Functional connectome extends the anatomical connectome by capturing the relations between neurons according to their activity and interactions. When these relations are causal, the functional connectome maps how neural activity flows within neural circuits and provides the possibility for inference of functional neural pathways, such as sensory-motor-behavioral pathways. While there exist various information approaches for non-causal estimations of the functional connectome, approaches that characterize the causal functional connectivity - the causal relationships between neuronal time series, are scarce. In this work, we develop the Neuro-PC algorithm which is a novel methodology for inferring the causal functional connectivity between neurons from multi-dimensional time series, such as neuronal recordings. The core of our methodology relies on a novel adaptation of the PC algorithm, a state-of-the-art method for statistical causal inference, to the multi-dimensional time-series of neural dynamics. We validate the performance of the method on network motifs with various interactions between their neurons simulated using continuous-time artificial network of neurons. We then consider the application of the method to obtain the causal functional connectome for recent multi-array electrophysiological recordings from the mouse visual cortex in the presence of different stimuli. We show how features of the mapping can be used for quantification of the similarities between neural responses subject to different stimuli.
The causal connectivity of a network is often inferred to understand the network function. It is arguably acknowledged that the inferred causal connectivity relies on causality measure one applies, and it may differ from the network's underlying structural connectivity. However, the interpretation of causal connectivity remains to be fully clarified, in particular, how causal connectivity depends on causality measures and how causal connectivity relates to structural connectivity. Here, we focus on nonlinear networks with pulse signals as measured output, $e.g.$, neural networks with spike out…
Neurofeedback is a non-invasive brain training with long-term medical and non-medical applications. Despite the existence of several emotion regulation studies using neurofeedback, further investigation is needed to understand interactions of the brain regions involved in the process. We implemented EEG neurofeedback with simultaneous fMRI using a modified happiness-inducing task through autobiographical memories to upregulate positive emotion. The results showed increased activity of prefrontal, occipital, parietal, and limbic regions and increased functional connectivity between prefrontal, …
As neuroscientists we want to understand how causal interactions or mechanisms within the brain give rise to perception, cognition, and behavior. It is typical to estimate interaction effects from measured activity using statistical techniques such as functional connectivity, Granger Causality, or information flow, whose outcomes are often falsely treated as revealing mechanistic insight. Since these statistical techniques fit models to low-dimensional measurements from brains, they ignore the fact that brain activity is high-dimensional. Here we focus on the obvious confound of common inputs:…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of neuron shape on the overall connectivity and dynamics of the emerging networks. The current work addresses this issue by considering simplified neuronal shapes consisting of circular regions (soma/axons) with spokes (dendrites). Networks are grown by placing these patterns randomly in the 2D plane and establishing connections whenever a piece of dendrite falls in…
Recent evidence in rodent cerebral cortex and olfactory bulb suggests that short-term dynamics of excitatory synaptic transmission is correlated to stereotypical connectivity motifs. It was observed that neurons with short-term facilitating synapses form predominantly reciprocal pairwise connections, while neurons with short-term depressing synapses form unidirectional pairwise connections. The cause of these structural differences in synaptic microcircuits is unknown. We propose that these connectivity motifs emerge from the interactions between short-term synaptic dynamics (SD) and long-term…
We apply Dynamic Causal Models to electrocorticogram recordings from two macaque monkeys performing a problem-solving task that engages working memory, and induces time-on-task effects. We thus provide a computational account of changes in effective connectivity within two regions of the fronto-parietal network, the dorsolateral prefrontal cortex and the pre-supplementary motor area. We find that forward connections between the two regions increased in strength when task demands increased, and as the experimental session progressed. Similarities in the effects of task demands and time on task …
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad principles underlying collective spiking activity in neural circuits. The first is that local features of network connectivity can be surprisingly effective in predicting global statistics of activity across a network. The second is that, for the important case of large networks with excitatory-inhibitory balance, correlated spiking persists or vanishes depending …
Background: Real-time functional magnetic resonance imaging neurofeedback (rtfMRI-nf) has proven to be a powerful technique to help subjects to gauge and enhance emotional control. Traditionally, rtfMRI-nf has focused on emotional regulation through self-regulation of amygdala. Recently, rtfMRI studies have observed that regulation of a target brain region is accompanied by connectivity changes beyond the target region. Therefore, the aim of present study is to investigate the use of connectivity between amygdala and prefrontal regions as the target of neurofeedback training in healthy individ…
