Successful Reconstruction of a Physiological Circuit with Known Connectivity from Spiking Activity Alone

Identifying the structure and dynamics of synaptic interactions between neurons is the first step to understanding neural network dynamics. The presence of synaptic connections is traditionally inferred through the use of targeted stimulation and paired recordings or by post-hoc histology. More recently, causal network inference algorithms have been proposed to deduce connectivity directly from electrophysiological signals, such as extracellularly recorded spiking activity. Usually, these algorithms have not been validated on a neurophysiological data set for which the actual circuitry is known. Recent work has shown that traditional network inference algorithms based on linear models typically fail to identify the correct coupling of a small central pattern generating circuit in the stomatogastric ganglion of the crab Cancer borealis. In this work, we show that point process models of observed spike trains can guide inference of relative connectivity estimates that match the known physiological connectivity of the central pattern generator up to a choice of threshold. We elucidate the necessary steps to derive faithful connectivity estimates from a model that incorporates the spike train nature of the data. We then apply the model to measure changes in the effective connectivity pattern in response to two pharmacological interventions, which affect both intrinsic neural dynamics and synaptic transmission. Our results provide the first successful application of a network inference algorithm to a circuit for which the actual physiological synapses between neurons are known. The point process methodology presented here generalizes well to larger networks and can describe the statistics of neural populations. In general we show that advanced statistical models allow for the characterization of effective network structure, deciphering underlying network dynamics and estimating information-processing capabilities.     

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

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. 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 functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. 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 estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.     

Impact of network topology on inference of synaptic connectivity from multi-neuronal spike data simulated by a large-scale cortical network model

Many mechanisms of neural processing rely critically upon the synaptic connectivity between neurons. As our ability to simultaneously record from large populations of neurons expands, the ability to infer network connectivity from this data has become a major goal of computational neuroscience. To address this issue, we employed several different methods to infer synaptic connections from simulated spike data from a realistic local cortical network model. This approach allowed us to directly compare the accuracy of different methods in predicting synaptic connectivity. We compared the performance of model-free (coherence measure and transfer entropy) and model-based (coupled escape rate model) methods of connectivity inference, applying those methods to the simulated spike data from the model networks with different network topologies. Our results indicate that the accuracy of the inferred connectivity was higher for highly clustered, near regular, or small-world networks, while accuracy was lower for random networks, irrespective of which analysis method was employed. Among the employed methods, the model-based method performed best. This model performed with higher accuracy, was less sensitive to threshold changes, and required less data to make an accurate assessment of connectivity. Given that cortical connectivity tends to be highly clustered, our results outline a powerful analytical tool for inferring local synaptic connectivity from observations of spontaneous activity.     

Graph theoretical analysis of complex networks in the brain

Since the discovery of small-world and scale-free networks the study of complex systems from a network perspective has taken an enormous flight. In recent years many important properties of complex networks have been delineated. In particular, significant progress has been made in understanding the relationship between the structural properties of networks and the nature of dynamics taking place on these networks. For instance, the 'synchronizability' of complex networks of coupled oscillators can be determined by graph spectral analysis. These developments in the theory of complex networks have inspired new applications in the field of neuroscience. Graph analysis has been used in the study of models of neural networks, anatomical connectivity, and functional connectivity based upon fMRI, EEG and MEG. These studies suggest that the human brain can be modelled as a complex network, and may have a small-world structure both at the level of anatomical as well as functional connectivity. This small-world structure is hypothesized to reflect an optimal situation associated with rapid synchronization and information transfer, minimal wiring costs, as well as a balance between local processing and global integration. The topological structure of functional networks is probably restrained by genetic and anatomical factors, but can be modified during tasks. There is also increasing evidence that various types of brain disease such as Alzheimer's disease, schizophrenia, brain tumours and epilepsy may be associated with deviations of the functional network topology from the optimal small-world pattern.     

A Multivariate Granger Causality Concept towards Full Brain Functional Connectivity

Detecting changes of spatially high-resolution functional connectivity patterns in the brain is crucial for improving the fundamental understanding of brain function in both health and disease, yet still poses one of the biggest challenges in computational neuroscience. Currently, classical multivariate Granger Causality analyses of directed interactions between single process components in coupled systems are commonly restricted to spatially low- dimensional data, which requires a pre-selection or aggregation of time series as a preprocessing step. In this paper we propose a new fully multivariate Granger Causality approach with embedded dimension reduction that makes it possible to obtain a representation of functional connectivity for spatially high-dimensional data. The resulting functional connectivity networks may consist of several thousand vertices and thus contain more detailed information compared to connectivity networks obtained from approaches based on particular regions of interest. Our large scale Granger Causality approach is applied to synthetic and resting state fMRI data with a focus on how well network community structure, which represents a functional segmentation of the network, is preserved. It is demonstrated that a number of different community detection algorithms, which utilize a variety of algorithmic strategies and exploit topological features differently, reveal meaningful information on the underlying network module structure.     

