Non-linear development of EEG coherence in adolescents and young adults shown by the analysis of neurophysiological trajectories and their covariance

To contribute to the understanding of changes in the factors governing the development of neural connectivity, the developmental structure of EEG coherence in adolescents and young adults was analyzed using the means, variances, and covariances of high alpha frequency band coherence measures from a set of 27 coherence pairs obtained from a sample of 1426 participants from the COGA study with 5006 observations over ages 12 through 31. Means and covariances were calculated at 96 age centers by a LOESS method. In the current study, trajectories of covariance matrices considered as individual units were determined by tensorial analysis: calculation of Riemannian geodesic (non-Euclidean) distances between matrices and application of both linear and non-linear dimension reduction techniques to these distances. Results were evaluated by bootstrap methods. Mean coherence trajectories for males and females were very similar, showing a steady upward trend from ages 12 to 20 which diminishes gradually from 20 to 25 and reaches stability from 25 to 31. In contrast, the individual covariance trajectories of males and female differed, with the male covariance levels becoming greater than that of females during the developmental process. Tensorial determination of the distances from the initial covariance matrix of subsequent covariance matrices to age 20 had the same trajectory as the mean coherence values. Tensorial determination of the trajectories of the covariance matrices of males and females based on their all pairs geodesic distances revealed a non-linear pattern in the multi-dimensional space of each of the trajectories: A steady increase in one dimension is accompanied by deviations from it peaking at age 20 which have both transient and lasting effects. There is a precise temporal parallelism of this pattern of covariance in males and females, while there is a consistent distance between the male and female covariance structures throughout the developmental process. Between region differences (anterior-posterior) within each sex are greater than between sex differences within regions. Examining development using multiple methods provides unique insight into the developmental process.