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Analysis of low-noise EEG in search of functional gamma band correlates Hamzei, Nazanin 2017

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Analysis of Low-Noise EEGin Search of Functional Gamma Band CorrelatesbyNazanin HamzeiB.Sc., Amirkabir University of Technology, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Electrical and Computer Engineering)The University Of British Columbia(Vancouver)April 2017© Nazanin Hamzei, 2017AbstractThe electroencephalogram (EEG) has proven to be a useful information source inanalysis of brain activity, diagnosis of neurological disorders, and developmentof brain-computer interfaces (BCI’s). Through numerous studies over the pastdecades, EEG activity in different frequency bands has been observed to corre-spond with various mental states. Clinical use of EEG, however, is often limitedto frequency ranges below 30 Hz, ignoring potentially informative patterns withinthe gamma band (30− 100 Hz). Indeed, the gamma band has received greaterscrutiny in recent years and is typically known to underlie and be modulated bysensorimotor behaviors and internal cognitive processes.In this study, we have investigated the potential of an ultra-low noise capsule atthe LSBB 1 for acquisition of clean EEG signals, with a focus on analysis of highfrequencies (gamma band) in search for novel activity patterns. Using a battery-operated EEG acquisition system, we acquired 64-channel EEG recordings from afew volunteers performing several cognitive, sensory, and motor tasks in both LSBBand a typical research laboratory. Upon analysis of this data using Stockwell Trans-form, we compared task-specific gamma band energy increases of signals acquiredat the two environments, observing more prominent functional EEG changes inLSBB. Moreover, we studied all recordings in both environments to examine sta-tistically significant spatial and spectral correlates of spontaneous EEG pertainingto each of the tasks.To further assess the task-induced changes in the EEG signals, we have alsoproposed a framework for analyzing gamma band connectivity; i.e. functional pat-terns of interaction between distinct channels of the EEG. Using this framework,1Laboratoire Souterrain a` Bas Bruit, Rustrel, Franceiiwe have analyzed directional connectivity on recordings pertaining to motor tasks,both in a batch-based (yielding a time-averaged pattern) and an instantaneous man-ner. Batch-based connectivity analysis of the data resulted in well-defined connec-tivity patterns among subjects, while instantaneous connectivity analysis was in-consistent due to limitations of the study protocol. The results obtained in this the-sis demonstrate the potential of the low-noise capsule and motivate further protocolenhancements and analysis methods for conducting high-frequency EEG studies atLSBB.iiiPrefaceThis dissertation is the original work of the author in collaboration with the Electri-cal and Computer Engineering in Medicine (ECEM) research group at the Univer-sity of British Columbia. The principal investigator, professor Guy A Dumont, wasresponsible for design of the experimental paradigm, recruitment of subjects (all ofwhom are interested researchers known to the principal investigator), and collec-tion of data, as approved by the UBC Research Ethics Board (certificate numberH14-02124, August 2014). The author was solely involved in concept formationand data analysis.The following article has been published out of the context of the work insection 2.3.2:• Hamzei, N., Bastany, Z., Jutzeler, C.R., Yedlin, M., Kramer, J.L., Steeves, J.D. andDumont, G.A., 2016. Ultra-low Noise EEG at LSBB: New results. In E3S Web ofConferences (Vol. 12, p. 05003). EDP Sciences.Additionally, the following articles will be written and submitted based on theframework laid out in this thesis:• High-frequency correlates of spontaneous EEG in response to cognitive andsensorimotor tasks• Topographical analysis of spontaneous Granger-causal connectivity duringmovement-related tasks: an EEG studyivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background And Basics of Electroencephalography . . . . . . . . 11.2 EEG Signal Analysis . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 EEG Patterns And Brain Waves . . . . . . . . . . . . . . 21.2.2 General Review of Analysis Techniques . . . . . . . . . . 61.3 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . 92 Time-frequency Analysis Using Stockwell Transform . . . . . . . . 112.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Data Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.1 Artifact Rejection . . . . . . . . . . . . . . . . . . . . . . 13v2.2.2 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . 172.3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.1 Stockwell Transform . . . . . . . . . . . . . . . . . . . . 192.3.2 Comparison of the Two Environments . . . . . . . . . . . 222.3.3 Task-specific EEG Changes in Both Environments . . . . 282.4 Discussion And Conclusions . . . . . . . . . . . . . . . . . . . . 373 Granger-Causal Connectivity Analysis . . . . . . . . . . . . . . . . . 393.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.1.1 Motivation for Connectivity Analysis . . . . . . . . . . . 393.1.2 Different Categories of Connectivity . . . . . . . . . . . . 403.1.3 Modeling And Estimation of Connectivity . . . . . . . . . 413.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2.1 Granger Causality . . . . . . . . . . . . . . . . . . . . . 433.2.2 MultiVariate AutoRegressive (MVAR) Models . . . . . . 443.2.3 Autoregressive Modeling of Nonstationary Data . . . . . 453.2.4 Representation in Frequency Domain . . . . . . . . . . . 463.2.5 Frequency Domain Estimators of Directed Connectivity . 473.3 Workflow, Methods, And Practical Considerations . . . . . . . . . 503.3.1 Pre-processing And Artifact Removal . . . . . . . . . . . 503.3.2 Model Fitting And Validation . . . . . . . . . . . . . . . 523.3.3 Computation of Connectivity Estimators . . . . . . . . . . 553.3.4 Tests for Statistical Significance . . . . . . . . . . . . . . 563.3.5 Visualization and Further Data Reduction . . . . . . . . . 583.4 Results And Discussion . . . . . . . . . . . . . . . . . . . . . . . 623.4.1 Static Connectivity Results . . . . . . . . . . . . . . . . . 643.4.2 Dynamic Connectivity Results . . . . . . . . . . . . . . . 713.4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 744 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78viBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80A Details of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 91A.1 The Underground Facility . . . . . . . . . . . . . . . . . . . . . . 91A.2 Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . . 91A.3 Study Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . 92viiList of TablesTable 2.1 Grouping of the electrodes in a 10-10 montage based on theirlocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Table 2.2 Different frequency bands used in our analysis. . . . . . . . . . 29viiiList of FiguresFigure 1.1 EEG electrode placement in the international 10-20 system. . 3Figure 1.2 EEG decomposition into standard subbands . . . . . . . . . . 4Figure 2.1 ICA decomposition of a noisy segment of EEG . . . . . . . . 15Figure 2.2 Stockwell transform magnitude of resting state as well as thatof a motor task at LSBB . . . . . . . . . . . . . . . . . . . . 21Figure 2.3 Stockwell transform magnitude of resting state as well as thatof a motor task at both LSBB and ICORD . . . . . . . . . . . 23Figure 2.4 Topographical map of electrode groups based on the classifi-cation in Table 2.1 . . . . . . . . . . . . . . . . . . . . . . . 24Figure 2.5 Box plots demonstrating the distribution of energy ratios acrosssubjects in different brain regions, conditions, and environments. 26Figure 2.6 Significance maps and Power Change Ratios of the backwardcounting task . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 2.7 Significance maps and Power Change Ratios of the matchingmemory task . . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 2.8 Significance maps and Power Change Ratios of the brushing task 33Figure 2.9 Significance maps and Power Change Ratios during the appli-cation of hot packs . . . . . . . . . . . . . . . . . . . . . . . 34Figure 2.10 Significance maps and Power Change Ratios of the ankle move-ment task . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Figure 2.11 Significance maps and Power Change Ratios of the wrist move-ment task . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36ixFigure 3.1 From raw time series to connectivity patterns: steps for es-timating effective connectivity based on multivariate autore-gressive models . . . . . . . . . . . . . . . . . . . . . . . . . 51Figure 3.2 Normalized auto and cross-correlations among all 60 channelsof the model residuals . . . . . . . . . . . . . . . . . . . . . 54Figure 3.3 Statistical significance testing methods for pair-wise static anddynamic connectivity estimation . . . . . . . . . . . . . . . . 57Figure 3.4 Visualization of the connectivity structure by plotting the sig-nificance matrix . . . . . . . . . . . . . . . . . . . . . . . . . 59Figure 3.5 Visualization of significant interactions by averaging channelinteractions within the brain regions specified in table 2.1. . . 60Figure 3.6 Representation of brain networks as graphs . . . . . . . . . . 61Figure 3.7 Significant directed pair-wise connections during ankle move-ment from three subjects in the two environments . . . . . . . 65Figure 3.8 Segmentation of significance matrices into hemispheric con-nections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 3.9 Overall strengths of inter and intra-hemispheric task-specificconnectivity during motor tasks . . . . . . . . . . . . . . . . 66Figure 3.10 Average regional interactions during motor tasks in eight sub-jects and two environments. . . . . . . . . . . . . . . . . . . 68Figure 3.11 Topographical plots showing the static graph-theoretical mea-sures calculated on the mean significance matrix during motortasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Figure 3.12 Topographical plots of instantaneous CAR values during thefirst five seconds of ankle movement . . . . . . . . . . . . . . 72Figure 3.13 Time course of gamma band interactions throughout the firstfive seconds of ankle movement from one subject at LSBB . . 73Figure A.1 EEG montage of the NRSign acquisition system . . . . . . . 92xList of AbbreviationsEEG ElectroencephalogramLSBB Laboratoire Souterrain a` Bas BruitICORD International Collaboration On Repair DiscoveriesBCI Brain-Computer InterfaceFMRI functional Magnetic Resonance ImagingERP Event-Related PotentialsSTFT Short-Time Fourier TransformWT Wavelet TransformICA Independent Component AnalysisDDTF direct Directed Transfer FunctionVAS Visual Analog ScalePCR Power Change RatioCNS Central Nervous SystemMVAR MultiVariate AutoRegressiveCAR Causal Asymmetry RatioxiAcknowledgementsMy gratitude goes out to my academic supervisor, professor Guy Dumont, forhis insightfulness, professionality, generosity, and unwavering support throughoutthis process. I would also like to thank Dr. John Kramer, Dr. John Steeves, Dr.Matthew Yedlin, Ms. Zoya Bastani, and Mr. Shahbaz Askari for their helpful andencouraging comments on this work.My sincere gratitude extends to my parents for all the sacrifices they made tosupport my aspirations. I am also indebted to my partner, Mahdi, who listenedpatiently to my occasional rants, set me straight at times when I staggered, andstayed lovingly by my side along the way.xiiChapter 1Introduction1.1 Background And Basics of ElectroencephalographyIn 1924, psychiatrist Hans Berger’s obsession with understanding the ”psychic en-ergy” led to one of the most remarkable developments in the history of neurology.His paper was published five years later, demonstrating that the electrical activity ofthe human brain can be recorded from the surface of the scalp. Using his method,later known as electroencephalography (EEG), he was the first to study changes inthe recorded EEG signal pertaining to specific mental processes, including arousal,memory, and consciousness. Application of EEG in detection of epilepsy followednot long after, when Gibbs et al. discovered the spike-and-wave discharge as afirst-ever clear EEG pattern particular to petit mal epilepsy [1]. Nowadays, EEGcontinues to be a valuable research and diagnosis tool in neurophysiology, withapplications ranging from diagnosis of brain injuries and mental disorders [2] tomonitoring the depth of anesthesia in the operating room [3] and design of sophis-ticated Brain-Computer Interfaces (BCI’s) [4].The physiological basis of brain’s electrical activity lies in that the core com-ponents of the central nervous system, i.e. neurons, have intrinsic electrical prop-erties. Neurons are electrically excitable cells capable of being activated by otherneurons through afferent electrochemical action potentials [5]. EEG is thereforehypothesized to comprise of the summed electrical activities (net electric field) ofthese post-synaptic potentials. A large cluster of synchronously activated neurons1are involved in generation of EEG, which is then propagated to the scalp surface.Passing through many layers before reaching the scalp, this signal is severely at-tenuated; and hence only large populations (thousands to millions) of neurons withcoherent orientations of electric fields can generate enough potential to be record-able using scalp electrodes.The EEG acquisition system is relatively simple and inexpensive compared toneuroimaging devices. It mainly comprises of electrodes distributed over the scalpin a standard and reproducible placement scheme (e.g. in the international 10-20montage shown in figure 1.1, the electrodes are placed at intervals which are 10%and 20% of the total front-back and left-right distance of the skull, respectively).Held in place on the scalp using conductive pastes, caps, or nets, each electrode isconnected to one input of a differential amplifier, with the other input connectedto a reference electrode. The signal picked up on the scalp surface is amplified,digitized and sampled, typically at sampling frequencies greater than 256 Hz, thusproviding a millisecond-range temporal resolution. Compared to other tools forexploring neural activity such as FMRI, this high temporal resolution is anotherattractive feature of EEG which provides the opportunity of studying brain functionin real time.1.2 EEG Signal AnalysisEEG traces recorded over time contain information about the brain state or poten-tial neural disorders. Clinical professionals with a trained eye typically obtain thisinformation by visual inspection of the time series. However, multichannel EEGis a highly complex signal in nature, holding many potentially valuable featureswhich cannot be visually discerned. The purpose of the current trend of researchon quantitative EEG signal analysis is, therefore, to extend and apply the conceptsof digital signal processing to the analysis of EEG to make use of this rich infor-mation source as a low-cost and non-invasive ’window to the brain’.1.2.1 EEG Patterns And Brain WavesDepending on the application, the patterns sought after in EEG are either rhythmicactivity or transients. Transient features of the signal, such as occurrence of spikes2Figure 1.1: EEG electrode placement in the international 10-20 system.There are a total of 19 recording electrodes spanned uniformly fromfront to back of the head (nasion to inion) and from left to right (be-tween pre-auricular points). Additionally, two reference electrodes (of-ten placed on ear lobes) and one or two ground electrodes (often placedon the nose) are included. Electrode names refer to their correspond-ing location, with F, C, P, T, and O denoting Frontal, Central, Parietal,Temporal, and Occipital lobes, respectively. A) side view, B) top view.and sharp waves (SSW), may represent seizures or interictal activity [6]. On theother hand, rhythmic oscillations, or the so-called notion of brain waves, refer tothe relative signal content within different frequency bands in the EEG spectrum(Figure 1.2). Conventionally, rhythmic activity of EEG is studied in a number ofspecific and standard frequency bands, including delta (0.1− 4Hz), theta (4−8Hz), al pha (8− 12Hz), beta (12− 30Hz), and gamma (30− 100Hz). Thesedistinctive categories are sometimes noted to have a certain spatial distribution overthe scalp and are often attributed to certain biophysical correlates such as particularbrain states [7]. The low-frequency, high-amplitude delta waves (< 4 Hz) are aprimary indicator of deep sleep in adults and the predominant activity in infantsduring the first two years of life, while hippocampal theta waves (∼ 4−8Hz) havebeen associated with drowsiness and deep meditation. Alpha oscillations (8−12Hz) are largest in the posterior regions of the brain and have been associated3F1C1CP1P1FP1AF3F3FC3C3CP3P3PO3O1AF7F5FC5C5CP5P51 2 3 4 5 6 7 8 9 10time(s)Multi-channel EEG time seriesPO70 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-20002007VOriginal EEG signal (5-second segment) - channel: P1-50050delta band content7V-50050theta band content7V-50050alpha band content7V-50050beta band content7V0.5 1  1.5 2  2.5 3  3.5 4  4.5 5  time (s)-50050gamma band content7VFigure 1.2: Top: typical 10 second-length multichannel EEG time series; la-bels on the vertical axis indicate channel names (chosen arbitrarily froma 10-10 montage). Bottom: first 5 seconds of the P1 signal filtered intoits corresponding standard sub-bands.4with relaxed wakefulness with eyes closed. Oscillations in the 12− 30 Hz rangeare generally smaller in amplitude compared to lower frequency waves, and areknown as beta oscillations. These rhythms are distributed symmetrically on thefronto-central regions and are associated with active thinking and focused attention[5].Gamma band oscillations, earlier defined as narrow-band 40 Hz waves andlater modified to the 30−100 Hz (and above) range, deserve more attention as theyhave been the subject of many EEG studies (including this thesis) during the pastdecades. These studies, however, typically lead to controversies. This is due to thefact that gamma band activity is observed in a multiplicity of cognitive processes,but it is not unique to any of these functions and is hence not regarded as a strictindicator of these processes [8]. Since the late nineteen-eighties, gamma band hasbeen linked to perceptual binding, i.e. the ability of the brain to fuse various aspectsof a stimulus into a coherent whole [9], [8], [5]. Later on, gamma band oscillationswere also associated with many