On imputing function to structure from the behavioural effects of brain lesions

What is the link, if any, between the patterns of connections in the brain and the behavioural effects of localized brain lesions? We explored this question in four related ways. First, we investigated the distribution of activity decrements that followed simulated damage to elements of the thalamocortical network, using integrative mechanisms that have recently been used to successfully relate connection data to information on the spread of activation, and to account simultaneously for a variety of lesion effects. Second, we examined the consequences of the patterns of decrement seen in the simulation for each type of inference that has been employed to impute function to structure on the basis of the effects of brain lesions. Every variety of conventional inference, including double dissociation, readily misattributed function to structure. Third, we tried to derive a more reliable framework of inference for imputing function to structure, by clarifying concepts of function, and exploring a more formal framework, in which knowledge of connectivity is necessary but insufficient, based on concepts capable of mathematical specification. Fourth, we applied this framework to inferences about function relating to a simple network that reproduces intact, lesioned and paradoxically restored orientating behaviour. Lesion effects could be used to recover detailed and reliable information on which structures contributed to particular functions in this simple network. Finally, we explored how the effects of brain lesions and this formal approach could be used in conjunction with information from multiple neuroscience methodologies to develop a practical and reliable approach to inferring the functional roles of brain structures.     

Time-variant estimation of directed influences during Parkinsonian tremor

The inference of interaction structures in multidimensional time series is a major challenge not only in neuroscience but in many fields of research. To gather information about the connectivity in a network from measured data, several parametric as well as non-parametric approaches have been proposed and widely examined. Today a lot of interest is focused on the evolution of the network connectivity in time which might contain information about ongoing tasks in the brain or possible dynamic dysfunctions. Therefore an extension of the current approaches towards time-resolved analysis techniques is desired. We present a parametric approach for time variant analysis, test its performance for simulated data, and apply it to real-world data.     

On directed information theory and Granger causality graphs

Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks can be used to assess Granger causality graphs of stochastic processes. We show that directed information theory includes measures such as the transfer entropy, and that it is the adequate information theoretic framework needed for neuroscience applications, such as connectivity inference problems.     

功能磁共振和脑电神经成像技术与大脑刺激相结合的研究进展

随着对神经机制问题阐述水平的迅速提高,所应用的神经成像技术、方法及各种工具的复杂程度也在不断提高．一方面是神经成像技术本身的不断发展,另一方面则是大脑直接刺激与神经成像技术同步记录方法的发展．经颅磁刺激-功能磁共振成像同步技术(TMS-fMRI)和经颅磁刺激-脑电技术(TMS-EEG)能为研究大脑网络的功能和有效连通性提供技术手段,该技术在多种认知领域的发展和应用,为神经科学、认知心理学、神经信息学等学科的研究者对人脑的研究开启了多条通道,更加有利于深入地理解人类大脑的工作机制．     

Imaging of functional connectivity in the mouse brain

Functional neuroimaging (e.g., with fMRI) has been difficult to perform in mice, making it challenging to translate between human fMRI studies and molecular and genetic mechanisms. A method to easily perform large-scale functional neuroimaging in mice would enable the discovery of functional correlates of genetic manipulations and bridge with mouse models of disease. To satisfy this need, we combined resting-state functional connectivity mapping with optical intrinsic signal imaging (fcOIS). We demonstrate functional connectivity in mice through highly detailed fcOIS mapping of resting-state networks across most of the cerebral cortex. Synthesis of multiple network connectivity patterns through iterative parcellation and clustering provides a comprehensive map of the functional neuroarchitecture and demonstrates identification of the major functional regions of the mouse cerebral cortex. The method relies on simple and relatively inexpensive camera-based equipment, does not require exogenous contrast agents and involves only reflection of the scalp (the skull remains intact) making it minimally invasive. In principle, fcOIS allows new paradigms linking human neuroscience with the power of molecular/genetic manipulations in mouse models.     

