Anil K. Seth

Wiener-Granger Causality: A well established methodology

For decades, the main ways to study the effect of one part of the nervous system upon another have been either to stimulate or lesion the first part and investigate the outcome in the second. This article describes a fundamentally different approach to identifying causal connectivity in neuroscience: a focus on the predictability of ongoing activity in one part from that in another. This approach was made possible by a new method that comes from the pioneering work of Wiener (1956) and Granger (1969). The Wiener-Granger method, unlike stimulation and ablation, does not require direct intervention in the nervous system. Rather, it relies on the estimation of causal statistical influences between simultaneously recorded neural time series data, either in the absence of identifiable behavioral events or in the context of task performance. Causality in the Wiener-Granger sense is based on the statistical predictability of one time series that derives from knowledge of one or more others. This article defines Wiener-Granger Causality, discusses its merits and limitations in neuroscience, and outlines recent developments in its implementation.

Granger Causality and Transfer Entropy Are Equivalent for Gaussian Variables

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience. More recently transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, has gained traction in a similarly wide field. While it has been recognized that the two concepts must be related, the exact relationship has until now not been formally described. Here we show that for Gaussian variables, Granger causality and transfer entropy are entirely equivalent, thus bridging autoregressive and information-theoretic approaches to data-driven causal inference.

An Interoceptive Predictive Coding Model of Conscious Presence

We describe a theoretical model of the neurocognitive mechanisms underlying conscious presence and its disturbances. The model is based on interoceptive prediction error and is informed by predictive models of agency, general models of hierarchical predictive coding and dopaminergic signaling in cortex, the role of the anterior insular cortex (AIC) in interoception and emotion, and cognitive neuroscience evidence from studies of virtual reality and of psychiatric disorders of presence, specifically depersonalization/derealization disorder. The model associates presence with successful suppression by top-down predictions of informative interoceptive signals evoked by autonomic control signals and, indirectly, by visceral responses to afferent sensory signals. The model connects presence to agency by allowing that predicted interoceptive signals will depend on whether afferent sensory signals are determined, by a parallel predictive-coding mechanism, to be self-generated or externally caused. Anatomically, we identify the AIC as the likely locus of key neural comparator mechanisms. Our model integrates a broad range of previously disparate evidence, makes predictions for conjoint manipulations of agency and presence, offers a new view of emotion as interoceptive inference, and represents a step toward a mechanistic account of a fundamental phenomenological property of consciousness.

Analysing connectivity with Granger causality and dynamic causal modelling

Highlights ► A brief introduction to the analysis of directed connectivity in brain networks. ► An overview of advances in Granger causality and dynamic causal modelling. ► A comparative evaluation of both approaches in terms of their pros and cons.

Measuring consciousness: relating behavioural and neurophysiological approaches

The resurgent science of consciousness has been accompanied by a recent emphasis on the problem of measurement. Having dependable measures of consciousness is essential both for mapping experimental evidence to theory and for designing perspicuous experiments. Here, we review a series of behavioural and brain-based measures, assessing their ability to track graded consciousness and clarifying how they relate to each other by showing what theories are presupposed by each. We identify possible and actual conflicts among measures that can stimulate new experiments, and we conclude that measures must prove themselves by iteratively building knowledge in the context of theoretical frameworks. Advances in measuring consciousness have implications for basic cognitive neuroscience, for comparative studies of consciousness and for clinical applications.

Knowing your own heart: Distinguishing interoceptive accuracy from interoceptive awareness

Interoception refers to the sensing of internal bodily changes. Interoception interacts with cognition and emotion, making measurement of individual differences in interoceptive ability broadly relevant to neuropsychology. However, inconsistency in how interoception is defined and quantified led to a three-dimensional model. Here, we provide empirical support for dissociation between dimensions of: (1) interoceptive accuracy (performance on objective behavioural tests of heartbeat detection), (2) interoceptive sensibility (self-evaluated assessment of subjective interoception, gauged using interviews/questionnaires) and (3) interoceptive awareness (metacognitive awareness of interoceptive accuracy, e.g. confidence-accuracy correspondence). In a normative sample (N=80), all three dimensions were distinct and dissociable. Interoceptive accuracy was only partly predicted by interoceptive awareness and interoceptive sensibility. Significant correspondence between dimensions emerged only within the sub-group of individuals with greatest interoceptive accuracy. These findings set the context for defining how the relative balance of accuracy, sensibility and awareness dimensions explain cognitive, emotional and clinical associations of interoceptive ability.