Neurofeedback cognitive training is a promising tool used to promote cognitive functions effectively and efficiently. In this study, we investigated a novel functional near-infrared spectroscopy (fNIRS)-based frontoparietal functional connectivity (FC) neurofeedback training paradigm related to working memory, involving healthy adults. Compared with conventional cognitive training studies, we chose the frontoparietal network, a key brain region for cognitive function modulation, as neurofeedback, yielding a strong targeting effect. In the experiment, 10 participants (test group) received three…
Primary visual cortex (V1) provides crucial insights into the selectivity and emergence of specific output features such as orientation tuning. Tuning and selectivity of cortical neurons in mouse visual cortex is not equivocally resolved so far. While many in-vivo experimental studies found inhibitory neurons of all subtypes to be broadly tuned for orientation other studies report inhibitory neurons that are as sharply tuned as excitatory neurons. These diverging findings about the selectivity of excitatory and inhibitory cortical neurons prompted us to ask the following questions: (1) How dif…
This paper indicates causality as the tool that unifies the analysis of both activations and connectivity of brain areas, obtained with fMRI data. Causality analysis is commonly applied to study connectivity, so this work focuses on demonstrating that also the detection of activations can be handled with a causality analysis. We test our method on finger tapping data, in which GLM and Granger Causality approaches are compared in finding activations. Granger causality not only performs the task well, but indeed we obtained a better localization (i.e. precision) of activations. As a result we cl…
Two recent experimental observations pose a challenge to many cortical models. First, the activity in the auditory cortex is sparse, and firing rates can be described by a lognormal distribution. Second, the distribution of non-zero synaptic strengths between nearby cortical neurons can also be described by a lognormal distribution. Here we use a simple model of cortical activity to reconcile these observations. The model makes the experimentally testable prediction that synaptic efficacies onto a given cortical neuron are statistically correlated, i.e. it predicts that some neurons receive ma…
A theoretical framework describing the set of interactions between neurons in the brain, or functional connectivity, should include dynamical functions representing the propagation of signal from one neuron to another. Green's functions and response functions are natural candidates for this but, while they are conceptually very useful, they are usually defined only for linear time-translationally invariant systems. The brain, instead, behaves nonlinearly and in a time-dependent way. Here, we use nonequilibrium Green's functions to describe the time-dependent functional connectivity of a contin…
When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with axonal conduction delays and spike timing dependent plasticity, representative of a cortical column or hypercolumn with large proportion of inhibitory neurons. Each neuron fires following a Hodgkin-Huxley like dynamics and it is interconnected randomly to other neurons. The network dynamics is investigated estimating Bandt and Pompe probability distribution f…
A fundamental goal in network neuroscience is to understand how activity in one region drives activity elsewhere, a process referred to as effective connectivity. Here we propose to model this causal interaction using integro-differential equations and causal kernels that allow for a rich analysis of effective connectivity. The approach combines the tractability and flexibility of autoregressive modeling with the biophysical interpretability of dynamic causal modeling. The causal kernels are learned nonparametrically using Gaussian process regression, yielding an efficient framework for causal…
Correlation-based Hebbian plasticity is thought to shape neuronal connectivity during development and learning, whereas homeostatic plasticity would stabilize network activity. Here we investigate another, new aspect of this dichotomy: Can Hebbian associative properties also emerge as a network effect from a plasticity rule based on homeostatic principles on the neuronal level? To address this question, we simulated a recurrent network of leaky integrate-and-fire neurons, in which excitatory connections are subject to a structural plasticity rule based on firing rate homeostasis. We show that …
Neurons in the primary visual cortex are more or less selective for the orientation of a light bar used for stimulation. A broad distribution of individual grades of orientation selectivity has in fact been reported in all species. A possible reason for emergence of broad distributions is the recurrent network within which the stimulus is being processed. Here we compute the distribution of orientation selectivity in randomly connected model networks that are equipped with different spatial patterns of connectivity. We show that, for a wide variety of connectivity patterns, a linear theory bas…
Discovering frequent episodes in event sequences is an interesting data mining task. In this paper, we argue that this framework is very effective for analyzing multi-neuronal spike train data. Analyzing spike train data is an important problem in neuroscience though there are no data mining approaches reported for this. Motivated by this application, we introduce different temporal constraints on the occurrences of episodes. We present algorithms for discovering frequent episodes under temporal constraints. Through simulations, we show that our method is very effective for analyzing spike tra…
A major challenge in neuroimaging is understanding the mapping of neurophysiological dynamics onto cognitive functions. Traditionally, these maps have been constructed by examining changes in the activity magnitude of regions related to task performance. Recently, network neuroscience has produced methods to map connectivity patterns among many regions to certain cognitive functions by drawing on tools from network science and graph theory. However, these two different views are rarely addressed simultaneously, largely because few tools exist that account for patterns between nodes while simul…