Individual differences in white-matter microstructure reflect variation in functional connectivity during choice

The relation between brain structure and function is of fundamental importance in neuroscience. Comparisons between behavioral and brain-imaging measures suggest that variation in brain structure correlates with the presence of specific skills. Behavioral measures, however, reflect the integrated function of multiple brain regions. Rather than behavior, a physiological index of function could be a more sensitive and informative measure with which to compare structural measures. Here, we test for a relationship between a physiological measure of functional connectivity between two brain areas during a simple decision-making task and a measure of structural connectivity. Paired-pulse transcranial magnetic stimulation indexed functional connectivity between two regions important for action choices: the premotor and motor cortex. Fractional anisotropy (FA), a marker of microstructural integrity, indexed structural connectivity. Individual differences in functional connectivity during action selection show highly specific correlations with FA in localized regions of white-matter interconnecting regions, including the premotor and motor cortex. Probabilistic tractography, a technique for identifying fiber pathways from diffusion-weighted imaging (DWI), was used to reconstruct the anatomical networks linking the component brain regions involved in making decisions. These findings demonstrate a relationship between individual differences in functional and structural connectivity within human brain networks central to action choice.     

Identifying and Tracking Simulated Synaptic Inputs from Neuronal Firing: Insights from In Vitro Experiments

Accurately describing synaptic interactions between neurons and how interactions change over time are key challenges for systems neuroscience. Although intracellular electrophysiology is a powerful tool for studying synaptic integration and plasticity, it is limited by the small number of neurons that can be recorded simultaneously in vitro and by the technical difficulty of intracellular recording in vivo. One way around these difficulties may be to use large-scale extracellular recording of spike trains and apply statistical methods to model and infer functional connections between neurons. These techniques have the potential to reveal large-scale connectivity structure based on the spike timing alone. However, the interpretation of functional connectivity is often approximate, since only a small fraction of presynaptic inputs are typically observed. Here we use in vitro current injection in layer 2/3 pyramidal neurons to validate methods for inferring functional connectivity in a setting where input to the neuron is controlled. In experiments with partially-defined input, we inject a single simulated input with known amplitude on a background of fluctuating noise. In a fully-defined input paradigm, we then control the synaptic weights and timing of many simulated presynaptic neurons. By analyzing the firing of neurons in response to these artificial inputs, we ask 1) How does functional connectivity inferred from spikes relate to simulated synaptic input? and 2) What are the limitations of connectivity inference? We find that individual current-based synaptic inputs are detectable over a broad range of amplitudes and conditions. Detectability depends on input amplitude and output firing rate, and excitatory inputs are detected more readily than inhibitory. Moreover, as we model increasing numbers of presynaptic inputs, we are able to estimate connection strengths more accurately and detect the presence of connections more quickly. These results illustrate the possibilities and outline the limits of inferring synaptic input from spikes.     

Efficient "Shotgun" Inference of Neural Connectivity from Highly Sub-sampled Activity Data

Inferring connectivity in neuronal networks remains a key challenge in statistical neuroscience. The “common input” problem presents a major roadblock: it is difficult to reliably distinguish causal connections between pairs of observed neurons versus correlations induced by common input from unobserved neurons. Available techniques allow us to simultaneously record, with sufficient temporal resolution, only a small fraction of the network. Consequently, naive connectivity estimators that neglect these common input effects are highly biased. This work proposes a “shotgun” experimental design, in which we observe multiple sub-networks briefly, in a serial manner. Thus, while the full network cannot be observed simultaneously at any given time, we may be able to observe much larger subsets of the network over the course of the entire experiment, thus ameliorating the common input problem. Using a generalized linear model for a spiking recurrent neural network, we develop a scalable approximate expected loglikelihood-based Bayesian method to perform network inference given this type of data, in which only a small fraction of the network is observed in each time bin. We demonstrate in simulation that the shotgun experimental design can eliminate the biases induced by common input effects. Networks with thousands of neurons, in which only a small fraction of the neurons is observed in each time bin, can be quickly and accurately estimated, achieving orders of magnitude speed up over previous approaches.     

