Functional connectivity and neuronal dynamics: insights from computational methods

International audienceBrain functions rely on flexible communication between microcircuits in distinct cortical regions. The mechanisms underlying flexible information routing are still, however, largely unknown. Here, we hypothesize that the emergence of a multiplicity of possible information routing patterns is due to the richness of the complex dynamics that can be supported by an underlying structural network. Analyses of circuit computational models of interacting brain areas suggest that different dynamical states associated with a given connectome mechanistically implement different information routing patterns between system's components. As a result, a fast, network-wide and self-organized reconfiguration of information routing patterns-and Functional Connectivity networks, seen as their proxy-can be achieved by inducing a transition between the available intrinsic dynamical states. We present here a survey of theoretical and modelling results, as well as of sophisticated metrics of Functional Connectivity which are compliant with the daunting task of characterizing dynamic routing from neural data. Theory: Function follows dynamics, rather than structure Neuronal activity conveys information, but which target should this information be-pushed‖ to, or which source should new information be-pulled‖ from? The problem of dynamic information routing is ubiquitous in a distributed information processing system as the brain. Brain functions in general require the control of distributed networks of interregional communication on fast timescales compliant with behavior, but incompatible with plastic modifications of connectivity tracts (Bressler & Kelso, 2001; Varela et al., 2001). This argument led to notions of connectivity based on information exchange-or more generically, an-interaction‖-between brain regions or neuronal populations, rather than based on the underlying STRUCTURAL CONNECTIVITY (SC, i.e. anatomic). An entire zoo of data-driven metrics has been introduced in the literature and this chapter will review some of them. Notwithstanding, they track simple correlation, or directed causal influence (Friston, 2011) or information transfer (Wibral et al., 2014) between time-series of activity. Thes

Model-free reconstruction of neuronal network connectivity from calcium imaging signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically unfeasible even in dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct approximations to network structural connectivities from network activity monitored through calcium fluorescence imaging. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time-series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the effective network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (e.g., bursting or non-bursting). We thus demonstrate how conditioning with respect to the global mean activity improves the performance of our method. [...] Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good reconstruction of the network clustering coefficient, allowing to discriminate between weakly or strongly clustered topologies, whereas on the other hand an approach based on cross-correlations would invariantly detect artificially high levels of clustering. Finally, we present the applicability of our method to real recordings of in vitro cortical cultures. We demonstrate that these networks are characterized by an elevated level of clustering compared to a random graph (although not extreme) and by a markedly non-local connectivity.Comment: 54 pages, 8 figures (+9 supplementary figures), 1 table; submitted for publicatio

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

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

Causality and synchronisation in complex systems with applications to neuroscience

This thesis presents an investigation, of synchronisation and causality, motivated by problems in computational neuroscience. The thesis addresses both theoretical and practical signal processing issues regarding the estimation of interdependence from a set of multivariate data generated by a complex underlying dynamical system. This topic is driven by a series of problems in neuroscience, which represents the principal background motive behind the material in this work. The underlying system is the human brain and the generative process of the data is based on modern electromagnetic neuroimaging methods . In this thesis, the underlying functional of the brain mechanisms are derived from the recent mathematical formalism of dynamical systems in complex networks. This is justified principally on the grounds of the complex hierarchical and multiscale nature of the brain and it offers new methods of analysis to model its emergent phenomena. A fundamental approach to study the neural activity is to investigate the connectivity pattern developed by the brain’s complex network. Three types of connectivity are important to study: 1) anatomical connectivity refering to the physical links forming the topology of the brain network; 2) effective connectivity concerning with the way the neural elements communicate with each other using the brain’s anatomical structure, through phenomena of synchronisation and information transfer; 3) functional connectivity, presenting an epistemic concept which alludes to the interdependence between data measured from the brain network. The main contribution of this thesis is to present, apply and discuss novel algorithms of functional connectivities, which are designed to extract different specific aspects of interaction between the underlying generators of the data. Firstly, a univariate statistic is developed to allow for indirect assessment of synchronisation in the local network from a single time series. This approach is useful in inferring the coupling as in a local cortical area as observed by a single measurement electrode. Secondly, different existing methods of phase synchronisation are considered from the perspective of experimental data analysis and inference of coupling from observed data. These methods are designed to address the estimation of medium to long range connectivity and their differences are particularly relevant in the context of volume conduction, that is known to produce spurious detections of connectivity. Finally, an asymmetric temporal metric is introduced in order to detect the direction of the coupling between different regions of the brain. The method developed in this thesis is based on a machine learning extensions of the well known concept of Granger causality. The thesis discussion is developed alongside examples of synthetic and experimental real data. The synthetic data are simulations of complex dynamical systems with the intention to mimic the behaviour of simple cortical neural assemblies. They are helpful to test the techniques developed in this thesis. The real datasets are provided to illustrate the problem of brain connectivity in the case of important neurological disorders such as Epilepsy and Parkinson’s disease. The methods of functional connectivity in this thesis are applied to intracranial EEG recordings in order to extract features, which characterize underlying spatiotemporal dynamics before during and after an epileptic seizure and predict seizure location and onset prior to conventional electrographic signs. The methodology is also applied to a MEG dataset containing healthy, Parkinson’s and dementia subjects with the scope of distinguishing patterns of pathological from physiological connectivity

