New complexity measures reveal that topographic loops of human alpha phase potentials are more complex in drowsy than in wake.

A number of measures, stemming from nonlinear dynamics, exist to estimate complexity of biomedical objects. In most cases they are appropriate, but sometimes unconventional measures, more suited for specific objects, are needed to perform the task. In our present work, we propose three new complexity measures to quantify complexity of topographic closed loops of alpha carrier frequency phase potentials (CFPP) of healthy humans in wake and drowsy states. EEG of ten adult individuals was recorded in both states, using a 14-channel montage. For each subject and each state, a topographic loop (circular directed graph) was constructed according to CFPP values. Circular complexity measure was obtained by summing angles which directed graph edges (arrows) form with the topographic center. Longitudinal complexity was defined as the sum of all arrow lengths, while intersecting complexity was introduced by counting the number of intersections of graph edges. Wilcoxon's signed-ranks test was used on the sets of these three measures, as well as on fractal dimension values of some loop properties, to test differences between loops obtained in wake vs. drowsy. While fractal dimension values were not significantly different, longitudinal and intersecting complexities, as well as anticlockwise circularity, were significantly increased in drowsy. Graphical abstract An example of closed topographic carrier frequency phase potential (CFPP) loops, recorded in one of the subjects in the wake (A) and drowsy (C) states. Lengths of loop graph edges, r(c j, c j + 1), plotted against the series of EEG channels with decreasing CFPP values, c j , in the wake (B) and drowsy (D) states. Conventional fractal analysis did not reveal any difference between them; therefore, three new complexity measures were introduced.