Large-Scale,High-Resolution Multielectrode-Array Recording Depicts Functional Network Differences of Cortical and Hippocampal Cultures

Understanding the detailed circuitry of functioning neuronal networks is one of the major goals of neuroscience. Recent improvements in neuronal recording techniques have made it possible to record the spiking activity from hundreds of neurons simultaneously with sub-millisecond temporal resolution. Here we used a 512-channel multielectrode array system to record the activity from hundreds of neurons in organotypic cultures of cortico-hippocampal brain slices from mice. To probe the network structure, we employed a wavelet transform of the cross-correlogram to categorize the functional connectivity in different frequency ranges. With this method we directly compare, for the first time, in any preparation, the neuronal network structures of cortex and hippocampus, on the scale of hundreds of neurons, with sub-millisecond time resolution. Among the three frequency ranges that we investigated, the lower two frequency ranges (gamma (30–80 Hz) and beta (12–30 Hz) range) showed similar network structure between cortex and hippocampus, but there were many significant differences between these structures in the high frequency range (100–1000 Hz). The high frequency networks in cortex showed short tailed degree-distributions, shorter decay length of connectivity density, smaller clustering coefficients, and positive assortativity. Our results suggest that our method can characterize frequency dependent differences of network architecture from different brain regions. Crucially, because these differences between brain regions require millisecond temporal scales to be observed and characterized, these results underscore the importance of high temporal resolution recordings for the understanding of functional networks in neuronal systems.     

Network enrichment analysis: extension of gene-set enrichment analysis to gene networks

ABSTRACT: BACKGROUND: Gene-set enrichment analyses (GEA or GSEA) are commonly used for biological characterization of an experimental gene-set. This is done by finding known functional categories, such as pathways or Gene Ontology terms, that are over-represented in the experimental set; the assessment is based on an overlap statistic. Rich biological information in terms of gene interaction network is now widely available, but this topological information is not used by GEA, so there is a need for methods that exploit this type of information in high-throughput data analysis. RESULTS: We developed a method of network enrichment analysis (NEA) that extends the overlap statistic in GEA to network links between genes in the experimental set and those in the functional categories. For the crucial step in statistical inference, we developed a fast network randomization algorithm in order to obtain the distribution of any network statistic under the null hypothesis of no association between an experimental gene-set and a functional category. We illustrate the NEA method using gene and protein expression data from a lung cancer study. CONCLUSIONS: The results indicate that the NEA method is more powerful than the traditional GEA, primarily because the relationships between gene sets were more strongly captured by network connectivity rather than by simple overlaps.     

Detecting effective connectivity in networks of coupled neuronal oscillators

The application of data-driven time series analysis techniques such as Granger causality, partial directed coherence and phase dynamics modeling to estimate effective connectivity in brain networks has recently gained significant prominence in the neuroscience community. While these techniques have been useful in determining causal interactions among different regions of brain networks, a thorough analysis of the comparative accuracy and robustness of these methods in identifying patterns of effective connectivity among brain networks is still lacking. In this paper, we systematically address this issue within the context of simple networks of coupled spiking neurons. Specifically, we develop a method to assess the ability of various effective connectivity measures to accurately determine the true effective connectivity of a given neuronal network. Our method is based on decision tree classifiers which are trained using several time series features that can be observed solely from experimentally recorded data. We show that the classifiers constructed in this work provide a general framework for determining whether a particular effective connectivity measure is likely to produce incorrect results when applied to a dataset.     

偏头痛患者体感刺激下脑电信号的功能连接（英文）

目的 偏头痛是一种复杂的脑功能障碍性疾病,全球范围内患病率为14.4%。功能连接测量两个神经信号之间的统计学相互依赖性,不同的功能连接反映了大脑区域协同工作的不同模式。因此,研究不同脑区的功能连接对于理解偏头痛的病理生理机制具有十分重要的意义。以往基于脑电图对偏头痛患者脑功能连接的分析主要集中在视觉和疼痛刺激。本文尝试研究偏头痛患者在发作间期对体感刺激的皮质反应,以进一步了解偏头痛的神经功能障碍,为偏头痛的预防和治疗提供线索。方法 招募23例无先兆偏头痛患者,10例有先兆偏头痛患者,28名健康对照者。所有受试者均进行详细的基本资料和病史采集,完善量表评估,在正中神经体感刺激下进行脑电图记录。计算68个脑区的相干性作为功能连接,并评估功能连接与临床参数的相关性。结果 在正中神经体感刺激下,无先兆偏头痛和有先兆偏头痛患者的脑电功能连接与对照组相比存在差异,异常的脑电功能连接主要位于感觉辨别、疼痛调节、情绪认知和视觉处理等区域。无先兆偏头痛和有先兆偏头痛患者的大脑皮层对体感刺激可能具有相同的反应方式。偏头痛患者的功能连接异常与临床特征之间存在相关性,可以部分反映偏头痛的严重程度。结论 本研究...     