other cognitive functions such as attention [10],arousal and alertness [11], perception and memory [12], [13], language processing[14], top-down modulation of sensory processes [15], movement-related tasks [16],and pain processing [17]. Nonetheless, a somewhat general explanatory theoryregarding the gamma band does not exist and the role of gamma band in cognitiveand sensorimotor processing is yet to be elucidated.Based on different activation patterns of gamma waves, Galambos [18] sug-gested the following categories for classification of studies on gamma band:1. Spontaneous gamma oscillations, which are essentially ongoing (background)gamma band activity in EEG without intentional stimulation; and can be de-fined at all times as the fraction of power in the gamma band in relation tothe total signal power.2. Induced gamma waves, which are caused by but not specifically time-lockedto a stimulus. The induced gamma responses usually occur at post-stimuluslatencies longer than 100 milliseconds and usually less than a second, andmay vary in latency from trial to trial. This kind of activity is the subject ofthe majority of gamma band studies in the literature.3. The evoked gamma responses, on the other hand, are precisely time-locked5to the stimulus, with post-stimulus latencies usually around 25 milliseconds.4. The emitted gamma band oscillations, occurring in cases when there is a re-sponse time-locked to a stimulus which is not presented. This might happenin paradigms when the subject is expecting a stimulus at a specific point intime, but is not presented with any.Contrary to Galambos’ classification in 1992, the current literature on gammaband makes loose distinctions between the terminology of induced, evoked, oremitted responses. However, it seems natural and essential to distinguish contin-uous spontaneous activity from transient time-locked responses caused by a stim-ulus. While very few studies have focused on the former (usually in the realmof sleep stages), the latter responses are studied extensively in the past decades.In fact, most of the studies on EEG oscillations focus on establishment of trial-averaged Event-Related Potentials (ERP’s) as physiological correlates of cognitive,sensory, and perceptual phenomena.1.2.2 General Review of Analysis TechniquesNumerous methods and techniques developed in electrical engineering and infor-mation theory have been utilized over the past decades to augment the power ofanalysis of EEG signals (See [19], [20], [21] for a review on these methods). Themain goal of all of these methods is to quantify and correlate changes observed inthe EEG signal with the underlying mental process or disorder which is believedto cause these changes. The methods range from time domain analysis, such asHjorth’s trio of descriptive statistics parameters [22], [23]; to parametric and non-parametric frequency domain (spectral analysis) methods [24], [25]; as well astime-frequency methods and the use of wavelet and short-time Fourier transforms[26], [27], [28], [29] to determine when specific spectral events happen in the EEG.On the other hand, non-linear signal processing methods such as mutual informa-tion studies [30], higher order spectral [31], [32], fractal [33], [34], and entropyanalysis methods [35], [36] have also been explored and used on EEG signals.There have been numerous attempts to solve the EEG inverse problem; namely,reconstructing the sources hypothesized to give rise to scalp signals [37], [38]. Inthis context, the scalp signals are assumed to be projected mixtures of an infi-6nite number of cortical sources at different locations within the brain. Hence, bysolving the inverse problem, one would be able to examine the source domain asopposed to the sensor (electrode) domain to have a more refined localization ofactivity patterns. This is of particular interest when scalp EEG is being used asa non-invasive tool to localize interictal spikes characteristic of epilepsy. Dipolesource localization methods [39], minimum-norm solutions [40], Low-resolutionElectromagnetic Tomography (LORETA) [41], Bayesian solutions [42], and Inde-pendent Component Analysis (ICA) [43] are among the popular source estimationtechniques found in literature.From another perspective, many neuro-scientific publications during the pastfew years have shifted their focus from segregated functional localization to func-tional connectivity analysis [44], [45], [46], [47], [48]. Specifically, it is nowcommonly accepted that during information processing, the brain is not merelystructured in separate, isolated parts. Rather, it behaves as a complex networkof different, possibly distant regions interacting with each other in various ways.Research in brain connectivity therefore refers to application of signal processingtechniques to quantify the information exchanged between different regions of thebrain in different states, tasks, or disorders; in order to shed some light on thebrain’s complex network structure. Connectivity estimation techniques range fromsimple coherence analyses to more sophisticated Dynamic Causal Models [49],Structrual Equation Models [50], and Multivariate Autoregressive-based models[44], [51].1.3 Thesis ObjectivesWith the end goal of performing innovative EEG studies and establishment of novellow-noise EEG benchmarks, our study was designed to make use of the unique un-derground laboratory (LSBB); an ultrashielded, ultra-low noise capsule used as across-disciplinary research facility for low-noise measurements (See Appendix A).We have collected high-resolution continuous EEG data from a number of subjectsboth in LSBB and in a typical research laboratory environment, ICORD 1, while1International Collaboration On Repair Discoveries, Blusson Spinal Cord Centre, Vancouver,BC7they performed several cognitive, sensory, and motor tasks. The main objective ofthis work is to analyze this data in search of task-specific EEG activity patterns,with a particular emphasis on gamma band oscillations. We attempt to find func-tional gamma band patterns in the subjects’ EEG which would correlate with thesubject performing a task, and could thus serve as functional biomarkers. We alsointend to see how these patterns are different in the low-noise LSBB as comparedto a typical noisy environment.The potential of the LSBB capsule for performing low-noise EEG measure-ments was previously assessed in a preliminary study [52], in which it was con-firmed that clean EEG signals can be acquired at LSBB without the need for notchfiltering. It was also shown that the battery-operated acquisition equipment doesnot introduce electromagnetic noise on the acquired signals. Moreover, due tohigher signal-to-noise ratio, task-specific EEG biomarkers at beta band were foundto be more prominent in signals acquired at LSBB compared to the hospital envi-ronment [52]. However, this preliminary study bore a number of limitations. First,the EEG system used was a clinical depth of hypnosis monitor designed for usein the operating room and only offered two EEG channels. Further, as it was afeasibility study, the experiments were not specifically designed to target functionsinvolving gamma band oscillations. Our study was an attempt to overcome theselimitations by upgrading the acquisition equipment to a 60-channel research-gradesystem, as well as improving the design of experiments by including a variety oftasks in which gamma band is deemed to play a role. Details of the acquisitionsystem, environments, and the study protocol are discussed in Appendix A.In more specific terms, the objectives of this thesis are twofold:1. To examine the task-specific gamma band content of the data in the time-frequency domain using Stockwell Transform (S-Transform) [53]. The S-Transform is an extension of the wavelet transform with properties whichmake it a suitable tool for analysis of high-frequency content in a signal.Using this tool, we have attempted to identify channels (brain regions) whichare actively generating gamma band activity when a particular task is beingperformed; and observed how these activity patterns differ across subjects.Moreover, we have used the S-Transform to compare task-specific gamma8band activity in data recorded at LSBB with those recorded in ICORD. Theend goal in this comparison is to search for EEG information, particularlywithin the gamma band, which is conspicuously present in LSBB but not inthe hospital environment and will lead us to better detection of task-specificbio-markers.2. To analyze the task-specific effective connectivity patterns in the data insearch of significant functional interactions among brain regions within thegamma band. Based on our observation from segregated time-frequencyanalysis, we will proceed with analyzing motor tasks, as the most consistentfunctional gamma band power increases were observed during these tasks.We have adopted two approaches for analyzing effective connectivity in ournon-stationary EEG data. One is to analyze connectivity in non-overlappingwindows (batches) and the other is to compute instantaneous connectivityparameters using an adaptive model.These objectives are addressed individually in chapters 2 and 3, respectively.Lastly, we have summarized our findings as well as outlined the major challenges,limitations of the dataset, and directions of future work in chapter 4.1.3.1 ContributionsRecapitulating, this work has made the following basic contributions:• The Stockwell transform was used for time-frequency analysis on this dataset,• Task-relevant gamma band energy increases were assessed and comparedacross subjects and brain regions between LSBB and the hospital environ-ment,• A pipeline for analysis of static (batch-averaged) and dynamic (instanta-neous) effective connectivity patterns is proposed for this dataset,• A multi-subject statistical inference scheme is proposed for group assess-ment of functional changes in EEG; both for time-frequency as well as staticand dynamic connectivity analysis,9• The direct Directed Transfer Function (DDTF), a multivariate measure ofconnectivity based on parametric auto-regressive modeling of EEG, wasused to measure batch-based connectivity in this dataset,• A Recursive Least Squares algorithm with forgetting factor, coupled withDDTF, was used to extend the batch-based analysis and adaptively modelinstantaneous connectivity in this dataset.10Chapter 2Time-frequency Analysis UsingStockwell Transform2.1 IntroductionFrequency analysis of the EEG signal goes back to when EEG was discovered byBerger in 1929. He was the first to study changes in oscillatory behavior of the EEGwhich were present in both normal and abnormal brains. Specifically, he reportedon oscillations with frequencies near 10 Hz, later termed as alpha waves; and theirsubstitution by the faster oscillating beta waves when the subject opened their eyes[54]. Following Berger’s pioneering work, and especially since the introductionof digital recordings and the Fast Fourier Transform, researchers have thoroughlystudied different EEG oscillation patterns and their correlation to various mentalstates, brain functions, and pathologies.Most studies of scalp EEG are concerned with measures on averages of re-sponses evoked by (precisely time-locked to) a stimulus presented in a series ofsimilar trials or epochs. It is assumed that by averaging multiple realizations of theprocess, background EEG and other sources of noise would be canceled out andwhat remains is the coherent time-and-phase-locked activity evoked by the stimu-lus, or the so-called Event-Related Potential (ERP). ERP’s are therefore brief (gen-erally less than 1 second), transient waves believed to represent the mental processof responding to a stimulus. Analysis of the EEG based on Event-Related Poten-11tials has a number of advantages. First, ERP’s are conceptually simple and fastand easy to implement with very few analysis parameters or assumptions. Thesestimulus-locked brain responses can be precisely characterized by means of ampli-tude and latency. Also, there is an extensive and decades-long ERP literature whichcan be used for validation and sanity check of the experimental conditions. For in-stance, the P300, a component elicited at latencies close to 300 milliseconds, is awell-established ERP component in neuroscience which reliably arises in oddballparadigms [55].The downside to the ERP approach is that responses are not necessarily stableacross trials, and averaging will remove any phase-incoherent activity not preciselytime-locked to the event, including potentially informative EEG activity whichis roughly time-locked but not phase-locked to the stimulus onset (i.e. inducedactivity). To characterize changes in the ongoing EEG induced by a stimulus,Pfurtscheller introduced Event-Related Synchronization (ERS) and Event-RelatedDesynchronization (ERD) [56] which represent short-lasting amplitude increasesand decreases of rhythmic activity, respectively. Examples of ERS are the betarebound after limb movement [57] and the induced gamma activity during visualprocessing [58]. It is important to stress here that both ERD and ERS measure in-duced changes in EEG oscillatory activity occurring shortly (a few seconds) beforeor after a stimulus, focusing on the time-locked mechanisms of cortical processing.On the other hand, a smaller portion of EEG studies, particularly studies onsleep patterns, analyze mean changes of spontaneous EEG power under variousconditions. In this type of analysis, the focus is not on transient dynamics of spec-tral properties in the temporal vicinity of a stimulus; rather, it is on overall spec-tral differences in ongoing oscillatory behavior between different states or groupsof pathologically different subjects. Our study falls into this category of spectralanalysis due to the nature of the experiment design. The main objective in thischapter is to find changes in oscillatory behavior which are specific to performinga task, and are manifested in the EEG by consequent regional power increases (ordecreases) in specific frequency bands.Our dataset consists of approximately 5 hours of continuous EEG data recordedin two environments: 1) The low-noise underground laboratory (LSBB), and 2)a research facility (ICORD). Using a battery-operated 60-channel acquisition sys-12tem, we have recorded the EEG while subjects performed a variety of cognitive andsensorimotor tasks. The cognitive tasks included backward counting from a largenumber, and an increasingly challenging ’matching’ memory task on an iPad. Inthe sensory stimulation phase, the subjects’ right thumb was brushed with a cottonswab as a tactile stimulation, and the subjects were asked to hold a hot pack in theirright hand as a noxious stimulus, while rating their pain experience using a visualanalog scale. Finally, as motor tasks, the subjects performed flexion movementsof the right ankle and the right wrist in separate sessions. Five subjects had volun-teered for data acquisition at ICORD, while seven subjects were present at LSBB,four of whom were common to both environments (see Appendix A for more de-tails on the protocol, acquisition system, and the underground environment).As our data analysis pipeline, we first clean the data of artifacts by removingcontaminated channels and rejecting artifactual time segments. We demonstrate insection 2.2.1 that for artifact rejection, ICA does not work effectively on our dataand we will henceforth resort to visual inspection to clean data of artifacts. Next,we introduce the theory and justify our use of the S-Transform in section 2.3.1. Wethen compare the task-to-rest S-transform energy ratios in ICORD and LSBB insection 2.3.2. Next, in section 2.3.3, we merge the data in the two environmentsto increase our sample size and use the same S-Transform information in hopesto find consistent task-specific gamma band activity patterns across all subjectsparticipating in the study. Lastly, we conclude and elaborate on our findings insection 2.4.2.2 Data Preparation2.2.1 Artifact RejectionEEG ArtifactsScalp EEG is almost always contaminated by noise and various artifacts whichobscure potentially informative cortical activity patterns. These sources of inter-ference are typically classified into physiological and extra-physiological artifacts.The latter refers to sources of noise and interference from the recording environ-13ment, including but not limited to poor electrical grounding, poor electrode con-tact, and powerline interference [5]. Extra-physiological artifacts can generally bemitigated by proper electrode attachment and recording the data in a controlledenvironment.Physiological artifacts, on the other hand, are the main sources of contamina-tion of the EEG signal and the main focus of studies on artifact rejection. Theyoriginate from inherent bio-physiological processes irrelevant to the EEG, andtherefore can rarely be avoided. The most prevalent physiological contaminants ofthe EEG are subject’s movements, cardiac activity or the electrocardiogram (ECG),the electromyogram (EMG) artifact caused by contraction of the muscles, and theelectrooculogram (EOG) artifacts caused by blinks and eye movements [59].Irrespective of their cause, the artifacts distort the signal and need to be elim-inated prior to quantitative analysis of EEG. Artifact suppression is typically per-formed by means of offline processing methods; a simple, classical example beingfiltering. For instance, notch filtering is often performed to remove the 50/60 Hzpowerline interference and its harmonics, and high-frequency noise is eliminatedby means of lowpass filtering. However, the majority of artifacts overlap in fre-quency content with the desired background EEG, and hence cannot be removedby bandpass filtering. Therefore, alternative techniques are typically developed,such as adaptive filtering [60], blind source separation (BSS) methods includingIndependent Component Analysis (ICA) [61] and Signal-Space Projection [62], orwavelet methods [63].The ICA MethodOne particularly popular artifact rejection technique in the EEG literature is Inde-pendent Component Analysis (ICA), which is an information-theoretical methodfor decomposition of a mixture of signals into additive subcomponents, such thatthese components are maximally independent at all times [64]. Essentially, ICAfinds a set of fixed spatial filters which together perform a linear change of ba-sis from the sensor domain to the so-called ’virtual channel’ (component) domain.Using this approach, locally coherent activity patterns are decomposed into inde-pendent components (IC’s), where each component could either correspond to a145 10 15 20 25 30time(s)(a) Channel activities versus time5 10 15 20 25 30time(s)(b) ICA