls (Gillebert et al., 2013; Vandenberghe andGillebert, 2013) to study spatial reorienting and attentional selection betweencompeting stimuli (Figure 3.1B). Originally based on the Posner spatial cueingparadigm (Posner, 1980), it probes attentional selection between competingstimuli as well as attentional reorienting following invalid cues within a sameexperiment.

The ECoG signal was analyzed in different, complementary ways: Event-related potentials (ERP), event-related spectral perturbation analysis (ERSP),intertrial coherence (ITC) and weighted phase lag index (wPLI). The eventrelated measures (ERP, ERSP, and ITC) offer complementary advantages tounderstand the neurophysiological mechanisms of cognitive tasks (Makeig et al.,2004). The ERP indicates overall stimulus-related amplitude changes with ahigh temporal precision that are simple and fast to compute. However, ERPmay not often pick up small variations in a particular frequency band which canbe of neurophysiological importance and occur at particular temporal intervals.In contrast to ERP, ERSP and ITC are based on time-frequency decompositionsensitive to power change and phase synchronizations, respectively, in aparticular frequency band. ITC measures an evoked effect that results ina strong phase synchrony across trials. ITC is closely related to the ERP asthe ERP depends on the ITC and the response amplitude. ERSP measuresthe mean change in spectral power compared to the baseline. Such a powerchange may or may not be picked up by ITC analysis. ERSP and ITC arenot necessarily coupled and can be interpreted independently of each other.Phase-based measures like ITC are less sensitive to common noise due to sourcemixing in comparison to power amplitude based measures such as ERSP. Ourfourth measure, the weighted Phase Lag Index, is a measure of phase leadsor lags between sensors (Stam et al., 2007). As a measure of synchronizationbetween sensors, it is relatively invariant against the presence of common sources(e.g. volume conduction or active reference electrodes) (Stam et al., 2007).


3.2 Materials and Methods

3.2.1 Subject

A right-handed 31 year old female patient with MRI-negative refractory partialepilepsy was hospitalized for a presurgical workup, including continuous videoand ECoG recordings from a surgically implanted subdural grid covering the leftparietal cortex (Figure 3.1A). She suffered from cryptogenic partial epileptic andsecondarily generalized seizures starting with sensory symptoms in the right leg.EEGs, 18F-fluorodeoxyglucose PET and ictal perfusion single-photon emissioncomputed tomography all suggested a left parietal focus. Her vision was normal,as was her interictal neurological examination. Conventional neuropsychologicalassessment revealed normal digit span forward and backwards, normal scores onthe Auditory Verbal Learning test (total learning 49/75, % delayed recall 92%),mild anomia (Boston Naming Test 42 out of 60), and scores within the normalrange in the executive domain. Total intelligence quotient on the Wechsler AdultIntelligence Scale was 94. During experimental testing the patient was treatedwith lacosamide, levetiracetam and oxcarbazepine for her seizures, alizapride,ondansetron and methylprednisolon for postoperative nausea and paracetamoland ketorolac for headache. The study participant provided written informedconsent in accordance with the declaration of Helsinki. The experiment wasapproved by the Ethics Committee of the University Hospitals Leuven.

3.2.2 Experimental paradigm

Stimuli were presented using Presentation 14.2 (Neurobehavioral Systems,Albany, CA, USA). The eye-screen distance was 70 cm. Testing was performedin a dimly lighted room. The hybrid spatial cueing paradigm was identicalto that used by (Gillebert et al., 2011; Vandenberghe and Gillebert, 2013) inpatients with parietal lesions and in healthy controls to study spatial reorientingand attentional selection between competing stimuli (Figure 3.1B). The patientwas instructed to fixate the central fixation point and to select a left or rightbutton depending on the orientation of the target grating, horizontal or vertical(covert orienting). In two thirds of the trials, the target grating appeared atthe cued location on its own at the cued location (validly cued trial) (Figure3.1B). In one sixth of the trials it appeared at the cued location together witha competing distracter in the opposite hemifield (competition trial). In thesetrials the cue was always valid. In another sixth of the trials the target appearedat the uncued location, without distracter (invalidly cued trial). Throughoutthe experiment a central white fixation dot (diameter 0.27 deg) was present,except during the cue phase. A trial started with a central arrow cue pointing

MATERIALS AND METHODS 37

Figure 3.1: (A) Distribution of the electrode positions on a surface renderingof the patient’s MRI. SPL and the postcentral sulcus are artificially dilated inorder to better show the position of the electrodes with respect to these sulci. (B)Hybrid spatial cueing paradigm (Gillebert et al., 2011).


to the left or the right (217 ms duration; size 0.59 deg x 0.66 deg), followed by adelay (217 ms duration) and the test phase during which one or two sinusoidalgratings appeared on the horizontal meridian at 7.6 deg eccentricity (duration217 ms; diameter 3.5 deg; 1.14 cycles/deg). In the validly cued single-gratingtrials (2/3 of trials) the target stimulus appeared on its own in the cued location.In the invalidly cued single-grating trials (1/6 of trials) a single grating appearedat a location contralateral to the cued location necessitating an attentionalshift. In the competition trials (1/6 of trials) two stimuli appeared in the testphase, one to each side of the fixation point. The cue and delay phase wasthe same between trial types. In trials with only a single grating, the subjecthad to respond to the single grating and the cue had a predictive value for thelocation of the target. In the competition trials short-term memory of the cuewas necessary to determine which of the gratings was the target. Note thatthis differs from the clinical visual extinction test where subjects have to detectboth targets under simultaneous stimulation conditions and there is no priorspatial cue. In case of two stimuli, the distracter and the target orientationdiffered in half of the trials. The onset of the subsequent trial was paced by thesubject’s response, with a 1650 ms interval between the patient’s response andthe next cue onset (Figure 3.1B) (Gillebert2011). The patient completed 20runs of 48 trials (960 trials in total). Conditions were balanced per run.

Eye movements were monitored using a horizontal EOG. In case of any deviationthe experimenter informed the subject online to maintain fixation. Forty-four(5.1%) trials were excluded from the analysis based on the presence of saccadeswhich occurred almost all near grating offset. There were no conditions thatcontained significantly more saccades although there were more saccades duringinvalidly cued trials with a right-sided target (11.1%) than during invalidlycued trials with a left-sided target (1.4%). Prior to the experimental runs, thepatient performed two practice runs of 48 trials with auditory feedback

3.2.3 ECoG and EOG acquisition and preprocessing

ECoG and EOG acquisition were performed with a Brainbox ECoG AmplifierEEG-1166 (Braintronics, Almere, The Netherlands) at a sampling frequency of4096 Hz, a resolution of 16 bit, a stopband frequency of 2048 Hz and a stopbandripple of -40 dB, using BrainRT Software Suite version 3 patch pack 1 build3874 (OSG, Rumst, Belgium). Two PMT Cortac grids (PMT Corporation,Chanhassen, USA) with 3 mm platinum contacts with an interelectrode spacingof 10 mm were implanted, grid A consisting of 4 x 5 contacts points andgrid B consisting of 4 x 1 contacts interhemispherically (Figure 3.1A). Atthe time of testing, channels A2, A5, A6 to A10, B1, B3 and B4 were nolonger usable due to the poor signal quality and were excluded from further


analysis. The two most anterior remaining contact points (A15, A20) werelocated above the primary motor cortex. Electrocortical stimulation elicited amotor response. These electrodes will not be considered in the further analysis.Three adjacent contact points (A4, A14, A19) overlayed the posterior bankof the postcentral sulcus. Somatosensory stimulation elicited a response atthese sites and they will also be excluded from further analysis. No motoror somatosensory responses were present in any of the remaining electrodes,which overlaid the upper and lower bank of the anterior (A13, A18) and middlesegment (A11, A12, A16, A17) of the left IPS, the lateral SPL (A3, A1) and leftmedial parietal cortex (B2). The last two runs had to be excluded due to poorsignal quality, leaving 864 trials. A 10 mm Ag/AgCl cup electrode at positionFpz was used as the hardware recording reference. Signal processing was doneon a Dell Optiplex 990 workstation running Windows 7 64 bit Service Pack 1(Microsoft, Redmond, USA) in MATLAB 7.8.0.347 (R2009a) (The MathWorksInc., Natick, MA, USA). ECoG and EOG data were imported into MATLABwith BRTToMatlab 4.0 (OSG, Rumst, Belgium) and downsampled to 1024 Hzand the remaining ECoG channels were rereferenced to the average of all gridelectrodes included in the analysis using EEGlab 9.0.8.6b (Schwarz Center forComputational Neuroscience, San Diego, USA). The EEG signal was notchfiltered using a Parks-McClellan notch filter and bandpass filtered between 0.15and 500 Hz using a butterworth filter with filter order 2 and removing DCoffset, as implemented in ERPlab 4.0.3.1 (UC-Davis Center for Mind & Brain,Davis, USA). Subsequently the data were epoched relative to grating onset.Baseline subtraction was performed -200 to 0 ms relative to cue onset. Epochswere included regardless of response accuracy. EOG data were scored for thepresence of saccades using an heuristic threshold of 22 µV within a 100-600 mstime window post grating onset.

Anatomical Region Electrode Label MNI coordinates (x,y,z)Primary motor cortex A15, A20 (-31, -27, 64), (-42, -24, 63)Postcentral sulcus A4, A14, A19 (-12, -40, 67), (-33, -36, 65),

(-43, -35, 58)Medial SPL B2 (-1, -57, 59)Lateral SPL A3, A1 (-14, -51, 62), (-16, -72, 52)Anterior IPS segment A13, A18 (-35, -47, 61),(-45, -46, 54)Middle IPS segment A17, A12, (-46, -56, 50), (-36, -57, 56),

A16, A11 (-46, -66, 45), (-37, -67, 52)

Table 3.1: MNI coordinates of the electrode positions.


3.2.4 Imaging

Structural brain MRI was obtained on a Siemens Magnetom Aera 1.5 T MRIscanner (Siemens AG, Munich, Germany) and a Toshiba Aquilion One ViSIONCT scanner (Toshiba Medical Systems Corporation, Tochigi-ken, Japan). Thepostoperative head CT scan was coregistered to a preoperative MRI scan byperforming a rigid transformation based on the maximization of the mutualinformation criterion (Maes et al., 1997) using SPM8 (Wellcome Trust Centrefor Neuroimaging, UCL, London, UK). Electrode positions were determined onthe coregistered postoperative CT. The coregistered CT-MRI and the electrodepositions were normalized to Montreal Neurological Institute (MNI) space usingSPM8. The MRI was segmented using BrainSuite 14b (build no. 1975) (Shattuckand Leahy, 2002). Electrode positions are visualized in figure 3.1A usingBrainstorm (Tadel et al., 2011)(http://neuroimage.usc.edu/brainstorm)and the MNI coordinates corresponding to the electrode positions are providedin Table 3.1.

3.2.5 Behavioral analyses

Performance in the patient was compared to that of a group of 22 healthy controlsfrom a previous study performing a highly similar paradigm. The controls hadto discriminate the orientation of the target grating. In the controls, the targetgrating could have an orientation of 45 deg minus or plus x deg. The valueof x was titrated so as to reach an accuracy of about 80-85%. In order totest for condition-dependent differences between the patient and controls, therevised standardized difference test was used (Crawford and Garthwaite, 2005).A Crawford-Howell modified t test was used to compare individual conditionsbetween the patient and the control group (Crawford and Garthwaite, 2005).

3.2.6 ECoG analysis

The main contrasts of prior interest were the contrast between invalidly andvalidly cued target trials (invalidity effect) and the contrast between competitiontrials and validly cued single-grating trials. The interaction effect betweenvalidity and direction of attention was also determined. Further effects ofdirection of attention were also determined: The effect of the direction of thecue, leftward or rightward from cue onset till grating onset, as well as the effectof the direction of attention from grating onset in the competition trials. For thedifferent contrasts the average evoked potentials were compared. Huynh-Feldtand Greenhouse Geisser were used to test for sphericity. Direct comparisons

http://neuroimage.usc.edu/brainstorm


between two conditions were carried out by means of a two-sided Student’s t testassuming equal variances repeated for every datapoint. Factorial analyses werecarried out by means of two-way ANOVA for unbalanced design. The statisticalsignificance threshold was set at P < 0.05 after Bonferroni correction for thenumber of electrodes (n = 9), with the additional requirement that significancehad to persist for a continuous time period of at least 10 ms. Adjacent timepoints are highly correlated and distant time points are not. As such Bonferronicorrection is not suited (not a form of repeated independent testing) and atime criterion is preferable. In the space domain the effects on the individualelectrodes (space) are less dependent, but not totally independent. Bonferronicorrection is used in order to select the most robust effects, although it couldbe argued that this method of correction is too stringent.

Event-related spectral perturbation (ERSP) analysis allows to determine theevent-related power in the spectrotemporal domain (1-150 Hz). Event-relatedspectral perturbation (ERSP) was calculated by means of the EEGlab newtimef()function in the frequency range 1-150 Hz at every 2 Hz using fast Fouriertransforms and Hanning window tapering. When ERSP revealed differentialeffects between conditions, each condition was compared to baseline in order todetermine whether the difference was due to either increased synchrony in onecondition or increased desynchronization in the other condition compared tobaseline. Hence, the terms (de)synchronization in the results section are basedon the contrast between each of the experimental conditions in combinationwith the contrast of the experimental condition with baseline.

For the sake of comparison with previous ECoG studies of the Posner spatialcueing paradigm (Daitch et al., 2013) we also performed an intertrial coherence(ITC) analysis within the theta frequency range. ITC, a phase locking factor,indicates a strength of phase alignment across trials at each time and frequencybin with magnitude scale 0 (weakest) to 1 (strongest). ITC was estimated alongwith ERSP using EEGlab newtimef() function with the same parameter settingsas for ERSP.

The significance levels of the ITC and ERSP were tested by bootstrap re-sampling method. The spectral estimates of a single trial from different timewindows of the baseline period were sampled 1000 times. This produceda baseline distribution and its percentile values were used as the thresholdmentioned. Statistical significance of a contrast of conditions was evaluatedbased on 1000 random permutations of the trials across conditions keeping thetotal number of trials in the dataset unchanged. Significance of the conditionand contrast were set at P < 0.05 corrected for the number of electrodes (n =9).

Weighted phase lag index analysis To study connectivity between time


series from the different channels, the weighted Phase Lag Index (wPLI) wascalculated (Vinck et al., 2011). The wPLI analysis was performed for all36 possible connections between the nine electrodes. The direction of theconnection was interpreted based on the sign of wPLI value. The Phase LagIndex is a measure of phase leads or lags between sensors (Stam et al., 2007).The weighting factor in wPLI is the magnitude of the imaginary component ofthe cross-spectrum (Vinck et al., 2011). wPLI is less sensitive to noise sourcesand has increased statistical power compared to PLI (Vinck et al., 2011). wPLIwas calculated as follows: The spectral power of the ECoG signals was estimatedusing the periodogram based Welch algorithm with a moving Hanning windowof 500 ms with 50% overlap. Based on spectral power peaks and local maximaidentified across all frequency bins and channels, two frequency bands wereselected: 6-10 Hz and 15-20 Hz. The data in these frequency bands werenarrow bandpass filtered. After a Hilbert transform, cross-spectral density(CSD) between two complex signals yi,n,k and yj,n,k of channels i and j foreach frequency band was calculated for each time point n and each trial k as:

CSDi,j,n,k = yi,n,k y∗j,n,k (3.1)

where * is the complex conjugate. wPLI was calculated across trials at eachtime point n according to:

wPLI(i,j,n) = (1/K)∑Kk=1 =(CSDi,j,n,k)

(1/K)∑Kk=1 | =(CSDi,j,n,k) |

(3.2)

where indicates the imaginary part of CSD and K equals the number of trials.wPLI was calculated for each condition separately. Statistical significanceof a pairwise contrast of conditions was evaluated based on 2000 randompermutations of the trials across datasets keeping the total number of trialsin the dataset unchanged. Significance of the contrast was set at P < 0.05corrected for the number of connections tested (n = 36).

3.3 Results

3.3.1 Behavioral analysis

The increase in reaction times in invalidly compared to validly cued single-grating trials was significantly larger in the patient (99 ms) than in the controls(31 ms) (modified t = 3.71, P < 0.002) (Figure 3.2B). For the invalidly cuedsingle-grating trials, the patient was significantly impaired for right-sided versus

RESULTS 43

left-sided targets compared to controls (modified t = 2.33, P < 0.03). Comparedto controls the patient was significantly less accurate (modified t = 3.27, P< 0.004) and slower (modified t = 8.69, P < 0.000001) for right-sided versusleft-sided targets in the competition trials (Figure 3.2A). Compared to validsingle-grating trials, competition trials were responded to less accurately (P <0.0001) and more slowly (P < 0.0001) by the healthy controls and this did notdiffer in the patient compared to controls (P < 0.1). In the competition trialsthe difference in accuracy and reaction times between right-sided and left-sidedattention trials was significantly larger in the patient compared to controls (P< 0.0001). Note that the overall difference in accuracy between the individualand the controls is not meaningful as the orientation difference in the patientwas fixed at 90 deg while in controls the difference was titrated to obtain anaccuracy around 85%.

3.3.2 Effects of the direction of attentional cue

The earliest effect of cue direction was seen in the most posterior IPS electrodes(A11, A17) approximately 384-390 ms after cue onset, with a negative deflectionfor rightward versus leftward attention in posterior IPS (Figure 3.3). There wasalso a positive ERP in SPL for rightward versus leftward attention with similartiming characteristics (Figure 3.3).

3.3.3 Invalidity effect

Early event-related potential (ERP) effects of invalidity occurred in SPL (Figure3.4A: A3, B2; Figure 3.4B: A1, A3) and in the upper bank of posterior IPS(Figure 3.4A: A12; Figure 3.4B: A11-12, A16). In medial SPL (B2) the invalidityeffect occurred as early as 163 ms following grating onset (Figure 3.4A). AnERP effect of invalidity was present in lateral SPL from 257 to 277 ms followingtarget onset (Figure 3.4A: site A3). ITC within the theta band was increasedfollowing invalidly versus validly cued targets as early as 200 ms followinggrating onset (A1 from 204 to 253 ms and A3 from 268 to 298 ms, respectively)(Figure 3.4B). An interaction analysis between the side of the relevant gratingand the invalidity effect did not reveal any significant ERP interaction effects.

There were also later effects which are less likely to be related to the spatialshift per se (Muller1998) (Figure 3.4B, 3.5A). Starting around 436 ms aftergrating onset, an invalidly cued trial elicited greater synchronization in thehigh gamma range than a valid trial (Figure 3.5A: electrode sites A17-18) andmore desynchronization in the high beta range (Figure 3.5A: electrode sitesA11, A16-17) in IPS. This effect did not depend on the target side.


Figure 3.2: (A) Accu-racy of the study par-ticipant in the differ-ent experimental condi-tions. (B) Reactiontimes of the study par-ticipant in the differentexperimental conditions(mean and S.D.). (C)Accuracy in the sameparadigm in a groupof 22 healthy controls.(D) Reaction times inthe same paradigm in agroup of healthy controls(mean and S.D.). Notethat the Y axis differsbetween the patient andthe controls given theoverall slower reactiontimes in the patient.

RESULTS 45

Figure 3.3: Leftward vs. rightward cueing trials: ERP analysis. Significanteffects that occur in the interval between cue onset and grating onset are markedby a green bar. Time point 0 refers to the onset of the grating. The significancethreshold is set at P < 0.05 corrected for the number of electrodes during aminimum continuous period of 10 ms. The plots for the different electrodesare positioned in accordance with their position on the cortical surface (Figure3.1A).

