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

Dynamical connectivity and nonlinearity in a whole-brain computational model

openTra la grande varietà di modelli per l'attività cerebrale su larga scala, gli "effective models" raggiungono un buon compromesso tra accuratezza e complessità del modello e possono essere adattati ai dati di risonanza magnetica funzionale dell'attività dei singoli soggetti. Useremo un modello delle dinamiche del cervello per analizzare i dati dell'attività cerebrale individuale dal Progetto Human Connectome (un grande database di neuroimaging) e affronteremo la relazione tra la non linearità del modello e la "connettività funzionale dinamica" (variazioni temporali nella correlazione tra i segnali di aree diverse). In particolare, ci concentreremo sulla "velocità di connettività funzionale dinamica", un indice scalare che misura la rapidità di variazione nei modelli di connettività, e indagheremo se il modello riproduce la sua distribuzione empirica e se quest'ultima è correlata alla non linearità del modello.Among the large variety of models for large-scale brain activity, effective models achieve a good trade-off between model accuracy and complexity and can be fit to activity data of individual subjects from functional magnetic resonance imaging. We will use an effective model of whole-brain dynamics to fit individual brain activity data from the Human Connectome Project (a large neuroimaging database) and address the relationship between the model nonlinearity and the "dynamic functional connectivity" (temporal variations in the correlation between signals of different areas). In particular, we will focus on the "dynamic functional connectivity speed", a scalar index measuring the rapidity of variation in connectivity patterns, and investigate whether the model reproduces its empirical distribution and whether the latter is related to the model's nonlinearity

Functional magnetic resonance imaging : an intermediary between behavior and neural activity

Blood oxygen level dependent (BOLD) functional magnetic resonance imaging is a non-invasive technique used to trace changes in neural dynamics in reaction to mental activity caused by perceptual, motor or cognitive tasks. The BOLD response is a complex signal, a consequence of a series of physiological events regulated by increased neural activity. A method to infer from the BOLD signal onto underlying neuronal activity (hemodynamic inverse problem) is proposed in Chapter 2 under the assumption of a previously proposed mathematical model on the transduction of neural activity to the BOLD signal. Also, in this chapter we clarify the meaning of the neural activity function used as the input for an intrinsic dynamic system which can be viewed as an advanced substitute for the impulse response function. Chapter 3 describes an approach for recovering neural timing information (mental chronometry) in an object interaction decision task via solving the hemodynamic inverse problem. In contrast to the hemodynamic level, at the neural level, we were able to determine statistically significant latencies in activation between functional units in the model used. In Chapter 4, two approaches for regularization parameter tuning in a regularized-regression analysis are compared in an attempt to find the optimal amount of smoothing to be imposed on fMRI data in determining an empirical hemodynamic response function. We found that the noise autocorrelation structure can be improved by tuning the regularization parameter but the whitening-based criterion provides too much smoothing when compared to cross-validation. Chapter~5 illustrates that the smoothing techniques proposed in Chapter 4 can be useful in the issue of correlating behavioral and hemodynamic characteristics. Specifically, Chapter 5, based on the smoothing techniques from Chapter 4, seeks to correlate several parameters characterizing the hemodynamic response in Broca's area to behavioral measures in a naming task. In particular, a condition for independence between two routes of converting print to speech in a dual route cognitive model was verified in terms of hemodynamic parameters

The connected brain: Causality, models and intrinsic dynamics

Recently, there have been several concerted international efforts - the BRAIN initiative, European Human Brain Project and the Human Connectome Project, to name a few - that hope to revolutionize our understanding of the connected brain. Over the past two decades, functional neuroimaging has emerged as the predominant technique in systems neuroscience. This is foreshadowed by an ever increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. In this article, we summarize pedagogically the (deep) history of brain mapping. We will highlight the theoretical advances made in the (dynamic) causal modelling of brain function - that may have escaped the wider audience of this article - and provide a brief overview of recent developments and interesting clinical applications. We hope that this article will engage the signal processing community by showcasing the inherently multidisciplinary nature of this important topic and the intriguing questions that are being addressed

Dynamical consequences of regional heterogeneity in the brain’s transcriptional landscape

Brain regions vary in their molecular and cellular composition, but how this heterogeneity shapes neuronal dynamics is unclear. Here, we investigate the dynamical consequences of regional heterogeneity using a biophysical model of whole-brain functional magnetic resonance imaging (MRI) dynamics in humans. We show that models in which transcriptional variations in excitatory and inhibitory receptor (E:I) gene expression constrain regional heterogeneity more accurately reproduce the spatiotemporal structure of empirical functional connectivity estimates than do models constrained by global gene expression profiles or MRI-derived estimates of myeloarchitecture. We further show that regional transcriptional heterogeneity is essential for yielding both ignition-like dynamics, which are thought to support conscious processing, and a wide variance of regional-activity time scales, which supports a broad dynamical range. We thus identify a key role for E:I heterogeneity in generating complex neuronal dynamics and demonstrate the viability of using transcriptomic data to constrain models of large-scale brain function

Spectral Dynamic Causal Modelling: A Didactic Introduction and its Relationship with Functional Connectivity

