Neural correlations during brain activation in arithmetical tasks – an approach using electroencephalographic data

Dissertação apresentada na Faculdade de Ciências e Tecnologiea da Universidade Nova de Lisboa, para obtenção do Grau de Mestre em Engenharia Biomédica

The present study aims at examining the correlation among different brain areas while the subjects performed an arithmetical task, and how these differ from the mental relations in the same subjects during a resting state. In order to this, both linear and nonlinear methods were used, i.e., both algorithms capable of detecting linear relations and algorithms capable of detecting correlations without assuming any type of parametric relationship between the signals were implemented. The first algorithm that was implemented was the cross-correlation function, which gives an estimate of how much two signals are linearly correlated, and estimates the delay between them, thus permitting to make inferences on causality. Furthermore, this algorithm was validated using the statistic method called surrogation, in order to test for the applicability of the algorithm on the signals that were to be processed. The next part of the study consisted on implementing two analogous algorithms, the coefficient of determination and the nonlinear regression coefficient. These coefficients both measure the fraction of reduction of variance that can be obtained by estimating the relationship between two signals according to a fitted line, the difference being that the former assumes a linear relation between both sets of samples and the latter doesn‟t previously assume any type of relationship between the signals. The main differences in correlation that were observed between the state of mental rest and between the arithmetic task performance were that in the former more brain sites were correlated, whereas during the task this synchrony was mainly verified between frontal and parietal areas, showing a decrease in the other locations. Furthermore, the estimates provided by the linear and nonlinear algorithms were very similar, suggesting that in this case the relationships among different neural networks were mainly linear, and thus validating the application of linear methods in this type of analysis in particular cases. Regarding the estimation of delays between signals and inferences on causality, no conclusive results were attained.