Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes

Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by mainly redundant or synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone

Causal interactions and delays in a neuronal ensemble

We analyze a neural system which mimics a sensorial cortex, with different input characteristics, in presence of transmission delays. We propose a new measure to characterize collective behavior, based on the nonlinear extension of the concept of Granger causality, and an interpretation is given of the variation of the percentage of the causally relevant interactions with transmission delays.Comment: 7 pages, 3 figures. To appear in the AIP seminar notes of 9th Granada seminar on Computational Physics: Computational and Mathematical Modeling of Cooperative Behavior in Neural System

On the interpretability and computational reliability of frequency-domain Granger causality

This is a comment to the paper 'A study of problems encountered in Granger causality analysis from a neuroscience perspective'. We agree that interpretation issues of Granger Causality in Neuroscience exist (partially due to the historical unfortunate use of the name 'causality', as nicely described in previous literature). On the other hand we think that the paper uses a formulation of Granger causality which is outdated (albeit still used), and in doing so it dismisses the measure based on a suboptimal use of it. Furthermore, since data from simulated systems are used, the pitfalls that are found with the used formulation are intended to be general, and not limited to neuroscience. It would be a pity if this paper, even written in good faith, became a wildcard against all possible applications of Granger Causality, regardless of the hard work of colleagues aiming to seriously address the methodological and interpretation pitfalls. In order to provide a balanced view, we replicated their simulations used the updated State Space implementation, proposed already some years ago, in which the pitfalls are mitigated or directly solved

Synergy and redundancy in the Granger causal analysis of dynamical networks

We analyze by means of Granger causality the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. Whilst we show that fully conditioned Granger causality is not affected by synergy, the pairwise analysis fails to put in evidence synergetic effects. In cases when the number of samples is low, thus making the fully conditioned approach unfeasible, we show that partially conditioned Granger causality is an effective approach if the set of conditioning variables is properly chosen. We consider here two different strategies (based either on informational content for the candidate driver or on selecting the variables with highest pairwise influences) for partially conditioned Granger causality and show that depending on the data structure either one or the other might be valid. On the other hand, we observe that fully conditioned approaches do not work well in presence of redundancy, thus suggesting the strategy of separating the pairwise links in two subsets: those corresponding to indirect connections of the fully conditioned Granger causality (which should thus be excluded) and links that can be ascribed to redundancy effects and, together with the results from the fully connected approach, provide a better description of the causality pattern in presence of redundancy. We finally apply these methods to two different real datasets. First, analyzing electrophysiological data from an epileptic brain, we show that synergetic effects are dominant just before seizure occurrences. Second, our analysis applied to gene expression time series from HeLa culture shows that the underlying regulatory networks are characterized by both redundancy and synergy

Retrieving the hemodynamic response function in resting state fMRI: methodology and application

In this paper we present a procedure to retrieve the hemodynamic response function (HRF) from resting state functional magnetic resonance imaging (fMRI) data. The fundamentals of the procedures are further validated by considering simultaneous electroencephalographic (EEG) recordings. The typical HRF shape at rest for a group of healthy subject is presented. Then we present the modifications to the shape of the HRF at rest following two physiological modulations: eyes open versus eyes closed and propofol-induced modulations of consciousness

The measure of randomness by leave-one-out prediction error in the analysis of EEG after laser painful stimulation in healthy subjects and migraine patients

