Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling

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

A Primer on Variational Laplace (VL)

This article details a scheme for approximate Bayesian inference, which has underpinned thousands of neuroimaging studies since its introduction 15 years ago. Variational Laplace (VL) provides a generic approach to fitting linear or non-linear models, which may be static or dynamic, returning a posterior probability density over the model parameters and an approximation of log model evidence, which enables Bayesian model comparison. VL applies variational Bayesian inference in conjunction with quadratic or Laplace approximations of the evidence lower bound (free energy). Importantly, update equations do not need to be derived for each model under consideration, providing a general method for fitting a broad class of models. This primer is intended for experimenters and modellers who may wish to fit models to data using variational Bayesian methods, without assuming previous experience of variational Bayes or machine learning. Accompanying code demonstrates how to fit different kinds of model using the reference implementation of the VL scheme in the open-source Statistical Parametric Mapping (SPM) software package. In addition, we provide a standalone software function that does not require SPM, in order to ease translation to other fields, together with detailed pseudocode. Finally, the supplementary materials provide worked derivations of the key equations

Linking fast and slow: the case for generative models

A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multi-scale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature.Comment: 20 pages, 5 figure

An information-theoretic analysis of resting-state versus task fMRI

Resting-state fMRI is an increasingly popular alternative to task-based fMRI. However, a formal quantification of the amount of information provided by resting-state fMRI as opposed to active task conditions about neural responses is lacking. We conducted a systematic comparison of the quality of inferences derived from a resting-state and a task fMRI paradigm by means of Bayesian Data Comparison. In this framework, data quality is formally quantified in information-theoretic terms as the precision and amount of information provided by the data on the parameters of interest. Parameters of effective connectivity, estimated from the cross-spectral densities of resting-state- and task time series by means of dynamic causal modelling (DCM), were subjected to the analysis. Data from 50 individuals undergoing resting-state and a Theory-of-Mind task were compared, both datasets provided by the Human Connectome Project. A threshold of very strong evidence was reached in favour of the Theory-of-Mind task (>10 bits or natural units) regarding information gain, which could be attributed to the active task condition eliciting stronger effective connectivity. Extending these analyses to other tasks and cognitive systems will reveal whether the superior informative value of task-based fMRI observed here is case specific or a more general trend

A tutorial on group effective connectivity analysis, part 2: second level analysis with PEB

This tutorial provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). This involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject's neuroimaging timeseries (e.g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i.e., posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors. We walk through this approach in detail, using data from a published fMRI experiment that characterised individual differences in hemispheric lateralization in a semantic processing task. The preliminary subject specific DCM analysis is covered in detail in a companion paper. This tutorial is accompanied by the example dataset and step-by-step instructions to reproduce the analyses

Ageing and the Ipsilateral M1 BOLD Response: A Connectivity Study.

Young people exhibit a negative BOLD response in ipsilateral primary motor cortex (M1) when making unilateral movements, such as button presses. This negative BOLD response becomes more positive as people age. In this study, we investigated why this occurs, in terms of the underlying effective connectivity and haemodynamics. We applied dynamic causal modeling (DCM) to task fMRI data from 635 participants aged 18-88 from the Cam-CAN dataset, who performed a cued button pressing task with their right hand. We found that connectivity from contralateral supplementary motor area (SMA) and dorsal premotor cortex (PMd) to ipsilateral M1 became more positive with age, explaining 44% of the variability across people in ipsilateral M1 responses. In contrast, connectivity from contralateral M1 to ipsilateral M1 was weaker and did not correlate with individual differences in rM1 BOLD. Neurovascular and haemodynamic parameters in the model were not able to explain the age-related shift to positive BOLD. Our results add to a body of evidence implicating neural, rather than vascular factors as the predominant cause of negative BOLD-while emphasising the importance of inter-hemispheric connectivity. This study provides a foundation for investigating the clinical and lifestyle factors that determine the sign and amplitude of the M1 BOLD response in ageing, which could serve as a proxy for neural and vascular health, via the underlying neurovascular mechanisms

