Statistical analysis of dynamic interdependence patterns in the cortex

This dissertation is an investigation of the sources of commonly observed event-related transients in statistical measures of interdependence: variance, cross-correlation, power spectrum density and coherence spectrum density time functions. These measures are often employed in the analysis of spatio-temporal interdependence patterns in neural activity. In order to understand the phenomenon, the origins of the variability of event-related responses are revisited. The time series of single trial cortical event-related potentials typically have a random appearance, and their trial-to-trial variability is commonly explained by the classic signal-plus-noise model, in which random ongoing background noise activity is linearly combined with a stereotyped evoked response. Here, we demonstrate that more realistic models, challenging both the linear superposition and the trial-to-trial stationarity of the event-related responses, can account for such event-related transients. In particular, two effects are considered: the nonlinear gain modulation in neural networks coupled through sigmoid functions and the trial-to-trial variability in amplitude and latency of the event phase-locked responses. An extensive analysis and characterization of both effects in interdependence measures is carried out through both analytical and numerical simulations in Chapter 2. Chapter 3 presents the outcome of testing the predicted effects on UP data recorded from implanted intracortical electrodes in monkeys performing a visuo-motor pattern discrimination task. Overall, the results point to a large contribution of the trial-to-trial variability of event phase-locked responses on the observed event-related transient in statistical interdependence measures. Because variability of the event-related responses is commonly ignored, event-related modulations in power spectral density, cross-correlation, and spectral coherence are often attributed to dynamic changes in functional connectivity within and among neural populations. It becomes then crucial the separation or removal of the trial-to-trial amplitude and latency variability effect from the statistical measures. In order to achieve this goal, the reconstruction of the single trial event phase-locked potentials is required. In Chapter 4, we approach this problem from a Bayesian inference perspective. The posterior probability density is derived for a specified number of event phase-locked components using data from single or multiple sensors. The Maximum A Posteriori solution is used to obtain the phase-locked component waveforms and their single trial parameters. The outcome is a further and definitive support for predominance of the effect of the nonstationarity of the phase-locked responses on the statistical quantities. Based on the theoretical and experimental analysis conducted in Chapters 2, 3 and 4, a framework for the statistical analysis of dynamic spatio-temporal interdependence patterns in Local Field Potential data is articulated.