Biscay, R. J. | Search bioRxiv

bioRxiv2017

Measures of time series coupling based on generalized weighted multiple regression

1.The sharing and the transmission of information between cortical brain regions is carried out by mechanisms that are still not fully understood. A deeper understanding should shed light on how consciousness and cognition are implemented in the brain. Research activity in this field has recently been focusing on the discovery of non-conventional coupling mechanisms, such as all forms of cross-frequency couplings between diverse combinations of amplitudes and phases, applied to measured or estimated cortical signals of electric neuronal activity. However, all coupling measures that involve phase computation have poor statistical properties. In this work, the conventional estimators for the well-known phase-phase (phase synchronization or locking), phase-amplitude, and phaseamplitude-amplitude couplings are generalized by means of the weighted multiple regression model. The choice of appropriate weights produces estimators that bypass the need for computing the complex-valued phase. In addition, a new coupling, denoted as the inhibitory coupling (InhCo), is introduced and defined as the dependence of one complex-valued variable on the inverse and on the conjugate inverse of another complex-valued variable. A weighted version denoted as wInhCo is also introduced, bypassing the need for computing the inverse of a complex variable, which has very poor statistical properties. The importance of this form of inhibitory coupling is that it may capture well- known processes, such as the observed inverse alpha/gamma relation within the same cortical region, or the inverse alpha/alpha relation between distant cortical regions.

neuroscience↗

bioRxiv2017

Innovations orthogonalization: a solution to the major pitfalls of EEG/MEG "leakage correction"

1.The problem of interest here is the study of brain functional and effective connectivity based non-invasive EEG-MEG inverse solution time series. These signals generally have low spatial resolution, such that an estimated signal at any one site is an instantaneous linear mixture of the true, actual, unobserved signals across all cortical sites. False connectivity can result from analysis of these low-resolution signals. Recent efforts toward \"unmixing\" have been developed, under the name of \"leakage correction\". One recent noteworthy approach is that by Colclough et al (2015 NeuroImage, 117:439-448), which forces the inverse solution signals to have zero cross-correlation at lag zero. One goal is to show that Colcloughs method produces false human connectomes under very broad conditions. The second major goal is to develop a new solution, that appropriately \"unmixes\" the inverse solution signals, based on innovations orthogonalization. The new method first fits a multivariate autoregression to the inverse solution signals, giving the mixed innovations. Second, the mixed innovations are orthogonalized. Third, the mixed and orthogonalized innovations allow the estimation of the \"unmixing\" matrix, which is then finally used to \"unmix\" the inverse solution signals. It is shown that under very broad conditions, the new method produces proper human connectomes, even when the signals are not generated by an autoregressive model.

neuroscience↗