Invalidity was also associated with a significant change in connectivity betweenIPS and SPL: From around 400 to 568 ms there was a transient phase leadof SPL with respect to IPS following an invalidly cued target compared to avalidly cued target, suggesting that for a brief period of time, activity in SPLwas preceding IPS activity (Figure 3.5B: A3 with respect to A12).

3.3.4 Selection between competing stimuli

The effects of a competing distracter differed drastically from the invalidityeffects in their time course, spatial distribution, and spectral power (Figure3.6 and 3.7). Along the lower and upper bank of IPS (A12-13, A18) and inSPL (A3, B2) the presence of a competing distracter caused a prolonged effect


Figure 3.4: (A) ERP during validly cued trials and during invalidly cued trials.Significant deficits following target onset between validly cued and invalidly cuedtrials are marked by a green bar. The significance threshold is set at P < 0.05corrected for the number of electrodes during a minimum continuous period of 10ms. The plots for the different electrodes are positioned in accordance with theirposition on the cortical surface. (B) ITC analysis within the theta band (4–7Hz) during invalid vs. valid cueing trials. The significance threshold is set at P< 0.05 corrected for the number of electrodes (n = 9) using a nonparametricbootstrapping approach with 1000 randomizations.

RESULTS 47

Figure 3.5: (A) Time-frequency plots during invalidly minus validly cued single-grating trials. The ERSP is thresholded at P < 0.05 corrected for the numberof electrodes (n = 9) using a nonparametric bootstrapping approach with 1,000randomizations. (B) wPLI analysis for the frequency band from 15 to 20 Hz,indicating the effect of invalidity on functional connection between IPS andSPL. A positive y value means that the phase lead is in the direction from A3to A12, as mentioned in the title of the plot, a negative y value that it goes inthe opposite direction. The significance threshold was P < 0.05 corrected forthe number of connections tested (n = 36) using a nonparametric bootstrappingapproach with 2,000 randomizations.


on the ERP from around 310 ms onwards (Figure 3.6A). The presence of acompeting distracter was associated with synchronization in the high gammarange (Figure 3.7A: A11, A17 and A1).

Rather uniquely for the competition trials, in the anterior electrodes in IPS(A18, A13) and SPL (A3) there was less desynchronization in the high betaband compared to single grating trials (Figure 3.7A). The distribution of thisbeta band effect co-localized with that of the ERP effect shown in Figure 3.6A.When a competing distracter was present, the directed influence of anterior onmiddle IPS remained positive for a longer period of time. This suggests that theeffect of anterior IPS to middle IPS regions was more prolonged in competitiontrials compared to single (Figure 3.7B). Within the 6-10 Hz frequency band,the directed influence of IPS on SPL also remained positive for a longer periodof time (Figure 3.7C).

3.4 Discussion

The current study provides for the first time the electrophysiological signatureof the spatial shifting signal in response to an invalidly cued spatial cueingtrial in SPL. The invalidly cued target requires a spatial shift, triggered by thestimulus appearing at an unexpected location. We propose that this spatialshift underlies the early SPL effects. The competition trials require selectionbetween two competing stimuli based on short-term memory of the directionof the prior spatial cue. In the past, we had proposed that the activation ofIPS during the competition trials was related to the attentional priority mapas described in LIP (for review see (Vandenberghe and Gillebert, 2009)). Thelong latency of the effect appears to exclude that IPS plays a role in setting theattentional weights in an early selection stage (Bundesen et al., 2005). The lateIPS response may reflect attentional priority setting in a late selection stage orresponse decision processes.

3.4.1 ECoG effects of invalidity in SPL

Around 200 ms, and as early as 167 ms, an ERP effect was found in SPL inresponse to an invalidly cued target compared to a validly cued target. Aroundthe same time and at approximately identical electrodes, an ITC effect waspresent that was congruent with the ERP effect. The congruency between theERP and the ITC effect strengthens the evidence that the invalidity effect inSPL is robust. Overall this timing is of the same order as that described for thebehavioral effect of exogenous reorienting (Müller and Rabbitt, 1989). wPLI

DISCUSSION 49

Figure 3.6: (A) ERP during competition trials compared to validly cued single-grating trials. Significant deficits following target onset between validly cuedand invalidly cued trials are marked by a green bar. The significance thresholdis set at P < 0.05 corrected for the number of electrodes during a minimumcontinuous period of 10 ms. The plots for the different electrodes are placed inaccordance with their position on the cortical surface (Figure 3.1A). (B) Inter-trial coherence during competition trials compared to validly cued single-gratingtrials. The significance threshold is set at P < 0.05 corrected for the numberof electrodes (n = 9) using a nonparametric bootstrapping approach with 1,000randomizations.


Figure 3.7: (A) Time-frequency plots during competition trials minus validlycued single-grating trials. The ERSP was thresholded at P < 0.05 corrected forthe number of electrodes (n = 9) using a nonparametric bootstrapping approachwith 1,000 randomizations. (B) wPLI analysis indicating the effect of competitiontrials compared to valid single-grating trials on functional connection betweenanterior and posterior IPS in the frequency band 15–20 Hz. The significancethreshold was P < 0.05 corrected for the number of connections tested (n =36) using a nonparametric bootstrapping approach with 2,000 randomizations.(C) wPLI analysis indicating the effect of competition trials compared to validsingle-grating trials on the functional connection between IPS and SPL in thefrequency band 6–10 Hz. Same significance threshold as in (B)

DISCUSSION 51

measures an entirely different dimension of the data, namely the phase lagbetween electrodes. Approximately 200 ms following the ITC/ERP effect insuperior parietal lobule there is a reversal of the direction of the phase lag sothat SPL leads IPS. Because of this long latency the reversal of the phase lagcannot be directly related to the mechanism of the spatial shift, which occursearlier, both behaviorally and electrophysiologically. The reversal of the phaselag may be related to a cognitive process after the shift, e.g. decision-relatedprocesses, a re-setting of the attentional set, or the increased cognitive controlrequired by an unpredicted event.

The Posner spatial cueing paradigm has been studied using ECoG in one previousstudy which principally focussed on changes in coherence of the signal withinand across network nodes (Gunduz et al., 2012; Daitch et al., 2013): Followingan invalidly cued target, theta synchronization was seen in both the dorsal andthe ventral attention network. This has been termed the theta band reorientingresponse (Daitch et al., 2013). ITC analysis of the current dataset allowed usto localize a theta reorienting response with higher anatomical specificity to thesuperior parietal lobule in invalid compared to valid trials as well as the upperbank of the posterior segment of IPS. The early theta reorienting response inSPL was specific for invalid trials (A1: Figure 3.4B versus Figure 3.6B) and wasnot present during competition trials at that recording site. In ERP, reorientingto distracters that share task-relevant features with the target is associated withchanges in the theta frequency band (Chang et al., 2016). In stroke patientswith left spatial neglect, the attentional benefit induced by task-relevant featuresof distracters upon the processing of targets is diminished (Ptak and Schnider,2010). This reduction is associated with a reduction of theta band connectivitywithin the structurally preserved dorsal attention network (Fellrath et al., 2016).Both task- and stimulus-driven factors may also play a role in the currentexperiment since the spatial shift to an invalidly cued target is triggered bythe grating appearing at an unexpected location and the shift also matchesthe task goal. The theta reorienting effect therefore most likely reflects bothstimulus-driven and task-driven attentional reorienting integrated. Althoughthe spatial shift following the cue is driven by a central arrow, the reorientingduring the target phase is partly driven exogenously by the appearance of thegrating at the uncued location.

Based on prior evidence (Gunduz et al., 2012; Daitch et al., 2013) and in order tolimit the number of comparisons we restricted the ITC analysis to the theta band.Electrophysiological studies based on surface EEG or magnetoencephalographyhave demonstrated alpha band desynchronization contralateral to the focus ofattention in bilateral posterior sensors at 300-600 ms following cue onset as wellas increases in alpha power contralateral to the ignored stimuli (RIHS et al.,2009). This alpha band desynchronization is considered a marker of allocation


of spatial attention (Capotosto et al., 2009; Hong et al., 2015; Wyart and Tallon-Baudry, 2008). Alpha desynchronization occurs principally at occipital sensorsoutside the cortical surface covered in the current study and also relatively latewith respect to the timing of the delay phase.

According to one of the most influential contemporary models of spatial attentionin the human brain, the spatial reorienting deficit during invalidly cued trials inthe Posner spatial cueing paradigm relates principally to inferior parietal lesionsof the ventral attention network, most notably the right angular gyrus and TPJ(Corbetta and Shulman, 2002). The current study provides information aboutthe contribution of superior parietal cortex to spatial attention. It demonstratesan early effect of spatial shifting in the superior parietal lobule. An importantoutstanding question is how the processes mediated by the superior parietallobule in invalidly cued trials relate to those performed by the inferior parietalareas during spatial shifts, such as cytoarchitectonic area PF (Gillebert et al.,2013), and how the timing differs between these regions. Further ECoG studieswith wider coverage would be needed to address this question. Ischemic lesionsof SPL that spare IPS structurally and functionally are extremely rare. Acase with bilateral damage to the SPL (MC) had a severe deficit in invalidlycued trials while performance on competition trials was relatively preserved(Vandenberghe et al., 2012). The nonhuman primate homologue of the SPLregion activated during spatial shifts has recently been identified as area V6/V6a(Caspari et al., 2015). The structural and functional connections between theSPL regions involved in shifting and the inferior parietal or prefrontal cortex area topic of ongoing research. Insight into these connections and the differenceswith IPS will be required in order to integrate the shifting-related activity inSPL into network models of spatial attention (Bartolomeo et al., 2012). It isalso important to note that the recordings were limited to the left hemisphereand that the link between the current findings and the clinical phenomenon ofright-hemispheric neglect (as opposed to visual extinction) is probably weak.

The absence of a directional effect in SPL is in full agreement with all previousstudies in humans and in nonhuman primates that the shifting effect in SPL isnot specific for the direction of the spatial shift (Vandenberghe et al., 2001; Yantiset al., 2002; Molenberghs et al., 2007; Caspari et al., 2015). In these studies, theshifting effect in SPL is systematically present in both hemispheres. We do notclaim that the response in SPL explains the contralesional shifting deficit seenin the current patient or in patients with lateralized spatial-attentional deficitsfollowing stroke. In fact, the effect of direction of attention following lesions isalmost certainly not mediated by SPL, but may, for instance, originate fromtopographically organized regions in IPS (Gillebert et al., 2011; Silver, 2005).

DISCUSSION 53

3.4.2 Relation to visual neglect and the clinical symptom ofextinction

The patient had no MRI-visible cortical lesions. The patient showed acontralesional shifting deficit and a contralesional deficit for the competitiontrials. A contralesional shifting deficit and a contralesional deficit on thecompetition trial does not imply neglect. In a previous study (Gillebert et al.,2011), among the 7 parietal lesion patients who had a contralesional shiftingor a contralesional selection deficit in the hybrid spatial cueing paradigm,only two had pathological scores on the clinical tests of target cancellation orclinical extinction. In another study of the competition trials in 20 (sub)acutestroke patients, all four patients who had neglect scored pathologically on thecompetition trials but one subject had a contralesional deficit on the competitiontrial but normal scores on the clinical neglect tests (Molenberghs et al., 2008).Hence the computerized tests are more sensitive than the conventional clinicalneglect tests. The right-hemispheric preponderance has been shown for theneglect syndrome but, as of yet, not for the current computerized tests. It isworth noting that in the canonical paper of the invalidity effect in parietal lesionpatients by (Posner et al., 1984), a contralesional shifting deficit was presentin both left- and right-hemispheric lesion patients. Neglect is a more severesyndrome that consists of multiple components (for review see (Vandenbergheet al., 2012)). The spatial-attentional deficits measured by our tests are alsopresent in neglect but are not sufficient to diagnose neglect. Patients who scorenormally on the clinical extinction test and who do not have neglect, may stillhave a contralesional shifting deficit and a contralesional competition effect onthese computerized tests which are more sensitive for spatial-attentional deficitsthan the clinical tests for neglect (see (Gillebert et al., 2011)). Currently thereis no evidence for hemispheric lateralization of the specific and subtle deficitsdetected by the hybrid spatial cueing paradigm, in contrast with neglect orvisual extinction where there is a right-hemispheric dominance.

3.4.3 Effects of cue direction during the delay phase

In the delay phase a direction-sensitive negativity occurred at the end of thedelay in the more posterior IPS electrodes. The spatial distribution of the effectof direction of attention differed from that of the reorienting effect. This fitswith nonhuman primate fMRI data showing a clear dissociation between theeffect of direction of attention (mainly localized to the Lateral Intraparietalarea, among other regions) and the effect of shifting attention (mainly localizedto V6/V6A) (Caspari et al., 2015). The timing of the cue direction effectmay seem relatively late but is in agreement with the timing characteristics


of the Early Directing Attention Negativity (EDAN) potential, a surface-EEGERP deflection contralateral to the direction of attention (Harter et al., 1989;Yamaguchi et al., 1994; Nobre et al., 2000; Grent-‘t Jong et al., 2007; Simpsonet al., 2011).

3.4.4 ECoG effects in IPS of a competing distracter

The current study provides a unique insight in the time course of the IPSresponse to competing distracters. In the past, we proposed that the fMRIresponse in middle IPS to the presence of competing distracters reflects thecompilation of the attentional priority map needed to prioritize between stimuli(Vandenberghe et al., 2005; Molenberghs et al., 2008). The ECoG data revealthat the latency of the IPS effect was more than 250 ms after the grating onset.Overall, this would rather suggest that the effect of stimulus competition in IPSmainly originates at a late-selection, post-perceptual stage. It could be relatedto the low frequency (1 out of 6 trials) of the competition and invalid cueingtrials compared to single valid trials, to the higher working memory demandsof competition trials, e.g. related to a higher load (Gillebert et al., 2012) orto the higher endogenous selection demands of competition trials (Duncan,2010). The data could still be compatible with a role in assigning attentionalpriorities to perceptual units at a late rather than an early selection stage.In an ECoG study of spatial attention using a different paradigm (Malhotraet al., 2009), ERSP in a time window from 400-600 ms revealed synchronizationin the high gamma band during the more demanding attentional task (Parket al., 2016). Desynchronization occurred in the theta, alpha and beta band insuperior parietal cortex during the spatial attention task from 400 to 800 msbilaterally (Park et al., 2016). In the current study, ERSP revealed in IPS anincrease in high gamma synchronisation in response to invalidly cued targets aswell as as to competition trials, similar to the effect described by (Park et al.,2016).

3.4.5 Study limitations

The study limitations are mainly related to the ethical restrictions imposed bythe clinical utility that is required for all aspects of the procedure. Foremost,this is a single-case report. In our opinion, the unique nature of the ECoGdata with its supreme spatial and temporal resolution compensates for thesingle-case nature. Second, interictal epileptic activity may have interfered withthe measurements. The clinical indication for the ECoG measurements impliesthat the cortical tissue from which recordings are made may be dysfunctional

DISCUSSION 55

and one should bear this in mind when drawing inferences regarding healthyintact neocortical tissue. Third, human IPS is a very convoluted sulcus with alarge part buried deeply within the sulcus itself. EEG recordings mainly detectsignal from the cortical surface and are less sensitive for activity arising fromwithin the depth of the sulcus. This is also the case for ECoG which uses asubdural grid instead of depth electrodes.

3.4.6 Conclusion

To conclude, the current study reveals the electrophysiological signature ofspatial-attentional shifting in the superior parietal lobule. In line with previousnonhuman primate studies (Caspari et al., 2015) the effect of spatial shifting isanatomically dissociable from the effect of the direction of attention, and alsofrom the effect caused by the presence of competing stimuli. In IPS the effect ofspatial cue direction in more posterior electrodes and the long-latency responseto the presence a competing distracter in more anterior electrodes reconciles aspatial interpretation of the role of IPS with its contribution to general-purposeattentional control processes (Duncan, 2010).

Chapter 4

Comparison of differentKalman filter approaches inderiving time varyingconnectivity from EEG data

Kalman filter approaches are widely applied to derive time varying effectiveconnectivity from electroencephalographic (EEG) data. For multi-trial data, aclassical Kalman filter (CKF) designed for the estimation of single trial data,can be implemented by trial-averaging the data or by averaging single trialestimates. A general linear Kalman filter (GLKF) provides an extension formulti-trial data. In this work, we studied the performance of the differentKalman filtering approaches for different values of signal-to-noise ratio (SNR),number of trials and number of EEG channels. We used a simulated modelfrom which we calculated scalp recordings. From these recordings, we estimatedcortical sources. Multivariate autoregressive model parameters and partialdirected coherence were calculated for these estimated sources and comparedwith the ground-truth. The results showed an overall superior performance ofGLKF except for low levels of SNR and number of trials.

This chapter has been published as: Ghumare, E., Schrooten, M., Vandenberghe, R.,and Dupont, P., Comparison of different Kalman filter approaches in deriving time varyingconnectivity from EEG data, Proc. Annu. Int. Conf. IEEE Eng. Med. Biol. Soc. EMBS,2015, pp. 2199–2202, 2015.

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58 COMPARISON OF DIFFERENT KALMAN FILTER APPROACHES IN DERIVING TIME VARYINGCONNECTIVITY FROM EEG DATA

4.1 Introduction

Effective or directed connectivity is receiving increased attention for exploringthe information processing in the human brain (Toppi et al., 2014; KoichiSameshima et al., 2014; Gow and Nied, 2014). Unlike functional connectivity,effective connectivity allows to study the information flow and interactiontimings among brain regions to understand the basis of cognitive functions.In contrast to functional magnetic resonance imaging (fMRI), data fromelectroencephalography (EEG) has an excellent time resolution. Using suchdata, we can study the effective connectivity to understand the spectral aswell as the temporal properties of these directed connections. Among thedifferent approaches proposed for effective connectivity analysis, MultivariateAutoregressive Modeling (MVAR) based on the concept of Granger causality(GC) is widely applied (Koichi Sameshima et al., 2014). GC based MVARmeasures give directed flow by estimating a linear causal relationship amongbrain regions. In this article, we focused on partial directed coherence (PDC),one of the commonly applied GC based frequency domain measures.

The estimation of PDC follows the multivariate autoregressive (MVAR) modelingof the EEG time series. The estimated MVAR parameters are transformed tothe frequency domain to calculate PDC values. Among all MVAR estimationapproaches, a Kalman filter based MVAR modeling gained wider applicationsdue to its accurate estimation of non-stationary and high dimensional EEG data(Arnold et al., 1998; Milde et al., 2010). Kalman filter based approaches areable to best follow transient changes in spectra of EEG data and give estimatesof the MVAR model at each time point, i.e. time varying MVAR (TV-MVAR).Hence time varying PDC (TV-PDC) can be calculated.

A Kalman filter can be implemented by a number of ways to estimate theTV-MVAR model. The classical Kalman filter (CKF) based approach can beused in case of single trial EEG or averaged event related potential (ERP)data (Giannakakis and Nikita, 2008). An alternative is to use the EEG of theindividual trials by estimating the TV-MVAR model of each single trial and byaveraging the model estimates across trials followed by TV-PDC calculation(Tang et al., 2013). A third approach is to calculate TV-PDC from the TV-MVAR estimates of each single trial and the final TV-PDC is obtained byaveraging TV-PDC across trials (Omidvarnia et al., 2014; Eftaxias and Sanei,2013). The General Linear Kalman filter (GLKF) provides an extension ofCKF to the case of multi-trial time series (Arnold et al., 1998). GLKF basedestimation allows the simultaneous fit of one MVAR model to all trials. Formulti-trial EEG data, GLKF is considered to be more effective to estimate theTV-MVAR model (Hu et al., 2012). However, to the best of our knowledge, nostudy directly comparing the accuracies of the different strategies is available.

