1. Abstract We present a method to obtain and display the significant changes in EEG dynamical connectivity (inferred from synchronization patterns) relative to the pre-stimulus state in a cognitive task. These changes are displayed as detailed Time-Frequency-Topography maps where specific synchronization patterns can be easily located in time and frequency and interactive segmentations may be performed. An analysis of different synchronization measures shows that most known synchrony measures can be classified in one of two groups: the first group matches the criteria of strict phase synchrony, where dynamical connections result in phase differences smaller than 10 ms; the second group consists of measures which involve some type of time-persistence and are highly correlated to the variance of the apparent phase measured at each electrode within a given time window, and thus, they may not be measuring true long-range synchrony. In our methodology, we avoid this problem by handling time-persistence separately by means of Bayesian estimation with a Markov Random Field model. We also present a mathematical model that explains many of these observations, which is based on the idea that the apparent phase measured at each electrode results from contributions of several subjacent neural subnetworks. Examples of the application of these techniques to the analysis of dynamic connectivity associated with specific cognitive tasks are presented as well. An EEG-based methodology for the study of dynamical brain connectivity during cognitive tasks Alba F.A.* 1, Marroquin, J.L. 1, Harmony T. 2 1 Centro de Investigación en Matemáticas, Guanajuato, Gto. (México) 2 Instituto de Neurobiología, Campus UNAM Juriquilla, Querétaro, Qro. (México) Overview of Procedure 1.- Run the EEG signals through bank of bandpass filters and extract apparent phase information 2.- Estimate the instantaneous mean phase-lock 3.- Estimate the likelihoods and prior distributions for the Markov Random Field (MRF) model using the instantaneous phase-lock values 4.- Use Bayesian estimation to find significant synchronization patterns that are persistent 5.- Display synchronization patterns as multitoposcopic graphs and time- frequency-topography (TFT) maps that can be interactively segmented.

2. Apparent phase for a population model 11 22  1 -   2 -  e1e1 e2e2  exp[i  1 ]  exp[i  2 ] A* exp[i  *] We model the signal at each electrode e as the sum of the contributions of a number of oscillators whose phase takes values from {  e,m }: The apparent amplitude and phase are those that are obtained from the EEG observations by band-pass filtering: Example: For a two-population model, there are only two possible phase values per electrode. This suggests |   e1 (t) –   e2 (t)| as synchrony criterion. Thus synchrony is characterized by: 1.- Significant phase-lock changes 2.- Persistence across a time window ERPA Phase-lock measure We have observed that measures which involve some sort of time-persistence are seriously affected by local phase scattering. Hence we decided to treat phase-locking and persistence separtely. Instantaneous synchrony measure: Instantaneous relative synchrony: Instantaneous mean relative synchrony: Bayesian classification of significant synchrony changes Bayesian estimation with a prior Markov Random Field (MRF) model [Marroquin, 1987] is used to classify significant changes in synchrony as higher (c=1), lower (c=-1) or equal (c=0), and also to include a persistence constraint. The posterior distribution of the class field c is given by: with The product h r (k) of prior distributions and likelihoods can be estimated from the data using kernel density estimation. Other common synchrony measures Phase-LockingStatistic (PLS): [Lachaux et al., 1999] Single-Trial PLS (STPLS): [Lachaux et al., 2000 ] Coherence: [Gardner, 1992] [Bressler et al., 1993, 1995]

3. Example Experiment (Words) A word is displayed onscreen and the subject is instructed to press one button if the word corresponds to an animal and starts with a consonant, and another button otherwise. Visualization Time-Frequency-Topography Histograms Interactively segmented maps Conclusions Influence of Local Phase Dispersion (LPD) For a given point in the TF map we employ a multitoposcopic view of the significant synchronization patterns. Red point = Significantly higher synchrony (class c = 1) Green point = Significantly lower synchrony (c = -1) Example: Words at 300 ms, 10 Hz. Significant changes in (1 – LPD) STPLS Coherence Correlation between pairs of measures We define LPD as: If we take the STPLS measure and fix the phase of one of the signals, we will be actually measuring the variance of the other signal’s phase in the given time window. Synchrony changes for ERPA are characterized by two properties: 1) a significant change in phase-lock, and 2) persistence of those changes across time. When these factors are combined into one measure, the results appear to be dominated by Local Phase Dispersion. We propose handling phase-locking and time-persistence separately. Phase-locking is measured simply by the magnitude of phase differences (as suggested by our population model), while significancy and persistence are taken into account using Bayesian estimation with a Markov Random Field model. We have also developed an user-friendly system with powerful visualization tools that allow an easy navigation of the TF plane, quick recognition of areas with homogeneous synchrony patterns, and a straightforward interactive segmentation of the TF plane. The Time-Frequency plane can be segmented in areas which show an homogeneous synchrony pattern. [Marroquin et al., 2004]