Granger causality is a method for identifying directed functional connectivity based on time series analysis of precedence and predictability. The method has been applied widely in neuroscience, ...however its application to functional MRI data has been particularly controversial, largely because of the suspicion that Granger causal inferences might be easily confounded by inter-regional differences in the hemodynamic response function. Here, we show both theoretically and in a range of simulations, that Granger causal inferences are in fact robust to a wide variety of changes in hemodynamic response properties, including notably their time-to-peak. However, when these changes are accompanied by severe downsampling, and/or excessive measurement noise, as is typical for current fMRI data, incorrect inferences can still be drawn. Our results have important implications for the ongoing debate about lag-based analyses of functional connectivity. Our methods, which include detailed spiking neuronal models coupled to biophysically realistic hemodynamic observation models, provide an important ‘analysis-agnostic’ platform for evaluating functional and effective connectivity methods.
► GC is invariant to confounding times-to-peak in hemodynamic responses applied to fMRI. ► We integrate theoretical analysis, simple simulations, and detailed spiking models. ► Our spiking/balloon model provides a ‘analysis-agnostic’ simulation test-bed. ► GC can't be applied naively to fMRI since downsampling and noise affect inference. ► We establish constraints & principles for functional connectivity analysis of fMRI.
•A “CTVAR” model for Neurophysiological processes is proposed.•Subsampling analysis based on an exact analytic solution of the model is performed.•Interactions between timescales of signal delay and ...sampling frequency are revealed.•GC detectability decays exponentially for sample intervals beyond causal delay time.•“Black spots” and “sweet spots” in GC detectability are discovered.
Granger causality is well established within the neurosciences for inference of directed functional connectivity from neurophysiological data. These data usually consist of time series which subsample a continuous-time biophysiological process. While it is well known that subsampling can lead to imputation of spurious causal connections where none exist, less is known about the effects of subsampling on the ability to reliably detect causal connections which do exist.
We present a theoretical analysis of the effects of subsampling on Granger-causal inference. Neurophysiological processes typically feature signal propagation delays on multiple time scales; accordingly, we base our analysis on a distributed-lag, continuous-time stochastic model, and consider Granger causality in continuous time at finite prediction horizons. Via exact analytical solutions, we identify relationships among sampling frequency, underlying causal time scales and detectability of causalities.
We reveal complex interactions between the time scale(s) of neural signal propagation and sampling frequency. We demonstrate that detectability decays exponentially as the sample time interval increases beyond causal delay times, identify detectability “black spots” and “sweet spots”, and show that downsampling may potentially improve detectability. We also demonstrate that the invariance of Granger causality under causal, invertible filtering fails at finite prediction horizons, with particular implications for inference of Granger causality from fMRI data.
Our analysis emphasises that sampling rates for causal analysis of neurophysiological time series should be informed by domain-specific time scales, and that state-space modelling should be preferred to purely autoregressive modelling.
On the basis of a very general model that captures the structure of neurophysiological processes, we are able to help identify confounds, and offer practical insights, for successful detection of causal connectivity from neurophysiological recordings.
Neuroimaging studies of the psychedelic state offer a unique window onto the neural basis of conscious perception and selfhood. Despite well understood pharmacological mechanisms of action, the ...large-scale changes in neural dynamics induced by psychedelic compounds remain poorly understood. Using source-localised, steady-state MEG recordings, we describe changes in functional connectivity following the controlled administration of LSD, psilocybin and low-dose ketamine, as well as, for comparison, the (non-psychedelic) anticonvulsant drug tiagabine. We compare both undirected and directed measures of functional connectivity between placebo and drug conditions. We observe a general decrease in directed functional connectivity for all three psychedelics, as measured by Granger causality, throughout the brain. These data support the view that the psychedelic state involves a breakdown in patterns of functional organisation or information flow in the brain. In the case of LSD, the decrease in directed functional connectivity is coupled with an increase in undirected functional connectivity, which we measure using correlation and coherence. This surprising opposite movement of directed and undirected measures is of more general interest for functional connectivity analyses, which we interpret using analytical modelling. Overall, our results uncover the neural dynamics of information flow in the psychedelic state, and highlight the importance of comparing multiple measures of functional connectivity when analysing time-resolved neuroimaging data.
