Order and Chaos in the Brain: Fractal Time Series Analysis of the EEG Activity During a Cognitive Problem Solving Task

Abstract

The study of brain dynamics has been approached from different mathematical strategies with the aim to obtain more information of the bioelectrical signals coming from an electroencephalogram (EEG). Although several of these tools try to conciliate the fact of using linear approaches to study a non-linear phenomenon, during the last years a set of complementary and alternative approaches has been used to mine deeper into the nature of the brain dynamics and its correlates with experience, thoughts and actions. One of these approaches comes from chaos theory and fractal geometry and considers a model where brain activity, as a time series of an electrical potential variation (EEG) recorded from the scalp, can be assumed as a dynamical state that moves in the range of 1/f α (fractal) noise. In this model it is possible to see brain dynamics as a functional state who moves from more chaotic or unpredictable dynamics (Brown or Gaussian uncorrelated noise), to quasi-chaotic or statistical noise (fractal or self-similar noise). The amount of order into the chaotic EEG background must be an indicator of the organization of brain procedural resources dealing with different circumstances. At the same time, it must reflect the degree of inter-individual differences and intra-individual variability in the way each different brain works. To test this hypothesis we implemented a study where EEG activity was recorded during the performing of a simple visual intelligent test (Raven test, abbreviated version of 15 questions) in a set of 10 adults to study their similarities and differences in the rendering of the test (estimated range of IQ) and in the process of solving the easy and the difficult part of the test. We estimated the Hurst exponent and the fractal dimension of the time series for each of the 14 EEG channels (Emotiv-Epoc® BCI headset) and searched for correlations and consistencies in the values of H and the difficulty level of the cognitive task. We found that order tend to emerge from a chaotic background when brain focuses on problem solving, rising the degree of predictability, self-similarity and persistent behavior of the EEG signal.