METHODS 59

The performance of GLKF was studied for different levels of signal to noise ratio(SNR) and number of trials (Astolfi et al., 2008; Toppi et al., 2012). A highnumber of trials is important to accurately estimate the model and to increasethe adaptation speed (i.e. the speed of change of MVAR estimates to minimizeprediction error). The SNR is an another factor which may strongly influencethe reliability of the approach. Although several papers have investigated theaccuracy of GLKF (Astolfi et al., 2008; Toppi et al., 2012), none have comparedCKF and GLKF approaches directly at different levels of trials and SNR.

4.2 Methods

4.2.1 Theoretical Background

Time varying MVAR (TV-MVAR) The time varying MVAR (TV-MVAR)process is described as:

Y (t) =p∑k=1

A(k, t) Y (t− k) + U(t) (4.1)

where Y(t) is the set of time series, p is the model order, A(k,t) is the matrixof time varying model parameters at time t for lag k =1, 2..., p and U(t) is avector of multivariate zero-mean uncorrelated white noise.

Time varying Partial directed coherence (TV-PDC) Partial directedcoherence (PDC) is a full multivariate spectral measure based on the conceptof Granger causality (GC) (Baccalá and Sameshima, 2001), used to determinethe directed influences between a pair of time series with the influence of theremaining time series removed. Using TV-MVAR parameters, we can obtaintime varying PDC (TV-PDC) values. TV-PDC from node j to node i iscalculated as a function of frequency and time as:

πij(f, t) = Aij(f, t)√m∑r=1

Arj(f, t) AHrj(f, t),∑i

|πij(f, t)|2 = 1 (4.2)


A(f, t) = I −p∑k=1

A(k, t)e−i2πfk (4.3)


where f is the normalized frequency in the interval [-.5,.5]. We used the squaredvalues of PDC i.e. |πij(f, t)|2 as measure of connectivity. Squared values ofPDC were shown to provide superior accuracy than PDC (Astolfi et al., 2006).

TV-MVAR model estimation using Kalman filtering A Kalman algorithmis applied in a linear state-space representation of the signal model. The linearstate equation can be represented as:

A(k, t) = A(k, t− 1) + V (k, t− 1) (4.4)

where A(k,t) is the state process i.e. TV-MVAR model parameters and V(k,t)is the additive noise in the state process. The measurement equation is givenby equation 4.1.

The Classical Kalman filter(CKF) approach models single trial EEG/ERP data.Details of this algorithm are described in (Arnold et al., 1998; Haykin, 2001).For multi-trial data we implemented the following 3 strategies to estimateTV-PDC.(1) TV-PDC is calculated from the averaged TV-MVAR estimates (CKF-AA)(Tang et al., 2013).(2) TV-PDC is obtained by averaging TV-PDC across trials (CKF-PA)(Omidvarnia et al., 2014; Eftaxias and Sanei, 2013).(3) CKF applied to the average of all trials (CKF-GA) (Giannakakis and Nikita,2008)The algorithm was implemented using the mvaar.m function available from thetime series analysis (TSA) toolbox (Schlögl, 2002).

The fourth strategy was General linear Kalman filter (GLKF) which wasimplemented in MATLAB as described in (Milde et al., 2010).

4.2.2 Simulated data

We used simulated data to compare the different approaches at various levels ofSNR, number of trials and number of EEG channels. We defined a ground-truthmodel at the level of cortical sources. Based on this model, we simulatedEEG scalp recordings. We linearly inverse estimated the cortical sources usingBrainstorm (v3.2). The estimated sources were compared with the ground-truthmodel.

Simulated cortical connectivity model The ground-truth model we used isbased upon a model described in a previous simulation study (Astolfi et al.,

METHODS 61

Figure 4.1: Connectivity pattern imposed among 3 nodes. The value of thecausal connection from S1→ S3 and S3→ S2 are time dependent (dotted arrow)and constant for the rest (continuous arrow). The theoretical (simulated) valuesare represented by the blue plots near each connection for the time lag given byTij (representing the constant delay in the propagation from node j to node i).For the other time lags, aij = 0. A time lag (model order) of 1 and 2 correspondto 4 and 8 ms, respectively.

2008) modified by adding a feedback connection to test the performance of thedifferent approaches in the presence of a feedback connection. The simulatedconnectivity pattern consisted of 3 nodes or time series with a predefined linearcausal TV-MVAR structure as depicted in figure 4.1.

To obtain simulated test signals similar to real cortical sources, the input time


series for node S1 was generated from auto regression (AR) parameters estimatedfrom a real cortical source which was estimated from a real EEG recording usingBrainstorm (Tadel et al., 2011). The AR parameters of signal S1 are shown infigure 4.1.

The remaining two signals were generated using TV-MVAR modeling (figure4.1). Values of Uj(t) were adjusted at each time point or sample to achieve theSNR level of 10. The model was constructed iteratively in time using the modelin figure 4.1 to generate single trial data. We repeated the procedure to obtain40 trials. The sampling frequency of the signal (Fs) was set to 256 Hz and thetotal number of time points (N) was set to 512 corresponding to two secondsrecording.

Simulated EEG recordings We assigned the simulated data in the three nodesof the model to 3 different cortical surface vertices modeled as current dipolesusing the default anatomy in Brainstorm. We positioned the dipoles in thefollowing Montreal neurological institute (MNI) coordinates (32, -108, -8), (33,-73, 56) and (66, -48, 20) for S1, S2 and S3, respectively. We choose thecoordinates based on previous studies on visuospatial attention from our lab(Gillebert et al., 2013). EEG channel files for different number of channels (32,64, 128 and 256) from ANT Neuro sensors were used. The forward matrix(G) was estimated for each channel file with the symmetric Boundary ElementMethod (Gramfort et al., 2010) implemented in Brainstorm. EEG scalp signalswere calculated with an average reference. The forward matrix of each EEGchannel file was used to simulate EEG data from the 3 simulated cortical sourcesS(t). Corresponding EEG recordings were generated using Brainstorm for eachEEG channel file and each trial of S(t) to generate multi-trial EEG data. Whitenoise was added on the simulated EEG data. SNR was defined as the ratio ofglobal power in the EEG recordings to variance of white noise added (Leistritzet al., 2013).

Source Modeling The diagonal noise covariance of the EEG data required forthe inverse estimation was calculated from EEG data in each trial separatelyusing the complete two second recording of the trial. For each trial, thesolution of the inversion kernel was achieved using the sLORETA (standardizedlow resolution brain electromagnetic tomography) method implemented inBrainstorm (Pascual-Marqui, 2002). We used the default settings in Brainstormto perform the source modeling. The orientations of the estimated dipoles arenormal to the cortical surface. The time series of the reconstructed sources wastaken as the cortical activity of the vertex point corresponding to the originalsource position.

METHODS 63

TV-MVAR estimation defaults The Kalman filter control parameters, alsoreferred as update constant and which control the adaptation speed of MVARparameters, were set to 0.02 (Astolfi et al., 2008; Leistritz et al., 2013). Weestimated the model order by fitting a stationary MVAR model to the simulateddata using the ARFIT algorithm from the Time series analysis toolbox (Schlögl,2002; Schneider and Neumaier, 2001). As criterion we used Schwarz’s BayesianCriterion because it is least affected by the presence of noise (Porcaro et al.,2009). In this study, we found model order 3.

4.2.3 Performance analysis

Factors and levels The SNR of the surface EEG, the number of trials and thenumber of EEG channels were chosen as factors to vary to test the performances.We used SNR = [0.1, 1, 3, 5, 10], number of trials = [1, 2, 3, 5, 10, 20, 40] andnumber of EEG channels = [32, 64, 128, 256]. We used 50 noise realizations foreach setting.

Theoretical TV-PDC We constructed the theoretical TV-PDC (Astolfi et al.,2008). We limited our analysis within the frequencies 0-30 Hz based on thespectral power of the signal assigned to node S1.

Figures of merit We used two figures of merit to capture the performance ofeach method at the level of detecting the TV-MVAR model parameters aij andat the level of TV-PDC. First, we used the mean square error (MSE) betweenthe theoretical and estimated TV-MVAR parameters (denoted as MVARfom)and second the MSE between the theoretical and estimated TV-PDC values(denoted as PDCfom). The diagonal elements were excluded from the calculationof PDCfom due to the column normalization properties of PDC.

Statistical testing We performed separate one-way repeated measuresANOVAs for MVARfom and PDCfom as dependent variable to compare thefour Kalman filter based approaches. This was done for each combination ofSNR, number of trials and number of EEG channels. A Greenhouse - Geissercorrection for sphericity was used. The post-hoc analysis was performed withthe Scheffé’s test. Statistical significance was set at p < 0.05.


Figure 4.2: Figures of merit (MVARfom and PDCfom) for different Kalman filterapproaches at various levels of trials, EEG channels and SNR for TV-MVARand TV-PDC estimation.

4.3 Results

Each figure of merit was calculated compared to the theoretical values fromthe ground-truth model for different number of trials, number of EEG channelsand SNR for each of the four possible Kalman filter approaches i.e. GLKF,CKF-GA, CKF-AA, CKF-PA.

DISCUSSION 65

Figure 4.2 shows the performance of different approaches on MVARfom andPDCfom at various levels of the factors investigated. The bar on each plotindicates the standard deviation of the mean value computed across 50realizations. Note that MVARfom for CKF-PA are not calculated since weused MVAR estimates of the individual trials. Based on one-way repeatedmeasure ANOVAs for MVARfom, the GLKF approach was significantly betterin performance compared to the other methods when SNR >3 and number oftrials >10. When SNR is low (≤ 1) CKF-GA performs best if the number oftrials is not too low (> 5). Based on PDCfom, GLKF is significantly better incase the number of trials is high enough (> 10) and SNR > 1. When the numberof trials is low (≤ 10) CKF-AA and CKF-PA showed superior performance whenSNR > 1. In contrast to other approaches CKF-GA showed higher varianceand no improved accuracy with increasing levels of SNR and number of trials.Interestingly, we also observed an improved performance when sources arereconstructed with an increasing number of EEG channels and this holds foreach approach.

4.4 Discussion

The results obtained from the simulated data clearly indicated differences in theaccuracy of the different Kalman filter approaches in TV-MVAR and TV-PDCestimation for multi-trial EEG or cortical source data.

Simulated data are often applied to study the effective connectivity (Toppiet al., 2012; Leistritz et al., 2013) directly at the level of sources or channels.However, we investigated the connectivity pattern at the level of cortical sourcesinversely re-estimated from the simulated EEG instead of the original sources.This provides a more realistic situation where accuracy of MVAR and TV-PDCestimation is evaluated after the source modeling which in itself may affect theaccuracy.

GLKF showed the best performance among the possible Kalman filterapproaches when SNR >3 and number of trials >10. These findings areconsistent with a previous study in which it was shown that certain levels ofSNR and number of trials were required for an accurate GLKF approach (Toppiet al., 2012). In addition to that, our study showed that in case the data containsa low number of trials, applying CKF-AA or CKF-PA can be an alternative toestimate TV-PDC. The exact levels of the factors when one method outperformsanother, can not be determined based on this study because it may depend onmany other factors like e.g. number of sources included in the analysis. However,this study gives some indication for the most suitable approach for the levels


of the factors included. CKF-PA and CKF-AA showed similar performances,however given the higher computation time required for CKF-PA, the CKF-AAapproach is preferred. In contrast to other approaches CKF-GA showed theworst performance when looking at TV-PDC. Averaging EEG data across trialsmay have disturbed the stochastic structure in the averaged data leading toan inferior accuracy. Indeed, a primary assumption of MVAR modeling is thateach single trial is considered as a stochastic process (Hu et al., 2012). Thisfinding can be important for future studies performing TV-MVAR or TV-PDCestimation on averaged ERP data.

4.5 Conclusions

The results showed that the general linear Kalman filter (GLKF) is the bestapproach when the number of trials and SNR are sufficiently high. If this is notthe case, a valid alternative is the classical Kalman filter approach in which timevarying partial directed coherence is calculated from the average time varyingmultivariate autoregressive model parameters (CKF-AA). The accuracy of aclassical Kalman filter approach applied on averaged EEG data across trials(CKF-GA) shows the worst performance in most cases.

Chapter 5

A time-varying connectivityanalysis from distributed EEGsources: a simulation study

Time-varying connectivity analysis based on sources reconstructed using inversemodeling of electroencephalographic (EEG) data is important to understandthe dynamic behaviour of the brain. We simulated cortical data from a visualspatial attention network with a time-varying connectivity structure, and thensimulated the propagation to the scalp to obtain EEG data. Distributed EEGsource modeling using sLORETA was applied. We compared different dipole(representing a source) selection strategies based on their time series in a regionof interest. Next, we estimated multivariate autoregressive (MVAR) parametersusing classical Kalman filter and general linear Kalman filter approaches followedby the calculation of partial directed coherence (PDC). MVAR parameters andPDC values for the selected sources were compared with the ground-truth. Wefound that the best strategy to extract the time series of a region of interestwas to select a dipole with time series showing the highest correlation with theaverage time series in the region of interest. Dipole selection based on poweror based on the largest singular value offer comparable alternatives. Amongthe different Kalman filter approaches, the use of a general linear Kalman filter

This chapter is resubmitted and under review as: Ghumare E., Schrooten M.,Vandenberghe R., and Dupont P., A time-varying connectivity analysis from distributedEEG sources: a simulation study, Brain Topography, under second review.

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68 A TIME-VARYING CONNECTIVITY ANALYSIS FROM DISTRIBUTED EEG SOURCES: ASIMULATION STUDY

was preferred to estimate PDC based connectivity except when only a smallnumber of trials are available. In the latter case, the classical Kalman filter canbe an alternative.

5.1 Introduction

Brain function fundamentally relies on the interaction between functional unitsat different scales. Electrophysiological measures such as electroencephalography(EEG) and magnetoencephalography (MEG) can provide unique insight intothe dynamic and directed interactions between anatomical regions, thanks totheir high temporal resolution (Leistritz et al., 2016; Lopes da Silva, 2013).This relies on the validity of methods and strategies used to derive time-varyingdirected connectivity from EEG and MEG when cortical sources are estimated(Siebenhühner et al., 2016; Mahjoory et al., 2016).

The technique to map EEG data from sensor space to cortical sources isreferred to as EEG source modeling. Popular approaches for distributed sourcemodeling are the weighted minimum-norm estimate (Jeffs et al., 1987) andsLORETA (standardized low-resolution brain electromagnetic tomography)(Pascual-Marqui, 2002). Both methods are widely used to study directed andtime-varying EEG-based connectivity between sources (Wang et al., 2016; Stortiet al., 2016; Hassan and Wendling, 2015; Plomp et al., 2016; Gao et al., 2015;Hassan et al., 2014). sLORETA is robust against noise, is less biased towardssuperficial sources and the solutions are very smooth. Once the sources aredetermined, the connectivity between these sources can be studied using avariety of methods such as Granger causality (Freiwald et al., 1999), phasesynchronisation (Campbell et al., 1980) or cross-spectrum (Blackman and Tukey,1958) among the reconstructed time series (Hassan et al., 2017; Haufe and Ewald,2016). All these methods heavily depend on the accuracy of the time series inthe selected sources. In the case of smooth distributed sources, the extraction ofthe correct representative time series is far from trivial while at the same time,this is critical for an accurate estimate of the connectivity measure (Mahjooryet al., 2016). Often, time series are averaged across the dipoles in a region ofinterest (ROI) which leads to an additional smoothing. An alternative is toextract the time series from a single dipole (Sohrabpour et al., 2016; Coito et al.,2016). However, when using such a strategy, it is important to evaluate theperformance of different dipole selection strategies within an ROI.

Once the time series are extracted in selected dipoles, directed and time-varying connectivity between these sources can be studied to determineinformation processing in the human brain (Leistritz et al., 2016; Lie and

INTRODUCTION 69

van Mierlo, 2017; Liu et al., 2016; Mao et al., 2016; Plomp et al., 2016). Unlikefunctional connectivity, directed and time-varying connectivity allows to studythe information flow and the timings of the interactions among brain regions tounderstand the basis of cognitive functions. Among the different approachesto derive directed and time-varying connectivity, multivariate autoregressivemodeling (MVAR) and the concept of Granger causality (GC), are widelyapplied (Baccalá and Sameshima, 2001). GC based measures give directed flowby estimating a linear causal relationship among brain regions. In this article,we focused on partial directed coherence (PDC), one of the commonly appliedGC based frequency domain measures. The estimation of PDC follows theMVAR modeling of EEG time series. The estimated MVAR parameters aretransformed to the frequency domain to calculate PDC values. The conventionalapproaches are based on stationary MVAR estimates of the data i.e. one modelis estimated for the entire length of the time series. However, EEG is highlynon-stationary, and stationarity will miss the dynamic interactions among brainregions. With a moving window approach, this would still require stationarityin a window and the size of the window will impose further limitations to theresults. Among all time-varying MVAR estimation approaches, a Kalman filterbased MVAR modeling gained wider applications in high-dimensional EEGdata due to its accurate estimation of non-stationary (Milde et al., 2010; Arnoldet al., 1998). Kalman filter based approaches can track transient changes inspectra of EEG data and give estimates of the MVAR model at each timepoint so that time-varying PDC can be calculated. A Kalman filter can beimplemented in a number of ways to estimate the time-varying MVAR model.

Here we present a methodological investigation on time-varying connectivitystarting from EEG source modeling. More specifically, our aim was:

1. To compare strategies for dipole selection within an ROI after sourcemodeling.

2. To compare the performance of time-varying directed connectivity methodsbased on different Kalman filtering approaches to derive partial directedcoherence based networks.

To perform a methodological investigation a ground truth time varyingconnectivity is required. Such validation is not possible with real data andsimulations are inevitable and the only way to compare different methods.Simple simulations are useful to gain insight into the behaviour of a methodunder different conditions like SNR, but ultimately we want to apply suchmethods in more complex situations, and therefore the development of morerealistic simulations is essential (Haufe and Ewald, 2016). We used simulatedEEG data with a known ground truth time-varying directed connectivity model.


A preliminary version of this work with a simple model consisting of 3 nodeshas been reported in (Ghumare et al., 2015).

5.2 Methods

5.2.1 Time-varying connectivity

We first describe the theoretical formulation of time-varying directed connectivitybased on Granger causality starting from time series in a set of sources.

For the discrete time series y ∈ R m×N measured in m channels with N samples,the time-varying MVAR process is described as:

y(n) =p∑k=1

Ak(n) y(n− k) + e(n) (5.1)

with n being the n-th time bin of the N samples, p is the model order, Ak(n) ∈R m×m is the matrix of the time-varying MVAR model parameters at timebin n for delay k, k = 1, 2..., p and e(n) is a vector of multivariate zero-meanuncorrelated white noise.

Partial directed coherence is a full multivariate spectral measure based on theconcept of Granger causality (Baccalá and Sameshima, 2001), used to determinethe directed influences between a pair of time series in sources i and j withthe influence of the remaining time series removed. Using time-varying MVARparameters, we can obtain time-varying PDC values from source j to source icalculated as a function of frequency and time:

πij(f, n) = Aij(f, n)√m∑r=1

Arj(f, n) AHrj(f, n),∑i

|πij(f, n)|2 = 1 (5.2)


A(f, n) = I −p∑k=1

Ak(n)e−i2πfk (5.3)

where f is the normalized frequency in the interval [-.5,.5]. We used the squaredvalues of PDC i.e. |πij(f, t)|2 as measure of connectivity. Squared values ofPDC were shown to provide superior accuracy and sensitivity compared to PDC(Astolfi et al., 2006).