component activities versus timeFigure 2.1: ICA decomposition of a noisy segment of EEG (a) into indepen-dent components (b). Artifacts have not been isolated into a few com-ponents.15cortical or artifactual source. By identifying the artifactual components, settingthem to zero in the component domain, and back-projecting the data to the sensordomain, it is possible to recover an artifact-free version of the data.In practice, however, ICA might not be able to completely group the artifactualsources into a few isolated components. In order to demonstrate whether ICA caneffectively remove different artifacts from our data, we have applied the infomax-ICA algorithm using the EEGLAB toolbox [65] on a raw segment of the multi-channel data in Figure 2.1. Figure 2.1a depicts 30 seconds of raw 60-channel EEGin the sensor domain, while Figure 2.1b demonstrates 60 Independent componentsfound in this data segment. It is observed that ICA fails to separate the artifacts intoa few identifiable components, as for instance, the muscle artifact seen during the8th and 22nd second of the recording has been spread out to most of the indepen-dent components in Figure 2.1b. Also, it appears that the eye movement artifactsbeginning on the 15th second have been successfully isolated into the first com-ponent. However, removing the first component does not fully eliminate the eyeartifacts, suggesting that other components are also contributing to these artifacts.In such cases where many components are found to be artifactual, artifacts can-not be eliminated by nullifying their corresponding components, as setting manycomponents to zero would amount to loss of cortical data.We speculate the following as potential reasons as to why the ICA method failsto separate the artifactual sources successfully. First, there is a trade-off between areliable decomposition and the signal stationarity. As suggested in [66], ICA meth-ods require a large number of data points for reliably decomposing the data. Thismeans that long segments of EEG are required to provide sufficient data points,while during these long segments the nature of the sources might vary significantlywith time. In this sense, ICA is able to isolate the artifactual sources which remainfairly constant in time and space, and does not guarantee to separate transient ar-tifacts occurring from time to time at random electrodes, as is the case with mostof the artifacts seen in our data. Second, ICA performs best in scenarios with thesame number of sources and sensors [64]. It is commonplace in EEG literatureto assume the number of independent sources to be the same as the number ofelectrodes, while there is no justification for the validity of this assumption. Infact, EEG is the summation of many complex cortical functions and sources, and16it might not be safe to assume that the number of cortical and artifactual sourcesdoes not exceed the number of electrodes. Lastly, ICA is based on the assumptionthat the independent components are maximally non-Gaussian. While true distri-butions of the EEG sources are not known, evidence to back the fact that corticalor artifactual sources are non-Gaussian is also lacking.Artifact Rejection by Visual InspectionGiven our observations, we have thus chosen not to use ICA for artifact rejection,and have instead rejected the artifactual channels or segments of the data by visualinspection. Approximately 5 hours of EEG recordings were visually inspectedin the time domain while artifactual channels and time segments were tagged forremoval using EEGLAB’s interface. Electrodes with frequent saturations and thosewith poor skin contact, judged by their abnormal activity patterns throughout thelength of the recording, were removed from the data and the analysis was based onstable channels. Time periods containing broadband muscle artifacts or any otherirregular activities were also removed from the data when possible. Occurrenceof eye blinks and eye movements was generally not a criterion for data rejectionsince their frequency content is usually below 15 Hz and does not overlap withthe gamma band frequencies. However, these artifacts were removed in case ofrarity to allow for alpha band analyses (in recordings such as those correspondingto the matching task, blinks happened very frequently and hence were not removedin order to preserve data). As for powerline interference, there was no need forapplication of 50 Hz notch filters to recordings acquired in LSBB. No 60 Hz notchfilter was used for recordings at ICORD either, owing to the fact that the battery-operated acquisition system was also able to minimize external electromagneticpower-line interference automatically using well-calibrated differential amplifiers.2.2.2 Pre-processingSegmentationAfter obtaining artifact-free recordings for all subjects and all tasks, we segmentthe long recordings corresponding to each task into consecutive non-overlapping17epochs of 10 seconds. Segmentation facilitates investigation of task-related changesin EEG and leads to more stable results, as it increases the number of samples perrecording and decreases the relative non-stationarity of longer epochs. Moreover,epochs appearing as ’outliers’ in the final results can easily be detected and re-moved as we are interested in broad spectral trends and not transient effects.Re-referencingEEG is a measure of voltage difference between an electrode placed at the positionof interest and a reference electrode. Dependence of the recorded multi-channeldata on the reference electrode causes any electrical activity on the reference elec-trode to be present in all other electrodes. In our data, the mid-prefrontal elec-trode FPZ was used as reference throughout all recordings. Since ocular artifactsusually have a topographical distribution peaking around the prefrontal channels,this choice of reference causes the ocular artifacts to spread to all other channels.Moreover, spatial proximity of an electrode to the reference electrode will causesmaller potentials to be picked from the electrode site. Hence, our choice of refer-ence might cause relative attenuation of frontal potentials and lead to topographicalbiases in the end results.To overcome problems of this sort, the data can be re-referenced to any otherreference channel or combination of channels. Because re-referencing is a lin-ear transformation of the data, it can be performed offline after the data has beenrecorded. We have chosen to reference the data to the average reference, which isa popular and theoretically sound choice of the new reference in high-dimensionalmontages. Re-referencing to the average reference is performed by subtractingfrom each electrode the instantaneous average across all electrodes as follows:xrere fi (t) = xi(t)−1NN∑j=1x j(t), i = 1, ...,N (2.1)where xrere fi denotes the re-referenced version of the signal xi at electrode i, andN is the total number of electrodes (60 in our case). From another point of view,average referencing can be regarded as spatial DC rejection of the multi-channelEEG in order to highlight and spatially sharpen the local activities over time.182.3 Data Analysis2.3.1 Stockwell TransformTime-frequency transforms are essential for analyzing non-stationary signals, i.e.signals whose statistical and spectral properties change over time. Two of themost commonly used time-frequency transforms in signal analysis are Short TimeFourier Transform (STFT), and Wavelet Transform (WT).The STFT was developed as an extension of the Fourier Transform by local-izing the frequency spectrum via a sliding window with smooth edges. Generally,one has to choose between a narrow window which results in poor frequency reso-lution, and a wide window which results in poor time resolution. This means thatSTFT is not a suitable tool for analysis of signals with relatively wide bandwidthswhich change rapidly with time. In order to overcome this limitation, the WaveletTransform was developed to analyze the signal with different resolutions at dif-ferent frequencies. WT performs a multi-resolution analysis by decomposing thesignal into a series of dilated and translated wavelets, such that high frequenciesare localized into a smaller time interval than low frequencies [67].Even though WT is an excellent tool in various applications such as denoisingand finding signal irregularities, it has a number of drawbacks as well. First, thephase information of the WT is not completely understood, as it is locally definedbased on the wavelet’s center point and it does not maintain a fixed reference.Moreover, the non-uniform time-frequency tiling on the analyzed signal may resultin biased energy representations. Specifically, the amplitude in WT is normalizedin such a way that higher frequency components are more attenuated than low-frequency components [67]. These properties are undesirable in applications whereintricate high-frequency components are the main attributes that are sought after ina signal.The Stockwell Transform [53], also known as the S-Transform, is a variant ofSTFT and/or an extension of WT developed in an attempt to overcome these issues.The S-transform of the signal x(t) is given byS(τ, f ) =∫ +∞−∞x(t)| f |2pie−(τ−t)2 f 22 e−i2pi f tdt (2.2)19The above formulation can be viewed as the STFT of x(t) windowed by alocalizing Gaussian function g(t) = 1√2piσ e−(t−τ)22σ2 , where the width of the Gaussianwindow σ = 1| f | is inversely proportional to frequency [67].From the point of view of WT, Eq. (2.2) can also be seen as a ’corrected’version of the continuous wavelet transform of x(t) using a complex Morlet waveletgiven by φ(t) = 12pi e− t22 e2piit :W (τ,a) =∫ +∞−∞x(t)1√|a|φ ∗( t− τa )dt=∫ +∞−∞x(t)1√|a| 12pi e− (t−τ)22a2 e−2pii(t−τa )=√|a|∫ +∞−∞x(t)12pi|a|e− (t−τ)22a2 e−2piita e2piiτa dt. (2.3)Where ∗ denotes complex conjugation. Letting a = 1| f | yieldsW (τ, f ) =1√| f |e2pii f τS(τ, f ), (2.4)Or equivalently,S(τ, f ) =√| f |e−2pii f τW (τ, f ). (2.5)Hence, the S-Transform is a generalization of the complex Morlet wavelettransform with the following modifications: 1) The multiplicative amplitude term√| f | causes the localizing Gaussian window to always have unit area, thus pro-viding a frequency-invariant amplitude response; and 2) the phase correction terme−2pii f τ which remains stationary while the Gaussian window is translated, enablesthe S-Transform to maintain absolute phase information relative to time τ = 0.Therefore, the S-Transform inherits the advantages of STFT and WT at the sametime, and it is in regard to these favorable properties that we choose it for analysisof high-frequency EEG.Given a segment of single-channel EEG, we can thus measure activity withinany frequency band and time window using the S-Transform in much the sameway as STFT. We will compute the total energy in the frequency band of interest20Figure 2.2: Stockwell transform magnitude of resting state (top) as well asthat of a motor task (bottom) from a single channel, single subject,and single environment (LSBB). The motor task has suppressed thelow-frequency activity and has caused increases in gamma band energythroughout the continuous recording.by integrating the S-transformed signal in the time-frequency space:E[ fL− fH ] =∫ fHfL∫ t fti|S(t, f )|2dtd f (2.6)where E[ fL− fH ] refers to the total energy of the S-Transform summed over fre-quencies fL to fH and times ti to t f . Figure 2.2 depicts the S-transform magnitude ofraw EEG signals of one subject during 30-second intervals of rest and a repetitivemotor activity (ankle movement) in the low-noise recording environment (LSBB)and a single parietal channel (P1). Comparing the figure on top (resting state)with the one on the bottom (motor task), we immediately observe that the motor21activity has caused power increases within the gamma band ( f > 30 Hz). Morespecifically, computing Eα , Eβ , and Eγ , leads to the observation that the total S-Transform energy in alpha, beta, and gamma band has changed from 7.8, 4.3, and2.6, to 5.6, 3.9, and 9.3, from the resting state to the motor condition, respectively.We can therefore conclude that for this specific EEG segment, subject, channel,and environment, the motor task has caused decreases in alpha and beta band andan increase in gamma band spontaneous activities.2.3.2 Comparison of the Two EnvironmentsOne of the main goals of conducting this study was to further assess the qualityof signals acquired in the low-noise environment by way of comparison with thoseacquired in a typical noisy environment. In particular, the objective is to searchfor task-specific changes in EEG, exhibited as power increases within the gammaband, and see if they are more prominent and better reflected in LSBB signals dueto higher signal to noise ratio. For this section, we will use data from four subjectswho are common to both environments in order to have an unbiased comparison ofthe two environments.Figure 2.3 depicts the same information shown in Figure 2.2, with similarrecordings (same subject, channel, and conditions) from the hospital environmentincluded for comparison. We observe that even though the motor activity hascaused gamma band power increases in both environments, this increase is moreprominent in LSBB than in ICORD.To quantitatively assess the task-specific changes in the gamma band EEGacross subjects, channels, and conditions, we calculate the task-rest gamma bandenergy ratios of the S-transform and compare them between LSBB and the hospitalenvironment.We measure the high frequency activity during each of the epochs by comput-ing the total gamma band energy of the epoch in the time-frequency space, definedin Equation (2.6) and with fL, fH , ti, and t f values set to 30 Hz,100 Hz, 0 s, and10 s, respectively. Consequently, responses to each task for each subject are ex-pressed as task-rest ratios; that is, given there are N epochs corresponding to therest condition and M epochs belonging to a particular task, we compute a total of22Figure 2.3: Stockwell transform magnitude of resting state (left) as well asthat of a motor task (right) from a single channel and a single subject,at both LSBB (top) and ICORD (bottom). The task-specific increase ingamma band energy is more prominent in LSBB.M×N ratios by dividing the total gamma band energy of each task epoch by thetotal gamma band energy of each of the resting-state epochs.This process is done in a channel-wise manner, resulting in MN task-rest ratiovalues for each channel. Since the high-dimensional results are difficult to interpretamong subjects and conditions, some data reduction across channels is necessary.In order to present the results in a more compact manner, we classify the electrodesinto nine functionally different brain regions (see Table 2.1 and Figure 2.4). Foreach task, we can then compare the entire set of ratios (including all four subjectscommon to both environments) in LSBB with that of the hospital environment ateach of these brain sites.The results from time-frequency analysis across epochs of all subjects in bothenvironments are summarized in Figure 2.5. These plots allow for comparisonof the distribution of gamma band task-rest ratios in LSBB and ICORD acrossdifferent brain regions.23Brain Region ElectrodesPrefrontal FPZ, FP1, FP2, AFZ, AF3, AF4, AF7, AF8Frontal FZ, F1, F2, F3, F4, F5, F6, F7, F8, FCZ, FC1, FC2, FC3, FC4Central CZ, C1, C2, C3, C4, CPZ, CP1, CP2, CP3, CP4Left Temporal FC5, FT7, C5, T7, CP5, TP7Right Temporal FC6, FT8, C6, T8, CP6, TP8Left Parietal P3, P5, P7, PO3, PO7Right Parietal P4, P6, P8, PO4, PO8Parietal PZ, P1, P2, POZOccipital OZ, O1, O2Table 2.1: Grouping of the electrodes in a 10-10 montage based on their lo-cationsFigure 2.4: Topographical map of electrode groups based on the classifica-tion in Table 2.1A quick look at Figure 2.5c reveals that for both of the motor tasks, the gammaband motor- rest ratios are significantly larger and more readily detected in LSBBacross all regions of the brain. While the median of motor-rest ratios at LSBB isalways greater than one, the median of ratios at the hospital stays close to one,suggesting that the gamma band activity in motor tasks was not readily detectable24Counting Matching1 3 5 Pre FrontalHospitalLSBBCounting Matching1 3 5 FrontalCounting Matching1 3 5 CentralCounting Matching1 3 5 Left TemporalCounting Matching1 3 5 Right TemporalCounting Matching1 3 5 ParietalCounting Matching1 3 5 Left ParietalCounting Matching1 3 5 Right ParietalCounting Matching1 3 5 Occipital(a) Cognitive TasksBrushing Heat Pack1 3 5 Pre FrontalHospitalLSBBBrushing Heat Pack1 3 5 FrontalBrushing Heat Pack1 3 5 CentralBrushing Heat Pack1 3 5 Left TemporalBrushing Heat Pack1 3 5 Right TemporalBrushing Heat Pack1 3 5 ParietalBrushing Heat Pack1 3 5 Left ParietalBrushing Heat Pack1 3 5 Right ParietalBrushing Heat Pack1 3 5 Occipital(b) Sensory Tasks25Ankle Wrist1 3 5 Pre FrontalHospitalLSBBAnkle Wrist1 3 5 FrontalAnkle Wrist1 3 5 CentralAnkle Wrist1 3 5 Left TemporalAnkle Wrist1 3 5 Right TemporalAnkle Wrist1 3 5 ParietalAnkle Wrist1 3 5 Left ParietalAnkle Wrist1 3 5 Right ParietalAnkle Wrist1 3 5 Occipital(c) Motor TasksFigure 2.5: Box plots demonstrating the distribution of task-rest gamma bandenergy ratios across different subjects in different brain regions, condi-tions, and environments. Subplots of each sub-figure correspond to thenine groups of electrodes (brain regions) according to Table 2.1. Wehave grouped the tasks into three categories: cognitive tasks (Fig. 3a)including counting and matching, motor tasks (Fig. 3b) including rightankle movement and right wrist movement, and right hand sensory tasks(Fig. 3c) including brushing and application of a heat pack. Tasks be-longing to each category are shown alongside each other. For each task,we have shown a boxplot of the task-rest ratios acquired in the hospitalenvironment (left) along with a boxplot of the ratios acquired at LSBB.Shown in the plots are the median value, as well as the 25% and 75%quartiles, and the whiskers representing ± 2.7σ or 99.3 percent cover-age given the data is normally distributed.at the hospital. Interestingly, LSBB ratios are consistently higher during the wristmovement task compared to the ankle movement task, while no significant differ-ence between wrist and ankle movement is observable at ICORD.26We have depicted the ratios for cognitive tasks in Figure 2.5a. Although hav-ing slightly higher values in ICORD, backward counting-rest ratios are mainlydistributed around one in both environments, suggesting that spontaneous gammaband activity may not correlate with continuous counting tasks. This was alsofound to be the case in a previous study [52]. On the other hand, the median ofmatching-rest ratios is mainly greater than one in both environments, and