Abstract
Phase transitions abound in nature and society, and, from species extinction to stock market collapse, their prediction is of widespread importance. In earlier work we showed that Global ...Transfer Entropy, a general measure of information flow, was found to peaks away from the transition on the disordered side for the Ising model, a canonical second order transition. Here we show that (a) global transfer entropy also peaks on the disordered side of the transition of finite first order transitions, such as ecology dynamics on coral reefs, which have latent heat and no correlation length divergence, and (b) analysis of information flow across state boundaries unifies both transition orders. We obtain the first information-theoretic result for the high-order Potts model and the first demonstration of early warning of a first order transition. The unexpected earlier finding that global transfer entropy peaks on the disordered side of a transition is also found for finite first order systems, albeit not in the thermodynamic limit. By noting that the interface length of clusters in each phase is the dominant region of information flow, we unify the information theoretic behaviour of first and second order transitions.
There is growing evidence that for a range of dynamical systems featuring complex interactions between large ensembles of interacting elements, mutual information peaks at order-disorder phase ...transitions. We conjecture that, by contrast, information flow in such systems will generally peak strictly on the disordered side of a phase transition. This conjecture is verified for a ferromagnetic 2D lattice Ising model with Glauber dynamics and a transfer entropy-based measure of systemwide information flow. Implications of the conjecture are considered, in particular, that for a complex dynamical system in the process of transitioning from disordered to ordered dynamics (a mechanism implicated, for example, in financial market crashes and the onset of some types of epileptic seizures); information dynamics may be able to predict an imminent transition.
Causal density and integrated information as measures of conscious level Seth, Anil K.; Barrett, Adam B.; Barnett, Lionel
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
10/2011, Letnik:
369, Številka:
1952
Journal Article
Recenzirano
An outstanding challenge in neuroscience is to develop theoretically grounded and practically applicable quantitative measures that are sensitive to conscious level. Such measures should be high for ...vivid alert conscious wakefulness, and low for unconscious states such as dreamless sleep, coma and general anaesthesia. Here, we describe recent progress in the development of measures of dynamical complexity, in particular causal density and integrated information. These and similar measures capture in different ways the extent to which a system's dynamics are simultaneously differentiated and integrated. Because conscious scenes are distinguished by the same dynamical features, these measures are therefore good candidates for reflecting conscious level. After reviewing the theoretical background, we present new simulation results demonstrating similarities and differences between the measures, and we discuss remaining challenges in the practical application of the measures to empirically obtained data.
A key challenge in neuroscience and, in particular, neuroimaging, is to move beyond identification of regional activations toward the characterization of functional circuits underpinning perception, ...cognition, behavior, and consciousness. Granger causality (G-causality) analysis provides a powerful method for achieving this, by identifying directed functional ("causal") interactions from time-series data. G-causality implements a statistical, predictive notion of causality whereby causes precede, and help predict, their effects. It is defined in both the time and frequency domains, and it allows for the conditioning out of common causal influences. In this paper we explain the theoretical basis and computational implementation of G-causality analysis in neuroimaging and, more broadly, in neurophysiology, noting both its exciting potential and the assumptions that govern its application and interpretation.
Multivariate Granger causality and generalized variance Barrett, Adam B; Barnett, Lionel; Seth, Anil K
Physical review. E, Statistical, nonlinear, and soft matter physics,
04/2010, Letnik:
81, Številka:
4 Pt 1
Journal Article
Odprti dostop
Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it ...only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables but may occur among groups or "ensembles" of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer additional justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy." Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.
PDF