METHODS 71

5.2.2 Time varying MVAR model estimation using Kalmanfiltering

The application of the Kalman filtering algorithm to MVAR modeling is basedon a linear state-space representation of the signal. A linear state-space modelconsists of two joined linear equations:the state equation

Ap(n+ 1) = Ap(n) + v(n) (5.4)

and a measurement equation

y(n) = Hp(n)Ap(n) + e(n) (5.5)

The state equation relates state Ap(n) of MVAR parameters at time bin n tothe state or MVAR estimates at time bin n+ 1 with v(n) ∼ N (0, V (n)), thestate white noise process and Hp(n) is a matrix with the p past data points ofthe measurement. The time-varying MVAR parameters Ap(n) are related tothe parameters Ak(n) (see appendix A and B).

The MVAR parameters Ap(n) are estimated using Kalman filtering recursionequations. There are mainly two different implementations of Kalman filteringto perform time-varying MVAR modeling: the classical Kalman filter (CKF)(Arnold et al., 1998) or the general linear Kalman filter (GLKF) (Milde et al.,2010). The former is implemented for a single trial while the latter has animplementation which takes into account multi-trial data and which is not astraightforward extension of the classical Kalman filter, i.e. it does not reduceto the classical Kalman filter if one would consider single trial data as a specialcase of multi-trial data. The details of the classical Kalman filter and thegeneral linear Kalman filter are given in Chapter 2.

For multi-trial EEG/ERP data, we can use the following strategies to estimatetime-varying PDC:

1. PDC values are calculated from the averaged single trial MVAR estimatesusing the classical Kalman filter (CKF-1) (Tang et al., 2013);

2. PDC values are calculated by averaging (across trials) single trial estimatesof the PDC values (CKF-2) calculated from MVAR estimates using theclassical Kalman filter (Eftaxias and Sanei, 2013; Omidvarnia et al., 2014);

3. PDC values are calculated from MVAR estimates obtained using thegeneral linear Kalman filter.


Previously, we have shown that averaging the trials before MVAR modelingwill result in inaccuracies (Ghumare et al., 2015) and therefore, this approachwill not be one of our strategies.

5.2.3 Simulated ground truth data

To compare the different strategies, we used simulated data with a ground-truthmodel at the level of cortical sources.

The simulated data consisted of a realistic large-scale model of the visualspatial attention system with a complex time-varying and directed connectivitystructure. The simulated directed connectivity model is shown in figure 5.1. Theconnectivity model was based on (Corbetta et al., 2008) and the time-varyinginformation was based on the timings of the significant effects observed indifferent regions as described in (Simpson et al., 2011) and (Vossel et al., 2014).The timings were specified for the presentation of a central cue in a visualspatial attention experiment.

To mimic the visual input to the cortical areas, the input signal was obtainedfrom a source estimated from real EEG data acquired during a visuospatialattention experiment in a healthy control. In this experiment, the trials startedwith a central cue presented for 200 ms indicating the direction of attentionto the left. After a delay phase of 300 ms from cue offset, a grating in the lefthemifield was shown in combination with a central fixation cross. We estimatedthe cortical sources using distributed source modeling (Pascual-Marqui, 2002)with the head model derived from a high-resolution anatomical MRI of thatsubject. To extract the visual input, a signal from 200ms before cue onsetuntil 500 ms after cue onset (the end of the delay phase) was extracted froma source in primary visual cortex (V1) and it was resampled with a samplingfrequency of 256Hz. The source in V1 was located at MNI coordinates (6.3,-82.3, -3.7) corresponding to a central position in the visual field according toretinotopic mapping studies (Dougherty et al., 2003). Because the timings ofthe effects were described in (Simpson et al., 2011; Vossel et al., 2014) for 1000ms after stimulus onset, we had to generate a new input signal for a longerduration. This was done as follow: 1) we estimated stationary autoregressiveparameters from the original input signal using the ARFIT package (Schneiderand Neumaier, 2001) and 2) we used the estimated parameters to simulate thenew input signal for a duration of 1000 ms after stimulus onset. This signal wasused as input for the model (figure 5.1). The model order for the stationaryautoregressive model was determined using Schwarz’s Bayesian Criterion (SBC)and was found to equal 10. The model order was further validated based onthe comparison of the power spectrum of the signal using a non-parametric

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Figure 5.1: The simulated visual spatial attention model consisting of an inputarea (V1), two visual areas (VA), the intraparietal sulcus (IPS), the frontaleye fields (FEF), the temporoparietal junction (TPJ), the anterior insula inthe ventral frontal cortex (VFC/AI) and the middle frontal gyrus (MFG). Themodel was taken from (Corbetta et al., 2008) with some minor modifications:connections between FEF, IPS, and MFG were slightly adapted, and the visualinput region was added. The arrows indicate directed interactions consistingof a stimulus-driven control (orange), top-down control (blue) and the visualinput signal (black). Bidirectional interhemispheric connections were modeledas stationary with a strength of 0.5. The time-varying MVAR connectivitywas imposed based on the timings of the significant effects observed in differentregions as described in (Simpson et al., 2011) and (Vossel et al., 2014) andare shown by the figures next to each directed connection. These time-varyingconnections were added on top of the stationary connection in which the latterhad a strength of 0.2. The time lag for MVAR parameters for the connection inblue and orange was chosen as 16 ms and for black as 4ms. The exact onset ofthe directional time-varying interactions, its amplitudes and duration as well asthe time lag were chosen arbitrarily.


Region x y zPrimary visual cortex (V1) 6.3 -82.3 -3.7Right visual area (R VA) 15 -71 5Right Intraparietal sulcus (IPS R) 42 -42 48Right Frontal eye fields (FEF R) 38 -6 56Right Temporoparietal junction (TPJ R) 66 -48 20Right Ventral frontal cortex/anterior insula (VFC/AI R) 39 0 39Right Middle frontal gyrus (MFG R) 47 38 29Left visual area (VA L) -14 -81 9Left Intraparietal sulcus (IPS L) -44 -57 48Left Frontal eye fields (FEF L) -43 -7 52

Table 5.1: MNI coordinates of the cortical ground truth sources

Welch and parametric Burg method (van Mierlo et al., 2013). Furthermore,the frequency spectrum of the simulated signal confirmed the presence of astandard 1/f function with a peak in the alpha band (8–12 Hz) as in a realEEG frequency spectrum.

The cortical signals of the ground truth model in the other regions weregenerated using the time-varying MVAR model shown in figure 5.1. Thesampling frequency was set to 256Hz. The noise amplitude was adjusted at eachtime point to achieve a constant SNR level of 20. The model was constructediteratively in time to generate single trial data. We repeated the procedure toobtain 100 trials to mimic multiple trial data. The time series in each trial wasgenerated for a duration of 1200 ms in which the first 200 ms were consideredbaseline.

Next, we associated the multi-trial ground truth time series to the corticalsources (dipoles) which were located on the cortical surface using the defaultanatomy (Colin27) in Brainstorm and which were closest to the MontrealNeurological Institute (MNI) coordinates described in table 6.1 based on theEuclidean distance. The MNI coordinates from table 6.1 were derived fromprevious studies on visuospatial attention (Gillebert et al., 2013; Simpson et al.,2011).

5.2.4 Simulated scalp EEG data

Using the data in the 10 dipoles, we simulated EEG measurements in 256electrodes derived from the ANT Neuro sensors available in Brainstorm. Theforward matrix G was estimated with the symmetric boundary element method

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(Gramfort et al., 2010) implemented in Brainstorm. This model consisted ofthree layers: skin, skull, and brain (including cerebrospinal fluid (CSF) ) withrelative values of the conductivities set as 1, 1/80 and 1 S/m respectively (Qinet al., 2010; Ahrens et al., 2012). The conductivity ratio between scalp and skullwas set to 1/80 which was the default value in Brainstorm. However, othershave argued that this ratio is rather between 1/20 and 1/10 (Oostendorp et al.,2000; Lai et al., 2005). By performing the simulations using the value 1/80, theproblems caused by the conductivity of the skull become more pronounced andit could be considered as a worst case scenario.

The brain sources were limited to the cortical surface with 15002 vertex pointswith a dipole orientation orthogonal to the cortical surface. For each time binn, we can calculate the surface EEG signal D(n) from the forward matrix Gand the signal S(n) in all dipoles:

D(n) = G · S(n) + e(n) (5.6)

in which e(n) is white noise mimicking measurement noise.

We applied an overall scale factor for S to obtain a peak amplitude in theEEG data in the same range as realistic measurements. EEG scalp signals werecalculated with an average reference.

We adapted the variance of the white noise to generate trials at a specific SNRlevel. SNR was defined as the ratio of the average power in the EEG recordings(over all trials, time and EEG electrodes) to the power of the white noise added(Leistritz et al., 2013). Final datasets consisted of 100 trials per SNR level.

5.2.5 Source modeling of simulated EEG data

We followed a realistic approach by performing a data-driven distributed sourcemodeling using Brainstorm.

The noise covariance of the EEG data required for the inverse estimation wascalculated using the baseline period of 200 ms of all simulated trials. Off-diagonal elements of the noise covariance were discarded to model uncorrelatedmeasurement noise. The parameter λ used in Brainstorm is required for theregularization of the ill-posed problem. λ is related to the level of noise presentin the measurements and is calculated as λ = 1/SNR2 in which SNR representsthe signal to noise ratio (Bradley et al., 2016). For each dataset, the simulatedSNR of the scalp EEG data was used to calculate λ. To regularize the noisecovariance matrix we used the default setting of 0.1 in Brainstorm. Duringthe source estimation, the orientations of the dipoles were constrained to benormal to the cortical surface. A shared inversion kernel for all the trials


was determined using sLORETA implemented in Brainstorm (Pascual-Marqui,2002). The estimated shared kernel was applied to each trial of EEG data toobtain the corresponding cortical signal in each dipole position in each of the15002 vertices.

5.2.6 Regions of interest and dipole selection

Using the scout menu in Brainstorm, we created a-priori regions of interest(ROIs) on the cortical surface around the location of the ground-truth dipoles(Table 6.1). Each ROI consisted of 40-50 vertex points (corresponding to an areaof 10 cm2) and was defined using the position of the ground-truth dipole as asseed. Within each ROI we selected a single dipole from the distributed sourcesobtained during source modeling. Extraction of a single time series in an ROIbetter overcomes the problem of smoothness of the inverse solution compared tothe averaged time course of all dipoles within that ROI (Rueda-Delgado et al.,2017). The set of time series of the selected dipoles was used to perform theconnectivity analysis.

We compared a number of strategies to select a single, representative dipolewithin an ROI. We used two different types of strategies for the dipole selection:1) strategies in which we used the ground truth information and 2) strategiesin which we use a data driven approach (as we would do in a real experiment).

Dipole selection using ground truth information In these approaches, weused the ground truth knowledge to select the representative dipole in eachROI. The following strategies were used:

1. The ground truth dipole was selected (GT1).

2. The dipole in the ROI with the highest correlation between the timeseries in that dipole and the ground truth time series was selected (GT2)(Babiloni et al., 2004).

Data driven methods for the dipole selection In these approaches, weselected a dipole without the knowledge of the ground truth data. Beforeselecting the dipole, we have to determine the dominant direction of the dipolesin an ROI followed by sign flipping the dipoles with opposite direction (Hassanet al., 2017). The reason for this approach is that the inverse solution obtainedby sLORETA is based on minimum norm estimates and the sign of theseminimum norm estimates depends on the dipole direction. In some of thestrategies, we make use of the resolution matrix of the inverse solution which

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is the product of the inverse kernel and the forward matrix. In the ideal case,the resolution matrix will be the identity when sources are perfectly separated.However, this is never the case because of the ill-posed nature of the problem.The selection strategies we have evaluated were:

1. The dipole with the highest correlation between the time series in thatdipole and the averaged time series across all dipoles in the ROI. Such adipole could best represent the regional fluctuations in the signal (DD1).

2. The dipole with the highest power (i.e. the mean squared amplitude)(DD2) (Rueda-Delgado et al., 2017).

3. The dipole showing the highest correspondence with the largest singularvalue based on a row singular vector (Sohrabpour et al., 2016). Such adipole can best explain the variability in the ROI (DD3).

4. The dipole with the resolution index closest to 1 in the ROI (DD4)(Stenroos and Hauk, 2013; Hauk et al., 2011). The resolution index is thediagonal value of the resolution matrix, and 1 indicates that the sourcesare optimally resolved.

5. The dipole with the highest cross-talk function (CTF) index in the regions(DD5). This index was defined as the ratio of the mean outflow CTF(the sum of the column elements of the resolution matrix) and the meaninflow CTF (the sum of the row elements of the resolution matrix). A"strong" dipole will have more outflow CTF due to the smooth solutionand a minimal inflow CTF indicating its closeness to the ideal solution(Farahibozorg et al., 2017; Hauk et al., 2011).

We used different parameters to evaluate the performance of the different dipoleselection strategies:

1. The Euclidean distance and the surface based distance between the positionof the selected dipole and the ground truth position.

2. The Pearson correlation coefficient between the time series in the selecteddipole and the ground-truth time series;

3. The mean squared error (MSE) between the linear fit of the time series inthe selected dipole and the ground-truth time series;

These parameters were estimated for different SNR levels.


5.2.7 Evaluation of different Kalman filtering approaches

The Kalman filtering approaches were applied to the time series extracted fromthe dipoles selected after source modeling to determine time-varying MVARparameters followed by time-varying PDC estimation.

The SNR of the surface EEG and the number of trials were chosen as factorsto vary when evaluating the different Kalman filter approaches. We used SNR= [1, 3, 5, 10] and number of trials = [3, 5, 10, 20, 40, 60, 80, 100]. For eachsetting, we used 100 noise realizations and each noise realization was obtained byrepeating the entire process starting from the simulated EEG surface recordings.

The update constant UC was set to 0.02 (Astolfi et al., 2008; Leistritz et al.,2013) and we used a fixed model order of 8 in all subsequent analyses. Thismodel order was obtained by fitting a stationary MVAR model to the groundtruth data using the ARFIT algorithm from the time series analysis toolbox(Schlögl, 2002; Schneider and Neumaier, 2001) and by applying the SBC criterionbecause it is least affected by the presence of noise (Porcaro et al., 2009).

Based on the theoretical time-varying MVAR parameters shown in figure 5.1,we constructed the theoretical time-varying PDC values (Astolfi et al., 2008).For the calculation of PDC, we limited our analysis to the frequency window1-40 Hz based on the spectral power of the ground truth source data. We usedtwo figures of merit to compare the performance of each method for MVARmodel parameters and PDC separately. The figures of merit were estimated perfactor level and per noise realization. Since it may make a difference whetherwe look at existing or non-existing connections in the ground truth model, weperformed a separate analysis for both types of connections.

The first figure of merit was the mean squared error (MSE) between thetheoretical and estimated time-varying MVAR parameters:

MSEMVAR = E[(Ap(n)estimated − Ap(n)theoretical)2] (5.7)

where p is the model order, n is the time bin.

The MSE between the theoretical and estimated time-varying PDC values wasused as another figure of merit:

MSEPDC = E[(|πij(f, n)estimated|2 − |πij(f, n)theoretical|2)2] (5.8)

where i and j refers to a pair of ROIs, f is the frequency bin, n is the timebin. In equation 5.8, the diagonal elements are excluded due to the columnnormalization properties of PDC.

We performed repeated-measures ANOVAs for MSEMVAR and MSEPDC tocompare the three Kalman filter based approaches. A Greenhouse-Geisser

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correction for sphericity was used. The posthoc analysis was performed usingScheffé’s method. The statistical significance was set at p<0.05 Bonferronicorrected for the number of pairwise tests performed.

5.3 Results

5.3.1 Dipole selection to extract ROI time series

We compared different dipole selection strategies using various performanceparameters in two different scenarios: 1) when the ground truth is known and2) using data-driven methods (figures 5.2-5.4).

For data driven dipole selection methods, we selected the dominant directionof the dipoles in the ROI without the ground truth knowledge similar to areal experiment. As a result, in four ROIs the sign of the dominant directionwas opposite to the ground truth direction. The dipole selection itself was notaffected but only the sign of the dipole time series. As a result, the localizationerror was not affected but the correlation with the ground truth time series andthe mean squared error with these time series was strongly affected. Therefore,we showed additional results for ROIS in which the extracted time series had acorrect or incorrect sign separately (panels (a) and (b) in figures 5.3-5.4).

Compared to the other data-driven strategies, DD1 showed the lowestlocalization error both using the Euclidean distance (figure 5.2a) and using thesurface distance (figure 5.2b) . The localization error improved with increasinglevels of SNR.

Looking at the correlation between the selected time series and the ground truthtime series, we observe that in ROIs with the correct sign for the dominantdirection, the dipole showing the highest correlation with the ROI averaged timeseries (DD1) also showed a high correlation with the ground truth time series(figure 5.3a). The performance of this strategy for this criterion was comparableto the ground truth based dipole selection strategies. For DD2 (power basedselection) and DD3 (based on SVD), the performance improved with increasinglevels of SNR and was comparable to DD1 when SNR=10 (figure 5.3a). Thestrategies based on resolution index (DD4) and the CTF index (DD5) showeda lower performance (figure 5.3a). For ROIs with an incorrect sign for thedominant direction, we observed almost an opposite pattern: using DD1, DD2and DD3 lead to strong negative correlations and using DD4 and DD5 wasfound to be superior (figure 5.3b). Based on the overall results for all ROIs, weobserved comparable performances of all the approaches for this criterion (figure5.3c). However, based on the median of the data, we considered DD1, DD2 and


Figure 5.2: The performance parameters for the dipole selection strategies atdifferent levels of SNR. Box-and-Whisker plots across all regions and 100 noiserealizations are shown. (a) Euclidean distance in mm from the ground truthlocation (b) Surface distance from the ground truth location along the cortex.

DD3 as superior compared to DD4 and DD5. Improvement in the performanceof using DD2 and DD3 with increasing SNR was consistently observed. AtSNR=10, DD2 and DD3 showed results comparable to DD1.

Looking at the mean squared error (MSE) between the linear fit of the selectedtime series and the ground truth time series, DD1 also showed the bestperformance for this criterion for ROIs with the correct sign of the dominantdirection (figure 5.4a). DD1 showed minimal variation across regions and noiserealizations compared to all other data-driven methods. Overall the errorreduced with increasing levels of SNR, and this was the case for all the dipoleselection strategies (figure 5.4a). Similar to the results for the correlationcoefficient, all methods showed for the ROIs with an incorrect sign of thedominant direction a large variability as well as a higher error compared to theROIs with a correct sign of the dominant direction (figure 5.4b). The overallresults also indicated a large variability (figure 5.4b) and DD4 and DD5 can beconsidered the best for this criterion.

In the remainder, we will show the performance of the Kalman filteringapproaches for dipole selection strategy DD1, DD2 and DD3 since they canbe considered the best taking all criteria into account. For comparison, wealso used the ground truth based selection strategy GT2 since this is also acorrelation based strategy.

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Figure 5.3: The correlation coefficient with corresponding ground truth timeseries for the dipole selection strategies at different levels of SNR. Box-and-Whisker plots across all regions and 100 noise realizations are shown. (a) ROIswith the correct sign of the dominant direction compared to the ground truthdirection (b) ROIs with an incorrect sign of the dominant direction compared tothe ground truth direction (c) Overall results.