is higherin LSBB at all brain regions except for the left temporal region. As an explanationfor why a global increase in ratios is not seen at LSBB, it could be claimed that theincrease in gamma band due to matching is more focused, contrary to the motorfunctions which exhibit a more global cortical response. Thus, in brain regionswhere the gamma-band content is boosted due to the cognitive activity associatedwith the matching task, the ratio increase is more prominent within the low-noisesettings at LSBB than in the hospital environment.Brushing-rest and noxious heat-rest ratios were also compared between thetwo environments in Figure 2.5b. This figure demonstrates that the median ofbrushing-rest ratios is slightly higher in LSBB compared to the hospital, thus re-vealing the potential of LSBB in identifying the brushing-induced high frequencyactivity. However, the heat-rest ratios are generally lower in LSBB than in the hos-pital environment. Explaining this issue, it is worth mentioning that the average ofthe VAS pain ratings across all recordings and all subjects was 5.5 at the hospitaland 1.5 at LSBB, suggesting that despite the efforts to keep the experiment condi-tions equal, the subjects reportedly experienced more pain in the hospital facilitythan in LSBB. We might therefore hypothesize that the lower ratios in LSBB arecaused by the lower pain experience in comparison with ICORD, which would inturn yield lower gamma band activity in LSBB as the strength of gamma band os-cillations has been shown to correlate well with the intensity of the perceived pain[17].Overall, our results demonstrate that functionally correlated gamma-band EEGpatterns can be better detected in low-noise conditions when compared with a typ-ical hospital environment. This motivates the design of more informative studieswith the end goal of defining potentially novel and predictive high-frequency EEG(gamma-band benchmarks) for a better understanding of central neuronal functionand CNS disorders.272.3.3 Task-specific EEG Changes in Both EnvironmentsThe analysis in section 2.3.2 was based on subjects common to both environmentsin order to have a fair comparison groundwork. However, another objective of thisthesis is to search for task-specific EEG correlates among all subjects, regardless ofthe recording environment. In this section, we will examine the spontaneous powerchanges in EEG using data from all subjects and all environments. Moreover, wewill also investigate other frequency bands in addition to gamma band. Our goalis to present a comprehensive analysis on the topographical and frequency-specificchanges in EEG between different conditions to observe the effect of each task onbrain’s rhythmic activity.We adopt two different approaches to analyze the effects of two variables inquestion: frequency and topology. The role of different frequency bands is quan-titatively assessed via Power Change Ratio (PCR), a measure nearly identical toS-Transform task-rest ratio introduced in the previous section. On the other hand,topographical analysis of different frequency bands is performed by strict statisti-cal significance testing to minimize spurious false-positive results in examinationof spatial patterns of EEG.• Power Change RatioWe define Power Change Ratio (PCR) from the i− th resting-state epoch Rito the j− th task epoch Tj in each frequency band B asPCRi, j =EBTj −EBRiEBRi(2.7)where EB(.) denotes the total epoch energy in the time-frequency space aselaborated in equation (2.6); and i and j range from 1 to the total number ofrest and task epochs, respectively. Contrary to task-rest ratios, task-specificincrease and/ or reduction in energy cause the PCR to elicit positive and neg-ative values, respectively, hence yielding a more intuitive measure of energychanges.In what follows, we use the PCR values to depict relative task-rest powerchanges at each region of the brain. Taking a similar approach as the previ-28ous section, we first compute MN channel-wise PCR values from all com-binations of N resting-state epochs and M epochs belonging to a particulartask. We then group these values according to the regioning scheme dis-cussed in section 2.3.2. Lastly, we examine the mean and standard deviationof all PCR values in a particular brain region across subjects, electrodes, andepochs, using all recordings from all eight subjects. This procedure is re-peated for different frequency bands; namely, alpha, beta, and our so-called’low gamma’ and ’high gamma’ sub-bands detailed in Table 2.2.Name of Frequency Band Lower And Upper Frequency Bounds (Hz)Alpha [7 − 12]Beta [12 − 30]Low Gamma [30 − 65]High Gamma [65 − 100]Table 2.2: Different frequency bands used in our analysis. Low Gamma andHigh Gamma bands are custom-defined ranges to allow for a more re-fined analysis of the gamma band.• Statistical Significance TestingFurthermore, in order to accurately infer the topographical distribution oftask-specific energy increases using all epochs at hand, we introduce ’signif-icance maps’: For each channel, the S-Transform energy of all task epochs isstatistically compared to energies of all rest epochs to test if the median of en-ergies in the task condition is greater than that of the resting-state condition.Since channel-wise energy values are not normally-distributed, we use thenonparametric Wilkoxon rank sum test to assess statistical significance be-tween the two conditions. This procedure yields a binary map M60×1 for eachsubject in which M(i) = 1 indicates statistically significant energy increaseat channel i. The significance maps for different subjects are then averagedto yield an average map of topographical S-Transform energy increases inthe desired frequency band. Finally, the resulting average significance mapM¯60×1 is arranged in topographical plots using spatial information from allelectrodes, where ’brighter’ spots represent local significant task-specific en-29ergy increases which have survived subject averaging. The algorithms usedin generating these plots typically utilize quadratic interpolation between thenearest electrodes to allow for smooth, more realistic transitions between thevalues of different electrodes, and hence aid in visual interpretation of theresults.In the following, we present the results of applying above analysis methods oneach of the tasks using the aggregate data from all subjects in ICORD and LSBB.We will categorize our results based on each of the cognitive, sensory, and motortasks.Cognitive TasksFigure 2.6a depicts significance maps of the backward counting task in alpha, beta,low gamma, and high gamma frequency bands. It is evident from the topograph-ical plots that during the counting task, spontaneous alpha and beta activity arelocalized more or less symmetrically on the parietal lobes, while prefrontal lobesas well as centro-parietal electrodes show more activation in the gamma band.Moreover, Figure 2.6b illustrates the quantitative PCR information for eachbrain region and frequency band, where the colored bars represent the averagePCR values among all subjects and all electrodes in a specific brain region, and theerror bars represent the standard deviations of the aforementioned PCR values. Weobserve that on average, spontaneous alpha band has the highest increase in energyduring counting. We believe that this was a side-effect of keeping the subjects’eyes closed during counting, and not a direct influence of the cognitive task, sincethese large power increases in the alpha band have not passed the significance testwhile being compared with resting-state energies in Figure 2.6a.Alpha and beta band patterns depicted in Figure 2.7 for the matching task areobserved to be more centralized and concentrated on the right parietal region. Sim-ilarly to Figure 2.5a, the matching task has caused more activity within the gammaband than the counting task. Interestingly, mid-parietal and occipital areas havereduced energies during matching in alpha and beta bands, while a global increasein gamma band energies (less so in central areas) is observed, and more areas ofthe brain are involved in cognitive processing in high gamma ranges compared to30(a)alpha beta lowgammahighgamma-1.5-1-0.500.511.522.53Power Change Ratio (PCR)Pre FrontalFrontalCentralLeft TemporalRight TemporalParietalLeft ParietalRight ParietalOccipital(b)Figure 2.6: a) Significance maps obtained from channel-wise statistical test-ing between the rest condition and backward counting task at four fre-quency bands; b) Power Change Ratios of the backward counting taskat different frequency bands and different brain sites.31(a)alpha beta lowgammahighgamma-1.5-1-0.500.511.522.533.5Power Change Ratio (PCR)Pre FrontalFrontalCentralLeft TemporalRight TemporalParietalLeft ParietalRight ParietalOccipital(b)Figure 2.7: a) Significance maps obtained from channel-wise statistical test-ing between the rest condition and the matching task at four frequencybands; b) Power Change Ratios of the matching task at different fre-quency bands and different brain sites.32the lower gamma rhythms.(a)alpha beta lowgammahighgamma-1.5-1-0.500.511.522.53Power Change Ratio (PCR)Pre FrontalFrontalCentralLeft TemporalRight TemporalParietalLeft ParietalRight ParietalOccipital(b)Figure 2.8: a) Significance maps obtained from channel-wise statistical test-ing between the rest condition and the brushing task at four frequencybands; b) Power Change Ratios of the brushing task at different fre-quency bands and different brain sites.Sensory TasksAccording to Figure 2.8, brushing of the right hand causes alpha, beta, and gammaenergy increases in the contralateral (left) central electrodes. With increasing fre-33(a)alpha beta lowgammahighgamma-1.5-1-0.500.511.522.533.5Power Change Ratio (PCR)Pre FrontalFrontalCentralLeft TemporalRight TemporalParietalLeft ParietalRight ParietalOccipital(b)Figure 2.9: a) Significance maps obtained from channel-wise statistical test-ing between the rest condition and application of hot packs at four fre-quency bands; b) Power Change Ratios during the application of hotpacks at different frequency bands and different brain sites.quency, centro-parietal lobes on the ipsilateral region (channels C4, CP4 and P6)also take part in information processing. On the other hand, Figure 2.9 demon-strates that holding hot packs has caused energy increases within the contralat-eral central region, most notably in the beta band, as well as significant prefrontalgamma band activity (Figure 2.9).34Motor Tasks(a)alpha beta lowgammahighgamma-1-0.500.511.522.533.54Power Change Ratio (PCR)Pre FrontalFrontalCentralLeft TemporalRight TemporalParietalLeft ParietalRight ParietalOccipital(b)Figure 2.10: a) Significance maps obtained from channel-wise statistical test-ing between the rest condition and the ankle movement task at fourfrequency bands; b) Power Change Ratios of the ankle movement taskat different frequency bands and different brain sites.Figure 2.10 illustrates the effect of ankle movement on EEG at different fre-quency bands. Most notable effects are alpha and gamma prefrontal energy en-hancements, symmetrical alpha and beta energy increases within temporal regions,and gamma energy enhancements on the contralateral P1 electrode. While beta35(a)alpha beta lowgammahighgamma-0.500.511.522.533.544.55Power Change Ratio (PCR)Pre FrontalFrontalCentralLeft TemporalRight TemporalParietalLeft ParietalRight ParietalOccipital(b)Figure 2.11: a) Significance maps obtained from channel-wise statistical test-ing between the rest condition and the wrist movement task at four fre-quency bands; b) Power Change Ratios of the wrist movement task atdifferent frequency bands and different brain sites.36band is minimally contributing to the energy increases during ankle movements, itis more active during wrist movements as seen in Figure 2.11. Moreover, gammaband activity seems to be more focused on the frontal areas during movements ofthe wrist in comparison with the ankle movement task.2.4 Discussion And ConclusionsIn this chapter, we used the Stockwell Transform to analyze spectral and spatialaspects of 60-channel EEG recordings corresponding to different cognitive andsensorimotor conditions.We first compared the gamma band (30−100 Hz) content of signals acquiredat the low-noise environment with those collected at the hospital facility in section2.3.2, and found significant differences between the two environments in their abil-ity to detect task-specific spontaneous gamma band oscillations, especially duringmotor tasks. In other words, we observed higher task-rest spontaneous gammaband energy ratios at LSBB in comparison with ICORD. This is clearly an advan-tage for studies in a low-noise environment such as LSBB, indicating its potentialfor detection of EEG benchmarks related to understanding central nervous system(CNS) control of basic motor tasks or early detection of disorders associated withchanges in motor behaviors (e.g. Epilepsy, Parkinsons disease, etc.). Low-noiseenvironments, like the LSBB, would also facilitate a greater understanding for po-tential subtle changes in cortical plasticity after CNS motor injuries (e.g. spinalcord or brain damage).In section 2.3.3 of this chapter, we used data from all subjects, including thosewho were not common to both environments, and carried out the same Stock-well transform time-frequency analysis method; though with slightly different ap-proaches to highlight functional differences of various frequency bands and differ-ent brain sites. Contrary to section 2.3.2 where the analysis was only based on thegamma band, in this section we also examined the role of alpha and beta bands, aswell as separated the upper and lower halves of the gamma frequency range intotwo subbands. Each of the tasks and conditions in our study protocol integrateunique and complex spectral and spatial EEG patterns. Since a detailed neurolog-ical analysis of each of the task-specific EEG patterns is beyond the scope of this37thesis, we have presented a brief summary of the observed patterns for each taskin section 2.3.3, and we will leave further analyses to future publications. We will,however, state one unifying observation among all of the tasks: high-frequencyEEG activity is not as centralized and localized to specialized brain areas as lower-frequency activity; rather, it seems that the brain tends to employ more and morelarge-scale neuronal networks with high-frequency synchronization in higher-levelstages of cognitive and sensorimotor information processing.This work bore a number of limitations. First, the number of subjects and hencethe size of our dataset was not large enough to yield statistically rigorous results.In fact, the large standard deviations seen in figures in section 2.3.3 as long errorbars is in part due to the high between-subject variability observed in the results.Moreover, the data at LSBB was improperly annotated. In other words, the dataduring each task was mixed with resting-state epochs, and the only markings on thedataset were put on rough start and end points of different tasks, not the resting-state epochs in between them (see Appendix A). This could have introduced biasesand imperfections in our data analysis pipeline. It also limits our scope of analysisof the data; for instance, since the correspondence between the VAS ratings forthe heat sensory task and actual time points in the dataset was unclear, the VASratings could not be used to correlate the strength of gamma band oscillations withsubjective pain experience. (the limitations of the study protocol are revisited indetail in section 4.2).To address the limitations of the current work, studies using a larger numberof subjects are necessary for more stringent statistical validation and more confi-dent conclusions. One might also consider designing a protocol for detection ofevoked and induced potentials with time-locked experimental trials as opposed tospontaneous EEG. Interactive automated acquisition systems, such as those usingcomputer-generated auditory or visual cues for start and end points of performingtasks would greatly enhance the capabilities of our future analyses.38Chapter 3Granger-Causal ConnectivityAnalysis3.1 Introduction3.1.1 Motivation for Connectivity AnalysisWith the dawn of the 21st century, the neuroscience community has emphasizedthe need to move beyond functional segregation, which refers to the existence ofspecialized neuronal populations to form functionally segregated cortical areas, tostudies of functional integration of the brain; i.e. viewing the brain as an intercon-nected system in which the interplay among different parts acts as a crucial elementin neural operation and formation of coherent cognitive and behavioral states [68].Historically, this notion of ’brain connectivity’ might have stemmed from Cajal’sneuron doctrine [69], stating that while the neuron is a separable entity in itself,its operation largely depends on the input gathered from other neurons. Over theyears, these ideas have resulted in a large number of multidisciplinary tools andmethodologies for studying the large-scale interactions between different, possiblyremote brain regions and unveiling the so-called human Connectome.Brain connectivity patterns are dynamic in nature; links among neuronal as-semblies may form or disappear in milliseconds [70], allowing for fast and tran-39sient information transfer among brain regions. Therefore, it is important to studyconnectivity in a framework that encompasses both time and space simultaneously.While the popular FMRI modality allows for high spatial resolution in studyingbrain function, efforts in fMRI are generally complicated by its relatively low tem-poral resolution. Moreover, recent research suggests that typical assumptions andstatistical methods used in fMRI introduce a high number of false positives andlead to erroneous conclusions [71]. On the other hand, the low-cost, non-invasivescalp EEG offers substantially higher temporal and spectral resolution. With theaid of proper computational data analysis tools and an acquisition system compris-ing of densely distributed electrodes, EEG is an attractive candidate for studyingrapidly changing spatiotemporal interactions among brain regions.3.1.2 Different Categories of ConnectivityConnectivity patterns of the brain can be studied from several perspectives. Gen-erally, studies of connectivity fall into one or more of three categories: anatomical,functional, and effective connectivity.Anatomical or structural connectivity aims at describing the biophysical (i.e.axonal) communication links between neuronal assemblies. One example of themethodologies in this field is the neuroanatomical tract tracing [72], an invasivetechnique to