Biology subjects

Pascual-Marqui, R.

Publications and source records attributed to Pascual-Marqui, R..

3 recordsLinked to original sources

bioRxiv2021

Linear causal filtering: definition and theory

1.This work provides a framework based on multivariate autoregressive modeling for linear causal filtering in the sense of Granger. In its bivariate form, the linear causal filter defined here takes as input signals A and B, and it filters out the causal effect of B on A, thus yielding two new signals only containing the Granger-causal effect of A on B. In its general multivariate form for more than two signals, the effect of all indirect causal connections between A and B, mediated by all other signals, are accounted for, partialled out, and filtered out also. The importance of this filter is that it enables the estimation of directional measures of causal information flow from any non-causal, non-directional measure of association. For instance, based on the classic coherence, a directional measure of strength of information flow from A to B is obtained when applied to the linear causal filtered pair containing only A to B connectivity information. This particular case is equivalent to the isolated effective coherence (doi.org/10.3389/fnhum.2014.00448). Of more recent interest are the large family of phase-phase, phase-amplitude, and amplitude-amplitude cross-frequency coupling measures which are non-directional. The linear causal filter makes it now possible to estimate the directional causal versions these measures of association. One important field of application is in brain connectivity analysis based on cortical signals of electric neuronal activity (e.g. estimated sources of EEG and MEG, and invasive intracranial ECoG recordings). The linear causal filter introduced here provides a novel solution to the problem of estimating the direction of information flow from any non-directional measure of association. This work provides definitions, non-ambiguous equations, and clear prescriptions for implementing the linear causal filter in diverse settings.

neuroscience↗

bioRxiv2021

Pervasive false brain connectivity from electrophysiological signals

1.Signals of brain electric neuronal activity, either invasively measured or non-invasively estimated, are commonly used for connectivity inference. One popular methodology assumes that the neural dynamics follow a multivariate autoregression, where the autoregressive coefficients represent the couplings among regions. If observation noise is present and ignored, as is common in practice, the estimated couplings are biased, affecting all forms of Granger-causality inference, both in time and in frequency domains. Significant nonsense coupling, i.e., nonsense connectivity, can appear when in reality there is none, since there is always observation noise in two possible forms: measurement noise, and activity from other brain regions due to volume conduction and low spatial resolution. This problem is critical, and is currently not being addressed, calling into question the validity of many Granger-causality reports in the literature. An estimation method that accounts for noise is based on an overdetermined system of high-order multivariate Yule-Walker equations, which give reduced variance estimators for the coupling coefficients of the unobserved signals. Simulation-based comparisons to other published methods are presented, demonstrating its adequate performance. In addition, simulation results are presented for a zero connectivity case with noisy observations, where the new method correctly reports no connectivity while classical analyses (as found in most software packages) report nonsense connectivity. For the sake of reproducible research, the supplementary material includes, in human readable format, all the time series data used here.

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↗