5.3.2 Performance of Kalman filtering approaches

The Kalman filtering approaches were compared at different levels of SNRand number of trials. The figures of merit were calculated separately for time-varying MVAR parameter estimates and PDC values. To distinguish betweenthe performance for existing versus non-existing connections in the groundtruth network, we applied the figures of merits separately for both types ofconnections.

Errors in existing connections

The figures of merit for the existing connections indicate the sensitivity tocapture the time-varying connectivity in the underlying brain network.


Figure 5.4: Mean square error (MSE) after linear fitting with ground truth timeseries for the dipole selection strategies at different levels of SNR. Box-and-Whisker plots across all regions and 100 noise realizations are shown. (a) ROIswith the correct sign of the dominant direction compared to the ground truthdirection (b) ROIs with an incorrect sign of the dominant direction compared tothe ground truth direction (c) Overall results.

The results of MSEMVAR for existing connections and the ground truth baseddipole selection (GT2) and data driven dipole selection strategies DD1, DD2and DD3 are shown in figure 5.5(a-h). For MSEMVAR, the use of the generallinear Kalman filter outperformed the other approaches (p < 0.05) when usingthe ground truth based dipole selection (GT2) (figure 5.5(a-b)). The figuresof merits calculated for the data-driven dipole selection methods (DD1, DD2and DD3) are shown in figure 5.5(c-h). Averaging of the MVAR estimates afterusing the classical Kalman filter (CKF-1) outperforms the other methods at alllevels of SNR and number of trials while GLKF showed the worst performance.We also observed in some cases an increase in error when the number of trialsincreased or when SNR increased. When looking at individual MVAR plots,this was caused by the sign flip in four of the time series as a result of the wrongdominant direction within the corresponding ROI.

For MSEPDC, the use of the general linear Kalman filter outperformed theother approaches when the dipole was selected based on the ground truth based

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Figure 5.5: MSEMVAR for different Kalman filtering approaches at variouslevels of SNR and number of trials for existing model connections and using theground truth based dipole selection GT2 and the data driven dipole selectionsDD1, DD2 and DD3.

strategy (GT2) except when the number of trials was <= 20 at SNR=10 inwhich case averaging PDC values across single trial estimates of the PDC valuesusing the classical Kalman filter is the best method (CKF-2) (figure 5.6(a-b)).For data driven dipole selection methods, the use of the general linear Kalmanfilter outperformed (p < 0.05) the other methods in most situations (figure5.6(c-h)). When using DD1, GLKF and CKF-2 gave comparable errors in PDCvalues (figure 5.6(c-d)).


Figure 5.6: MSEPDC for different Kalman filtering approaches at various levelsof SNR and number of trials for existing model connections and using the groundtruth based dipole selection GT2 and the data driven dipole selections DD1, DD2and DD3.

Errors in non-existing connections

The figures of merit for the non-existing connections is an indication for detectionof false positive connections.

The results of the figures of merit MSEMVAR for the non-existing connectionsand the ground truth based dipole selection (GT2) and data driven dipoleselection strategies DD1, DD2 and DD3 are shown in figure 5.7(a-h). Theresults indicate that averaging of the MVAR estimates after using the classicalKalman filter (CKF-1) outperforms the other methods (p < 0.05).

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Figure 5.7: MSEMVAR for different Kalman filtering approaches at various levelsof SNR and number of trials for non-existing connections of the model and usingthe ground truth based dipole selection GT2 and the data driven dipole selectionsDD1, DD2 and DD3

The results of the figures of merit MSEPDC for the non-existing connectionsand the ground truth based dipole selection (GT2) and data driven dipoleselection strategies DD1 , DD2 and DD3 are shown in figure 5.8(a-h). Similar toMSEMVAR, the results indicate that the classical Kalman filter with averagingof the MVAR estimates (CKF-1) outperforms the other methods (p < 0.05).

Overall performances

Overall the performance depends on the ratio of existing and non-existingconnections as well as on their actual errors. In our case, for MSEMVAR, the use


Figure 5.8: MSEPDC for different Kalman filtering approaches at various levelsof SNR and number of trials for non-existing connections of the model and usingthe ground truth based dipole selection GT2 and the data driven dipole selectionsDD1, DD2 and DD3

of the general linear Kalman filter outperformed all other approaches for theground truth based dipole selection. For data-driven dipole selection methodsDD1, DD2 and DD3, this was the case for averaging of the MVAR estimatesafter using the classical Kalman filter (CKF-1).

For MSEPDC, the use of the general linear Kalman filter outperformed the othermethods for all the dipole selection approaches (GT2, DD1, DD2 and DD3).

Interesting to note is that among the data-driven dipole selection methods,MSEMVAR and MSEPDC was lowest for DD1.

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5.4 Discussion

The pipeline to derive time-varying connectivity from EEG data can be dividedinto three stages: 1) Estimation of cortical sources (source modeling); 2)ROI selection and time series extractions; and 3) Estimating time-varyingconnectivity. There is abundant literature available about source modeling, andtherefore we investigated the remaining two stages of the pipeline that requiredfurther attention. We used simulated data with a ground-truth time-varyingconnectivity applied to regions involved in the visual spatial attention system.We studied two aspects: first, we compared strategies to select representativedipoles from which the time series could be used in the connectivity analysis andsecond, we compared the performance of different Kalman filtering approachesin deriving time-varying PDC based connectivity.

Some of the earlier work on time varying connectivity (Wilke et al., 2008) focusedon the application of the classical Kalman filter to compare the adaptive andthe stationary directed transfer function. In contrast, in this work, we focusedon the comparison between the classical Kalman filter and the more recentgeneral linear Kalman filter for the case of multi-trial data and their impact onthe estimation of the MVAR model parameters and the PDC values along withthe comparison of dipole selection methods. Previously, the methodologicalinvestigations on time-varying connectivity approaches were often based onsimulated EEG data with only a few network nodes with a simple time-varyingstructure and without EEG cortical source estimation (Wilke et al., 2008; Astolfiet al., 2008; Leistritz et al., 2013). However, in this study, we took it a stepfurther and used a model based on the visual spatial attention system. Thismodel of the attention system (Corbetta et al., 2008) has been highly influentialand had the regions sparsely distributed all over the cortical surfaces at variousdepths. Such a configuration allowed to compare the different approaches undermore realistic circumstances with respect to other simulations in which only afew regions with a simple time-varying connectivity structure are used.

In our model, we simulated 23 directed connections from 90 possible connections.The simulated directed connections allowed the modeling of feed-forward andfeedback mechanisms of the interaction between areas as is the case in a realbrain network (Corbetta et al., 2008). Furthermore, time-varying influences ontop of baseline connectivity mimic cognitive processes and flow of informationbetween regions. However, the exact choices of the time-varying values ofMVAR parameters were arbitrary but consistent with the timings describedin (Simpson et al., 2011; Vossel et al., 2014) specified for the presentation of acentral cue in a visual spatial attention experiment.

The source modeling included in the simulation pipeline is essential for the


comparison of the performance because this is what we do in a real experiment.We used a realistic head model in combination with the symmetric boundaryelement method and constrained the orientation of the sources orthogonal tothe cortical surface. However, we did not want to include the effect of thecreation of the head model on the dipole selection and the comparison ofthe performance of different Kalman filtering approaches, and therefore wemade the same choices for the head model while simulating the surface EEGdata from the ground truth model. The distributed source estimation usingminimum norm is giving the network that best matched the ground-truth(Hassan et al., 2017). Among minimum norm algorithms, sLORETA is widelyapplied due to its standardization applied to the estimates to reduce the error indepth localization. However, the performance of sLORETA to uncover multiplesource configurations with different strengths and cortical depths is still underinvestigation (Becker et al., 2016; Dümpelmann et al., 2012) although theapproach is a promising candidate and performs well as compared to otherlinear approaches for source localizations (Dümpelmann et al., 2012; Wagneret al., 2003).

The smoothed distributed sources, obtained using sLORETA, result in mixingof sources due to cross-talk and impose a primary challenge to estimate theconnectivity. A reliable estimation of the true connectivity is possible if the shapeand fluctuations of the source’s time series are well estimated. Often the timeseries of an ROI is obtained by averaging the time series across dipoles withinthat ROI (Hassan et al., 2017), However, this would further worsen the problemfor Granger causality and phase based connectivity measures (Ghumare et al.,2015; Makeig, 2002). To overcome this problem, choosing a single representativedipole is recommended (Rueda-Delgado et al., 2017; Sohrabpour et al., 2016;Coito et al., 2016). We compared a number of strategies for dipole selection. Alarge correlation indicates a strong matching of the shape of the ground-truthand the time series in the selected dipole (Stenroos and Hauk, 2013; Babiloniet al., 2004, 2003). Another criterion often applied is mean squared errorbetween times series in estimated and true sources. However, compared toconventional criteria, we used MSE between the time series in the true sourceand a linear fit of time series in the estimated source. Due to the ill-posednature, the strength of estimated sources is underestimated compared to thestrength of true sources with a factor of about 10−3 (Stenroos and Hauk, 2013).MSE calculated by the direct comparison between estimated sources and truesources would lead to a dipole selection with higher amplitude but with lesssimilarity in signal fluctuations. However, the fluctuations are essential toextract the time-frequency characteristics and connectivity. Our approach oflinear fitting of estimated time series to the ground truth time series ensuredthat the selected dipole time series has a similar shape as the true source. Notethat we did not perform the connectivity calculations with scaled data but

DISCUSSION 89

performed it with the unscaled estimated time series.

For the sources estimated with constrained orientations (normal to the cortex),the sign of the estimated time series can be an issue. A strategy that is oftenused, is to determine the dominant direction of the ROI based on the scalarproduct of the orientations followed by a sign flip of the dipole time series thatare not in the dominant direction (Hassan et al., 2017). For the regions usedin this study, we found four ROIs in which the sign of the dominant directionwas opposite compared to the ground truth. This has no impact on the dipoleselected but it has an impact on the sign of the time series which will be usedin the connectivity analysis. When we evaluated the dipole selection methods,we found that the methods based on highest correlation (DD1), highest power(DD2) or using SVD (DD3) performed comparatively well. Dipole selectionbased on the resolution matrix showed the worst performance. This is causedby selecting a dipole with (almost) no signal since such dipoles can also havea resolution index of 1 or can have a high cross-talk function index when thedipole is surrounded by very low signal dipoles resulting in a low denominator(inflow cross-talk function).

The comparison of different Kalman filtering approaches to derive time-varyingPDC was performed using four dipole selection strategies (one which was basedon knowledge of the ground-truth and three purely data-driven methods). Thefigures of merit calculated for time-varying MVAR indicated how well thesimulated model is extracted. We found that averaging of the MVAR estimatesafter using the classical Kalman filter (CKF-1) gave the best result for all datadriven dipole selection strategies. In this analysis we included four time serieswith the wrong sign because the dominant direction in the corresponding ROIswas sign flipped compared to the ground truth. As a result, we observed adecline in the performance with increasing levels of SNR or number of trials. Butif we are interested in directed connectivity, we are using the MVAR parametersto calculate the PDC values and these were not much affected by the sign flip.However, the accuracy of MVAR parameters is usually considered importantfor the generalization of the results to other measures (Sameshima et al., 2015).

Overall, based on the MSEPDC results, the best Kalman filtering approachdepends on the number of trials and the SNR in the data. However, some cleartrends can be observed. For existing connections, a higher number of trials isrequired for the approach in which we use the general linear Kalman filter inorder to outperform the other strategies (Ghumare et al., 2015). There shouldbe sufficient data compared to the number of estimated parameters dependingon the model order and the number of time series (Schlögl and Supp, 2006).For the case of non-existing connections, the noise in the data can often leadto false positive connections. In that case, the best performance was obtainedwhen averaging MVAR estimates across trials (CKF-1), and this is caused by


the improved SNR while averaging. The use of the general linear Kalman filtershowed poor performance for the non-existing connections. However, the errorwas much lower compared to the existing connections and therefore, this methodwas overall the best one in most cases. However, if we look at the ground truthbased method GT2, we speculate that the general linear Kalman filter eventuallywould outperform CKF-1 in case of non-existing connections if we would haveincluded a higher number of trials. For the data-driven approaches, this is abit more complicated because in that case the influence of the incorrect sign ofsome of the time series is also playing a role.

Interestingly, based on MSEMVAR and MSEPDC, we observed a lower error usingthe ground truth based (GT2) and data driven DD1 dipole selection methodcompared to the other data driven methods DD2 and DD3. This also supportsour idea that for time-varying connectivity studies, the dipole selection shouldnot be based on amplitude but on the fluctuations in the signal which are morerelevant in that case.

There are a number of limitations in our analysis. Firstly, often in sourcesimulation studies, random noise is added to dipoles besides the ground truthdipoles to mimic the background brain activity (Haufe and Ewald, 2016; Babiloniet al., 2004, 2003). However, there are several noise configurations possible. Inreality, each noise configuration can lead to slightly different results, and nonecan be considered as the best choice. In our analysis, noise in the ground truthsources is required due to the intrinsic property of MVAR approaches being awhite noise process. Therefore, we added only a small amount of noise to theground truth sources (SNR = 20) to mimic the background noise. Furthermore,we added noise at the level of the scalp in various amounts. Therefore, we didnot add any noise in the dipoles besides the ground truth dipoles to modelbackground brain activity but rather considered it negligible. Secondly, in thedipole selection strategies, the results were based on a surface ROI. We haveperformed additional analyses with a surface ROI of smaller size comparedto the original analysis and a spherical ROI of 1 cm radius. These additionalanalyses showed similar results in the dipole selection strategies.

5.5 Conclusions

We compared approaches for single dipole based extraction of time series fromthe inversely reconstructed EEG sources in regions of interest. We showed thata single dipole can be selected to represent the time series based on the highestcorrelation with the averaged time series in the region of interest. The dipoleselected based on the highest power or based on a singular value decomposition

CONCLUSIONS 91

are good alternatives. The comparison of different approaches based on Kalmanfiltering to estimate time-varying partial directed coherence (PDC) showed thatthe best approach is based on the use of the general linear Kalman filteringin case of existing connections whereas the classical Kalman filter with trialaveraged multivariate autoregressive model estimates is the best approach fornon-existing connections. Based on the overall performance, the general linearKalman filter is the best choice.

Chapter 6

Time-varying connectivity inthe parietal cortex duringvisuospatial attention

6.1 Introduction

The cognitive processes during visuospatial attention consist of dynamicactivations of a large-scale network. The network mainly consists of frontal,parietal and occipital areas in the human brain. The areas are hierarchicallyorganised to carry out a diverse set of functions in visual attentional processing.The lower level areas in the hierarchy, mainly the visual cortex, influence thehigher level areas of the parietal and frontal cortex. In a fast feedback fromhigher level areas to lower level, the behavioural goals can be achieved byattentional selection, reorientation or neglect (Meehan et al., 2017; Plompet al., 2016; Ptak, 2012). The bidirectional hierarchical processes are referredto as bottom-up and top-down attention (Katsuki and Constantinidis, 2014).Although the interactions between lower and higher areas have been shown tooccur, understanding the modulation or reorganisation of such interactions isimportant (Meehan et al., 2017). The areas that interact in bottom-up andtop-down attention form functionally and anatomically overlapping networks.Network models are proposed to understand the mechanism of the interactionsin the system (Corbetta et al., 2008; Corbetta and Shulman, 2002).

In a magnetoencephalography (MEG) study by (Simpson et al., 2011), examined

93

94 TIME-VARYING CONNECTIVITY IN THE PARIETAL CORTEX DURING VISUOSPATIAL ATTENTION

the activity time course in several areas when attention was oriented to the leftor right hemifield. The activity is the result of the information flow from visualareas to higher parietal and frontal areas. The higher areas, the intraparietalsulcus (IPS) and frontal eye fields (FEF) are activated after a certain delaywith the visual system (Simpson et al., 2011). Based on connectivity studies infMRI, the parietal cortex and FEF are found to mutually influence each otheras well as the visual system in order to change behaviour according to the taskdemands (Bressler et al., 2008; Plomp et al., 2016).

Furthermore, in an EEG study, a large-scale synchronous network in the gammaband was found in the contralateral visual cortex and other cortical areaswhen directing attention to the left or the right (Doesburg et al., 2008). In anevent-related potential (ERP) study, it was shown that attentional processingnot only was associated with the spatial hierarchy but also with the temporalcascade of the activity in these regions (Shomstein et al., 2012). Comparedto bottom-up, top-down interactions occur at much longer latencies indicatingprocessing time of the stimulus and decision making in the brain (Bressler et al.,2008; Doesburg et al., 2008). Therefore, not only the timing of the activationin different regions but also a clear and consistent temporal hierarchy of theirconnections requires further investigation (Nobre and Mesulam, 2014).

Among the different lobes of the brain involved in spatial attention, the parietalcortex is the most important. Lesion mapping studies have uncovered thecritical role of the parietal cortex in visuospatial attention (Gillebert et al.,2011). Within parietal cortex, anatomically and functionally distinct systemsexist for selection and reorientation of attention (Vossel et al., 2014; Bartolomeoet al., 2012; Corbetta and Shulman, 2002). Several attention studies have utilizeda spatial cueing paradigm modified from the Posner paradigm to understand therole of the parietal cortex in the attentional selection and reorienting (Schrootenet al., 2017; Gillebert et al., 2013; Vandenberghe et al., 2005). In that paradigm,presentation of competing stimuli allows studying spatially selective attention.These studies have also provided ample evidence of the functionally distinctrole of the different anatomical areas from parietal lobule (Vandenberghe andGillebert, 2013). During competing stimuli, the middle IPS is consistentlyactivated indicating a role in attentional selection (Molenberghs et al., 2008).In posterior IPS, activity levels change with the direction of attention (left orright) (Vandenberghe et al., 2005). Furthermore, based on cytoarchitectonicmapping of parietal cortex, various bilateral areas in the inferior parietal lobule(IPL) were found to be associated with attentional shifting and selection.

In spite of the progress in understanding the role of parietal areas, directedinformation flow and timing of the attentional process remain poorly understood.This requires the study of the underlying directed connectivity model withinthe parietal lobule at high temporal resolution.

METHODS 95

To investigate the dynamics of the directed connectivity model in attentionalprocessing within the parietal lobule, we applied time-varying directed connec-tivity measures with high temporal resolution using electroencephalography(EEG) data. Among several functional imaging modalities, EEG has an excellenttime resolution. Using EEG data acquired during the spatial cueing paradigmwith competing stimuli, combined with EEG source modeling can lead to anopportunity to understand timings of cortical directed interactions (McDermottet al., 2017; Plomp et al., 2016). Among several connectivity methods, Grangercausality based partial directed coherence (PDC) is widely applied becauseit gives directed, frequency dependent strength of the connections (Baccaláand Sameshima, 2001). To estimate PDC, multivariate autoregressive (MVAR)modeling is required. Using Kalman filtering, a time-varying MVAR modelingcan be performed (Milde et al., 2010; Toppi et al., 2012; Arnold et al., 1998).In this way, time-varying PDC values, and thus time-varying connectivity, canbe obtained. These methods are validated in several studies using simulatedand real data (Lie and van Mierlo, 2017; Hu et al., 2012; Astolfi et al., 2008;Ghumare et al., 2015). Recent studies have clearly shown the advantage ofusing a dynamic directed connectivity model in real applications using EEGmeasurements in epilepsy patients or during cognitive processing (van Mierloet al., 2017; Staljanssens et al., 2017; McDermott et al., 2017; Coito et al., 2016;Plomp et al., 2016).

