Biology subjects

Kochi, K.

Publications and source records attributed to Kochi, K..

8 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↗

bioRxiv2018

Measuring Granger-causal effects in multivariate time series by system editing

1.What is the role of each node in a system of many interconnected nodes? This can be quantified by comparing the dynamics of the nodes in the intact system, with their modified dynamics in the edited system, where one node is deleted. In detail, the spectra are calculated from a causal multivariate autoregressive model for the intact system. Next, without re-estimation, one node is deleted from the model and the modified spectra at all other nodes are re-calculated. The change in spectra from the edited system to the intact system quantifies the role of the deleted node, giving a measure of its Granger-causal effects (CFX) on the system. A generalization of this novel measure is available for networks (i.e. for groups of nodes), which quantifies the role of each network in a system of many networks. For the sake of reproducible research, program codes (PASCAL), executable file, and toy data in human readable format are included in the supplementary material.

neuroscience↗

bioRxiv2018

A comparison of bivariate frequency domain measures of electrophysiological connectivity

1The problem of interest here concerns electrophysiological signals from two cortical sites, acquired as invasive intracranial recordings, or from non-invasive estimates of cortical electric neuronal activity computed from EEG or MEG recordings (see e.g. https://doi.org/10.1101/269753). In the absence of other sources, these measured signals consist of an instantaneous linear mixture of the true, actual, unobserved local signals, due to low spatial resolution and volume conduction. A connectivity measure is unreliable as a true indicator of electrophysiological connectivity if it is not invariant to mixing, or if it reports a significant connection for a mixture of independent signals. In (Vinck et al 2011 Neuroimage 55:1548) it was shown that coherence, imaginary coherence, and phase locking value are not invariant to mixing, while the phase lag index (PLI) and the weighted version (wPLI) are invariant to mixing. Here we show that the lagged coherence (LagCoh) measure (2007, https://arxiv.org/abs/0711.1455), not studied in Vinck et al, is invariant to mixing. Additionally, we present here a new mixture-invariant connectivity statistic: the \"standardized imaginary covariance\" (sImCov). We also include in the comparisons the directed PLI (dPLI) by Stam et al (2012 Neuroimage 62:1415). Fourier coefficients for \"N\" trials are generated from a linear unidirectional causal time domain model with electrophysiological delay \"k\" and regression coefficient \"b\". 1000 random data sets of \"N\" trials are simulated, and for each one, and for each connectivity measure, non-parametric randomization tests are performed. The \"true positive detection rate\" is calculated as the fraction of 1000 cases that have significant connectivity at p<0.05, 0.1, and 0.2. The connectivity methods were compared in terms of detection rates, under non-mixed and mixed conditions, for small and large sample sizes \"N\", with and without jitter for \"k\", and for different values of signal to noise. Under mixing, the results show that LagCoh outperforms wPLI, PLI, dPLI, and sImCov. Without mixing, LagCoh and sImCov outperform wPLI, PLI, and dPLI. Finally, it is shown that dPLI is an invalid estimator of flow direction, i.e. it reverses and \"goes against the flow\" by merely changing the sign of one of the time series, a fact that violates the basic definition of Granger causality. For the sake of reproducible research, the supplementary material includes Delphi Pascal source code and all detailed result files in human readable format.

neuroscience↗

bioRxiv2018

Comparing EEG/MEG neuroimaging methods based on localization error, false positive activity, and false positive connectivity

1.EEG/MEG neuroimaging consists of estimating the cortical distribution of time varying signals of electric neuronal activity, for the study of functional localization and connectivity. Currently, many different imaging methods are being used, with very different capabilities of correct localization of activity and of correct localization of connectivity. The aim here is to provide a guideline for choosing the best (i.e. least bad) imaging method. This first study is limited to the comparison of the following methods for EEG signals: sLORETA and eLORETA (standardized and exact low resolution electromagnetic tomography), MNE (minimum norm estimate), dSPM (dynamic statistical parametric mapping), and LCMVBs (linearly constrained minimum variance beamformers). These methods are linear, except for the LCMVBs that make use of the quadratic EEG covariances. To achieve a fair comparison, it is assumed here that the generators are independent and widely distributed (i.e. not few in number), giving a well-defined theoretical population EEG covariance matrix for use with the LCMVBs. Measures of localization error, false positive activity, and false positive connectivity are defined and computed under ideal no-noise conditions. It is empirically shown with extensive simulations that: (1) MNE, dSPM, and all LCMVBs are in general incapable of correct localization, while sLORETA and eLORETA have exact (zero-error) localization; (2) the brain volume with false positive activity is significantly larger for MN, dSPM, and all LCMVBs, as compared to sLORETA and eLORETA; and (3) the number of false positive connections is significantly larger for MN, dSPM, all LCMVBs, and sLORETA, as compared to eLORETA. Non-vague and fully detailed equations are given. PASCAL program codes and data files are available. It is noted that the results reported here do not apply to the LCMVBs based on EEG covariance matrices generated from extremely few generators, such as only one or two independent point sources.

neuroscience↗

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↗

bioRxiv2017

The Cross-Frequency Mediation Mechanism Of Intracortical Information Transactions

1. AbstractIn a seminal paper by von Stein and Sarnthein (2000), it was hypothesized that \"bottom-up\" information processing of \"content\" elicits local, high frequency (beta-gamma) oscillations, whereas \"top-down\" processing is \"contextual\", characterized by large scale integration spanning distant cortical regions, and implemented by slower frequency (theta-alpha) oscillations. This corresponds to a mechanism of cortical information transactions, where synchronization of beta-gamma oscillations between distant cortical regions is mediated by widespread theta-alpha oscillations. It is the aim of this paper to express this hypothesis quantitatively, in terms of a model that will allow testing this type of information transaction mechanism. The basic methodology used here corresponds to statistical mediation analysis, originally developed by (Baron and Kenny 1986). We generalize the classical mediator model to the case of multivariate complex-valued data, consisting of the discrete Fourier transform coefficients of signals of electric neuronal activity, at different frequencies, and at different cortical locations. The \"mediation effect\" is quantified here in a novel way, as the product of \"dual frequency RV-coupling coefficients\", that were introduced in (Pascual-Marqui et al 2016, http://arxiv.org/abs/1603.05343). Relevant statistical procedures are presented for testing the cross-frequency mediation mechanism in general, and in particular for testing the von Stein & Sarnthein hypothesis.

neuroscience↗