Causal measures of structure and plasticity in simulated and living neural networks

Coupling of in vitro Neocortical-Hippocampal Coculture Bursts Induces Different Spike Rhythms in Individual Networks

Brain-state alternation is important for long-term memory formation. Each brain state can be identified with a specific process in memory formation, e.g., encoding during wakefulness or consolidation during sleeping. The hippocampal-neocortical dialogue was proposed as a hypothetical framework for systems consolidation, which features different cross-frequency couplings between the hippocampus and distributed neocortical regions in different brain states. Despite evidence supporting this hypothesis, little has been reported about how information is processed with shifts in brain states. To address this gap, we developed an in vitro neocortical-hippocampal coculture model to study how activity coupling can affect connections between coupled networks. Neocortical and hippocampal neurons were cultured in two different compartments connected by a micro-tunnel structure. The network activity of the coculture model was recorded by microelectrode arrays underlying the substrate. Rhythmic bursting was observed in the spontaneous activity and electrical evoked responses. Rhythmic bursting activity in one compartment could couple to that in the other via axons passing through the micro-tunnels. Two types of coupling patterns were observed: slow-burst coupling (neocortex at 0.1–0.5 Hz and hippocampus at 1 Hz) and fast burst coupling (neocortex at 20–40 Hz and hippocampus at 4–10 Hz). The network activity showed greater synchronicity in the slow-burst coupling, as indicated by changes in the burstiness index. Network synchronicity analysis suggests the presence of different information processing states under different burst activity coupling patterns. Our results suggest that the hippocampal-neocortical coculture model possesses multiple modes of burst activity coupling between the cortical and hippocampal parts. With the addition of external stimulation, the neocortical-hippocampal network model we developed can elucidate the influence of state shifts on information processing.

Transfer Entropy between Intracranial EEG Nodes Highlights Network Dynamics that Cause and Stop Epileptic Seizures

Transfer entropy (TE) is used to examine the connectivity between nodes and the roles of nodes in epileptic neural networks during rest, moments before seizure, during seizure, and moments after seizure. There is a set of nodes that dominate information flow to epileptogenic zone (EZ) nodes, regions that trigger seizure, and non-EZ nodes during rest. The TE from the dominant to the EZ nodes decreases shortly before a seizure event and reaches a minimum during seizure. During the seizure, the dominant nodes cease or only weakly interact with the EZ nodes. This supports the hypothesis that seizure occurs when some nodes stop inhibiting the EZ nodes. The TE from the dominant to the EZ nodes peaks immediately after seizure, suggesting that seizure may stop when the brain exerts the highest level of information flow/activation/communication to the EZ nodes. The information flow from the dominant to EZ nodes is different from that to non-EZ nodes. This TE dynamics entering and exiting seizures may identify more accurately the EZ nodes, which may improve surgical planning.

The Flow of Axonal Information Among Hippocampal Subregions: 1. Feed-Forward and Feedback Network Spatial Dynamics Underpinning Emergent Information Processing

The tri-synaptic pathway in the mammalian hippocampus enables cognitive learning and memory. Despite decades of reports on anatomy and physiology, the functional architecture of the hippocampal network remains poorly understood in terms of the dynamics of axonal information transfer between subregions. Information inputs largely flow from the entorhinal cortex (EC) to the dentate gyrus (DG), and then are processed further in the CA3 and CA1 before returning to the EC. Here, we reconstructed elements of the rat hippocampus in a novel device over an electrode array that allowed for monitoring the directionality of individual axons between the subregions. The direction of spike propagation was determined by the transmission delay of the axons recorded between two electrodes in microfluidic tunnels. The majority of axons from the EC to the DG operated in the feed-forward direction, with other regions developing unexpectedly large proportions of feedback axons to balance excitation. Spike timing in axons between each region followed single exponential log-log distributions over two orders of magnitude from 0.01 to 1 s, indicating that conventional descriptors of mean firing rates are misleading assumptions. Most of the spiking occurred in bursts that required two exponentials to fit the distribution of inter-burst intervals. This suggested the presence of up-states and down-states in every region, with the least up-states in the DG to CA3 feed-forward axons and the CA3 subregion. The peaks of the log-normal distributions of intra-burst spike rates were similar in axons between regions with modes around 95 Hz distributed over an order of magnitude. Burst durations were also log-normally distributed around a peak of 88 ms over two orders of magnitude. Despite the diversity of these spike distributions, spike rates from individual axons were often linearly correlated to subregions. These linear relationships enabled the generation of structural connectivity graphs, not possible previously without the directional flow of axonal information. The rich axonal spike dynamics between subregions of the hippocampus reveal both constraints and broad emergent dynamics of hippocampal architecture. Knowledge of this network architecture may enable more efficient computational artificial intelligence (AI) networks, neuromorphic hardware, and stimulation and decoding from cognitive implants.