Dynamics of large-scale electrophysiological networks: a technical review

For several years it has been argued that neural synchronisation is crucial for cognition. The idea that synchronised temporal patterns between different neural groups carries information above and beyond the isolated activity of these groups has inspired a shift in focus in the field of functional neuroimaging. Specifically, investigation into the activation elicited within certain regions by some stimulus or task has, in part, given way to analysis of patterns of co-activation or functional connectivity between distal regions. Recently, the functional connectivity community has been looking beyond the assumptions of stationarity that earlier work was based on, and has introduced methods to incorporate temporal dynamics into the analysis of connectivity. In particular, non-invasive electrophysiological data (magnetoencephalography / electroencephalography (MEG/EEG)), which provides direct measurement of whole-brain activity and rich temporal information, offers an exceptional window into such (potentially fast) brain dynamics. In this review, we discuss challenges, solutions, and a collection of analysis tools that have been developed in recent years to facilitate the investigation of dynamic functional connectivity using these imaging modalities. Further, we discuss the applications of these approaches in the study of cognition and neuropsychiatric disorders. Finally, we review some existing developments that, by using realistic computational models, pursue a deeper understanding of the underlying causes of non-stationary connectivity

Conditional network measures using multivariate partial coherence analysis for spike train data with application to multi-electrode array recordings

This thesis proposes a novel approach for functional connectivity studies of neuronal signal recordings based on statistical signal processing analysis in the frequency domain using Multivariate Partial Coherence (MVPC) combined with network theory measures. MVPC is applied to spike trains signals to make inferences about the underlying network structure. The presence of connections between single unit spike trains is estimated using both coherence and MVPC analysis. Scalability of MVPC analysis is investigated through application to simulated spike train data with up to 100 simultaneous spike trains generated from a network of excitatory and inhibitory cortical neurons. Stable MVPC estimates were obtained with up to 198 predictors in partial coherence estimates, using a combination of simulated cortical neuron data and additional Poisson spike train predictors. MVPC provides higher order partial coherence analysis for multi-channel spike trains signals, removing effects of common influences in pairwise connectivity estimates. Network measures applied to binary and weighted adjacency measures derived from coherence and partial coherence are compared to determine the differences in unconditional and conditional networks of spike train interactions. A combination of MVPC analysis along with network theory analysis provides a systematic approach for multi-channel spike train signals. The proposed method is applied to simulated and multi-electrode array (MEA) spike train data. The MEA data consists of 19 single unit channels recorded from a study of connectivity in a model of kainic acid (KA) induced epileptiform activity for mesial temporal lobe epilepsy (mTLE) in a rat. The network theory analysis uses basic measures on both conditional and unconditional network, which highlights the differences in network structure and characteristics between the two representations. Complex analysis on conditional networks is useful in describing the properties of integration and segregation in the network

Modelling and analysis of cortico-hippocampal interactions and dynamics during sleep and anaesthesia