In this study, we combined EEG source imaging using a subject-specific headmodel with time-varying PDC estimation. Based on the regions in the parietallobule selected based on the prior knowledge, we studied the underlyingconnectivity model which is directed, spectral as well as time-varying. UsingEEG data acquired during a spatial cueing paradigm, we investigated timevarying connectivity specific to directing attention to the left or the right andto the competition effect. We used a predefined set of regions for which westudied time-varying directed connectivity. These regions were selected basedon previous studies in our lab with a similar paradigm (Vandenberghe et al.,2005; Gillebert et al., 2013; Neyens et al., 2017). EEG source estimation wasapplied separately for the cue locked and stimulus-locked data.

6.2 Methods

6.2.1 Subjects

14 right-handed healthy volunteers, between 18 and 35 years of age, withnormal or corrected to normal vision, without a personal or family history of aneuropsychiatric or an ophthalmological disorder and not taking any neurotropic


drugs were recruited amongst university students from the Biomedical Sciencesgroup of the University of Leuven and hospital personnel of the UniversityHospitals Leuven through advertisements. The experiment was approved bythe Ethics Committee of the University Hospital Leuven (S51126) and wasperformed according to the World Medical Association Declaration of Helsinki.All subjects provided informed consent. Inclusion criteria were assessed using aquestionnaire. Subjects with a handedness score below 85%, quantified usingthe Edinburgh inventory of handedness (Oldfield, 1971), were excluded.

6.2.2 Stimulus presentation and paradigm

Stimuli were presented using Presentation [14.2] (Neurobehavioral Systems,Albany, CA, USA) on a 17-inch liquid-crystal display with a vertical refresh rateof 60 Hz (Dell [type], Dell Inc., Austin, TX, USA). The eye-screen distance was70 cm. Experiments took place in a dimly lit room. Throughout the experiment,a white fixation cross with a diameter of 1.3° was continuously shown in thecenter of the screen, except when the cue was present.

At the start of the trial, a central symbolic cue was presented for 212ms. Thecue consisted either of a grey triangle pointing left (in 1/4 of the trials), agrey triangle pointing right (in 1/4 of the trials) or a grey square (in 1/2 ofthe trials) with a diameter of 1.3°. Subjects were instructed to perform theperipheral task following a triangle cue and to perform the central task followinga square cue. Following cue offset, there was a fixation only preparation intervalof 288 ms (in 1/2 of the trials) or 388 ms (in 1/2 of the trials). Subsequently,the peripheral and central stimuli were shown for 212 ms. The peripheralstimuli were circular grayscale sinusoid gratings, presented either unilaterally orbilaterally with a contrast of 90%, using four cycles per circle and five differentrandomized equidistant cycle phases. The grating was presented at a (gratingcenter) horizontal eccentricity of 5° with a diameter of 3.4°. In 1/2 of thetrials, the grating was rotated clockwise about a reference grating rotated 45°clockwise compared to a vertical grating and in the other 1/2, the grating wasrotated anticlockwise. The contralateral competing grating, present in 1/2 ofthe cases, could either be rotated anticlockwise (1/3 of the trials), not rotated(1/3 of trials) or rotated clockwise (1/3 of the trials) in reference to the referencegrating. The central stimulus was the 1.3° fixation cross with either the vertical(1/2) or the horizontal (1/2) line dimmed. There was an interval of 1650 msbetween target stimulus offset and the next cue onset. We defined the responsewindow between 50 ms after target stimulus onset and the next stimulus onset.A complete run consisted of 192 trials.

Subjects were instructed to continuously fixate at the center of the screen.

METHODS 97

Following a peripheral cue (triangle), subjects were asked to judge if theperipheral target grating was rotated clockwise or anticlockwise. There were noinvalid cues. Following a central cue (square), subjects were asked to discriminatewhich of the lines of the fixation cross had dimmed. Subjects had to respondby pressing the left button (Cedrus RB-820, Cedrus Corporation, San Pedro,CA, USA) for anticlockwise gratings or vertical lines dimmed, and the rightbutton for clockwise gratings or horizontal lines dimmed, using the index fingerof the right hand (speeded two-choice task). They were instructed to press abutton as soon as they were sure about their answer and before the next cue.All subjects performed 1 or more practice runs, 2 or more titration runs andfinally four runs that were used for the analysis. In case the investigator noticedfixation problems on the electrooculogram (EOG), the subject was informedto maintain fixation. In case the subject kept making frequent errors at theend of a practice run, additional practice run(s) were done. After the practicerun(s), the grating deviance to the reference stimulus and the line dimming ofthe fixation cross were titrated for every subject, until an accuracy of around80% was reached. Titration was performed to assure the attentional load duringthe actual experiment was significantly high to constantly keep the subjectsmotivated to focus their attention and to have a comparable level of attentionbetween subjects. We used trials in the conditions as described in table 6.1.

Condition label DescriptionCondition-1 the peripheral attention task of a single target grating

appearing in the left hemifieldCondition-2 the peripheral attention task of a single target grating

appearing in the right hemifieldCondition-3 the peripheral attention task of a grating appearing

in both hemifields with the target in the left hemifieldCondition-4 the peripheral attention task of a grating appearing

in both hemifields with the target in the right hemifieldControl-1 the central attention task while a grating appeared

in the left hemifieldControl-2 the central attention task while a grating appeared

in the right hemifieldControl-3-4 the central attention task while a grating appeared

in both hemifields

Table 6.1: List of conditions and corresponding control tasks


6.2.3 MRI data acquisition

For each subject, a structural scan was acquired using a 3T Philips Achievaequipped with a 32-channel head volume coil according to a T1-weighted 3Dturbo-field-echo sequence (repetition time=9.6 ms, echo time=4.6 ms, in-planeresolution= 0.97 mm, slice thickness=1.2 mm).

6.2.4 EEG recording and processing

EEG acquisition was performed with a WaveGuard 64-channel EEG cap,following the 10/20 system of electrode placement, an Advanced Source Analysis(ASA) amplifier at a sampling frequency of 1024 Hz and a resolution of 22 bit,using active shielding and the ASA software version 4.6.0.8 Advanced NeuroTechnology (ANT), Enschede, The Netherlands). During all measurements,impedances for all electrodes were kept below 5 kΩ. Data were acquired withAFz as common hardware reference and were stored with the linked mastoidelectrodes as a reference. Both a horizontal and vertical EOG were recorded.During the EEG session, 3D electrode layouts positions for each participant weredigitized with reference to subject’s nasion (NAS), left and right pre-auricular(LPA and RPA) positions using the Brainsight (Rogue Research, MontrealCanada).

Recorded EEG data were bandpass filtered using ASA software version 4.6.0.8and Experiment Manager version 8.8 (ANT, Enschede, The Netherlands), witha high-pass filter of 0.3 Hz and a low pass filter of 40 Hz using a slope of 24dB. Further data processing was done in MATLAB R2014b (The MathWorksInc., Natick, MA, USA), with the following MATLAB toolboxes and plugins:signal processing toolbox, EEGlab version 9.0.8.6b (Delorme and Makeig, 2004),ANT EEGlab import plugin version 1.09 (ANT, Enschede, The Netherlands)and Automatic Artifact Removal (AAR) 1.3 (R060409) plug-in for EEGLAB(http://www.cs.tut.fi/ gomezher/projects/eeg/aar.htm). In case the subjectcorrected his/her response, the response latency was defined as the latency ofthe first response, but the interpretation (correct/incorrect) of the response wasmade on the corrected response. Muscle artifacts were subtracted with the AARplugin for EEGlab relying on a blind source separation technique using canonicalcorrelation (Wim De Clercq et al., 2006). Blink artifacts were subtracted usingthe second order blind identification (SOBI) algorithm (Belouchrani and Abed-Meraim, 1993). The source correlating best with a subject specific blink artifacttopography map, was subtracted from the corresponding EEG data segment,provided the correlation exceeded a predefined heuristic threshold of 0.9. Further,the data were re-referenced to the average reference and downsampled to 256Hz.

METHODS 99

Subsequently, data were epoched to obtain 2 different set of data, first lockedat cue onset and second locked at grating onset. Baseline subtraction wasperformed. The baseline was defined between 200ms to 0ms relative to cue onsetwhich correspond to -600 ms and -400 ms relative to grating onset. Epochscontaining signals above 75 µV or below -75 µV in any channel between thestart of the baseline and the end of the epoch were rejected. Epochs withincorrect responses, misses or responses outside of the response window, werealso rejected. EOGs were visually scored, and subjects showing frequent saccadeswere excluded from the analysis. For the behavioural analysis, we calculatedresponse time and percentage accuracy (number of correct responses/totalnumber of trials) in each subject for each.

6.2.5 Processing for source modeling

Tesselated cortical, inner skull, outer skull, and scalp surfaces of each subjectwere obtained using segmentations of the subject specific structural scan inBrainsuite software (version BrainSuite v.15b 64-bit Windows) (Shattuck andLeahy, 2002). Further processing was done in Brainstorm software (version170528) which is an open source application for source modeling (Tadel et al.,2011). The segmented brain surfaces, MRI, EEG layout and 3D electrodepositions were imported into Brainstorm. Using a 3D distance minimizationalgorithm, the electrode layout was co-registered with the subject specific MRI.

The forward matrix was estimated with the symmetric Boundary ElementMethod (BEM) (Gramfort et al., 2010) implemented in Brainstorm. The BEMmodel consisted of three layers: skin, skull, and brain (including CSF) withrelative values of the conductivities set as 1, 0.0125 and 1 S/m respectively (Qinet al., 2010; Ahrens et al., 2012). The brain sources were limited to the corticalsurface with vertex points in the range of 15000-15200 based on the individualanatomy. We obtained the cortical current density time-series for each epochusing a distributed linear inverse solution. We used minimum norm estimate(MNE) based standardized low-resolution brain electromagnetic tomography(sLORETA), implemented in Brainstorm.

The noise covariance of the EEG data required for the inverse estimationwas calculated using the baseline period of all the trials per subject. Off-diagonal elements of the noise covariance were discarded to model uncorrelatedmeasurement noise (Engemann and Gramfort, 2015). Due to a large numberof trials used for noise covariance calculation, no further regularization wasapplied (Engemann and Gramfort, 2015). Using the diagonal noise covariance,we estimated the whitening operator required for whitening of the scalp data.The regularization parameter (λ) required for MNE is related to the level of

100 TIME-VARYING CONNECTIVITY IN THE PARIETAL CORTEX DURING VISUOSPATIALATTENTION

noise present in the whitened measurements. In Brainstorm, this regularizationparameter is selected based on the amplitude SNR of the data. We applied thewhitening operator from each subject to each EEG trial to obtain whitenedmeasurements before estimating the SNR. The data covariance was calculatedusing all the whitened trials. Further, eigenvalues of the data covariance matrixwere calculated, and the highest eigenvalue was considered as the signal andthe remaining as the noise. The mean of the noise related eigenvalues was usedas the average power of noise (σnoise) in the data. For the EEG data of timeseries y ∈ R M×N×K measured in M channels with N samples and K trials,the signal power Psignal was calculated (Hamid et al., 2014) as:

Psignal =

K∑k=1

N∑n=1

M∑m=1|y(m,n, k)|2

MNK− σnoise (6.1)

dividing both sides by the noise power (σnoise) we obtained the power SNR as

SNRpower =

K∑k=1

N∑n=1

M∑m=1|y(m,n, k)|2

σnoiseMNK− 1 (6.2)

Finally, a square root of this value was used in Brainstorm for source modeling.This was done for each subject. Sources were obtained with sLORETA witha dipole orientation constrained orthogonal to the cortical surface. A sharedinverse kernel was obtained for each subject and was applied to each EEG trialseparately to obtain source time series for each trial.

6.2.6 Regions of interest and time series extraction

We selected 7 different regions based on previous studies on visual spatialattention performed with an experimental paradigm containing bilateral stimuli.We selected middle and posterior IPS (mIPS and pIPS), fusiform gyrus (FG)bilaterally, and right inferior parietal lobule (IPL) (Vandenberghe et al., 2005;Gillebert et al., 2013; Neyens et al., 2017). A previous study using fMRIshowed the role of middle and posterior IPS in the endogenous selection andthe processing of bilateral stimuli and attentional enhancement (Vandenbergheet al., 2005). Furthermore, another study using a hybrid cueing paradigmshowed a diverse role of cytoarchitectonic areas of IPL in attentional selectionbetween competing stimuli and spatial reorienting based on the spatial patternof functional connectivity (Gillebert et al., 2013). The selected regions weredefined based on a probabilistic cytoarchitectonic atlas in SPM (the anatomytoolbox) as described in table 6.2 (Eickhoff et al., 2005). The fusiform gyrus

METHODS 101

was selected as the combination of area FG1 and FG2, the middle IPS was acombination of area hIP1, hIP2 and hIP3 and for the IPL area right PF wasselected as described in table 6.2. The volume of interests from the anatomytoolbox were transformed to surface regions using the Colin27 template inBrainstorm. We selected two more regions in the left and right Posterior IPS(pIPS). For pIPS, we used MNI coordinates described in a previous study(Neyens et al., 2017). The dipoles corresponding to the MNI coordinates weredetermined, and the final ROI was generated by including all dipoles in a10cm2 area along the cortical surfaces with the selected dipoles as a seed. Foreach subject, the surface regions from the Colin27 atlas were transformed tosubject space using the transformation calculated in Brainstorm. To obtain thetransformation, for each subject’s anatomy, a co-registration with the Colin27template was computed using a unified segmentation approach (Ashburner andFriston, 2005). As a result, seven subject-specific surface ROIs were used forfurther analysis.

Region Name in the atlas orMNI coordinates

Right fusiform gyrus (FG R) Right area FG1+ Area FG2Right middle Intraparietal sulcus (mIPS R) Right area hIP1+ hIP2+ hIP3Right posterior Intraparietal sulcus (pIPS R) (16, -86, 34)Right inferior parietal lobule (IPL R) Right area PFLeft fusiform gyrus (FG L) Left area FG1+ Area FG2Left middle Intraparietal sulcus (mIPS L) Left area hIP1+ hIP2+ hIP3Left posterior Intraparietal sulcus (pIPS L) (-20, -86, 30)

Table 6.2: Regions selected from (Eickhoff et al., 2005; Neyens et al., 2017)

For each ROI, the dominant direction of the dipoles was identified by singularvalue decomposition of the direction vectors and the signs of the time seriesof all dipoles were flipped when the direction was >=180 degrees deviatingfrom the dominant direction. We extracted time series for each ROI froma single representative dipole to avoid averaging the data which can lead toadditional smoothing and frequency doubling (Coito et al., 2016; Rueda-Delgadoet al., 2017; Sohrabpour et al., 2016). To obtain the time series in a singlerepresentative dipole, we calculated the average time series across dipoles inthe ROI and the individual dipole time series correlating best with this averagetime series was selected for further analysis (Chapter 4). The dipole selectionwas performed using all the trials per condition per subject. By using a separatedipole selection for each condition takes into account any anatomical dissociationwithin the ROI between different conditions (Gillebert et al., 2013). Finally, persubject and per condition, multi-trial time series of each ROI were obtained.


6.2.7 Time varying connectivity estimation

Time varying connectivity estimation was performed separately for each dataset,locked at the cue or grating onset, for each condition and each subject. For eachsubject, we estimated the model order p required for multivariate autoregressive(MVAR) modeling. This was done using all the trials irrespective of theconditions. As a criterion to find the optimal model order, we used the AkaikeInformation Criterion (AIC). We fixed the model order across subjects by takingthe rounded average model order. An additional comparison of the frequencyspectrum of the data using a non-parametric Welch with parametric Burgmethod was made to check the quality of the selected model order.

To fix the update coefficient (UC), we estimated time varying MVAR for eachsubject and calculated the frequency power spectrum for the range of UC values.Based on the spectrum, UC required for time varying MVAR estimation was setat 0.001. We used the general linear Kalman filter (GLKF) for the estimationof the time-varying MVAR model (Milde et al., 2010; Ghumare et al., 2015).We estimated the time-varying MVAR model per condition and per subject.The time-varying MVAR parameters were transformed to the frequency domain,and partial directed coherence (PDC) was calculated in the frequency range of1-40 Hz. We used the squared values of PDC since squared values show superiorsensitivity to the underlying connectivity and can be interpreted in terms ofthe fraction of the source power (Astolfi et al., 2006).

6.2.8 Time frequency analysis

We obtained the spectral power of each subject using Welch algorithm in thefrequency range 1-40 Hz with 1 Hz bins. This was done including all trialsregardless of the condition. We used a 0.5 s sliding Hanning time windowwith a 50% overlap. We identified spectral power peaks in each subject. Thefrequency bands were defined for the whole group taking into account variabilityacross subjects, and these were used in the connectivity analysis. Based on thisanalysis, we selected standard frequency bands as Delta (1-3Hz), Theta (4-7Hz),Alpha (8-13Hz) and Beta (14-30Hz) for the further analysis.

6.2.9 Statistical analysis

For cue locked data, we looked at the contrast between different types of thecue to study the differential effect. We averaged time-varying PDC values ineach frequency band identified in the previous step. For statistical analysis,we compared the PDC values in each frequency band between each pair of

RESULTS 103

cue type (cue indicating attention to the left, right or central) using a pairedrandom permutation test. The statical threshold was set to 0.05 corrected forthe number of directed connections, which in our case was 42.

For grating locked data we averaged the time-varying PDC values in eachfrequency band identified in the previous step. To observe the effect specific toperipheral attention, PDC connectivity values of control tasks were subtractedfrom the corresponding PDC values of the peripheral task in each subject. Weobtained subtracted PDC maps for the following conditions:

1. single left (condition-1 - control-1)

2. single right (condition-2 - control-2)

3. double left (condition-3 - control-3-4)

4. double right (condition-4 - control-3-4)

Using a paired random permutation test, we calculated the main and interactioneffects of the number of gratings (double or single) and the hemifield of theexpected target (left or right). The statical threshold was set to 0.05 correctedfor the number of directed connections.

6.3 Results

6.3.1 Cue related effects

To study the cue-related effects, we analyzed the data locked at cue onset fora period of 500ms after cue onset. We analyzed three pairs of contrasts ofcue orientations. The results are depicted in figure 6.1. Comparing the cue tothe left with the cue to the center, we observed a decreased directed influencefrom left fusiform gyrus to right mIPS in the delta band. This effect was alsomoderately present when comparing the cues to the right and to the centerbut it did not reach significance at the corrected level. Furthermore, we founda decreased influence from right mIPS to left mIPS in the delta band whena cue to the left was shown compared to a cue to the center. This effect wassignificant during the cue presentation as well as in the period thereafter (thedelay period). In the same delta band, we also found a decreased influence fromright pIPS to right IPL very early after cue onset. However, when a cue to theright was shown, these effects did not reach significance. In the other frequencybands, no significant difference between the cue to the left or right versus cueto the center was found. When directly comparing the cue to the right with


the cue to the left, we found a significant increased influence from right pIPSto right IPL in the delta band in the delay period and in the theta band veryearly after cue onset.

Figure 6.1: Time varying PDC connectivity for the cue locked data for threedifferent contrasts of the type of cue

6.3.2 Grating related effects

We analysed the main and interaction effects of the number of gratings (singles vsdouble) and the direction of attention (left vs right) using a random permutationtest with 5000 realisations. The analysis was limited to the time period fromstimulus onset up to 850ms thereafter. The influences described below are based

RESULTS 105

on substracted squared PDC values calculated by substracting the squared PDCvalues of the central attention task from the values from the correspondingsensorially matched peripheral attention condition.