Experimental Platform to Study Spiking Pattern Propagation in Modular Networks In Vitro

The structured organization of connectivity in neural networks is associated with highly efficient information propagation and processing in the brain, in contrast with disordered homogeneous network architectures. Using microfluidic methods, we engineered modular networks of cultures using dissociated cells with unidirectional synaptic connections formed by asymmetric microchannels. The complexity of the microchannel geometry defined the strength of the synaptic connectivity and the properties of spiking activity propagation. In this study, we developed an experimental platform to study the effects of synaptic plasticity on a network level with predefined locations of unidirectionally connected cellular assemblies using multisite extracellular electrophysiology.

An EEG channel selection method for motor imagery based brain-computer interface and neurofeedback using Granger causality

Motor imagery (MI) brain-computer interface (BCI) and neurofeedback (NF) with electroencephalogram (EEG) signals are commonly used for motor function improvement in healthy subjects and to restore neurological functions in stroke patients. Generally, in order to decrease noisy and redundant information in unrelated EEG channels, channel selection methods are used which provide feasible BCI and NF implementations with better performances. Our assumption is that there are causal interactions between the channels of EEG signal in MI tasks that are repeated in different trials of a BCI and NF experiment. Therefore, a novel method for EEG channel selection is proposed which is based on Granger causality (GC) analysis. Additionally, the machine-learning approach is used to cluster independent component analysis (ICA) components of the EEG signal into artifact and normal EEG clusters. After channel selection, using the common spatial pattern (CSP) and regularized CSP (RCSP), features are extracted and with the k-nearest neighbor (k-NN), support vector machine (SVM) and linear discriminant analysis (LDA) classifiers, MI tasks are classified into left and right hand MI. The goal of this study is to achieve a method resulting in lower EEG channels with higher classification performance in MI-based BCI and NF by causal constraint. The proposed method based on GC, with only eight selected channels, results in 93.03% accuracy, 92.93% sensitivity, and 93.12% specificity, with RCSP feature extractor and best classifier for each subject, after being applied on Physionet MI dataset, which is increased by 3.95%, 3.73%, and 4.13%, in comparison with correlation-based channel selection method.

Ictal High-Frequency Oscillation for Lateralizing Patients With Suspected Bitemporal Epilepsy Using Wavelet Transform and Granger Causality Analysis

Identifying lateralization of bilateral temporal lobe epilepsy (TLE) is a challenging issue; scalp electroencephalography (EEG) and routine band electrocorticography (ECoG) fail to reveal the epileptogenic focus for further temporal lobectomy treatment. High-frequency oscillations (HFOs) can be utilized as a biomarker for lateralizing the onset zone in suspected bitemporal epilepsy. Except subjective vision detect the HFOs, objective verification should be performed to raise the accuracy. In the present research, we prospectively studied 10 patients with refractory temporal seizures and who underwent ECoG with wide-band frequency amplifiers (2,048 Hz); all patients had a class I outcome after temporal resection. Pre- and ictal HFOs will be analyzed by wavelet transform (WT) and Granger causality (GC) to objectively verify lateralization of the seizure onset zone (SOZ). WT analysis showed ictal HFOs in 10 patients mainly covered from 80 to 115 Hz (average, 92.59 ± 10.23 Hz), and there was distinct bandpass boundary between pre-ictal HFOs and ictal HFOs. GC analysis showed five patients (2, 4, 5, 6, and 7), no matter the pre-ictal or ictal state, had the highest GC degree in SOZ itself. The remaining patients (1, 3, 8, 9, and 10) had the highest GC degree in SOZ with its adjacent regions in the pre-ictal and ictal stages. GC analysis further confirmed the result of the WT and suggested HFOs are initiated and propagated in the local brain region mainly, afterward, transmitting to adjacent brain regions. These results indicated that the combination of WT and GC analyses significantly contributes to accurate lateralization in patients with suspected bitemporal epilepsy.