Variational representational similarity analysis

© 2019 The Authors This technical note describes a variational or Bayesian implementation of representational similarity analysis (RSA) and pattern component modelling (PCM). It considers RSA and PCM as Bayesian model comparison procedures that assess the evidence for stimulus or condition-specific patterns of responses distributed over voxels or channels. On this view, one can use standard variational inference procedures to quantify the contributions of particular patterns to the data, by evaluating second-order parameters or hyperparameters. Crucially, this allows one to use parametric empirical Bayes (PEB) to infer which patterns are consistent among subjects. At the between-subject level, one can then assess the evidence for different (combinations of) hypotheses about condition-specific effects using Bayesian model comparison. Alternatively, one can select a single hypothesis that best explains the pattern of responses using Bayesian model selection. This note rehearses the technical aspects of within and between-subject RSA using a worked example, as implemented in the Statistical Parametric Mapping (SPM) software. En route, we highlight the connection between univariate and multivariate analyses of neuroimaging data and the sorts of analyses that are possible using component modelling and representational similarity analysis

Representation of contralateral visual space in the human hippocampus

The initial encoding of visual information primarily from the contralateral visual field is a fundamental organizing principle of the primate visual system. Recently, the presence of such retinotopic sensitivity has been shown to extend well beyond early visual cortex to regions not historically considered retinotopically sensitive. In particular, human scene-selective regions in parahippocampal and medial parietal cortex exhibit prominent biases for the contralateral visual field. Here we used fMRI to test the hypothesis that the human hippocampus, which is thought to be anatomically connected with these scene-selective regions, would also exhibit a biased representation of contralateral visual space. First, population receptive field mapping with scene stimuli revealed strong biases for the contralateral visual field in bilateral hippocampus. Second, the distribution of retinotopic sensitivity suggested a more prominent representation in anterior medial portions of the hippocampus. Finally, the contralateral bias was confirmed in independent data taken from the Human Connectome Project initiative. The presence of contralateral biases in the hippocampus - a structure considered by many as the apex of the visual hierarchy - highlights the truly pervasive influence of retinotopy. Moreover, this finding has important implications for understanding how this information relates to the allocentric global spatial representations known to be encoded therein.SIGNIFICANCE STATEMENT:Retinotopic encoding of visual information is an organizing principle of visual cortex. Recent work demonstrates this sensitivity in structures far beyond early visual cortex, including those anatomically connected to the hippocampus. Here, using population receptive field modelling in two independent sets of data we demonstrate a consistent bias for the contralateral visual field in bilateral hippocampus. Such a bias highlights the truly pervasive influence of retinotopy, with important implications for understanding how the presence of retinotopy relates to more allocentric spatial representations

Directed coupling in multi-brain networks underlies generalized synchrony during social exchange

Advances in social neuroscience have made neural signatures of social exchange measurable simultaneously across people. This has identified brain regions differentially active during social interaction between human dyads, but the underlying systems-level mechanisms are incompletely understood. This paper introduces dynamic causal modeling and Bayesian model comparison to assess the causal and directed connectivity between two brains in the context of hyperscanning (h-DCM). In this setting, correlated neuronal responses become the data features that have to be explained by models with and without between-brain (effective) connections. Connections between brains can be understood in the context of generalized synchrony, which explains how dynamical systems become synchronized when they are coupled to each another. Under generalized synchrony, each brain state can be predicted by the other brain or a mixture of both. Our results show that effective connectivity between brains is not a feature within dyads per se but emerges selectively during social exchange. We demonstrate a causal impact of the sender's brain activity on the receiver of information, which explains previous reports of two-brain synchrony. We discuss the implications of this work; in particular, how characterizing generalized synchrony enables the discovery of between-brain connections in any social contact, and the advantage of h-DCM in studying brain function on the subject level, dyadic level, and group level within a directed model of (between) brain function