Psychiatric research has been hampered by an explanatory gap between psychiatric symptoms and their neural underpinnings, which has resulted in poor treatment outcomes. This situation has prompted us to shift from symptom-based diagnosis to data-driven diagnosis, aiming to redefine psychiatric disorders as disorders of neural circuitry. Promising candidates for data-driven diagnosis include resting-state functional connectivity MRI (rs-fcMRI)-based biomarkers. Although biomarkers have been developed with the aim of diagnosing patients and predicting the efficacy of therapy, the focus has shift…
Small-World Networks (SWNs) represent a fundamental model for the comprehension of many complex man-made and biological networks. In the central nervous system, SWN models have been shown to fit well both anatomical and functional maps at the macroscopic level. However the functional microscopic level, where the nodes of a network are composed of single neurons, is still poorly understood. At this level, although recent evidences suggest that functional connectivity maps exhibit small-world organization, it is not known whether and how these maps, distributed in multiple brain regions, change …
There has been a substantial amount of research on the relationship between hippocampal neurogenesis and behaviour over the past fifteen years, but the causal role that new neurons have on cognitive and affective behavioural tasks is still far from clear. This is partly due to the difficulty of manipulating levels of neurogenesis without inducing off-target effects, which might also influence behaviour. In addition, the analytical methods typically used do not directly test whether neurogenesis mediates the effect of an intervention on behaviour. Previous studies may have incorrectly attribute…
In the study of biological networks, one of the major challenges is to understand the relationships between network structure and dynamics. In this paper, we model in vitro cortical neuronal cultures as stochastic dynamical systems and apply a method that reconstructs directed networks from dynamics [Ching and Tam, Phys. Rev. E 95, 010301(R), 2017] to reveal directed effective connectivity, namely the directed links and synaptic weights, of the neuronal cultures from voltage measurements recorded by a multielectrode array. The effective connectivity so obtained reproduces several features of c…
The analysis of the activity of neuronal cultures is considered to be a good proxy of the functional connectivity of in vivo neuronal tissues. Thus, the functional complex network inferred from activity patterns is a promising way to unravel the interplay between structure and functionality of neuronal systems. Here, we monitor the spontaneous self-sustained dynamics in neuronal cultures formed by interconnected aggregates of neurons (clusters). Dynamics is characterized by the fast activation of groups of clusters in sequences termed bursts. The analysis of the time delays between clusters' a…
Parkinsons disease (PD) is a movement disorder and the second most common neurodengerative disease but despite its relative abundance, there are no clinically accepted neuroimaging biomarkers to make prognostic predictions or differentiate between the similar atypical neurodegenerative diseases Multiple System Atrophy and Progressive Supranuclear Palsy. Abnormal connectivity in circuits including the motor circuit and basal ganglia have been previously shown as early markers of neurodegeneration. Therefore, we postulate the combination patterns of interregional dysconnectivity across the brain…
Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivity. Understanding how low-dimensional computations on mixed, distributed representations emerge from the structure of the recurrent connectivity and inputs to cortical networks is a major challenge. Here, we study a class of recurrent network models in which the connectivity is a sum of a random part and a minimal, low-dimensional structure. We show that, in such networks, the d…
Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a si…
Qualitatively, some real networks in the brain could be characterized as 'small worlds', in the sense that the structure of their connections is intermediate between the extremes of an orderly geometric arrangement and of a geometry-independent random mesh. Small worlds can be defined more precisely in terms of their mean path length and clustering coefficient; but is such a precise description useful to better understand how the type of connectivity affects memory retrieval? We have simulated an autoassociative memory network of integrate-and-fire units, positioned on a ring, with the network…
Developmental dyslexia is characterized by the inability to acquire typical reading and writing skills. Dyslexia has been frequently linked to cerebral cortex alterations; however recent evidence also points towards sensory thalamus dysfunctions: dyslexics showed reduced responses in the left auditory thalamus (medial geniculate body, MGB) during speech processing in contrast to neurotypical readers. In addition, in the visual modality, dyslexics have reduced structural connectivity between the left visual thalamus (lateral geniculate nucleus, LGN) and V5/MT, a cerebral cortex region involved …
Analysis of brain activity in resting-state is of fundamental importance in identifying functional characteristics of neuronal system. Although resting brain has been extensively investigated for low frequency synchrony between brain regions, namely Functional Connectivity (FC), the other main stream of brain connectivity analysis that seeks causal interactions between brain regions, Effective Connectivity (EC), has been little explored in spontaneous brain oscillations. Inherent complexity of brain activities in resting-state, as is observed in BOLD (Blood Oxygenation-Level Dependant) fluctua…
In dynamical models of cortical networks, the recurrent connectivity can amplify the input given to the network in two distinct ways. One is induced by the presence of near-critical eigenvalues in the connectivity matrix W, producing large but slow activity fluctuations along the corresponding eigenvectors (dynamical slowing). The other relies on W being nonnormal, which allows the network activity to make large but fast excursions along specific directions. Here we investigate the tradeoff between nonnormal amplification and dynamical slowing in the spontaneous activity of large random neuron…