provide information about direct axonal connections in vivo. Anatom-ical connectivity can also be studied non-invasively, though with lower spatial reso-lution, by means of diffusion weighted imaging techniques such as diffusion tensorMRI (DTI) [73].The goal of functional connectivity, on the other hand, is not to understandthe physical capability of axonal links. Rather, functional connectivity is con-cerned with finding evidences of statistical dependence among large-scale neuronalunits, regardless of the presence of direct anatomical connections. The dependenceamong brain regions is typically examined by means of cross-correlation, spectralcoherence, or mutual information, and therefore has no notion of direction or cau-sation. Primary tools for the analysis of functional connectivity, including fMRIand Positron Emission Tomography (PET), have shown that functional connectiv-ity is related to behavior in a variety of different tasks [74].40In addition to functional connectivity, effective connectivity attempts to under-stand causation among neural units, i.e. the influence that one neural system hasover another. In other words, in comparison with functional connectivity, effectiveconnectivity provides additional information about the direction of interactions aswell as their presence. Current techniques for determining effective connectivityinclude Granger-causal modeling, dynamic causal modeling, structural equationmodeling, and transfer entropy, applied to neuroimaging data such as fMRI as wellas EEG/MEG time series [75]. Methodologies implemented in this chapter typ-ically fall under the category of task-relevant effective connectivity. It is worthmentioning that there is not always a sharp distinction between the terminology ofeffective and functional connectivity, as sometimes directed connectivity relevantto a particular function might be called functional connectivity.3.1.3 Modeling And Estimation of ConnectivityVarious methods have been devised for quantification of connectivity patterns overthe past decades. While most of these methods rely completely on the data to in-fer connectivity patterns (data-driven approaches), there are also techniques whichassert specific prior assumptions on the connectivity structure (model-based ap-proaches). Dynamic causal modeling (DCM) [49] is a popular example of a model-based technique which relies on comparing different models of connectivity basedon the relative evidence for one model compared to another [50]. Structural Equa-tion Modeling (SEM) is another hypothesis-driven approach based on explainingthe observed covariance among several variables by a defined anatomical network[76]. On the other hand, correlation-based methods and information-theoretic tech-niques such as transfer entropy [77] and mutual information [78] exemplify meth-ods that do not depend on prior assumptions on the model and try to find connectiv-ity structure solely based on the data. The model-based methods are valuable whenthere is some validated pre-existing knowledge about the underlying dynamics ofconnectivity, which is usually not the case in the current state of neuroscience withso many unknown patterns of interactions that are yet to be discovered.From a different perspective, the connectivity estimation metrics can be classi-fied into either linear or nonlinear measures. Typically, most of the methods in the41literature are based on linear assumptions; while information-theoretic approachesor methods such as the imaginary part of coherency [79], do not assume linear re-lations among variables. Linear methods are generally easy to implement and aresufficient for detection of interactions such as coupling of oscillations at similarfrequencies, while nonlinear methods are useful if we are interested in nonlinearforms of coupling, such as cross-frequency coupling at two different frequencies[80]. Moreover, while it may seem counter-intuitive to apply linear methods toproblems of highly nonlinear nature such as EEG, it has been shown that manybiomedical signals can be sufficiently characterized and analyzed by means of lin-ear methods [81].Connectivity metrics may also be classified into bivariate or multivariate mea-sures. Bivariate measures find patterns of interaction among a multiplicity of sig-nals by calculating pair-wise connectivity separately for each channel pair. Onthe other hand, for computing multivariate measures all channels are taken intoaccount at once by fitting a full multivariate model. Most of the nonlinear connec-tivity measures such as mutual information and phase synchronization are bivariate[48]. It is shown that in the case of densely inter-connected networks, multivariatemeasures are strongly preferred since bivariate measures may lead to misleadingand spurious connectivity patterns [48].Through the rest of this thesis, we focus on a model-based, linear, and mul-tivariate method based on Granger causality [82]. Originated from the field ofeconomic time series, Granger causality describes a framework for quantifying theinfluence of signal A(t) on another signal B(t) by the ability of A to predict sub-sequent instances of B. Due to their simplicity, interpretability, and the minimalprior assumptions posed on the data, Granger-causal methods have been exten-sively used in biomedical data analysis [83]; and their use has been extended tomore than two signals by means of MultiVariate AutoRegressive (MVAR) modeling[84]. Moreover, many of these methods operate in the frequency domain and haveproper adaptive variants to deal with nonstationarity of the multivariate signals,thus being good candidates for analysis of connectivity within specific frequencybands of a nonstationary multivariate process such as EEG.Until recently, analysis of connectivity was based on the implicit assumptionthat the pattern of interactions among brain regions remains fairly constant over the42course of performing a task or the period of data collection [74]. This assumptionhas led to an extensive number of studies contributing to our understanding oflarge-scale interactions. However, results of these studies typically represent theaggregate or average connectivity patterns ’smeared’ across time. In cases such asstudying the formation and propagation of epileptic seizures, however, analysis ofchanges in dynamic connectivity over smaller, near instantaneous time scales willlead to greater insights into the fundamentals of brain networks [85]. In this thesis,we have analyzed our data both from a static and dynamic perspective, with theresults of the former and latter approaches presented in sections 3.4.1 and 3.4.2,respectively.This chapter is organized as follows. In section 3.2 we describe the theorybehind MVAR modeling and Granger-causal methods and introduce a number ofconnectivity measures based on Granger causality. Section 3.3 discusses the prac-tical issues faced when these theories are to be implemented on real EEG data, aswell as our methods and approaches in solving these issues. Once the theory andmethods are introduced, the results of applying the static measures on our data arepresented in section 3.4.1. In section 3.4.2, we extend our use of these measuresto the time-varying case in order to incorporate time evolutions of the connectivitypatterns.3.2 Theory3.2.1 Granger CausalityGranger’s original definition of causality [82] is based on the fact that causes pre-cede their effects in time, and that knowledge of the cause aids in predicting theeffect. Specifically, let us assume that we are interested in predicting the value of atime series x1 at time t based on a linear combination of its p previous values:x1(t) =p∑i=1A11(i)x1(t− i)+ ε(t) (3.1)where ε(t) is the prediction error. If, in predicting the current value of x1(t), weincorporate also q previous values of another signal x2(t), we will attain a different43prediction error ε ′(t):x1(t) =p∑i=1A′11(i)x1(t− i)+q−1∑j=0A12( j)x2(t− j)+ ε ′(t) (3.2)In this context, x2 is said to Granger-cause x1 if it can be shown that ε ′ is an im-provement over ε . This improvement in the prediction error needs to be assessedin a statistical sense, e.g. by performing an F-test on the variances of ε(t) and ε ′(t),given assumptions of covariance stationarity on x1(t) and x2(t).3.2.2 MultiVariate AutoRegressive (MVAR) ModelsGranger-causal relations between signals x1(t) and x2(t) in equation 3.2 can alsobe inferred through parameters A′11(i), i = 1, ..., p and A12( j), j = 0, ...,q− 1.These parameters, along with a similar set of parameters relating x2(t) with pastvalues of itself and x1(t), comprise an autoregressive (AR) model. Autoregressivemodeling is a simple yet effective approach for characterization of time series andtheir spectra. The order of the model (p, q, etc.) is the number of precedingobservations included in the model and depends on the dynamics of the signal. Thecoefficients Ai j are essentially features carrying information about the behavior ofthe time series. In the context of Granger causality, these features represent theamount by which past values of a signal aid in prediction of the current values ofanother signal (hence an implicit notion of causation).Multivariate autoregressive (MVAR) models extend this approach to more thantwo time series by predicting each of the signals based on the previous values ofall other signals. Specifically, let X denote a K-dimensional stochastic multivariateprocess of length T . In our case, X corresponds to the set of K = 60 channelsof EEG recorded over T time points. A value of this process at time instant t isthe K-dimensional data vector X(t) =(X1(t),X2(t), ...,Xk(t))′. This vector can beestimated as a regression on its p previous values (a vector autoregressive process)as:X(t) =p∑m=1AmX(t−m)+E(t) (3.3)44Here, Am’s are K ×K model coefficient matrices where Am(i, j) represents theeffect (weight) of sub-process X j on Xi at lag m; and E(t) is a K-dimensionalzero-mean white noise process with a non-singular covariance matrix Σ. We haveassumed, without loss of generality, that X1(t),X2(t), ...,Xk(t), k = 1, ...,K arezero-mean sub-processes and that the same model order p is required to regress onall signals.Relating equations 3.2 and 3.3, extension of Granger causality to more thantwo variables thus involves fitting an MVAR model to the data. In this context, atime series Xi(t) is called a Granger cause of the time series X j(t) if at least at onelag m, m = 1, ..., p , the corresponding element of the coefficient matrix Am(i, j)is significantly greater than zero in absolute value sense [86], [87].3.2.3 Autoregressive Modeling of Nonstationary DataIn practice, autoregressive models are typically restricted to stationary time seriesso that an accurate model fit can be realized. However, many biomedical signals,specially the EEG, are highly nonstationary in nature. There are two approachesfor modeling nonstationarity EEG time series:I. Segmentation: We may assume that segments of EEG in small overlappingwindows are at least quasi-stationary, so an MVAR model can be accuratelyfit to each of the segments. Adopting a similar concept to Short Time FourierTransform (STFT), we therefore model local sections of a multivariate signalas it changes over time.A problem with this approach is the concern of having sufficient data pointsfalling within each segment. Fitting an MVAR model to a high-dimensionaltime series amounts to determining a large number of parameters relating eachchannel to lagged values of other channels. Therefore, a large number of datapoints are needed to have a well-posed fitting problem and this restricts ourability to choose a short window length for satisfying assumptions of quasi-stationarity. Nonetheless, fitting MVAR models to long segments of EEGhas been suggested in the literature [88], [89], and can be justified as beinguseful in assessing the aggregate connectivity structure within each window,disregarding the transients. In section 3.4.1, we will fit models to 10-second45epochs of EEG and average the results over all epochs. This may lead us toan overview of the average connectivity structure inferred from a full-lengthrecording during a specific task.II. Adaptive models: Alternatively, we can model the nonstationary EEG usingadaptive variants of the MVAR process, i.e. assuming that the model itselfvaries over time in accordance with the data. In this sense, the matrices Am(and hence the connectivity structure) are dependent on time and the equation3.3 can be modified to represent instantaneous model parameters:X(t) =p∑m=1Am(t)X(t−m)+E(t) (3.4)This approach will capture the transient features of effective connectivity andresult in dynamic task-specific connectivity analysis. Details regarding adap-tive MVAR modeling are discussed in section 3.3.2.Through the rest of this chapter, we have used a constant parameter matrixnotation A. It goes without saying that in the adaptive case, this matrix (andits corresponding variants) can be implicitly substituted with A(t), its instan-taneous value at time t.3.2.4 Representation in Frequency DomainThe formulation in section 3.2.2 can be transformed to the frequency domain tostudy couplings in different frequencies, as is common with EEG analysis. Specif-ically, rearranging 3.3 and assuming Aˆ0 = I and Aˆm =−Am,E(t) =p∑m=0AˆmX(t−m). (3.5)Transforming 3.5 into the frequency domain, we getE( f ) = A( f )X( f ) (3.6)A( f ) =p∑m=0Aˆmexp(−2piim f/ fs) (3.7)46where fs is the sampling frequency. 3.6 can also be rearranged in the followingform:X( f ) = A−1( f )E( f ) = H( f )E( f ) (3.8)Equation 3.8 suggests that the AR approach models the process X as a filter actingon the white noise process E. Since the spectrum of white noise is flat over allfrequencies, information about the spectral content of X is contained in the matrixH( f ), A−1( f ), also known as the transfer matrix. From the transfer matrix H( f )and the prediction error covariance matrix Σ, the spectral density matrix S of theprocess can be calculated asS( f ) = X( f )X∗( f ) = H( f )E( f )E∗( f )H∗( f ) = H( f )ΣH∗( f ) (3.9)where ∗ denotes complex conjugation. As we shall see in the following section,matrices S( f ), H( f ), and A( f ) derived from the EEG process carry informationabout directed connectivity, and several quantitative connectivity metrics have beendefined in the literature based upon these matrices, each targeting a different aspectof information flow.3.2.5 Frequency Domain Estimators of Directed ConnectivityHere we introduce and define a selection of quantitative metrics for effective con-nectivity in a coherence and/or Granger-causal sense, derived from the matricesdefined in the previous sub-section. Our goal is not to provide a comprehensive re-view on these measures, so the list goes well beyond the few measures introducedherein.• Coherency (Coh): Perhaps the simplest measure of coupling in the fre-quency domain is Coherency, defined in terms of the spectral matrix S asCi j( f ) =Si j( f )√Sii( f )S j j( f )(3.10)Coherency measures the degree of synchrony among the subprocesses at dif-ferent frequencies and is not a directional measure. The directional versions47of coherency, such as Directed Coherence [90] are limited to bivariate mod-els and do not fully consider the multivariate nature of the process [91].• partial Coherence (pCoh): In a multivariate process, coherence betweentwo subprocesses might be influenced by all other variables. The PartialCoherence [92], [93] attempts to find the portion of coherence between twosubprocesses which cannot be explained by a linear combination of othercommon inputs. Partial Coherence is defined as:Pi j( f ) =Mi j( f )√Mii( f )M j j( f )(3.11)where Mi j is a minor determinant of S with the i−th row and j−th columnremoved. It can be shown [94] that (3.11) is equivalent toPi j( f ) =Sˆi j( f )√Sˆii( f )Sˆ j j( f )(3.12)where Sˆ( f ) = S−1( f ).• Partial Directed Coherence (PDC): Another estimator based on the ma-trix A( f ), the Partial Directed Coherence (PDC), has been proposed in [95].PDC is defined in terms of the coefficient matrix A as:pii j( f ) =Ai j( f )√∑Kk=1 |Ak j|2(3.13)The complex quantity pii j( f ) can be interpreted as the causal flow from chan-nel j to channel i normalized by all outflows from channel j. Since it is basedon the values Ai j (the parameters of the MVAR model), PDC can be viewedas a frequency-domain equivalent of multivariate Granger causality [96].• Directed Transfer Function (DTF): Similarly to PDC, the Directed Trans-fer Function (DTF) [84] is a multivariate directional measure defined based48on the elements of the transfer matrix H asγ2i j( f ) =|Hi j( f )|2∑Kk=1 |Hik( f )|2(3.14)γ2i j represents the directional flow from channel j to channel i normalizedby the sum of flow from all channels to channel i. The normalization inthe original definition of DTF (3.14) is done in order to compare directedcomponents in signals with different power spectra [97]. However, DTF canalso be defined in a simpler, non-normalized format as:θ 2i j( f ) = |Hi j( f )|2 (3.15)It is argued in [86] that DTF does not represent Granger Causality. Rather,DTF and Granger causal tools such as PDC focus on different and comple-mentary aspects of the connectivity structure.• full-frequency Directed Transfer Function (ffDTF): Integrating the de-nominator in (3.14) over frequency leads to a variant of DTF, full-frequencyDTF (ffDTF) [98]:λ 2i j( f ) =|Hi j( f )|2∑ f ∑Kk=1 |Hik( f )|2(3.16)Compared to DTF, ffDTF allows for better interpretation of the estimatorcharacteristics at different frequencies.