Granger Causality Analysis in Neuroscience and Neuroimaging

### Introduction 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

Superficial white matter fiber systems impede detection of long-range cortical connections in diffusion MR tractography

Significance It is widely recognized that studying the detailed anatomy of the human brain is of great importance for neuroscience and medicine. The principal means for achieving this goal is presently diffusion magnetic resonance imaging (dMRI) tractography, which uses the local diffusion of water throughout the brain to estimate the course of long-range anatomical projections. Such projections connect gray matter regions through axons that travel in the deep white matter. The present study combines dMRI tractography with histological analysis to investigate where in the brain this method succeeds and fails. We conclude that certain superficial white matter systems pose challenges for measuring cortical connections that must be overcome for accurate determination of detailed neuroanatomy in humans. In vivo tractography based on diffusion magnetic resonance imaging (dMRI) has opened new doors to study structure–function relationships in the human brain. Initially developed to map the trajectory of major white matter tracts, dMRI is used increasingly to infer long-range anatomical connections of the cortex. Because axonal projections originate and terminate in the gray matter but travel mainly through the deep white matter, the success of tractography hinges on the capacity to follow fibers across this transition. Here we demonstrate that the complex arrangement of white matter fibers residing just under the cortical sheet poses severe challenges for long-range tractography over roughly half of the brain. We investigate this issue by comparing dMRI from very-high-resolution ex vivo macaque brain specimens with histological analysis of the same tissue. Using probabilistic tracking from pure gray and white matter seeds, we found that ∼50% of the cortical surface was effectively inaccessible for long-range diffusion tracking because of dense white matter zones just beneath the infragranular layers of the cortex. Analysis of the corresponding myelin-stained sections revealed that these zones colocalized with dense and uniform sheets of axons running mostly parallel to the cortical surface, most often in sulcal regions but also in many gyral crowns. Tracer injection into the sulcal cortex demonstrated that at least some axonal fibers pass directly through these fiber systems. Current and future high-resolution dMRI studies of the human brain will need to develop methods to overcome the challenges posed by superficial white matter systems to determine long-range anatomical connections accurately.

Distinguishing Causal Interactions in Neural Populations

We describe a theoretical network analysis that can distinguish statistically causal interactions in population neural activity leading to a specific output. We introduce the concept of a causal core to refer to the set of neuronal interactions that are causally significant for the output, as assessed by Granger causality. Because our approach requires extensive knowledge of neuronal connectivity and dynamics, an illustrative example is provided by analysis of Darwin X, a brain-based device that allows precise recording of the activity of neuronal units during behavior. In Darwin X, a simulated neuronal model of the hippocampus and surrounding cortical areas supports learning of a spatial navigation task in a real environment. Analysis of Darwin X reveals that large repertoires of neuronal interactions contain comparatively small causal cores and that these causal cores become smaller during learning, a finding that may reflect the selection of specific causal pathways from diverse neuronal repertoires.

Granger causality analysis of steady-state electroencephalographic signals during propofol-induced anaesthesia

Changes in conscious level have been associated with changes in dynamical integration and segregation among distributed brain regions. Recent theoretical developments emphasize changes in directed functional (i.e., causal) connectivity as reflected in quantities such as ‘integrated information’ and ‘causal density’. Here we develop and illustrate a rigorous methodology for assessing causal connectivity from electroencephalographic (EEG) signals using Granger causality (GC). Our method addresses the challenges of non-stationarity and bias by dividing data into short segments and applying permutation analysis. We apply the method to EEG data obtained from subjects undergoing propofol-induced anaesthesia, with signals source-localized to the anterior and posterior cingulate cortices. We found significant increases in bidirectional GC in most subjects during loss-of-consciousness, especially in the beta and gamma frequency ranges. Corroborating a previous analysis we also found increases in synchrony in these ranges; importantly, the Granger causality analysis showed higher inter-subject consistency than the synchrony analysis. Finally, we validate our method using simulated data generated from a model for which GC values can be analytically derived. In summary, our findings advance the methodology of Granger causality analysis of EEG data and carry implications for integrated information and causal density theories of consciousness.