In this paper, we developed a model-based and a data-driven estimator for directed information (DI) to infer the causal connectivity graph between electrocorticographic (ECoG) signals recorded from brain and to identify the seizure onset zone (SOZ) in epileptic patients. Directed information, an information theoretic quantity, is a general metric to infer causal connectivity between time-series and is not restricted to a particular class of models unlike the popular metrics based on Granger causality or transfer entropy. The proposed estimators are shown to be almost surely convergent. Causal …
Universidad de Málaga（马拉加大学）；Northumbria University（诺森比亚大学）
While the brain connectivity network can inform the understanding and diagnosis of developmental dyslexia, its cause-effect relationships have not yet enough been examined. Employing electroencephalography signals and band-limited white noise stimulus at 4.8 Hz (prosodic-syllabic frequency), we measure the phase Granger causalities among channels to identify differences between dyslexic learners and controls, thereby proposing a method to calculate directional connectivity. As causal relationships run in both directions, we explore three scenarios, namely channels' activity as sources, as sink…
We apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown {\it in vitro}. We infer connectivity between two neurons via the measurement of the mutual information between their spike trains. In addition we measure higher point multi-informations between any two spike trains conditional on the activity of a third cell, as a means to identify and distinguish classes of functional connectivity among three neurons. The use of a conditional three-cell measure removes some in…
A method of data assimilation (DA) is employed to estimate electrophysiological parameters of neurons simultaneously with their synaptic connectivity in a small model biological network. The DA procedure is cast as an optimization, with a cost function consisting of both a measurement error and a model error term. An iterative reweighting of these terms permits a systematic method to identify the lowest minimum, within a local region of state space, on the surface of a non-convex cost function. In the model, two sets of parameter values are associated with two particular functional modes of ne…
Neuroengineering is faced with unique challenges in repairing or replacing complex neural systems that are composed of many interacting parts. These interactions form intricate patterns over large spatiotemporal scales, and produce emergent behaviors that are difficult to predict from individual elements. Network science provides a particularly appropriate framework in which to study and intervene in such systems, by treating neural elements (cells, volumes) as nodes in a graph and neural interactions (synapses, white matter tracts) as edges in that graph. Here, we review the emerging discipli…
Dynamics and function of neuronal networks are determined by their synaptic connectivity. Current experimental methods to analyze synaptic network structure on the cellular level, however, cover only small fractions of functional neuronal circuits, typically without a simultaneous record of neuronal spiking activity. Here we present a method for the reconstruction of large recurrent neuronal networks from thousands of parallel spike train recordings. We employ maximum likelihood estimation of a generalized linear model of the spiking activity in continuous time. For this model the point proces…
Many different analysis techniques have been developed and applied to EEG recordings that allow one to investigate how different brain areas interact. One particular class of methods, based on the linear parametric representation of multiple interacting time series, is widely used to study causal connectivity in the brain. However, the results obtained by these methods should be interpreted with great care. The goal of this paper is to show, both theoretically and using simulations, that results obtained by applying causal connectivity measures on the sensor (scalp) time series do not allow in…
NeuroStrata: An Electroencephalographic Connectivity-Aware Deep Representation Learning Framework for Dynamic Brain Network Analysis of Mental Stress
Institute for Intelligent Systems Research and Innovation (IISRI), Deakin University（迪肯大学智能系统研究与创新研究所）；Centre for Health Research, University of Southern Queensland（南昆士兰大学健康研究中心）；School of Science, Engineering and Digital Technologies, University of Southern Queensland（南昆士兰大学科学、工程与数字技术学院）
Neuronal networks are controlled by a combination of the dynamics of individual neurons and the connectivity of the network that links them together. We study a minimal model of the preBotzinger complex, a small neuronal network that controls the breathing rhythm of mammals through periodic firing bursts. We show that the properties of a such a randomly connected network of identical excitatory neurons are fundamentally different from those of uniformly connected neuronal networks as described by mean-field theory. We show that (i) the connectivity properties of the networks determines the loc…
Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity, related to the more elusive question "Which areas cause the present activity of which others?". Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that a dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study me…
Cellular neural circuit and networks consisting of interconnected neurons and glia are ulti- mately responsible for the information processing associated with information processing in the brain. While there are major efforts aimed at mapping the structural and (electro)physiological connectivity of brain networks, such as the White House BRAIN Initiative aimed at the devel- opment of neurotechnologies capable of high density neural recordings, theoretical and compu- tational methods for analyzing and making sense of all this data seem to be further behind. Here, we propose and provide a summa…