The standard memory consolidation model assumes that new memories are temporarily stored in the hippocampus and later transferred to the neocortex, during deep sleep, for long-term storage, signifying the importance of studying functional and structural cortico-hippocampal interactions. Our work offers a thorough analysis on such interactions between neocortex and hippocampus, along with a detailed study of their intrinsic dynamics, from two complementary perspectives: statistical data analysis and computational modelling. The first part of this study reviews mathematical tools for assessing directional interactions in multivariate time series. We focus on the notion of Granger Causality and the related measure of generalised Partial Directed Coherence (gPDC) which we then apply, through a custom built numerical package, to electrophysiological data from the medial prefrontal cortex (mPFC) and hippocampus of anaesthetized rats. Our gPDC analysis reveals a clear lateral-to-medial hippocampus connectivity and suggests a reciprocal information flow between mPFC and hippocampus, altered during cortical activity. The second part deals with modelling sleep-related intrinsic rhythmic dynamics of the two areas, and examining their coupling. We first reproduce a computational model of the cortical slow oscillation, a periodic alteration between activated (UP) states and neuronal silence. We then develop a new spiking network model of hippocampal areas CA3 and CA1, reproducing many of their intrinsic dynamics and exhibiting sharp wave-ripple complexes, suggesting a novel mechanism for their generation based on CA1 interneuronal activity and recurrent inhibition. We finally couple the two models to study interactions between the slow oscillation and hippocampal activity. Our simulations propose a dependence of the correlation between UP states and hippocampal spiking on the excitation-to-inhibition ratio induced by the mossy fibre input to CA3 and by a combination of the Schaffer collateral and temporoammonic input to CA1. These inputs are shown to affect reported correlations between UP states and ripples

Effective influences in neuronal networks : attentional modulation of effective influences underlying flexible processing and how to measure them

Selective routing of information between brain areas is a key prerequisite for flexible adaptive behaviour. It allows to focus on relevant information and to ignore potentially distracting influences. Selective attention is a psychological process which controls this preferential processing of relevant information. The neuronal network structures and dynamics, and the attentional mechanisms by which this routing is enabled are not fully clarified. Based on previous experimental findings and theories, a network model is proposed which reproduces a range of results from the attention literature. It depends on shifting of phase relations between oscillating neuronal populations to modulate the effective influence of synapses. This network model might serve as a generic routing motif throughout the brain. The attentional modifications of activity in this network are investigated experimentally and found to employ two distinct channels to influence processing: facilitation of relevant information and independent suppression of distracting information. These findings are in agreement with the model and previously unreported on the level of neuronal populations. Furthermore, effective influence in dynamical systems is investigated more closely. Due to a lack of a theoretical underpinning for measurements of influence in non-linear dynamical systems such as neuronal networks, often unsuited measures are used for experimental data that can lead to erroneous conclusions. Based on a central theorem in dynamical systems, a novel theory of effective influence is developed. Measures derived from this theory are demonstrated to capture the time dependent effective influence and the asymmetry of influences in model systems and experimental data. This new theory holds the potential to uncover previously concealed interactions in generic non-linear systems studied in a range of disciplines, such as neuroscience, ecology, economy and climatology

Modelling and analysis of cortico-hippocampal interactions and dynamics during sleep and anaesthesia

The standard memory consolidation model assumes that new memories are temporarily stored in the hippocampus and later transferred to the neocortex, during deep sleep, for long-term storage, signifying the importance of studying functional and structural cortico-hippocampal interactions. Our work offers a thorough analysis on such interactions between neocortex and hippocampus, along with a detailed study of their intrinsic dynamics, from two complementary perspectives: statistical data analysis and computational modelling. The first part of this study reviews mathematical tools for assessing directional interactions in multivariate time series. We focus on the notion of Granger Causality and the related measure of generalised Partial Directed Coherence (gPDC) which we then apply, through a custom built numerical package, to electrophysiological data from the medial prefrontal cortex (mPFC) and hippocampus of anaesthetized rats. Our gPDC analysis reveals a clear lateral-to-medial hippocampus connectivity and suggests a reciprocal information flow between mPFC and hippocampus, altered during cortical activity. The second part deals with modelling sleep-related intrinsic rhythmic dynamics of the two areas, and examining their coupling. We first reproduce a computational model of the cortical slow oscillation, a periodic alteration between activated (UP) states and neuronal silence. We then develop a new spiking network model of hippocampal areas CA3 and CA1, reproducing many of their intrinsic dynamics and exhibiting sharp wave-ripple complexes, suggesting a novel mechanism for their generation based on CA1 interneuronal activity and recurrent inhibition. We finally couple the two models to study interactions between the slow oscillation and hippocampal activity. Our simulations propose a dependence of the correlation between UP states and hippocampal spiking on the excitation-to-inhibition ratio induced by the mossy fibre input to CA3 and by a combination of the Schaffer collateral and temporoammonic input to CA1. These inputs are shown to affect reported correlations between UP states and ripples