Emergent functional properties of neuronal networks with controlled topology

The interplay between anatomical connectivity and dynamics in neural networks plays a key role in the functional properties of the brain and in the associated connectivity changes induced by neural diseases. However, a detailed experimental investigation of this interplay at both cellular and population scales in the living brain is limited by accessibility. Alternatively, to investigate the basic operational principles with morphological, electrophysiological and computational methods, the activity emerging from large in vitro networks of primary neurons organized with imposed topologies can be studied. Here, we validated the use of a new bio-printing approach, which effectively maintains the topology of hippocampal cultures in vitro and investigated, by patch-clamp and MEA electrophysiology, the emerging functional properties of these grid-confined networks. In spite of differences in the organization of physical connectivity, our bio-patterned grid networks retained the key properties of synaptic transmission, short-term plasticity and overall network activity with respect to random networks. Interestingly, the imposed grid topology resulted in a reinforcement of functional connections along orthogonal directions, shorter connectivity links and a greatly increased spiking probability in response to focal stimulation. These results clearly demonstrate that reliable functional studies can nowadays be performed on large neuronal networks in the presence of sustained changes in the physical network connectivity.     

The research of constructing dynamic cognition model based on brain network

Estimating the functional interactions and connections between brain regions to corresponding process in cognitive, behavioral and psychiatric domains is a central pursuit for understanding the human connectome. Few studies have examined the effects of dynamic evolution on cognitive processing and brain activation using brain network model in scalp electroencephalography (EEG) data. Aim of this study was to investigate the brain functional connectivity and construct dynamic programing model from EEG data and to evaluate a possible correlation between topological characteristics of the brain connectivity and cognitive evolution processing. Here, functional connectivity between brain regions is defined as the statistical dependence between EEG signals in different brain areas and is typically determined by calculating the relationship between regional time series using wavelet coherence. We present an accelerated dynamic programing algorithm to construct dynamic cognitive model that we found that spatially distributed regions coherence connection difference, the topologic characteristics with which they can transfer information, producing temporary network states. Our findings suggest that brain dynamics give rise to variations in complex network properties over time after variation audio stimulation, dynamic programing model gives the dynamic evolution processing at different time and frequency. In this paper, by applying a new construct approach to understand whole brain network dynamics, firstly, brain network is constructed by wavelet coherence, secondly, different time active brain regions are selected by network topological characteristics and minimum spanning tree. Finally, dynamic evolution model is constructed to understand cognitive process by dynamic programing algorithm, this model is applied to the auditory experiment, results showed that, quantitatively, more correlation was observed after variation audio stimulation, the EEG function connection dynamic evolution model on cognitive processing is feasible with wavelet coherence EEG recording.     

Changes of Functional and Effective Connectivity in Smoking Replenishment on Deprived Heavy Smokers: A Resting-State fMRI Study

Previous researches have explored the changes of functional connectivity caused by smoking with the aid of fMRI. This study considers not only functional connectivity but also effective connectivity regarding both brain networks and brain regions by using a novel analysis framework that combines independent component analysis (ICA) and Granger causality analysis (GCA). We conducted a resting-state fMRI experiment in which twenty-one heavy smokers were scanned in two sessions of different conditions: smoking abstinence followed by smoking satiety. In our framework, group ICA was firstly adopted to obtain the spatial patterns of the default-mode network (DMN), executive-control network (ECN), and salience network (SN). Their associated time courses were analyzed using GCA, showing that the effective connectivity from SN to DMN was reduced and that from ECN/DMN to SN was enhanced after smoking replenishment. A paired t-test on ICA spatial patterns revealed functional connectivity variation in regions such as the insula, parahippocampus, precuneus, anterior cingulate cortex, supplementary motor area, and ventromedial/dorsolateral prefrontal cortex. These regions were later selected as the regions of interest (ROIs), and their effective connectivity was investigated subsequently using GCA. In smoking abstinence, the insula showed the increased effective connectivity with the other ROIs; while in smoking satiety, the parahippocampus had the enhanced inter-area effective connectivity. These results demonstrate our hypothesis that for deprived heavy smokers, smoking replenishment takes effect on both functional and effective connectivity. Moreover, our analysis framework could be applied in a range of neuroscience studies.