• direct Directed Transfer Function (dDTF): DTF and its variants show notonly direct but also indirect, mediated interactions [98]. For instance, if twonon-interacting channels A and B are influencing channel C such that A→Cand B→C, then DTF will falsely detect the indirect interaction A→ B. Amore robust variant of DTF that is able to distinguish between direct andindirect flows among channels is introduced in [98] as the product of full-49frequency DTF and partial coherence:δ 2i j( f ) = λ2i j( f )P2i j( f )=|Hi j( f )|2∑ f ∑Kk=1 |Hik( f )|2× (Sˆi j( f ))2Sˆii( f )Sˆ j j( f )(3.17)Direct DTF (dDTF) is thus a multivariate directional measure which com-bines information from both DTF and Partial Coherence.A comparison of some of the measures introduced above is presented in [99],where it is concluded that all measures perform nearly equivalently under reason-able recording conditions. In this thesis, we proceed with dDTF as our measure ofeffective connectivity since it has the combined advantages of ffDTF and PartialCoherence.3.3 Workflow, Methods, And Practical ConsiderationsIn section 3.2 we outlined the theory underlying Granger-causal analysis and in-troduced a number of connectivity estimators. We concluded that we can estimateeffective connectivity in multi-channel EEG using an approach based on linearMultivariate Autoregressive models; and that this approach can be used adaptivelyto infer instantaneous connectivity patterns. The detailed procedure for obtainingan estimate of the connectivity structure from raw EEG data is depicted in Figure3.1. In the following, we will discuss methods and practical issues related to eachstep of the procedure.3.3.1 Pre-processing And Artifact RemovalThe first step is to remove artifacts from the data as outlined in section 2.2.1, thoughmore stringent criteria need to be exercised for removal of artifacts. In other words,contrary to the previous chapter, here we also reject, as much as possible, portionsof data corresponding to blinks and low-frequency artifacts as they affect and dis-tort the parameters of the MVAR model, especially in the adaptive, time-varyingcase.Extra caution needs to be exercised in pre-processing of the EEG for estimation50MVAR Model FittingComputation of Connectivity EstimatorsStatistical Significance TestsInterpretation of significant StructuresVisualizationPre-processingModel ValidationFigure 3.1: From raw time series to connectivity patterns: steps for estimat-ing effective connectivity based on multivariate autoregressive modelsof the connectivity measures. Since these measures are dependent on the signalphase, any filtering with phase distortion would invalidate the final results. Re-referencing is another procedure that would distort the estimates, as the choice ofreference is shown to have a significant impact on the derived network attributes[100], and average-rereferencing mixes the signals and introduces false correla-tions between them. We thereby chose to have as little pre-processing steps aspossible, bypassing the conventional pre-filtering steps. We do, however, normal-ize every channel by removing the mean and dividing by the standard deviationaccording to the Equation (3.18) below prior to segmentation and MVAR model-ing:xnormk (t) =xk(t)− xk(t)σk, k = 1, ...,K (3.18)51where xk(t) and σk refer to the temporal mean and the temporal standard de-viation of the signal at electrode k, respectively. Since many of the connectivitymeasures described in section 3.2.5 are highly dependent on scale and variances ofthe signals, this step is performed to scale the variances among different signals toa comparable range in order to prevent model misspecifications.3.3.2 Model Fitting And ValidationHaving ensured that the data is free of artifacts, the next step would be to fit anMVAR model to the time series. Model fitting refers to implementation of analgorithm for computing the coefficient matrices Am, m = 1, ..., p and the errorcovariance matrix Σ (See Equation 3.3) given the process time series X collectedover T time points. Here we discuss our choice of the fitting algorithm and thecriterion for choosing the model order p.The Model Fitting AlgorithmAs discussed in section 3.2.3, there are two approaches for MVAR modeling ofnonstationary EEG time series: 1) Segmentation, which results in batch-averagedconnectivity estimation, and 2) Adaptive MVAR modeling, resulting in instanta-neous (dynamic) connectivity estimation.Static MVAR models can be fitted to a batch of signals falling within a windowusing various methods including least-squares (Yule-Walker) approaches, Burg’smethod, and the Vieira-Morf algorithm. In this thesis, we have used an efficientstep-wise least squares method proposed in [101] and [102]. The only considera-tion here is the choice of the window length, which is dependent upon the minimumanalysis frequency and the number of parameters of the MVAR model. We chosethe window length to be 10 seconds as in [88] and [89]. Considering the estima-tion problem, there are K2 p free parameters to estimate in an MVAR model andas a rule of thumb, at least 10 times more data samples are needed for an accurateestimation ([51]). With a generic order of p = 8, we have 602 ∗8≈ 29000 param-eters to estimate and we need at least 290000 data points, which are provided ina 10-second window (60(channels) ∗ 500(Hz) ∗ 10(s) = 300000). Therefore, theselected window length of 10 s seems to be a reasonable choice. We have also52included an overlap of 50% (5 seconds) between windows in order to have morebatches of available data as well as a smoother distribution of connectivity param-eters.In addition to batch-based models, adaptive MVAR models are estimated us-ing the Recursive Least Squares (RLS) algorithm with forgetting factor [103]. TheRLS algorithm was preferred over methods such as Kalman filtering due to be-ing better suited for high-dimensional data. Specifically, in Kalman-filter basedapproaches, the required matrix inversions cannot be avoided [103] and this is spe-cially undesirable in cases when the dimension of the time series is large. Also, it isshown in [103] that the model dimension has no influence on the RLS algorithm’sadaptation speed and its estimation properties. The only tuning parameter of thealgorithm, the forgetting factor, represents the trade-off between adaption speedand the variance of the estimation (this parameter was empirically set to 0.002 andwas fixed throughout all recordings).Choice of the Model OrderIn an autoregressive model, the order p is the number of lags used for regression onthe previous process values. Since the order is not known a priori, we need a data-driven criterion that would determine an optimal value for p given the multivariatetime series. The most popular methods to this end are information-theoretical ap-proaches such as Akaike’s Final Prediction Error (FPE) [104], and the SchwarzBayesian Criterion (SBC) [105]. Generally, these methods attempt to minimizean entropy-based objective function comprising of a prediction error term and apenalty term for including too many parameters (large model orders). By mini-mizing both terms over a range of model orders, they search for an order which isoptimal in the sense that it is both parsimonious and that it predicts the data well.The FPE and SBC methods function rather conservatively and impose too higha penalty for large model orders; that is, when used on a 10-second segment of ourEEG data, FPE and SBC criteria yield optimal orders of 3 and 1 respectively, whichare likely too low for accurate spectral identification. Therefore, we have used arather heuristic approach for picking a proper model order. This approach is basedon the fact that if the model is accurately representative of the data, the correlation53structure of the data will be completely described by the model. Hence the residu-als U(t) = X(t)−∑pm=1 AˆmX(t−m) should not exhibit significant correlation, andvalidating the model amounts to checking the whiteness (uncorrelatedness) of itsresiduals. This can be assessed by computing cross-correlations of the residuals upto some maximum lag, and checking whether they will be sufficiently small withthe current choice of the model order.-50 -40 -30 -20 -10 0 10 20 30 40 50Lag (samples)-0.8-0.6-0.4-0.200.20.40.60.81Correlation valueFigure 3.2: Normalized auto and cross-correlations among all 60 channels ofthe model residualsWe found that a model order p = 10 is enough to keep the normalized covari-ance of the residuals reasonably small. Figure 3.2 depicts the correlation structureof the residuals of a model with p = 10 fitted to a 10-second segment of the data(the 602 autocovariance and cross-covariance sequences for all combinations of theresidual dimensions are overlaid on the same plot). We observe that with p = 10,residual correlations will be bounded by ±0.05 for all lags other than zero. Hence,we may claim that with %95 confidence, the residuals are white and the modelis valid. We have also empirically assumed that this choice of the optimal modelorder is sufficient to keep the residuals white among all of the recordings. Based54on this observation, the order was also kept fixed at p = 10 for dynamic MVARmodeling in the RLS algorithm.3.3.3 Computation of Connectivity EstimatorsOnce we have fitted a valid MVAR model to the data, we may proceed to computingthe quantitative measures of effective connectivity described in section 3.2.5 fromthe parameters of the model. As shown in section 3.2.2, fitting MVAR models tothe time series data would result in K-by-K parameter matrices Am, m = 1, ..., p.These parameter matrices are then transformed to the frequency domain (Equation3.7) to yield arrays of the form A( f ) (K×K×Nt ×N f ), where• Nt is, for the static connectivity case, the number of overlapping windows(segments) extracted from the whole length of the recording; whereas in thedynamic connectivity case Nt is the number of discrete time samples;• N f is the number of discrete frequency values at which A( f ) is evaluated.These four-dimensional arrays encapsulate the model parameter information interms of time (or epoch), frequency, and channel-wise interactions. Once com-puted, they are passed to functions calculating the connectivity estimators ex-plained in section 3.2.5, which in turn yield connectivity arrays of a similar form C(K×K×Nt×N f ). As a case in point, assuming we have calculated the connectiv-ity measure DTF (Equation 3.15), the element (i, j, t, f ) in the connectivity array Crepresents the causal interaction of channel j on channel i at time t and frequencyf as measured by the metric DTF.An issue arising in computation of dynamic (time-dependent) connectivity struc-tures is that these arrays can easily become so large that they exceed the availablecomputer memory and cause programs to be unresponsive. For instance, whencalculating the time-varying dynamic connectivity of 10 seconds of data in 50 fre-quency points, the connectivity array will take up to 60×60×10×500(Fs)×50×8(bytes per array element) = 7200 megabytes in memory. Considering the factthat these arrays are to be further manipulated through the rest of the program andcompared among conditions and subjects, they are impractical to use unless some-how compressed and reduced. To this end, we have eliminated the third dimension55(frequency) by integrating the measures over frequency in the bands of interest.Moreover, in this thesis, we have examined the time-varying connectivity structureonly during a short period of time after the beginning of performing a task (usuallythe first 5 seconds).3.3.4 Tests for Statistical SignificanceProper interpretation of connectivity patterns is not achievable without a suitablestatistical testing scheme which is able to distinguish significant interactions frominsignificant ones. Specifically, we have seen that computation of any connectivityestimator on a segment of EEG at a particular time and frequency yields K2 values,each corresponding to the directional flow from one channel to another. Thesevalues often need to be compared between two conditions and assessed amongsubjects to infer significant and consistent patterns. Similar to our approach in theprevious chapter, we have compared pair-wise connectivity values during each taskto those of the resting state. In this sense, a task-specific connection from channel Ato channel B is deemed significant if and only if its connectivity value is greater (ina statistical sense) than that of the resting state. Our methods for statistical testingare customized to the static and dynamic connectivity estimation as follows:• In the case of static connectivity, we are comparing frequency-integrated ar-rays Crest(K ×K ×Nrest) and Ctask(K ×K ×Ntask). Each directed pair ofchannels has Nrest realizations (hence a ’distribution’ of connectivity val-ues) in the resting state and Ntask realizations during performance of the task(Figure 3.3a). For each directed pair of channels, we can therefore com-pare means of the two distributions for the rest and task conditions using aWilkoxon signed rank test. Once the means of all resting-state batches arecompared with those of the task state, a K ×K ’significance matrix’ S ofzeros and ones is derived in which S(i, j) = 1 implies that for the interac-tion from channel j to channel i, the mean connectivity value during task issignificantly greater than the mean connectivity value during rest, and hencethe connection from j to i is task-specific. By comparing the means of thetwo distributions, we are essentially examining the time-averaged (or morespecifically, batch-averaged) connectivity over all epochs of the rest and task56recordings.0 5 10 15 20Crest(i,j) and Ctask(i,j)00.020.040.060.080.10.12Crest(i,j)Ctask(i,j)(a)2 4 6 8 10 12Crest(i,j)00.0050.010.0150.020.0250.030.0350.040.045Normalized HistogramEmpirical CDF Ccrit(i,j)(b)Figure 3.3: Our statistical significance testing method for determination ofsignificant pair-wise interactions. The directed pair whose connectivityvalues are depicted above are FC2 and F3, with C(i, j) signifying thedirected interaction FC2→ F3. (a) In static connectivity estimation, allvalues of pair-wise interactions at rest are compared with those duringtask in an offline manner; (b) In dynamic connectivity estimation, in-stantaneous values of interactions during task are compared with a crit-ical value obtained from the cumulative distribution of all resting-statevalues.• As for dynamic connectivity, significant interactions need to be identified atevery instant throughout the length of the recording. Hence, pair-wise distri-butions of rest and task connectivity values cannot be assessed in an offlinemanner that leads to loss of temporal information. Rather, we may gatherall resting-state connectivity realizations (at all time instants) into a ’base-line distribution’, and examine at what point in time the connectivity valueduring a task is exceeding a ’critical’ value (Figure 3.3b). In this context,the critical connectivity value Ccrit(i, j) for each directed pair of channelsis defined as the value at which the cumulative distribution of resting-stateconnectivity values reaches 1−α , where α is some significance level. Es-sentially, significant connectivity values during a task are values which areunlikely to occur during rest; and that is the rationale behind looking at the57tail of the resting-state distribution. The significance matrix S in this casewould be of size K×K×Nt and would comprise of the instantaneous sig-nificant interactions evolving over time.It is worth mentioning that simultaneous comparison of a large number of in-teractions will raise the chances of occurrence of type 1 errors. Hence, the signifi-cance level needs to be corrected and set to a more conservative value to decreasethe number of false-positive significant interactions. We have used the Bonferronicorrection method for this purpose, i.e. lowered the significance level from α toα/K2.3.3.5 Visualization and Further Data ReductionSo far, we have fitted MVAR models to batches or instants of the time series, com-puted the connectivity metrics, and assessed the statistical significance of thesemetrics. At this point, we need to be able to visualize and interpret a vast number(i.e. 602) of significant and insignificant interactions that may or may not differamong subjects and even different instances within the same recording. Visualiza-tion of a connectivity structure is not an easy task, especially when the number ofelectrodes is large and in scenarios like ours where the notion of direction needs tobe preserved by the visualization method.Perhaps the most readily available visualization scheme is to plot the signifi-cance matrix as an image, such that each pixel corresponds to a directed pair-wiseinteraction and its color indicates whether or not the interaction is significant. Fig-ure 3.4 depicts such an image obtained from comparison of gamma band staticconnectivity between the ankle movement and rest conditions for subject 1. Eventhough a few high-level features can be identified from this figure (see section 3.4),it contains too much detail to be informative of the overall connectivity structure inthe first glance. Moreover, the significance matrix changes instantly in the dynamicscenario, making it extremely difficult to follow the patterns. There is thus an in-evitable need to reduce this information and represent it in a compact and moreinterpretable manner.To this end, we may utilize the same approach as in section 2.3.2 for furtherreducing the significance matrix, i.e. grouping the neighboring electrodes into nine58AFZ FZ FCZ CZ PZ POZ OZ F1FC1 C1 CP1 P1 FP1AF3 F3 FC3 C3 CP3 P3 PO3 O1 AF7 F5 C5 CP5 P5 PO7 F7 FT7 T7 P7 F2 FC2 C2 CP2 P2 FP2AF4 F4 FC4 C4 CP4 P4 PO4 O2 AF8 F6 FC6 C6 CP6 P6 PO8 F8 FT8 T8 TP8 P8AFZFZFCZCZPZPOZOZF1FC1C1CP1P1FP1AF3F3FC3C3CP3P3PO3O1AF7F5C5CP5P5PO7F7FT7T7P7F2FC2C2CP2P2FP2AF4F4FC4C4CP4P4PO4O2AF8F6FC6C6CP6P6PO8F8FT8T8TP8P8Figure 3.4: Visualization of the connectivity structure by plotting the signif-icance matrix. Starting from top left, the i j-th element represents theconnection from channel j (corresponding column below the pixel) tochannel i (corresponding row to the left). Yellow pixels correspond tostatistically significant interactions, while blue ones represent insignifi-cant connections.specified brain regions. In this sense, the 602 channel-wise interactions will bereduced to 92 regional interactions, where the i j-th element in the ’regional inter-action matrix’ indicates the average number of significant interactions from the j-thto the i-th brain region, where the average is taken over all directed channel pairsbetween the two regions. Application of this averaging procedure on the connec-tivity structure in Figure 3.4 yields Figure 3.5, where brighter colors show strongersignificant interactions. This figure represents information not directly perceivablefrom Figure 3.4, such as the strong frontal-to-parietal interaction. Nonetheless, amajor shortcoming of the brain regioning approach is that regardless of the choice59Averaged significant interactionsPreFrontalFrontalCentralParietalLeftParietalRightParietalLeftTemporalRightTemporalOccipitalPreFrontalFrontalCentralParietalLeftParietalRightParietalLeftTemporalRightTemporalOccipital00.10.20.30.40.50.60.70.80.91Figure 3.5: Reduction of Figure 3.4 by averaging channel interactions withinthe brain regions specified in table 2.1, where the average is taken overall directed channel pairs (e.g. the regional interaction value from regioni to region j is calculated by taking the average of all Ni ×N j pair-wise connectivity values between the two regions, where Ni and N j are,respectively, the number of channels in regions i and j). Each coloredblock represents the average strength of directional connections fromthe region below the block to the region on its left. For illustrative