Statistical Methods and Nonlinear Dynamics for Analyzing Brain Activity. Theoretical and Experimental Aspects

Abstract

In this paper, we propose statistical methods and nonlinear dynamics for analyzing brain activity in epileptic patients, using the PhysioNet database. Thus, the analysis by statistical methods (the time variation of the standard deviation of the component signals of the electroencephalogram, the time variation of the signal variance, the time variation of the skewness, the time variation of the kurtosis, the construction of the recurrence maps corresponding to both normal functioning of the brain, as well as of the pre-crisis period, respectively of the crisis, the evolution in time of the spatial–temporal entropy, the variations of the Lyapunov coefficients, etc.) allows us to determine not only the epilepsy time based on a specific strange attractor but also that the entry into the epileptic seizure can be determined at least twenty minutes in advance. Finally, utilyzing elements of nonlinear dynamics and chaos, one builds in the states space certain attractors corresponding to a wide “class” of signals of encephalographic type. These classes dictate the normal or the abnormal functioning (the epileptic one) of the brain so that a possible classification of the types of epilepsy can be given.