Evaluation of connectivity estimates using spiking neuronal network models

The flow of information between different regions of the cortex is fundamental for brain function. Researchers use causality detection techniques, such as Granger causality, to infer connectivity among brain areas from time series. Generalized partial directed coherence (GPDC) is a frequency domain linear method based on vector autoregressive model, which has been applied in electroencephalography, local field potential, and blood oxygenation level-dependent signals. Despite its widespread usage, previous attempts to validate GPDC use oversimplified simulated data, which do not reflect the nonlinearities and network couplings present in biological signals. In this work, we evaluated the GPDC performance when applied to simulated LFP signals, i.e., generated from networks of spiking neuronal models. We created three models, each containing five interacting networks, and evaluated whether the GPDC method could accurately detect network couplings. When using a stronger coupling, we showed that GPDC correctly detects all existing connections from simulated LFP signals in the three models, without false positives. Varying the coupling strength between networks, by changing the number of connections or synaptic strengths, and adding noise in the times series, altered the receiver operating characteristic (ROC) curve, ranging from perfect to chance level retrieval. We also showed that GPDC values correlated with coupling strength, indicating that GPDC values can provide useful information regarding coupling strength. These results reinforce that GPDC can be used to detect causality relationships over neural signals.

Altered structural and causal connectivity in frontal lobe epilepsy

Background

Albeit the few resting-state fMRI neuroimaging studies in frontal lobe epilepsy (FLE) patients, these studies focused on functional connectivity. The aim of this current study was to examine the effective connectivity based on voxel-based morphometry in FLE patients.

Methods

Resting-state structural and functional magnetic resonance imaging (fMRI) data were acquired from 19 FLE patients and 19 age and gender-matched healthy controls using the 3.0 Tesla magnetic resonance imaging (3.0 T MRI). The investigations were done by acquiring the structural information through voxel-based morphometry, then based on the seed obtained, Granger causality analysis was used to evaluate the causal flow of the designated seed to and from other significant voxels.

Results

Our results showed altered structural and effective connectivity. Compared with healthy controls, FLE patients showed reduced grey matter volume in bilateral putamen and right caudate as well as altered causality with increased, and decreased causal outflow from the right caudate (seed region) to inferior frontal gyrus-triangular, from bilateral putamen (seed regions) to right middle frontal gyrus and frontal gyrus medial-orbital representing the frontal executive areas, respectively. Also, significantly increased and decreased inflow from left calcarine to right caudate and from cerebellum_6 and vermis_6 to bilateral putamen, respectively. Moreover, we found that the causal alterations to and from the seed regions (from vermis_6 to right putamen and from left putamen to right middle frontal gyrus) negatively correlated with clinical scores (duration of epilepsy).

Conclusions

The findings point to the impairment within the executive and motor-controlled system including the cerebellum, frontal, caudate and putamen regions in FLE patients. These results would therefore enhance our understanding of structural and effective mechanisms in FLE.

Identification of excitatory-inhibitory links and network topology in large-scale neuronal assemblies from multi-electrode recordings

Functional-effective connectivity and network topology are nowadays key issues for studying brain physiological functions and pathologies. Inferring neuronal connectivity from electrophysiological recordings presents open challenges and unsolved problems. In this work, we present a cross-correlation based method for reliably estimating not only excitatory but also inhibitory links, by analyzing multi-unit spike activity from large-scale neuronal networks. The method is validated by means of realistic simulations of large-scale neuronal populations. New results related to functional connectivity estimation and network topology identification obtained by experimental electrophysiological recordings from high-density and large-scale (i.e., 4096 electrodes) microtransducer arrays coupled to in vitro neural populations are presented. Specifically, we show that: (i) functional inhibitory connections are accurately identified in in vitro cortical networks, providing that a reasonable firing rate and recording length are achieved; (ii) small-world topology, with scale-free and rich-club features are reliably obtained, on condition that a minimum number of active recording sites are available. The method and procedure can be directly extended and applied to in vivo multi-units brain activity recordings.