andcomparison purposes, interaction matrices are normalized to have unitFrobenius norm.of boundaries, neighboring electrodes do not always fall into the same group (e.g.in Figure 2.4, channels FC4 and FC6 are immediate neighbors, but belong to twodistinct groups). In other words, ’spatial discretization’ of the electrodes does nottake into account the interactions between adjacent electrodes near the boundaries,resulting in a relatively smeared representation of regional interactions.Graph-theoretical MeasuresIn order to overcome these limitations and further reduce the high-dimensional datafor visualization (especially in the case of dynamic connectivity patterns), we may60turn to graph theory. The main idea behind graph-theoretical measures is that largeconnectivity datasets have the same characteristics as ’networks’ emerging in biol-ogy, economy, internet, and other fields; and their properties can be characterizedas holistic, compact, meaningful, and easily computable network measures. Graphtheory is a field of mathematics defined to study these networks and their propertiesand has been extensively used in the past decade for the analysis of brain networks[106].Edges&(E)&Ver+ces&(V)&G$=$(V,E)Figure 3.6: A graph G (shown on the left) is an inter-connected set of vertices(V ) and edges (E). Brain networks can be represented as graphs. Thenon-causal connectivity network depicted on the right can be obtainedby thresholding the connectivity values and discarding their direction.In mathematics, a graph is a structure consisting of a set of ’nodes’ havingsome sort of inter-connections represented as ’edges’ (Figure 3.6). In the contextof brain networks, nodes represent channels and edges represent the strength (orpresence) of the connectivity measures. Once the computed connectivity structureis defined in terms of a graph, features of the network can be summarized in termsof quantitative graph-theoretical measures such as centrality, clustering coefficient,efficiency, path length etc. [106]. In this thesis, we have used a few basic graph-theoretical measures that are outlined below; including inflow, outflow, and causalasymmetry ratio [107]. Denoting the computed connectivity measure from channelj to channel i by ci j,• Inflow (Ii) is defined as the sum of causal information flowing from the restof the system toward channel i: Ii = ∑Kj=1 ci j,61• Outflow (O j) is defined as the sum of causal information flowing from chan-nel j toward the rest of the system: O j = ∑Ki=1 ci j,• Causal Asymmetry Ratio (CARi) is a normalized value indicating asymme-try of information flowing in and out of channel i: CARi = Oi−IiOi+Ii .Based on definitions above, a high value of outflow indicates that the channelacts as a source (causally influencing the system), and channels having high inflowvalues acts as sinks (being causally influenced by the system). The causal asymme-try ratio has values ranging from−1 to 1, with positive values close to 1 indicatingsource behavior and negative values close to −1 suggesting that the channel influ-ences the system more as a sink. A CAR value around zero would indicate thatthe channel is relatively passive in that the amount of influence it imposes on thenetwork is equalized by the amount of influence it receives from the network.Since these measures are summing the pairwise connectivity values to obtainchannel-wise values, they essentially reduce the dimensionality of the connectivitystructure from K2 to K. In addition to being compact, these measures are intu-itive and neurologically insightful. They can easily be computed and visualized ona topographical plot, circumventing the enforced abstraction of location informa-tion (as in Figures 3.4 and 3.5) and hence simplifying visualization of the directedconnectivity structure.3.4 Results And DiscussionHaving laid the foundations and a framework for estimation of effective connectiv-ity, we now present the results of applying this framework to the data at hand. Forsimplicity and based on results from the previous chapter, we only consider mo-tor tasks for connectivity estimation and will analyze the rest of our data in futurepublications.We begin by presenting the results of batch-averaged (static) connectivity insection 3.4.1. To clarify and sum up, the results presented in section 3.4.1 areobtained by:1. cleaning the raw recordings by rejecting artifactual channels (yielding K′ <K clean channels per recording) and rejection of transient artifactual time62segments,2. extracting 10-second epochs with 50% overlap from clean rest and taskrecordings (usually, around 130 rest epochs and 30 task epochs are extractedper subject),3. fitting an MVAR model (p = 10) to each epoch, calculating the epoch dDTFmeasure (Equation (3.17)), and integrating the dDTF values in the gammaband,4. statistically comparing the motor dDTF values with those of the resting state(section 3.3.4) and obtaining the K×K pair-wise significance matrices persubject, where values corresponding to the rejected channels are left empty1,5. averaging the K×K pair-wise significance matrices (ignoring empty values)across subjects to determine significant dDTF connections which are com-mon to all subjects and hence survive averaging.Steps 4 and 5 above outline our strategy for group-level (between-subjects)analysis: we first obtain subject-specific significance matrices by statistically com-paring the two conditions for each individual subject. This procedure rules out,for each subject, any connection which is not task-specific. Subsequently, group-level results are obtained by averaging these significance matrices across subjects.Averaging promotes general trends among all subjects by preserving common con-nections and suppressing connections which are specific only to a single subject.Next, results from dynamic connectivity analysis are presented in section 3.4.2.Similarly, these results have been obtained by:1. cleaning the raw recordings by rejecting artifactual channels and transientartifactual time segments,2. extracting the first 5 seconds from the rest and task recordings per subject,1In MATLAB, empty matrix values are implemented as NaN, the IEEE arithmetic representationfor Not-a-Number.633. fitting an instantaneous MVAR model (p= 10) using the RLS algorithm, cal-culating the dDTF measure at each instant, and integrating the instantaneousdDTF values in the gamma band,4. statistically comparing the instantaneous motor dDTF values with the overallresting state values and obtaining the K′×K′ pair-wise significance matricesfor all time instants.For reasons explained in section 3.4.2, dynamic connectivity is not analyzedon a group-level basis and is inspected for all subjects individually.3.4.1 Static Connectivity ResultsFigure 3.7 depicts the significance matrices of three subjects in both environmentsfor one of the motor tasks (ankle movements). Although somewhat too detailed, anumber of overall structural properties can be deduced from these figures.First, in many cases, one or more well-defined columns of the significancematrix with connections to most of the channels can be seen. These columns rep-resent prominent sources of information flow and can be useful in identification of’critical nodes’ in the network. However, we observed that these sources are notconsistent as they differ among subjects, and even among different recordings ofthe same subject. They are thus not reported here in isolation, but re-examinedshortly using Graph-theoretical measures.Interestingly, we also observe that for a specific subject, more significant con-nections are present in recordings at LSBB than their counterparts at the hospitalenvironment. This is a direct consequence of low-noise conditions, and is in ac-cordance with our findings in section 2.3.2, as task-specific effective connectivityis another gamma band correlate which is enhanced and better detected in the low-noise environment.Another property deducible from Figure 3.7 is laterality and the amount of in-ter and intra-hemispheric connections. Based on the arrangement of electrodes de-picted in detail in Figure 3.4, and the 10-10 montage shown in Figure 2.4, entries ina significance matrix can be classified according to the corresponding hemispheresthey are connecting. Figure 3.8 below shows a mapping of all of the pixels to their64(a) Subject 1, Hospital (b) Subject 2, Hospital (c) Subject 3, Hospital(d) Subject 1, LSBB (e) Subject 2, LSBB (f) Subject 3, LSBBFigure 3.7: Significant connections during ankle movement from three sub-jects in the two environments (chosen arbitrarily from the four subjectscommon to both environments). Electrode labels are not shown on theaxes, as the overall structures are the main point of notice. ’Global’sources of activity, i.e. channels with connections to the majority ofother channels are evident in subfigures (d) and (e); while more localsources, connected only to a subgroup of electrodes, can be spotted inother subfigures.corresponding inter and intra-hemispheric connections. This crude classificationof electrodes leads to the observation that on average, there are more connectionswithin the same hemisphere than between hemispheres, since the yellow pixels(significant connections) are more densely distributed in the top-left and bottom-right corners of the images in Figure 3.7.In Figure 3.9 we have quantified the inter and intra-hemispheric connectionsacross all of the significance matrices, as well as those corresponding to wrist65Mid$Line(Area(Mid$Line(Area(L!L  R!L  L!R  R!R  Figure 3.8: Segmentation of significance matrices into hemispheric connec-tions. This particular arrangement stems from the ordered sequence ofelectrodes in Figure 3.4, having the mid-line electrodes first (names end-ing in ’Z’), electrodes in the left hemisphere second (names ending withan odd number), and lastly, electrodes in the right hemisphere (namesending with an even number). L→ L denotes connections within theleft hemisphere, L→ R denotes connections from the left hemisphere tothe right, and so on.L --> L R --> L L --> R R --> R0.010.030.050.070.09(a) Ankle MovementsL --> L R --> L L --> R R --> R0.010.030.050.070.09(b) Wrist MovementsFigure 3.9: Overall strengths of inter and intra-hemispheric task-specific con-nectivity during motor tasks in eight subjects and two environments.Box plots represent the median and quartiles of the distribution of hemi-spheric strength values across all subjects in both environments. Eachstrength value is essentially the number of significant connections fromone hemisphere to the other, divided by the total number of significantconnections.66movements. Each entry is the result of calculating the ratio of significant inter-actions to the total number of possible interactions within the regions designatedin Figure 3.8, discarding the pixels falling in the mid-line areas. The figure con-firms our previous observation that the number of significant intra-hemisphericconnections is more than the number of inter-hemispheric connections. The overallnumber of connections is also shown to be slightly higher in the left (contralateral)hemisphere than in the right. This suggests that, in a Granger-causal sense, the con-tralateral hemisphere is more gamma-band-inter-connected during ankle and wristmovements than the ipsilateral hemisphere. Further, there is seemingly more left-to-right connectivity than from the right hemisphere to the left during both ankleand wrist movements. Left-to-right connections are also less variable (as measuredby the inter-quartile range of their distribution) among different subjects than otherinter and intra-hemispheric connections. They might therefore be deemed, with rel-atively higher confidence, as subject-independent movement correlates. However,these observations may vary if more subjects are added to the analysis.To further assess which local regions of the brain contribute the most to thetask-specific connectivity structure, we can count the number of significant interac-tions within the brain regions specified in Figure 2.4. In Figure 3.10, we have illus-trated the mean region-wise significant interactions averaged over all of the record-ings (the process is explained in section 3.3.5). Figure 3.10a demonstrates thatduring ankle movements, frontal and central regions have the most inter-relationsrelative to other sites of the brain, with frontal-to-frontal and frontal-to-central ac-tivities being the most prominent region-wise interactions. In contrast, the mid-and left parietal regions are relatively less active in the connectivity process, whilethere is noticable information flow from the right parietal and left temporal regionsto the frontal region. Figure 3.10b shows the same characteristics for the wristmovements, although the overall connectivity pattern seems to be more structuredand focused around the frontal and central areas compared to ankle movements(i.e. connections between other areas are sparser and connections between frontaland central areas are stronger).More accurate and interpretable results are obtained using the Graph-Theoretical(GT) measures described in section 3.3.5. We begin by computing the average ofsignificance matrices across all subjects and environments. We will then compute67PreFrontalFrontalCentralParietalLeftParietalRightParietalLeftTemporalRightTemporalOccipitalPreFrontalFrontalCentralParietalLeftParietalRightParietalLeftTemporalRightTemporalOccipital00.10.20.30.40.50.6(a) Ankle MovementsPreFrontalFrontalCentralParietalLeftParietalRightParietalLeftTemporalRightTemporalOccipitalPreFrontalFrontalCentralParietalLeftParietalRightParietalLeftTemporalRightTemporalOccipital00.10.20.30.40.50.6(b) Wrist MovementsFigure 3.10: Average regional interactions during motor tasks in eight sub-jects and both environments. We have recorded the number of signif-icant interactions between the nine previously defined regions of thebrain, in an attempt to represent the data in Figure 3.7 in a more com-pact manner, and extend the analysis of hemispheric connections.68the channel-wise GT measures of inflow, outflow, and Causal Asymmetry Ratioon the average significance matrix. The resulting GT values can then be shown ontopographical scalp plots, allowing for a more intuitive representation of signifi-cant sources and sinks of information flow. Figure 3.11 illustrates the results forsignificant gamma band activity, averaged over recordings from eight subjects, forboth of the motor tasks.According to Figure 3.11a, on average, a cluster of frontal electrodes on theright hemisphere (F4, F6, FC2) as well as another cluster of parietal electrodeson the left hemisphere (P5, CP5) are identified as the most prominent sources ofgamma band activity during ankle movement. These sources propagate informa-tion within the gamma band to the central and posterior parts of the brain on theleft hemisphere, most notably to the fronto-central and parietal nodes such as FC1,C5, CP1, CZ, and PZ. Meanwhile, Figure 3.11b shows a similar structure for wristmovements, with dominant pre-frontal and parietal sources slightly shifted towardthe midline in comparison with ankle movements. An interesting observation isthat for both of the motor tasks, almost all channels with high values of inflow(sinks of information) are located on the contralateral hemisphere and clusteredaround fronto-central and parietal regions. On the other hand, sources of gammaband activity exist on both hemispheres, feeding information to the rest of the sys-tem while being organized in the form of several separate clusters on fronto-central(on the right hemisphere) and parietal (on the left hemisphere) regions of the brain.It is argued in [108] that gamma band activity in the prefrontal cortex is linkedto the maintenance of the behaviorally relevant items. This can explain the ob-served prefrontal sources of gamma band during the motor activity, as they couldbe responsible for planning of the next repetitive movement. This information thendrives the specific part of the brain known to be responsible for motor function,namely, the central nodes within the contralateral hemisphere, in order to performthe act of movement. It is important to stress here that the confidence of these con-clusions is confined by the limited number of subjects in the study, as the objectiveof this thesis was not to reach rigorous neurological discoveries, but rather to reportthe results on available data as a pilot gamma band study.69(a) Ankle Movements (b) Wrist MovementsFigure 3.11: Topographical plots showing the static channel-wise graph-theoretical measures calculated on the mean significance matrix duringmotor tasks. Top: outflow; middle: inflow; bottom: Causal Asymme-try Ratio (CAR).703.4.2 Dynamic Connectivity ResultsAs explained before, dynamic or instantaneous connectivity is the result of lettingthe parameters of the model (and hence the connectivity values) vary adaptivelywith time. Due to memory limitations, calculation of connectivity parameters frommodel parameters is done one at a time for small consecutive time windows of 5seconds. Given the fact that a huge volume of data is generated in this manner, wehave resorted to observing only the first 5 seconds of connectivity values in orderto see which interactions dominate the connectivity structure at the initial stages ofperforming a task.In terms of visualization of the results, all of the Figures in the previous sectionwould turn into videos whose frames depict instantaneous connectivity structures.Naturally, the least detailed and most illustrative videos would be those correspond-ing to graph-theoretical topographical plots. In Figure 3.12, we have illustrated afew video snapshots from three subjects showing the evolution of the ankle move-ment connectivity structure throughout the first five-second interval in one-secondsteps. Shown in the plots is the instantaneous CAR value calculated on gammaband significance matrices obtained from recordings at LSBB.Alternatively, if the directed interaction between a specific pair of channelsA→ B is of interest, we can plot the time course of the computed connectivitymeasure (integrated within the gamma band) flowing from A to B. For instance,having identified the major sources (CP2, P5, F4, FC4) and sinks (C3, CP1, CZ,PZ, CP6) of significant gamma band activity for a single subject from plots similarto those in Figure 3.11a, we might be curious to know the specific times at whichconnections between each of these channels are stronger during ankle movements.Figure 3.13 depicts such information obtained from the first five-second interval ofankle movements from subject 1 at LSBB. The figure illustrates the variability ofinteractions over time. Specifically, we observe that