We present a didactic introduction to spectral Dynamic Causal Modelling (DCM), a Bayesian state-space modelling approach used to infer effective connectivity from non-invasive neuroimaging data. Spectral DCM is currently the most widely applied DCM variant for resting-state functional MRI analysis. Our aim is to explain its technical foundations to an audience with limited expertise in state-space modelling and spectral data analysis. Particular attention will be paid to cross-spectral density, which is the most distinctive feature of spectral DCM and is closely related to functional connectivity, as measured by (zero-lag) Pearson correlations. In fact, the model parameters estimated by spectral DCM are those that best reproduce the cross-correlations between all variables--at all time lags--including the zero-lag correlations that are usually interpreted as functional connectivity. We derive the functional connectivity matrix from the model equations and show how changing a single effective connectivity parameter can affect all pairwise correlations. To complicate matters, the pairs of brain regions showing the largest changes in functional connectivity do not necessarily coincide with those presenting the largest changes in effective connectivity. We discuss the implications and conclude with a comprehensive summary of the assumptions and limitations of spectral DCM

Estimating Neural Signal Dynamics in the Human Brain

Although brain imaging methods are highly effective for localizing the effects of neural activation throughout the human brain in terms of the blood oxygenation level dependent (BOLD) response, there is currently no way to estimate the underlying neural signal dynamics in generating the BOLD response in each local activation region (except for processes slower than the BOLD time course). Knowledge of the neural signal is critical if spatial mapping is to progress to the analysis of dynamic information flow through the cortical networks as the brain performs its tasks. We introduce an analytic approach that provides a new level of conceptualization and specificity in the study of brain processing by non-invasive methods. This technique allows us to use brain imaging methods to determine the dynamics of local neural population responses to their native temporal resolution throughout the human brain, with relatively narrow confidence intervals on many response properties. The ability to characterize local neural dynamics in the human brain represents a significant enhancement of brain imaging capabilities, with potential applications ranging from general cognitive studies to assessment of neuropathologies

A tutorial on group effective connectivity analysis, part 1: first level analysis with DCM for fMRI

Dynamic Causal Modelling (DCM) is the predominant method for inferring effective connectivity from neuroimaging data. In the 15 years since its introduction, the neural models and statistical routines in DCM have developed in parallel, driven by the needs of researchers in cognitive and clinical neuroscience. In this tutorial, we step through an exemplar fMRI analysis in detail, reviewing the current implementation of DCM and demonstrating recent developments in group-level connectivity analysis. In the first part of the tutorial (current paper), we focus on issues specific to DCM for fMRI, unpacking the relevant theory and highlighting practical considerations. In particular, we clarify the assumptions (i.e., priors) used in DCM for fMRI and how to interpret the model parameters. This tutorial is accompanied by all the necessary data and instructions to reproduce the analyses using the SPM software. In the second part (in a companion paper), we move from subject-level to group-level modelling using the Parametric Empirical Bayes framework, and illustrate how to test for commonalities and differences in effective connectivity across subjects, based on imaging data from any modality

The impact of regional heterogeneity in whole-brain dynamics in the presence of oscillations

Large variability exists across brain regions in health and disease, considering their cellular and molecular composition, connectivity and function. Large-scale whole-brain models comprising coupled brain regions provide insights into the underlying dynamics that shape complex patterns of spontaneous brain activity. In particular, biophysically grounded mean-field whole-brain models in the asynchronous regime were used to demonstrate the dynamical consequences of including regional variability. Nevertheless, the role of heterogeneities when brain dynamics are supporting by synchronous oscillating state, which is a ubiquitous phenomenon in brain, remains poorly understood. Here, we implemented two models capable of presenting oscillatory behaviour with different levels of abstraction: a phenomenological Stuart Landau model and an exact mean-field model. The fit of these models informed by structural-to-functional–weighted MRI signal (T1w/T2w) allowed to explore the implication of the inclusion of heterogeneities for modelling resting-state fMRI recordings from healthy participants. We found that disease-specific regional functional heterogeneity imposed dynamical consequences within the oscillatory regime in fMRI recordings from neurodegeneration with specific impacts in brain atrophy/structure (Alzheimer patients). Overall, we found that models with oscillations perform better when structural and functional regional heterogeneities are considered showing that phenomenological and biophysical models behave similarly at the brink of the Hopf bifurcation.Fil: Sanz Perl Hernandez, Yonatan. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentina. Universidad de San Andrés; Argentina. Universitat Pompeu Fabra; EspañaFil: Zamora Lopez, Gorka. Universitat Pompeu Fabra; EspañaFil: Montbrió, Ernest. Universitat Pompeu Fabra; EspañaFil: Monge Asensio, Martí. Universitat Pompeu Fabra; EspañaFil: Vohryzek, Jakub. Universitat Pompeu Fabra; España. University of Oxford; Reino UnidoFil: Fittipaldi, María Sol. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; Argentina. University of California; Estados Unidos. Trinity College; IrlandaFil: Gonzalez Campo, Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; ArgentinaFil: Moguilner, Sebastian Gabriel. University of California; Estados Unidos. Trinity College; Irlanda. Universidad Adolfo Ibañez; ChileFil: Ibañez, Agustin Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; Argentina. University of California; Estados Unidos. Trinity College; Irlanda. Universidad Adolfo Ibañez; ChileFil: Tagliazucchi, Enzo Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentina. Universidad de San Andrés; Argentina. Universidad Adolfo Ibañez; ChileFil: Yeo, B. T. Thomas. National University of Singapore; SingapurFil: Kringelbach, Morten L.. University of Oxford; Reino Unido. University Aarhus; Dinamarca. Universidade do Minho; PortugalFil: Deco, Gustavo. Universitat Pompeu Fabra; España. Max Planck Institute for Human Cognitive and Brain Sciences; Alemania. Monash University; Australi