Objective: We aimed to perform a quantitative analysis of event-related modulation of EEG activity, resulting from a not-warned and a warned paradigm of painful laser stimulation, in migraine patients and controls, by the use of a novel analysis, based upon a parametric approach to measure predictability of short and noisy time series. Methods: Ten migraine patients were evaluated during the not-symptomatic phase and compared to seven age and sex matched controls. The dorsum of the right hand and the right supraorbital zone were stimulated by a painful CO2 laser, in presence or in absence of a visual warning stimulus. An analysis time of 1 s after the stimulus was submitted to a time–frequency analysis by a complex Morlet wavelet and to a crosscorrelation analysis, in order to detect the development of EEG changes and the most activated cortical regions. A parametric approach to measure predictability of short and noisy time series was applied, where time series were modeled by leave-one-out (LOO) error. Results: The averaged laser-evoked potentials features were similar between the two groups in the alerted and not alerted condition. A strong reset of the beta rhythms after the painful stimuli was seen for three groups of electrodes along the midline in patients and controls: the predictability of the series induced by the laser stimulus changed very differently in controls and patients. The separation was more evident after the warning signal, leading to a separation with P-values of 0.0046 for both the hand and the face. Discussion: As painful stimulus causes organization of the local activity in cortex, EEG series become more predictable after stimulation. This phenomenon was less evident in migraine, as a sign of an inadequate cortical reactivity to pain. Significance: The LOO method enabled to show in migraine subtle changes in the cortical response to pain

The touch and zap method for in vivo whole-cell patch recording of intrinsic and visual responses of cortical neurons and Glial cells

Whole-cell patch recording is an essential tool for quantitatively establishing the biophysics of brain function, particularly in vivo. This method is of particular interest for studying the functional roles of cortical glial cells in the intact brain, which cannot be assessed with extracellular recordings. Nevertheless, a reasonable success rate remains a challenge because of stability, recording duration and electrical quality constraints, particularly for voltage clamp, dynamic clamp or conductance measurements. To address this, we describe "Touch and Zap", an alternative method for whole-cell patch clamp recordings, with the goal of being simpler, quicker and more gentle to brain tissue than previous approaches. Under current clamp mode with a continuous train of hyperpolarizing current pulses, seal formation is initiated immediately upon cell contact, thus the "Touch". By maintaining the current injection, whole-cell access is spontaneously achieved within seconds from the cell-attached configuration by a self-limited membrane electroporation, or "Zap", as seal resistance increases. We present examples of intrinsic and visual responses of neurons and putative glial cells obtained with the revised method from cat and rat cortices in vivo. Recording parameters and biophysical properties obtained with the Touch and Zap method compare favourably with those obtained with the traditional blind patch approach, demonstrating that the revised approach does not compromise the recorded cell. We find that the method is particularly well-suited for whole-cell patch recordings of cortical glial cells in vivo, targeting a wider population of this cell type than the standard method, with better access resistance. Overall, the gentler Touch and Zap method is promising for studying quantitative functional properties in the intact brain with minimal perturbation of the cell's intrinsic properties and local network. Because the Touch and Zap method is performed semi-automatically, this approach is more reproducible and less dependent on experimenter technique

Brain networks under attack : robustness properties and the impact of lesions

A growing number of studies approach the brain as a complex network, the so-called ‘connectome’. Adopting this framework, we examine what types or extent of damage the brain can withstand—referred to as network ‘robustness’—and conversely, which kind of distortions can be expected after brain lesions. To this end, we review computational lesion studies and empirical studies investigating network alterations in brain tumour, stroke and traumatic brain injury patients. Common to these three types of focal injury is that there is no unequivocal relationship between the anatomical lesion site and its topological characteristics within the brain network. Furthermore, large-scale network effects of these focal lesions are compared to those of a widely studied multifocal neurodegenerative disorder, Alzheimer’s disease, in which central parts of the connectome are preferentially affected. Results indicate that human brain networks are remarkably resilient to different types of lesions, compared to other types of complex networks such as random or scale-free networks. However, lesion effects have been found to depend critically on the topological position of the lesion. In particular, damage to network hub regions—and especially those connecting different subnetworks—was found to cause the largest disturbances in network organization. Regardless of lesion location, evidence from empirical and computational lesion studies shows that lesions cause significant alterations in global network topology. The direction of these changes though remains to be elucidated. Encouragingly, both empirical and modelling studies have indicated that after focal damage, the connectome carries the potential to recover at least to some extent, with normalization of graph metrics being related to improved behavioural and cognitive functioning. To conclude, we highlight possible clinical implications of these findings, point out several methodological limitations that pertain to the study of brain diseases adopting a network approach, and provide suggestions for future research