We observed significant main effects for the number of gratings (single vs double)in different frequency bands as depicted in figure 6.2. In single grating trialscompared to double gratings, there was a lower directed influence for a briefperiod from left FG to left mIPS in the delta band. Similar significantly lowerinfluences during the single gratings were observed in the delta band for a longerperiod from right pIPS to left mIPS during the presence of the grating(s) andlater around 500-600ms after grating offset. Similarly, in the theta band, weobserved main effects with lower influence from right FG and right pIPS toleft mIPS after stimulus offset in single grating compared to double gratingtrials. In single gratings, the influence from left mIPS to right pIPS was lowerfor a brief period after the grating onset. In the alpha band, around 200msafter the grating offset, the directed influence from left mIPS to right pIPS wassignificantly lower during the double gratings. During the stimulus period anddouble gratings, a lower influence was observed from right FG to left FG inthe beta band. In single gratings, a lower directed influence was observed fromstimulus offset upto 500ms thereafter from right IPL to right mIPS.

We observed no significant main effects for the direction of the attention.

We observed significant interaction effects for time varying substracted squaredPDC values between the number of gratings and direction of attention indifferent frequency bands as depicted in figure 6.3. In the delta band, thedifference of the substracted squared PDC values between double and singlegratings was higher in left-sided target compared to right sided from left FGto left mIPS. This was also true for the influence from left FG to right mIPSbut at a later time (around 300 ms after stimulus offset). Furthermore, in thedelta band, the influence from right mIPS to right pIPS between double versussingel gratings was higher in trials with a left-sided target compared to a rightsided target in multiple time intervals (during the stimulus period, shortly afterstimulus offset and around 400-500 ms after stimulus offset).

In the theta band, the interaction effect was present for directed influences fromright FG to left mIPS after stimulus offset for a longer period. For the influencefrom right pIPS to right FG, there was an interaction effect lasting for a briefperiod around 500ms after stimulus offset. There were no significant interactioneffects found in the alpha band. In the beta band, interaction effects were alsofound in the directed influence from left to right FG as well as from right pIPSto right mIPS. In this latter case the interaction effect lasted for a longer periodfrom 100-500ms after stimulus offset.


Figure 6.2: The main effects of the number of gratings (singles vs double) forthe substracted time varying squared PDC connectivity

6.4 Discussion

We studied the time varying directed interactions between different areas ofthe parietal cortex in a visual spatial attention task. The task consisted of

DISCUSSION 107

Figure 6.3: The interaction effects between the number of gratings (singles vsdouble) and the direction of attention (left vs right) for the substracted timevarying squared PDC connectivity

a presentation of a single or double stimulus. We used a combined approachof EEG source modeling using subject-specific anatomy and time varyingconnectivity measured with partial directed coherence (PDC). The studiednetwork consisted of 7 regions selected on the basis of visuospatial attentionstudies using an experimental paradigm similar to the current study. Thesubtraction of squared PDC values between the task of interest and the


corresponding central task allowed us to remove sensorial effects. The resultingeffects can be attributed to peripheral attention. We observed several significantearly and late effects specific to the presentation of the cue or the numberof gratings (singles vs doubles). The competition trials, i.e. when double(bilateral) gratings are shown, require selection between two competing stimuliassociated with the direction of the prior spatial cue. Given the lower temporalresolution of fMRI, the measured activity usually reflects the sum of differentcognitive processes underlying the presentation of a spatial cue and gratings(Vandenberghe and Gillebert, 2015). A high temporal resolution technique likeEEG is better suited to investigate the timing effects.

After the cue presentation, the left FG exerted bottom-up influences to the rightmIPS. A significant bilateral communication between the right and left mIPSwas observed where the earlier significant effect might correspond to endogenousdirecting of attention to the left or right while maintaining fixation to thecentre whereas the later effect may correspond to sustained attention (Meehanet al., 2017; Vossel et al., 2012; Lauritzen et al., 2009). There was a significanttop-down influence from right mIPS to right FG in the delay phase. We alsofound an increased influence from right pIPS to right IPL immediately afterthe cue onset. However, this effect may not be specific to directing attentionsince it was present before the cue onset although it didn’t reached significance.

After the grating)(s) appeared, we found interactions from IPS to and frominferior parietal and fusiform gyrus in different frequency bands. Comparedto the posterior third of IPS, the middle part exerted and received moresignificant directed influences bilaterally. This supports the critical role of mIPSin competing stimuli (Gillebert et al., 2013; Vandenberghe and Gillebert, 2009).Interestingly, there was an interaction effect from FG to bilateral mIPS afterthe stimulus offset and these effects were more pronounced in doubles versussingle gratings when left-sided compared to right sided targets were shown. Theeffects might be due to the prolonged processing of the distractor (Schrootenet al., 2017) and were observed in different frequency bands in this study. In thebeta band, there a similar prolonged interaction effect was seen on the influencefrom right pIPS to right mIPS.

This study has a number of methodological limitations. The PDC measure isoutflow normalised and therefore any change in one outflow connection affectsthe PDC values of the other connections. Furthermore, we used substractedPDC which are also determined by the central task. We suspect that some ofthe effects can be driven by subtle differences in the task requirements. Thenumber of subjects was limited to 14 in this study, however further analysiswith more subjects is required.

Chapter 7

General discussion

In this chapter, we briefly summarise the most important findings of the thesisin section 7.1 and suggestions for future research directions are given in section7.2.

7.1 General Conclusion

The estimation of time varying connectivity requires careful selection of theimaging modalities and consideration as well as validation of several technicalsteps. Throughout this work, we discussed methods to calculate time varyingconnectivity from the sources of real EEG data or EEG data generated withsimulations. We applied the methods to understand the dynamic connectivityunderlying the visuospatial attention tasks. We proposed a pipeline for theEEG source modeling and the calculation of time varying connectivity (Chapter2). We applied phase synchronisation based time varying connectivity in ECoGdata to investigate timings of the directed interactions occurring at a partof the parietal cortex during attentional reorienting and attention selection(Chapter 3). In the next stage, using simulated data, we investigated moreadvanced techniques for time varying connectivity based on MVAR modelingusing Kalman filtering and a Granger causality based measure, more specificallypartial directed coherence (PDC) (Chapter 4). We simulated more complexconnectivity model to investigate the dipole selection to extract the time seriesfrom of estimated sources and further validated Kalman filtering approaches(Chapter 5). Finally, we applied this technique to EEG data acquired in avisuospatial attention experiment in a group of healthy subjects to understand

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the connectivity among regions in the parietal cortex during visual spatialattention (Chapter 6).

We started with constructing a pipeline for source modeling from surface EEGdata and the calculation of time-varying connectivity from the estimated sources.For EEG source modeling, several algorithms have been proposed. Due to thelimited number of EEG channel data available to estimate a large number ofsources, the estimation is underdetermined. The conventional way to overcomethis problem is to perform single dipole (source) fitting of the EEG data orindependent components of EEG. However, this approach is limited by theselection of a single or a few dipoles (Grech et al., 2008). Therefore, data-drivenapproaches based on distributed source modeling are proposed. The mostcommonly applied approaches are Minimum Norm Estimate (MNE) and itsweighted formulation (wMNE), low-resolution brain electromagnetic tomography(LORETA) and its standardised version (sLORETA), LAURA, MUSIC andbeamforming (Becker et al., 2015; Song et al., 2015). However, among all thesemethods, sLORETA requires minimal modeling assumptions and produces nodepth localisation errors (Pascual-Marqui, 2002). Superior approaches comparedto sLORETA for the localisation of multiple sources are proposed (Jatoi et al.,2014; Wagner et al., 2003; Dümpelmann et al., 2012; Saha et al., 2015). However,these approaches still require more study to understand the behavior of thesealgorithms in different situations. Furthermore, the source localisation accuracygreatly depends on the accuracy of the head model. Using head models derivedfrom the individual subject specific anatomy, sLORETA may become a valuableapproach as applied in this work (Saha et al., 2015).

As mentioned before, the head model construction is a crucial step for accuratesource modeling. In this thesis, we used a 3-layer realistic head modelconstructed using a symmetric boundary element method. Furthermore, bymodeling anisotropic conductivity in the different tissues by a finite elementmethod (FEM), an even higher accuracy can be obtained compared to surface-based models (Mosher et al., 1999; Vorwerk et al., 2017). However, using moretissue classes like skin, fat and muscle, grey and white matter, brain stemand eye, a better reconstruction can be obtained (Liu et al., 2017). ClassicalBEM is based on an integral formulation of double layer potentials. Comparedto classical BEM, symmetric BEM is based on a combination of single aswell as double layer potentials and this method is demonstrated to be muchmore accurate. Furthermore, based on the relative difference measure (RDM)calculated using an analytical reference solution, the superiority of symmetricBEM compared to FEM was shown (Clerc 2010, Vorwerk 2012). However, thenumber of layers in symmetric BEM is limited to 4 because the layers need tobe encapsulated. In contrast, FEM can use a higher number of tissue classesand respective conductivities and in that case, FEM will outperform symmetric

GENERAL CONCLUSION 111

BEM (Liu 2016). However, we must take into account the segmentation qualitywhich can drop if we include more tissue classes as well as the computationalcost of FEM. In our pipeline, we have limited the analysis to symmetric BEMand have included the most essential tissue classes, i.e, skin, skull and braintissues (CSF, GM, WM) (Vorwerk 2014).

To investigate the connection between different brain areas several connectivitymeasures are proposed. The measures differ based on the underlying assumptionof the connections and dimensions that they can measure (Cekic et al., 2017; Millet al., 2017a; Hassan et al., 2017; Mill et al., 2017b). The traditional correlation-based measures can lead to spurious connectivity due to the presence of indirectlinks. To overcome this problem, partial correlations are applied (Vandenbergheet al., 2013). However, partial correlations do not give information about thedirection of the connections. Furthermore, to estimate time-varying connectivitycorrelations can be calculated in short time windows. The extent to whichthe connectivity can capture the changes strongly depends on the size of thewindow. Granger causality and phase based connectivity measures are superioralternatives in such case (Cekic et al., 2017). They can give information aboutthe direction of the connectivity as well as the time-varying interaction betweenbrain areas.

We mainly focused on two approaches (1) time-varying multivariate autore-gressive modeling (TV-MVAR) of the data followed by calculation of partialdirected coherence (PDC), a Granger Causality (GC) based multivariate spectralmeasure. There are several forms of Granger causality measures available in theliterature and the most common alternative for PDC is the directed transferfunction (DTF). However, DTF suffers from spurious connectivity due to theindirect links. Therefore, direct DTF (dDTF) was proposed to overcome thisproblem. However, squared values of PDC can be put in direct relation with thesource power. This makes it more sensitive to the underlying causal interactioncompared to DTF or dDTF (Astolfi et al., 2008, 2006). PDC measure is basedon linear MVAR models. The nonlinear relationships across time series canalso be described effectively with linear MVAR models (Astolfi et al., 2008,2006). In a previous study (Winterhalder et al., 2005) linear MVAR models wereapplied to simulated data with nonlinear coupling and it was demonstrated thatMVAR models are sensitive in detecting nonlinear interactions in multivariatesystems (Astolfi et al., 2008). (2) In a second approach, the phase lag index(PLI), a phase synchronisation based measure, was used. We also used PLIweighted with the cross-spectral power, referred to as weighted PLI (wPLI),to improve the noise performance. The latter measure is relatively invariantagainst the presence of common sources (e.g. volume conduction or activereference electrodes) (Kida et al., 2016). Compared to different phase lockedmethods, wPLI allows to pick up the connectivity changes specific to true phase


lags. Based on the sign the wPLI value, the direction of the connection can beestimated, and this is an advantage compared to other phase-based methods.However, wPLI still suffers from the issue of indirect connection.

In the first study, we applied the time-varying connectivity framework toelectrocorticography (ECoG) data acquired during a visual spatial attentiontask. To study connectivity between different channels, the weighted Phase LagIndex (wPLI) was calculated in each condition (Kida et al., 2016). Unlike EEG,for ECoG data, the solution of EEG inverse problem is not required as it ismeasured at the cortical surface at much higher SNR. The study provided forthe first time the electrophysiological signature of the spatial shifting signal inresponse to an invalidly cued spatial cueing trial in the superior parietal lobule(SPL). A number of studies have investigated the connectivity to understand themechanisms specific to different attention processes (Meehan et al., 2017; Weiszet al., 2014; Vossel et al., 2012; Prado et al., 2011; Lauritzen et al., 2009). Thesestudies uncovered the directed influences between IPS and frontal eye fields andthe occipital cortex. Furthermore, based on fMRI studies, the critical role ofSPL in attentional reorienting was highlighted (Caspari, 2015; Vandenbergheet al., 2012; Gillebert et al., 2013). Based on time-varying connectivity, wewere able to understand changes in the direction of the influence between IPSand SPL in invalid trials. Furthermore, a prolonged effect was observed fromanterior IPS to middle IPS regions which can be due to a higher cognitiveload in competition trials. Such observations are not possible with undirectedtime-invariant connectivity. In the ECoG study, we had only a limited coverageof the brain and investigation of the influences from SPL to other regions in alarge-scale network and vice versa is an interesting question for future research.

Then, we moved a step further by comparing methods to estimate the timevarying connectivity based on PDC. In these methods, an accurate estimationof the time varying MVAR model is essential. The Kalman filtering basedapproaches such as the classical Kalman filter (CKF) and the General LinearKalman filter (GLKF), offer a robust framework to MVAR estimation. Theresults indicated that based on accuracy and computation time, GLKF is thebest choice in most cases except when the number of trials is too low. Here, itimportant to understand that the accuracy of MVAR estimation greatly relieson the number of data points available to estimate the model (Schlögl andSupp, 2006). This number depends on the number of channels and model order.Unlike conventional approaches for Kalman filtering based MVAR models, thelength of time series is not an influential factor because the model is estimatedat each time point. In the implementation of CKF the single trial data arereplicated using the Kronecker product to have sufficient data for reliable modelestimation (Schlögl, 2000, 2002). However, this is not the case for GLKF wherethe number of data points depends on the number of trials used. Depending on

GENERAL CONCLUSION 113

the SNR, a certain number of trials are required for reliable estimation (Toppiet al., 2014, 2012). Hence, the number of trials and SNR are the crucial factorsin the comparison as applied in this study. Furthermore, dual extended Kalmanfilter can be applied to uncover the nonlinearity in the data (Rajabioun et al.,2017; Omidvarnia et al., 2011). However, nonlinear approaches still require acareful validation. A Kalman smoother can be applied in addition to CKF andGLKF and during this operation, the MVAR estimates of previous time pointsare smoothed based on the current time point Hu et al. (2012). However, inour work, we did not find any noticeable improvement using this approach in apreliminary test. Although our study focussed on PDC measures, the findingscan be very well generalised to other measures based on the MVAR modelingbecause we also investigated the performance at the level of MVAR parameters.

The connectivity analyses require the definition of the regions of interest andconnectivity is estimated from the time series of the regions. There exist twobasic ways to obtain time series in a region: calculating an average time seriesin the region or determining a representative time series in a single dipolein the region. Due to the regularization of the ill-posed nature of the EEGsource modeling problem when using sLORETA, the sources are smooth, andaveraging would lead to a destruction of phase information and dynamics, leadingto inaccurate connectivity metrics. To overcome this problem, a selection of asingle dipole to extract the time series is often applied. We showed that thedipole with time series showing the highest correlation with the region averagetime series also showed the highest correlation with the ground truth time seriesand it has the lowest localisation error compared to other strategies. The areaof the ROI can play a crucial role here, however, in our analysis we used avariable size of the ROI to investigate this issue.

Later, we studied temporal networks related to a visual spatial attentionexperiment in the human brain. The role of the parietal lobe in visual spatialattention is well established. However, there exist anatomically and functionallydissociable regions in the parietal lobe. To uncover the mechanisms of attention,the underlying connectivity between parietal regions need to be investigated.We applied EEG source modeling combined with time-varying connectivityestimation based on partial directed coherence. With this approach, we studieda directed network at high temporal resolution using pre-defined regions mainlyin the parietal lobe.


7.2 Future research directions

In this thesis, several aspects of time-varying connectivity and their applicationto understand visual spatial attention are presented. However, as a new field,there are still a lot of open questions which need to be addressed in thefuture. Here we discuss several important ideas which might be interestingand important. First, there are several formulations of PDC proposed inthe literature. A clear validation and comparison of these PDC and othermeasures are required. Second, such connectivity approaches can be studiedwith a much more accurate head model. Furthermore, regional time seriesextraction strategies can be improved. Third, more careful attention to thestrategies to integrate fMRI information with time varying connectivity fromEEG is required to obtain high spatiotemporal resolution networks. Fourth, itis important to investigate how we can constrain the time varying functionalconnectivity based on structural connections to relate brain function to anatomy.Fifth, investigation and development of graph theoretical metrics of temporalnetworks are increasingly required. In the following subsections, we describethese issues or ideas step by step.

7.2.1 Partial directed coherence (PDC)

Since PDC was first introduced, several formulations have been proposed inorder to improve the interpretation (Toppi et al., 2016; Baccalá and Sameshima,2001). The squared versions of outflow (column) normalised PDC is usuallyadopted, due to a higher stability and accuracy. However, in order to improvephysiological inference, inflow (row) normalised PDC (rPDC) was proposed(Plomp et al., 2014). The results from rPDC indicated better temporal resolutioncompared to column-wise normalized PDC. However, to our knowledge, the row(inflow) normalisation or column (outflow) normalisation of PDC should dependon the research questions under investigation. Furthermore, weighing of thePDC with the instantaneous spectral power of the source node was proposed(Plomp et al., 2014). This allowed more clearer identification of critical drivers.However, in case of EEG source modeling, the time series from the region canhave a huge impact on the scale because of varying depth of the sources andregularisation or smoothing. In such a case, weighting PDC with the power canbe misleading, and this is an important issue to investigate further. Furthermore,another optimisation includes renormalized PDC that also allows calculation ofstatistical properties of the PDC and improved interpretation (Schelter et al.,2009; Gao et al., 2015). From the group proposing PDC for the first time,two more formulations have come up. First one was generalised PDC to dealwith the effect of scale difference between time series (Baccala et al., 2007) and

FUTURE RESEARCH DIRECTIONS 115

second information PDC to interpret PDC in relation to information theory(Takahashi et al., 2010). Despite several formulations described, it is worth toperform a clear validation or comparison of the formulation and its relation tounderlying true connectivity.

7.2.2 Source modeling and dipole selection

The estimation of time-varying connectivity is more challenging when EEGcortical sources are estimated. This requires not only a more accurate headmodel and inverse model but also careful selection of time series to estimatethe connectivity. In this thesis we used a 3-layer realistic head model, howeverwith more detailed segmentation of the head tissue up to 6 or 12 compartmentscan be obtained (Liu et al., 2017). Furthermore, volume-based head modelsusing finite element methods (FEM) are considered more accurate compared tosurface-based models (Mosher et al., 1999; Vorwerk et al., 2017). There is alsoroom for improvement in the quality of the segmentation of the individual tissueclasses, mainly high resistive skull (Lanfer et al., 2012). It will be importantto investigate how the accuracy of the head model will affect the estimatedconnectivity structure. The connectivity results between estimated sources arequite variable across different EEG inverse methods (Mahjoory et al., 2017).This leads to considerable uncertainty in the results. Further comparison ofdistributed source modeling methods to estimate time-varying connectivity isan important investigation to carry out. Furthermore, depending on the inversemodeling one or more parameters need to be carefully selected. In case ofminimum norm-based methods, the selection of the regularisation parametersis required (Hincapié et al., 2016; Engemann and Gramfort, 2015). Theseparameters impose the smoothness of the solution and can greatly influencethe time series amplitude and fluctuations leading to an erroneous result. Forfuture research, it will be important to consider the effect of such parameters.

