232 research outputs found

    Granger causality analysis in neuroscience and neuroimaging

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    Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling

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    Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of (ie, hypotheses about) network architectures and implicit coupling functions in terms of their Bayesian model evidence. These methods are collectively referred to as dynamical casual modelling (DCM). We focus on a relatively new approach that is proving remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems

    Causality within the Epileptic Network: An EEG-fMRI Study Validated by Intracranial EEG

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    Accurate localization of the Seizure Onset Zone (SOZ) is crucial in patients with drug-resistance focal epilepsy. EEG with fMRI recording (EEG-fMRI) has been proposed as a complementary non-invasive tool, which can give useful additional information in the pre-surgical work-up. However, fMRI maps related to interictal epileptiform activities (IED) often show multiple regions of signal change, or "networks," rather than highly focal ones. Effective connectivity approaches like Dynamic Causal Modeling (DCM) applied to fMRI data potentially offers a framework to address which brain regions drives the generation of seizures and IED within an epileptic network. Here, we present a first attempt to validate DCM on EEG-fMRI data in one patient affected by frontal lobe epilepsy. Pre-surgical EEG-fMRI demonstrated two distinct clusters of blood oxygenation level dependent (BOLD) signal increases linked to IED, one located in the left frontal pole and the other in the ipsilateral dorso-lateral frontal cortex. DCM of the IED-related BOLD signal favored a model corresponding to the left dorso-lateral frontal cortex as driver of changes in the fronto-polar region. The validity of DCM was supported by: (a) the results of two different non-invasive analysis obtained on the same dataset: EEG source imaging (ESI), and "psycho-physiological interaction" analysis; (b) the failure of a first surgical intervention limited to the fronto-polar region; (c) the results of the intracranial EEG monitoring performed after the first surgical intervention confirming a SOZ located over the dorso-lateral frontal cortex. These results add evidence that EEG-fMRI together with advanced methods of BOLD signal analysis is a promising tool that can give relevant information within the epilepsy surgery diagnostic work-up

    Analysing connectivity with Granger causality and dynamic causal modelling

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    This review considers state-of-the-art analyses of functional integration in neuronal macrocircuits. We focus on detecting and estimating directed connectivity in neuronal networks using Granger causality (GC) and dynamic causal modelling (DCM). These approaches are considered in the context of functional segregation and integration and — within functional integration — the distinction between functional and effective connectivity. We review recent developments that have enjoyed a rapid uptake in the discovery and quantification of functional brain architectures. GC and DCM have distinct and complementary ambitions that are usefully considered in relation to the detection of functional connectivity and the identification of models of effective connectivity. We highlight the basic ideas upon which they are grounded, provide a comparative evaluation and point to some outstanding issues

    Understanding DCM: ten simple rules for the clinician.

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    Despite almost a decade since the introduction of Dynamic Causal Modelling (DCM), there remains some confusion within the wider neuroimaging, neuroscience and clinical communities as to what DCM studies are probing, and what all the jargon means. We provide ten simple rules, and a theoretical example to gently introduce the reader to the rationale behind DCM analyses, and how one should consider neuroimaging data and experiments that use DCM. It is deliberately written as a primer or orientation for non-technical imaging neuroscientists or clinicians who have had to contend with the technical intricacies of understanding DCM

    Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

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    In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

    Causal Modelling and Brain Connectivity in Functional Magnetic Resonance Imaging

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    Recent advances in data analysis and modeling allow the use of fMRI data to ask not just which brain regions are involved in various cognitive and perceptual tasks, but also how they communicate with each other. Karl Friston examines two different state-of-the-art approaches to modeling brain connectivity using neuroimaging

    Adiabatic dynamic causal modelling

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    This technical note introduces adiabatic dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow changes in variables (e.g., extracellular ion concentrations or synaptic efficacy) that underlie phase transitions in brain activity (e.g., paroxysmal seizure activity). The scheme is efficient and yet retains a biophysical interpretation, in virtue of being based on established neural mass models that are equipped with a slow dynamic on the parameters (such as synaptic rate constants or effective connectivity). In brief, we use an adiabatic approximation to summarise fast fluctuations in hidden neuronal states (and their expression in sensors) in terms of their second order statistics; namely, their complex cross spectra. This allows one to specify and compare models of slowly changing parameters (using Bayesian model reduction) that generate a sequence of empirical cross spectra of electrophysiological recordings. Crucially, we use the slow fluctuations in the spectral power of neuronal activity as empirical priors on changes in synaptic parameters. This introduces a circular causality, in which synaptic parameters underwrite fast neuronal activity that, in turn, induces activity-dependent plasticity in synaptic parameters. In this foundational paper, we describe the underlying model, establish its face validity using simulations and provide an illustrative application to a chemoconvulsant animal model of seizure activity

    Combining optogenetic stimulation and fMRI to validate a multivariate dynamical systems model for estimating causal brain interactions

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    State-space multivariate dynamical systems (MDS) (Ryali et al., 2011) and other causal estimation models are being increasingly used to identify directed functional interactions between brain regions. However, the validity and accuracy of such methods is poorly understood. Performance evaluation based on computer simulations of small artificial causal networks can address this problem to some extent, but they often involve simplifying assumptions that reduce biological validity of the resulting data. Here, we use a novel approach taking advantage of recently developed optogenetic fMRI (ofMRI) techniques to selectively stimulate brain regions while simultaneously recording high-resolution whole-brain fMRI data. ofMRI allows for a more direct investigation of causal influences from the stimulated site to brain regions activated downstream and is therefore ideal for evaluating causal estimation methods in vivo. We used ofMRI to investigate whether MDS models for fMRI can accurately estimate causal functional interactions between brain regions. Two cohorts of ofMRI data were acquired, one at Stanford University and the University of California Los Angeles (Cohort 1) and the other at the University of North Carolina Chapel Hill (Cohort 2). In each cohort optical stimulation was delivered to the right primary motor cortex (M1). General linear model analysis revealed prominent downstream thalamic activation in Cohort 1, and caudate-putamen (CPu) activation in Cohort 2. MDS accurately estimated causal interactions from M1 to thalamus and from M1 to CPu in Cohort 1 and Cohort 2, respectively. As predicted, no causal influences were found in the reverse direction. Additional control analyses demonstrated the specificity of causal interactions between stimulated and target sites. Our findings suggest that MDS state-space models can accurately and reliably estimate causal interactions in ofMRI data and further validate their use for estimating causal interactions in fMRI. More generally, our study demonstrates that the combined use of optogenetics and fMRI provides a powerful new tool for evaluating computational methods designed to estimate causal interactions between distributed brain regions
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