Brain criticality through nonadditive entropic analysis of electroencephalograms

Abstract

On the grounds of nonadditive entropies -- appropriate for complex systems -- we investigate the electroencephalogram amplitudes of typical and ADHD children. The corresponding probability distributions are $q$-Gaussians, i.e., $\ddot{I}(x)\propto e_q^{-{\hat{I}}^2{x}^2}\equiv [1+(q-1){\hat{I}}^2{x}^2{]}^{1/(1-q)}$, where $(q,{\hat{I}}^2)$ are, respectively, the entropic index characterizing complexity and the inverse width. We show that $q$ tends to monotonically vary with ${\hat{I}}^2$ for both typical and ADHD subjects, thus revealing critical behavior of the brain. Moreover, we verify that ADHD subjects have a higher complexity than the typical ones. Consistently, biomarkers for objective phychyatric diagnosis could emerge along this path. We show that $q$ tends to monotonically vary with ${\hat{I}}^2$ for both typical and ADHD subjects, thus revealing critical behavior of the brain. Moreover, we verify that ADHD subjects have a higher complexity than the typical ones. Consistently, biomarkers for objective phychyatric diagnosis could emerge along this path.

7 pages and 6 figures