7.2.3 EEG-fMRI integration

In this thesis, we focused on the analysis of networks derived from a singlemodality, i.e. EEG. However, to obtain cortical sources, EEG inverse modelingis required. To overcome the ill-posed nature of the modeling, a regularisation isimposed. This results in much lower spatial resolution in EEG compared to fMRI.Approaches to integrate fMRI/EEG functional data are receiving attention (Leiet al., 2011; Babiloni et al., 2005). But these studies are restricted to integrationat the level of the activities between individual modalities. Obviously, eachmodality has specific advantages, but they also have limitations. Both modalities


give information about the functional relationships among regions. By combiningthese modalities, we can construct and study a directed dynamical functionalnetwork with higher spatial resolution. Usually, fMRI information is used asprior information for EEG source modeling (Lei et al., 2011; Babiloni et al.,2005). However, in another approach, fMRI information was used to select theregions of interest for connectivity analysis (Plomp et al., 2016). The strategiesto integrate fMRI and EEG need further study to better understand the meritsand weaknesses of the different approaches.

7.2.4 Structurally constrained functional connectivity

The relation between human brain function and its structure is not yet fullyunderstood at region and network level. There is great urge to study functionaland structural properties of these networks, and their relationship as these willlead to further insights into a basis for information processing, perception andcognition in the human brain. With functional connectivity, we often estimatea relation between two regions which may be structurally indirectly connectedthrough some other region. The functional connections should be constrainedby the underlying structural connections. This will lead to a functional networkmore closely related to the underlying biological network. This calls for theinvestigation of how prior knowledge of structural connections can be used toconstrain functional connectivity estimates between a pair or set of regions.Recently, such an approach was demonstrated with real and simulated datafor partial correlations measured with Gaussian graphical models to constrainestimates of partial correlation coefficients (Guillemot et al., 2013). In anotherapproach, a correlation of structural connectivity derived from diffusion imagingwith EEG time varying functional connectivity was calculated (Amico et al.,2017). In another study, functional connectivity was mapped on the fibre tractand time varying connectivity was estimated (Calamante et al., 2017). Anotherstrategy includes formulating a prior distribution for functional connectivitythat depends upon the probability of structural connectivity between brainregions (Xue et al., 2015). It is worth applying these strategies to more realmeasurements to understand and interpret cognitive processes.

7.2.5 Graph theoretical analysis of time varying directednetworks

Graph theoretical approaches have successfully uncovered the topologicalfeatures and quantification of biological connections. However, with stationaryor time invariant connectivity such quantification is limited to spatial features

FUTURE RESEARCH DIRECTIONS 117

of the network. With the advent of directed time varying networks, topologicalfeatures as functions of time and frequency can be estimated. In addition tospatial metrics, several temporal graph metrics can be estimated to understandtemporal hierarchy in the information processing (Nicosia et al., 2013; Tayloret al., 2017). The development of temporal graph metrics offers an excellentopportunity for future research to quantify the time varying networks.

Appendix A

Conflict of interest statement,Acknowledgements andPersonal Contribution

Conflict of interest statementThere are no conflicts of interest relevant to the thesis manuscript.

AcknowledgementsThe research of this PhD was funded by KU Leuven Grant OT/12/097, FWOgrants G0A0913N and G093616N, and Federal Wetenschapsbeleid Belspo Inter-University Attraction Pole Grant P7/11.

Personal ContributionFor the shared first author paper described in chapter 3 of this thesis: I wasmainly involved in the data analysis (ERP, ERSP, ITC and wPLI). For thewPLI analysis, I performed the conceptualization, methodology, implementation,analysis and writing. I repeated the ERP, ERSP and ITC analyses with differentsettings by modifying the scripts from Maarten Schrooten. I generated allthe figures in the manuscript together with some modifications by MaartenSchrooten. I was involved in writing and reviewing of the manuscript alongwith the other co-authors.

For the shared first author paper described in chapter 6 of this thesis: Istarted from EEG data, and MRI scans acquired and pre-processed by MaartenSchrooten. I performed the entire EEG source modelling pipeline and time-varying connectivity analysis. I performed the conceptualisation, methodology,

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120 CONFLICT OF INTEREST STATEMENT, ACKNOWLEDGEMENTS AND PERSONALCONTRIBUTION

implementation, analysis, figures and writing.

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Curriculum vitae

Personal DetailsEshwar Gorakhnath GhumareNationality of IndiaBorn on 4 September 1984Married

AddressIjzerenmolenstraat, 28/208, 3001, Heverlee, Belgium

ContactMobile: +32 499 89 66 59Mail to: [email protected]

Webhttps://www.linkedin.com/in/eshwargg/https://twitter.com/eshwargg

Research and Education2013 - 2017PhD in Biomedical Sciences (Brain connectivity)KU Leuven, BelgiumLaboratory for Cognitive Neurology, Dept. of Neuroscience

Title of the thesis: Time-varying connectivity in large scale networks in thehuman brainPromotor: Prof. dr. Patrick DupontImaging modalities: EEG, ECoG, MRI, fMRIHighlights: EEG source modelling • Connectivity methods/measures •Granger causality • Time-varying connectivity • Visuospatial attention •Simulations/real data • Integration of EEG/fMRI • Graph theory • Cognitiveneuroscience • Time-frequency analysis

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146 CURRICULUM VITAE

2012 - 2013Postgraduate studies in Advanced Medical ImagingKU Leuven, BelgiumFaculty of Medicine, KU LeuvenScore: Magna cum laude

Title of the thesis: The effect of preprocessing on the network derived from18F-FDG PET in Temporal lobe epilepsy: a Pilot study in brain imaging.Main subjects: Kinetic modeling using PET • MRI techniques in neuroimagingand cardiology • Ultrasound imaging• Image analysis • Graph theory •Advanced statistics

2002 - 2006Bachelor of Biomedical EngineeringUniversity of Mumbai, IndiaMGM college of engineering and technology, Navi MumbaiScore: DistinctionTitle of the thesis: Electrooculography and its applications.Main subjects: Medical imaging • Biomedical instrumentation • Signal andimage processing • Computer programming • Biomechanics

Experience2009 - 2012Innovation Engineer - R&DPhilips Healthcare, Pune, IndiaDiagnostic X-ray imaging systems for Cardiovascular and Neuro applications

2008 - 2009Service and Application EngineerPhilips Healthcare, Navi Mumbai, IndiaDiagnostic X-ray imaging systems for Cardiovascular and Neuro applications

2007 - 2008Service and Application EngineerAlpha X-ray Technologies, Navi Mumbai, IndiaDiagnostic X-ray imaging systems for Cardiovascular and Neuro applications

2006 - 2007Sales and Service EngineerBiomedicon systems, Mumbai, IndiaSurgical and Vessel sealing systems

2005 - 2005InternshipLarsen and Toubro (Medical Division), Mysore, India

CURRICULUM VITAE 147

Ultrasound imaging (2D, 3D and Doppler)

Professional Specialties and Summary:CathLab, C-arm, and X-ray generators • Service design and development• Verification and validation during new product release • Technical andclinical applications support • Radiation safety, and quality assurance tests •Diagnostic image quality • CompTIA CTT+ and PHILIPS Healthcare academycertified technical trainer • Service instruction manuals

Awards and Recognitions2013KU Leuven scholarship for doctoral studiesKU Leuven, Leuven, Belgium

20102 spot recognition awardsPhilips Healthcare, IndiaExceptional handling of technical escalations in Egypt and India

20061st prize in the national level technical paper presentation contestUniversity of Mumbai, IndiaPaper title: Electrooculography & its application

2000The Ideal Student of the yearSmt. Radhikabai Meghe Vidyalaya, Navi Mumbai, India

Other InformationReviewing activities: IEEE EMBS conference proceedings (4 page papers).

Volunteer experience: Organising travel trips for students as a part of IndianStudents Association Leuven (ISAL), a non profit organisation subsidised byKU Leuven (2015-2017).

Publications

Articles in internationally peer-reviewed academic journals :

Ghumare E., Schrooten M., Vandenberghe R., and Dupont P., A time-varyingconnectivity analysis from distributed EEG sources: a simulation study, BrainTopography, under second review.

Schrooten, M.*, Ghumare, E.*, Seynaeve, L., Theys, T., Dupont, P., VanPaesschen, W., and Vandenberghe, R., Electrocorticography of Spatial Shiftingand Attentional Selection in Human Superior Parietal Cortex, Frontiers inHuman Neuroscience, 2017. DOI: 10.3389/fnhum.2017.00240*shared first author

Wang, Y., Ghumare, E., Vandenberghe, R., and Dupont, P., Comparisonof Different Generalisations of Clustering Coefficient and Local Efficiency forWeighted Undirected Graphs, Neural Computation, vol. 29(2), pp. 313-331,2017.

Papers at international scientific conferences, published in full in proceed-ings :

Oral presentation

Ghumare, E., Schrooten, M., Vandenberghe, R., and Dupont, P., Comparisonof different Kalman filter approaches in deriving time varying connectivity fromEEG data, Proc. Annu. Int. Conf. IEEE Eng. Med. Biol. Soc. EMBS, 2015,pp. 2199–2202, 2015.

Meeting abstracts, presented at international scientific conferences :

Poster presentation

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150 PUBLICATIONS

Ghumare, E., Schrooten, M., Vandenberghe, R., and Dupont, P., Comparingtime-varying connectivity methods using simulated data of a visuospatialattention network, The Organization for Human Brain Mapping (OHBM).Vancouver, Canada, 25-29 June 2017.

Schrooten, M., Ghumare, E., Vandenberghe, R., and Dupont, P., Peripheralversus central visual spatial attention: an fMRI study, The Organization forHuman Brain Mapping (OHBM). Vancouver, Canada, 25-29 June 2017.

Vandenberghe R., Ghumare E., Seynaeve L., Dupont P., Van Paesschen W.,Theys T., Schrooten M., Dissociation between spatial shifting and attentionalselection in superior parietal cortex: An electrocorticography study. The annualmeeting of the Society for Neuroscience. San Diego, 2016.

Ghumare, E., Vunckx, K., Goffin, K., Wang, Y., Van Paesschen, W., Dupont,P., (2014). FDG-PET based connectivity in patients with mesial temporal lobeepilepsy with hippocampal sclerosis, The Organization for Human Brain Mapping(OHBM). Hamburg, Germany, 8-12 June 2014.

Acknowledgements

After finishing my bachelor studies in Biomedical engineering in 2006, I startedworking with Philips Healthcare India. In the year 2012, I decided to movetowards more challenging tasks in the field of medical imaging. I decided toquit the job and start postgraduate studies in Advanced Medical Imaging atKU Leuven. I was so glad to be at such a prestigious university known for itshigh-quality education and Research. My promotor Prof. Patrick Dupont wasthe first person I knew and met at KU Leuven. I was fortunate that based onmy motivation and performance during the postgraduate studies, he offered mea PhD position. Since then my PhD has been a thrilling adventure with twistand turns. It would not have been possible to complete it without the help,support and company of all the kind people, to whom I owe a debt of gratitude.

Beyond doubt, first and foremost, I am incredibly thankful to Prof. PatrickDupont for not only giving me an opportunity to start my PhD but also guidingmy thesis work with a noble vision, great wisdom, unlimited patience and tirelesshelp. He has always been a role model. He provided excellent support andencouraged me to become an independent, honest and high-quality researcher.His trust and care drove me through the difficult moments in my research. Iam thankful that in spite of his busy schedule, he was always finding the timefor me. I am flabbergasted by his resourceful nature and attention to minutedetails. His timely feedback, reminders and continuous attention helped memaintained a crisp balance between technical depth and multitasking. I haveundoubtedly learnt a lot from him, and his guidance is the foundation of myscientific career. He not only taught to be a high-quality scientist but also tobe a good and humble human. He will be remembered at every milestone I willachieve throughout my life. I am fortunate to have met him and proud of beinghis student!

I am also grateful to my co-promotor, Prof. Rik Vandenberghe for providingme with his deep expertise in cognitive neuroscience. His work and guidancehelped me realise how important and challenging it are to interpret different

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152 ACKNOWLEDGEMENTS

techniques about neuroscience-related questions. I am amazed and inspired byhis meticulous attention to the scientific details. I thank him for always showinggreat trust and recognition to my work. His valuable comments, discussionsand remarks are the cornerstone of my PhD. I feel privileged to have workedwith such a great scientist!

I would like to thank my dear colleague, Dr Maarten Schrooten for anextraordinary collaboration during my PhD. The acquired and preprocesseddata and tools developed by him are the essential foundations of my PhD. He isingenious and a great team player who is always willing to give the extra mileto get the job done. I am astonished by his technical ability and programmingskills being a medical doctor. You are simply outstanding!

I would like to acknowledge and thank the members of my thesis committee,Prof. Frederik Maes, Prof. Dante Mantini, Prof. Pieter Van Mierlo and Prof.Laura Astolfi for their comments and feedback to elaborate this thesis and theirparticipation in the examination. The timely feedback and suggestions from myinternal jury members, Prof. Frederik Maes and Prof. Dante Mantini, have keptme on track in pursuing this PhD. It is also a great honour for me to have Prof.Pieter Van Mierlo and Prof. Laura Astolfi in my examining committee. Thecritical and constructive comments and suggestions I received have improvedthe work substantially. I would also like to thank Prof. Rudi Vennekens forchairing the thesis committee.

It was great to have the fantastic and friendly working atmosphere in ourgroup, and gratitude goes to all my dear colleagues at Laboratory for cognitiveneurology: Gabriella Liuzzi, Jolien Schaeverbeke, Veerle Neyens, Yu Wang,Rose Bruffaerts, Qian Ran, Tarik Jamoulle, Silvy Gabel, Karen Meersmans,Kate Adamczuk. I would like to say thank you for all the support and thenice moments during discussions in the office, the lunch, the parties and on allpossible occasions. Many of you have become real friends in the meanwhile.Special thanks to Gabriella, Jolien, Veerle and Yu Wang for always willing tohelp me on several technical and neuroscience issues. I still remember the daywhen Gabriella and Jolien suggested and recommended me to one of the visitingprofessors for a postdoc position. Your great sense of care and trust on severaloccasions mean a lot to me. You guys are awesome!

My special thanks to Prof. Dante Mantini and Dr. Quanying Liu for dedicatingtime to guide me through the NET toolbox they are developing and severalscientific discussions. Many thanks to Prof. Jan Van den Stock for alwayshelping me with the technical as well as social issues and being a great friend. Ithank colleagues from the other labs Mansoureh, Ehsan, Flavio, Yun-An Huangfor all technical discussions.

ACKNOWLEDGEMENTS 153

I must mention some of the unsung heroes in my life who motivated me to cometo Leuven and start the PhD. The first and foremost Dr. Janaki Rangarajan,who gave me selfless guidance for my postgraduate studies and choosing PhDcareer. Many thanks to Shashank Totre and Ameya Atre for motivating me tocome to Leuven for the postgraduate studies. Thank you guys for giving methe spark of your thoughts.

My colleagues from Philips India made a significant contribution to my career.I express my immense gratitude to Surendra Deolekar and Tushar Bhaleraofor proving their guarantee for the loan application I needed to become aself-supporting student for the postgraduate studies. Without their selflesssupport, this dream was impossible. It is always difficult to leave a well-settledjob and start self-supporting studies. I also would like to thank my colleague’sfrom Philips Healthcare India and Netherlands Frank Spronk, Jitendra Shitole,Gurpreet Singh Bedi, Alwyn van den Berg, Deepak Bharambe, MaheswarapuSR Dikshit, Debashish Bhattacharya, Ramakant Navle and Nitin Walunjkarfor providing me guidance, encouragement and recommendation for the furtherstudies.

In Leuven, many friends have given their time, help and care generously. Iam especially grateful to Chandan Kadur, Shweta Saini, Bharat Gadakh andChetan Kulkarni. You guys are the cornerstone of my enriched life besidesresearch in Leuven. I cannot forget the immense support and encouragementyou gave during my good and bad times. I remember the financial help thatChandan and Bharat gave me during initial days and always being there forme whatever the occasion and moment may be. It was so kind of Shweta (thevibrant girl) for always finding time for me, offering every help that she can,taking immense care and bringing a variety of sweets that she was making.Buddy, we share an amazing friendship. Chetan, the mesmerising trips wemade together across Europe and the great time we spent at Campus Arenaresidence are unforgettable. Their amazing partners Deepthi Shashtry, SumitSaini, Sujata Aher and Kirti Kulkarni always showed an equally great affectionto me and treated me as a family. I am simply blessed to have you guys therefor me!

During my stay in Leuven, some people have not only been great friends butalso helped through several technical issues and discussions. I am very gratefulto Saurabh Jain, Bharat HN, Satwant Dagar, Susheel Kumar and PradeepKuravi for all their help and time. I cannot forget to mention their partnersNeha Jain, Vidya Moorthy and Khushboo Verma for all the kind gestures andaffections. I am very thankful to Mandar Thite, who made my apartment homeduring the postgraduate studies and giving many more memories in later yearswith his wife, Nishigandha.

154 ACKNOWLEDGEMENTS

Many more friends have been part of my fabulous social life in Leuven. Iwould like to thank Parimal Naik, Abhishek Singh and Suravi, Manish Gupta,Anjan Dhumal Rao and Sravya, Abhijit Shinde, Parveen Dabas, Arun KumarTharkeshwar, Siva Ramesh, Raghavendra Mall, Sagnik Chatterjee and MilindSaudi for their support and for making me feel at home. Guys, love you loads! Iwould also like to thank all the members of Indian Student Association Leuvenwhom I met during organising and volunteering several events and trips.

I cannot forget some of the great social interactions I had with Jose George,Niraj Mishra, Suresh Vajrala, Rahul Patil, Tarun, Shibesh, Pravov, Bala, Suraj,Manoj, Vamsi, Saurab Vig, Ritesh, Shawez, Mohit, Bidisha, Ilaya, Surya, Gokul,Sanish, Sriram, Sajin, Jehan, Srini, Tamal, Amit,Vikas and Omprakash. Thanka ton friends for everything!

My parents Gorakhnath (Nana) and Shobha (Aai) have been the most significantsource of inspiration, and I have no words to express my broad sense of reverenceto them. Without their unconditional love, sacrifices and contributions I wouldnot have become the person I am today. Many thanks to my lovely sister Krupaand brother Dnyneshwar (Mauli) for cheering me up on every occasion. Yourimmense faith in me gave me all the strength I need. Love you so much!

Last but not the least, one of the most beautiful things this life gave me, mydear and gorgeous wife, Priya. You are the most adorable and innocent personI ever met. I owe many thanks to you. You took great care of me and stayedcalm in most stressful moments. You celebrated every small success I made.You made me smile for no reason and realise what is most important in life.Behind successful me, you are the woman! Thank you and love you very much!

Eshwar Gorakhnath GhumareLeuven, Belgium

07.12.2017

FACULTY OF MEDICINEDEPARTMENT OF NEUROSCIENCES

LABORATORY FOR COGNITIVE NEUROLOGYHerestraat 49, ON-2, box 1027

3000 Leuven, [email protected]

http://med.kuleuven.be/lcn/

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