connections F4→C3, F4→CP1, and P5→CZ are mainly inactive during this period. Moreover, while FC4 ispropagating activity only during the initial stages of the task, connections such asP5→C3 are activated at later times, and connections P5→CP1 and CP2→CP1are consistently active throughout the whole five-second period.Unfortunately, interpretability of these results and performing a multi-subject71013245time(s)(a) Subject 1 (b) Subject 2 (c) Subject 3Figure 3.12: Topographical plots of instantaneous significant CAR valuesduring the first five seconds of ankle movement for three subjects inLSBB.72 CP2 --> C3  P5 --> C3  F4 --> C3  FC4 --> C3  CP2 --> CP1  P5 --> CP1  F4 --> CP1  FC4 --> CP1  CP2 --> CZ  P5 --> CZ  F4 --> CZ  FC4 --> CZ  CP2 --> PZ  P5 --> PZ  F4 --> PZ  FC4 --> PZ 1 2 3 4 5Time (s)01Significant Connection(binary) CP2 --> CP6  P5 --> CP6  F4 --> CP6  FC4 --> CP6 Figure 3.13: Time course of significant gamma band interactions between aselected array of sources and sinks throughout the first five seconds ofankle movement (subject 1, LSBB). Shaded areas represent the pres-ence of significant gamma band interactions across time (horizontalaxis).analysis is severely limited by the protocol definition and design of experiments.It is apparent from Figures 3.12 and 3.13 that the connectivity structure changesrapidly over short instances of time. Hence, in order to be able to compare thetime-dependent patterns across subjects and recordings to find consistent connec-tivity patterns, the movement tasks need to be performed at repeatable epochs,commenced at precisely known start times and executed at closely similar paces.On the contrary, task start times in our dataset were not properly annotated, andthe movements were performed at varying self-selected paces. In other words, thesubjects in Figure 3.12 are likely in different stages of ankle and wrist movements73due to the high uncertainty in task start times, and hence their activities cannot becompared across time.3.4.3 ConclusionBrain connectivity structure comprises networks of different brain sites connectedby anatomical, functional, or causal (effective) associations. In this chapter, we ex-tended the segregated analysis of chapter 2 to search for the presence and directionof task-specific gamma band connectivity links in our EEG dataset during motortasks.Using the parameters from a data-driven auto-regressive model, we calculateda Granger-causal measure of connectivity, the direct Directed Transfer Function(dDTF), on 10-second segments of the continuous data. This gave rise to a batch-averaged (so-called static) manifestation of the connectivity structure, signifyingthe general patterns of interaction between channels within the whole batch pe-riod. Using the dDTF values obtained from different batches of the same record-ing, we devised a statistical significance selection procedure based on the distri-bution of dDTF values across channel pairs, conditions, and subjects in order todistinguish significant connections from insignificant ones. Moreover, to presentthe high-dimensional results in a compact manner, we introduced graph-theoreticalmeasures of inflow, outflow, and Causal Asymmetry Ratio. The static connectivityresults indicated high inter-connectivity across a wide range of brain regions withinthe gamma band. Hemispherical analysis demonstrated more intra-hemisphericthan inter-hemispheric connectivity, and more left-to-right connections than right-to-left (for tasks involving movements of the right hand/ foot). Frontal and centralregions contained the most number of significant connections during motor tasks,while significant sources and sinks of information were also seen in other (e.g.parietal) regions.Furthermore, we extended the auto-regressive model to the adaptive, time-varying case (so-called dynamic connectivity) to incorporate the dimension of timein the analysis. We observed that patterns of connectivity change very rapidly overtime, limiting interpretability of the results given the uncertainty of task start timesin the current dataset.74Apart from the timing of the experiments, statistical rigor of the results ob-tained from this dataset is also limited by the small number of participants. Moreso than any other biological phenomenon, task-specific EEG correlates are knownto differ significantly in topology, time-frequency, and connectivity patterns acrosssubjects. Substantial variability was observed even between recordings obtainedfrom the same subject at different times. Hence, many subjects (more than 30,according to the Central Limit Theorem) are needed to obtain more consistent andreliable results, as well as many trials of the same task performed by the samesubject. The thorough pipeline and methods introduced in this thesis would be ofvalue to the future studies addressing these limitations.75Chapter 4Conclusion4.1 SummaryThis thesis was aimed at analysis of high-frequency EEG activity patterns in adataset consisting of high-dimensional continuous task-specific recordings from anumber of subjects in a low-noise environment as well as a typical hospital environ-ment. The analysis was performed both from a segregated and an integrated (con-nectivity) perspective; with the former investigating isolated channel behaviors andthe latter attempting to discern patterns of interaction between different brain sites.Due to its well-suited properties in high frequencies, the Stockwell transform waschosen to reveal gamma band energy enhancements pertaining to specific tasks inthe segregated analysis. Using this transform, we analyzed the data from all sub-jects in search of significant task-specific activity patterns in different frequencybands, and found activity patterns highly dependent on topology (spatial locationof the electrode), frequency, and condition (the task being performed). We alsoused S-Transform to compare the data collected at the low-noise environment withsimilar data in the hospital environment, and found greater task-relevant gammaband energy increases in LSBB, especially during motor tasks. Based on this obser-vation, the subsequent connectivity analysis was performed solely on motor tasksusing a linear, data-driven method based on multivariate Granger causality. A rig-orous framework for block-averaged as well as instantaneous connectivity analysiswas proposed and implemented on the data. Block-averaged connectivity analysis76revealed well-defined patterns during ankle and wrist movements, possibly valu-able for further neurological analysis if more subjects are included in the study. Onthe other hand, unrepeatability of task-specific epochs, resulting from the lack oftime-locked task performances, limited the multi-subject analysis of instantaneousconnectivity patterns.4.2 LimitationsThis work was limited by a number of issues stemming from imperfections indata collection, most notably lack of precisely annotated data. To elaborate, thedata was continuously recorded in the NRSign software with annotations denotingstart and end times of different phases of the experiment (e.g. onset of a countingepoch immediately following rest). These annotations were manually added on-line, giving rise to human errors in orders of seconds which increase with increas-ing recording time. Moreover, the alternating epochs of rest/task in LSBB were notannotated at all. As a case in point, a two-minute recording of backward countingconsists of two episodes of a 30-second counting epoch followed by 30 seconds ofrest; whereas the annotations in LSBB denoted the whole two minutes as counting,leaving the onsets of resting epochs unknown. This was an issue because despitethe efforts to keep the duration of epochs fixed at 30 seconds, examining the an-notated epochs at ICORD showed that in some cases the length of each rest/taskepoch differed from 30 seconds by a few seconds. Due to lack of annotations atLSBB, in this thesis we have regarded the mixed task-and-rest recordings (such asthe cound-and-rest recording described above) as task recordings, comparing themwith resting-state recordings which we knew for sure corresponded to the restingcondition. The reasoning behind this approach was that if the gamma band en-ergy is increased during a task, more gamma band energy would be present in atask-and-rest recording than in a recording solely comprising of resting-state data.However, we acknowledge that this procedure might obscure some task-specificfeatures and make baseline comparisons difficult, as well as compromise on task-rest statistical significance results.Furthermore, while the focus of our study was on continuous gamma bandoscillations in relatively long periods of time, most studies of cognitive and sensory77gamma band correlates were performed in an induced (e.g. ERP) framework withtime-locked stimuli. This might be the reason why no major task-specific gammaband increases were observed during cognitive and sensory tasks in section 2.3.2.Time-locked experiments with proper annotation schemes, such as auditory cueswith automated timing, could be important and valuable to examine in future work.Another limitation in the dataset was the fact that the number of uncontami-nated channels differed between subjects, recordings and environments. While insome cases two or three channels were rejected due to artifacts for one subject, asmany as ten channels were rejected for another subject. This could have obscuredimportant information and biased the results, especially during identification ofsources and sinks in connectivity analysis. This issue is also the main reason why acomparative analysis of connectivity structures in ICORD and LSBB was not per-formed, since the artifactual channels rejected from subjects’ recordings differedin the two environments.On a different note, choosing the prefrontal electrode FPZ as the referenceelectrode might not have been the safest choice in that it causes blink and eyemovement artifacts to appear in all other electrodes. While the data can be eas-ily re-referenced offline for segregated analysis, re-referencing is not an optionfor connectivity analysis since it introduces false inter-relations between channels.Generally, ear lobes (averaged mastoids) might be a safer choice for positioningthe reference electrodes and mitigation of blink artifacts, since they record activitywhich is not drastically different from other electrodes while recording less brainactivity.4.3 Future WorkFuture improvement efforts can be twofold: 1) efforts to address the limitationsof the current study protocol (inclusion of more subjects, precise data annotations,and time-locked experiments, as well as online data monitoring from time to timeto ensure quality of all recording electrodes); and 2) efforts to improve the dataanalysis framework, including but not limited to:• use of more rigorous statistical testing methods, such as mixed-model de-signs, repeated measures ANOVA, permutation testing and bootstrap,78• use of machine learning and Markovian models in dynamic connectivity toexamine potentially consistent patterns (e.g. two regions following eachother consistently but in a transient fashion),• including nonlinear analysis methods (entropy, measures of signal complex-ity, mutual information),• inclusion of more abstract graph-theoretical measures (such as path length,global efficiency, and measures of centrality and modularity) and their task-specific correlates.These methods will be inspected for feasibility and implemented in future pub-lications. 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Modeling cortical sourcedynamics and interactions during seizure. In 2011 Annual InternationalConference of the IEEE Engineering in Medicine and Biology Society,pages 1411–1414. IEEE, 2011. → pages 6189[108] F Roux, M Wibral, H Mohr, W Singer, and P Uhlhaas. Gamma-bandactivity in human prefrontal cortex codes for the number of relevant itemsmaintained in working memory. Journal of Neuroscience,32(36):12411–12420, 2012. → pages 69[109] G Waysand, S Gaffet, J Virieux, A Chwala, M Auguste, D Boyer,A Cavaillou, Y Guglielmi, and D Rodrigues. The laboratoire souterrain basbruit (lsbb) in rustrel-pays d’apt (france): A unique opportunity forlow-noise underground science. In EGS General Assembly ConferenceAbstracts, volume 27, page 3869, 2002. → pages 9190Appendix ADetails of the StudyA.1 The Underground FacilityThe Laboratoire Souterrain a` Bas Bruit (LSBB) is a unique low-noise facility underthe karstic Lube´ron plateau in Rustrel, France. Formerly used as a ground basedcomponent of the French nuclear missile system, this underground capsule is robustto radioactive clouds, thermal and mechanical waves and electromagnetic interfer-ence, and has now been progressively used as a cross disciplinary laboratory. The28×8 meter capsule is located 500 meters underground and is surrounded by 1 cmof steel in addition to 2 m of reinforced concrete, thus being a completely shieldedFaraday cage with a residual electromagnetic noise lower than 2 f T/Hz above 10Hz [109]. The absence of sources of electromagnetic interference makes LSBB anideal environment for performing low-noise measurements of physiological sig-nals such as EEG, particularly in frequencies above 30 Hz which are specificallysusceptible to high-frequency noise.A.2 Acquisition SystemIn this project, we have used a research-grade EEG system 1 capable of non-invasive acquisition of scalp EEG. The system works on battery and has 64 chan-1NR SIGN EEG 5000Q 64-channel (NR SIGN Inc., New Westminster, BC, Canada),http://www.nrsign.com/eeg/eeg-5000q91nels 2 (see Fig. A.1), thus offering considerably higher spatial resolution for thescalp potentials than the previous two-channel system. The system allows for aprogrammable sample rate of 500 Hz to 2 KHz with resolution of 16 bits. Due toacquiring progressively longer data segments and limitations faced in storing thedata, the sampling rate was fixed at 500 Hz. Data was transferred using a USBcable to a laptop computer (also running on battery power) through the NR SIGNEEG application software. The raw data was then exported to MATLAB (R2015b)in an offline procedure for quantitative analysis.Figure A.1: EEG montage of the NRSign acquisition system. The 1cm sur-face scalp electrodes are placed as per the 10-10 international EEG sys-tem (higher density of electrodes than the 10-20 system shown in Fig1.1) for standardized reproducibility.A.3 Study ProtocolEEG was first acquired using the above system in the LSBB capsule. For compari-son purposes, the same equipment and recording protocol was then used to acquire2 There were 60 actual channels recording meaningful data out of the total 64 channels in thesystem: two channels are implemented for recording surface EMG (Electromyogram), one channelis used for recording ECG (these channels are usually helpful in epilepsy applications and hence,they were not set to record data in our experimental paradigm), and channel FPZ was used as thereference electrode (set to zero at all times). The ground electrode was placed on the wrist.92control recordings at a hospital environment (the International Collaboration OnRepair Discoveries (ICORD) in Vancouver General Hospital).Seven subjects (three females) varying in age from early thirties to early six-ties participated in data acquisition at LSBB in France; while five subjects (twofemales) participated in the acquisition at ICORD in Vancouver. All subjects wereright-hand dominant. Due to the logistically challenging nature of taking replicaterecordings on different continents, only four subjects (two females) were commonto both environments.During a recording period at either LSBB or the hospital environment, subjectsperformed a number of cognitive, sensory, and motor tasks with ample time be-tween experiments so that each subject was rested, comfortable, and ready to moveon to the next task. Each five-hour recording period consisted of the followingphases:1. Resting state EEG:The subjects were placed supine in a darkened room, lying as still as possiblewhile EEG was being recorded for seven minutes. The subjects were askedto open/close their eyes every 30 seconds for five minutes, and keep theireyes closed during the last two minutes.2. Cognitive EEG:(a) Counting - With eyes closed, the subjects counted backwards for four30-second periods with 30-seconds periods of rest in between (totalcounting period of two minutes). Counting started from some largerandomly selected number and decremented by 7 or 6 at each step.(b) Matching - Subjects then performed an increasingly challenging mem-ory task on an iPad which required recalling and matching the locationof identically-shaped objects. Similarly to the counting task, match-ing was performed for two minutes (four 30-second intervals) with twominutes (four 30-second intervals) of rest in between.3. EEG during pain and sensory stimulation:93(a) Light touch (brushing) - As an innocuous tactile stimulus, a cottonswab was used to ’brush’ the adductor pollicis region (proximal jointof thumb) of the right hand. Brushing was performed at a constant rate(~2 Hz) for five minutes, during which the subjects opened and closedtheir eyes in ten alternating 30-second intervals.(b) Noxious EEG (heat) - First, skin temperature was measured by ap-plication of a temperature sensor to the skin surface for a period of 1minute. Consequently, as a noxious tactile stimulation phenomenon,hot packs were applied to the adductor pollicis region for five minutes,with 30-second periods alternating between eyes-open and eyes-closedconditions. At the end of each 30-second period, the subjects rated theintensity of their perceived pain based on a (0-10, 10 being the mostpainful) visual analog scale (VAS). Finally, skin temperature over theadductor pollicis was measured and recorded again to evaluate the ef-fect of the heat pack.4. EEG during motor function:(a) Ankle movements - Subjects performed reciprocal dorsal and plantarflexion movements of the right ankle for five minutes, with 30 secondsof movement alternating with 30 seconds of rest. Movements were per-formed with closed eyes at a self-selected speed (~1.5 Hz) and subjectswere asked to silently count and report the total number of movementsat the end of each 30-second movement period.(b) Wrist movements - Subjects performed repeated upwards flexion andextension movements of the right wrist (fingers held straight) for fiveminutes, with alternating 3-second periods of rest in between. Move-ments were performed with closed eyes at a self-selected pace (~1.5Hz) and subjects were asked to silently count and report the total num-ber of movements at the end of each 30-second movement period.94

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