The balance between excitation and inhibition is fundamental for proper brain functions and for this reason is precisely regulated in adult cortices. Impaired excitation/inhibition balance is often associated with several neurological disorders, such as epilepsy, autism and schizophrenia. However, estimating functional inhibitory connections is not an easy task and few methods are available to identify such connections from electrophysiological data. Here we present a cross-correlation based method to identify both excitatory and inhibitory functional connections in large-scale neuronal networks. The method is applicable to both in vitro and in vivo spike data recordings. Once a connectivity map (i.e. a graph) is obtained, we characterized the associated topology by means of classical graph theory metrics to unveil functional architecture. In this work, we analyze in vitro cortical networks probed by means of large-scale microelectrode arrays (i.e., 4096 sensors) and we derive network topologies from spike data. The functional organization found is called “small-world and scale-free” and is the same organization found in cortical in vivo brain regions by means of different experimental methods. We also show that to obtain reliable information about network architecture at least a network with a hundred of nodes-neurons is needed.

Microphysiological Human Brain and Neural Systems-on-a-Chip: Potential Alternatives to Small Animal Models and Emerging Platforms for Drug Discovery and Personalized Medicine

Translational challenges associated with reductionist modeling approaches, as well as ethical concerns and economic implications of small animal testing, drive the need for developing microphysiological neural systems for modeling human neurological diseases, disorders, and injuries. Here, we provide a comprehensive review of microphysiological brain and neural systems-on-a-chip (NSCs) for modeling higher order trajectories in the human nervous system. Societal, economic, and national security impacts of neurological diseases, disorders, and injuries are highlighted to identify critical NSC application spaces. Hierarchical design and manufacturing of NSCs are discussed with distinction for surface- and bulk-based systems. Three broad NSC classes are identified and reviewed: microfluidic NSCs, compartmentalized NSCs, and hydrogel NSCs. Emerging areas and future directions are highlighted, including the application of 3D printing to design and manufacturing of next-generation NSCs, the use of stem cells for constructing patient-specific NSCs, and the application of human NSCs to 'personalized neurology'. Technical hurdles and remaining challenges are discussed. This review identifies the state-of-the-art design methodologies, manufacturing approaches, and performance capabilities of NSCs. This work suggests NSCs appear poised to revolutionize the modeling of human neurological diseases, disorders, and injuries.

Inferring neuronal network functional connectivity with directed information

A major challenge in neuroscience is to develop effective tools that infer the circuit connectivity from large-scale recordings of neuronal activity patterns. In this study, context tree maximizing (CTM) was used to estimate directed information (DI), which measures causal influences among neural spike trains in order to infer putative synaptic connections. In contrast to existing methods, the method presented here is data driven and can readily identify both linear and nonlinear relations between neurons. This CTM-DI method reliably identified circuit structures underlying simulations of realistic conductance-based networks. It also inferred circuit properties from voltage-sensitive dye recordings of the buccal ganglion of Aplysia. This method can be applied to other large-scale recordings as well. It offers a systematic tool to map network connectivity and to track changes in network structure such as synaptic strengths as well as the degrees of connectivity of individual neurons, which in turn could provide insights into how modifications produced by learning are distributed in a neural network.NEW & NOTEWORTHY This study brings together the techniques of voltage-sensitive dye recording and information theory to infer the functional connectome of the feeding central pattern generating network of Aplysia. In contrast to current statistical approaches, the inference method developed in this study is data driven and validated by conductance-based model circuits, can distinguish excitatory and inhibitory connections, is robust against synaptic plasticity, and is capable of detecting network structures that mediate motor patterns.

Thalamic amplification of cortical connectivity sustains attentional control

While interactions between the thalamus and cortex are critical for cognitive function^1–3, the exact contribution of the thalamus to these interactions is often unclear. Recent studies have shown diverse connectivity patterns across the thalamus ^4,5, but whether this diversity translates to thalamic functions beyond relaying information to or between cortical regions⁶ is unknown. Here, by investigating prefrontal cortical (PFC) representation of two rules used to guide attention, we find that the mediodorsal thalamus (MD) sustains these representations without relaying categorical information. Specifically, MD input amplifies local PFC connectivity, enabling rule-specific neural sequences to emerge and thereby maintain rule representations. Consistent with this notion, broadly enhancing PFC excitability diminishes rule specificity and behavioral performance, while enhancing MD excitability improves both. Overall, our results define a previously unknown principle in neuroscience; thalamic control of functional cortical connectivity. This function indicates that the thalamus plays much more central roles in cognition than previously thought.

T-type calcium channel blocker Z944 restores cortical synchrony and thalamocortical connectivity in a rat model of neuropathic pain

Oscillations are fundamental to communication between neuronal ensembles. We previously reported that pain in awake rats enhances synchrony in primary somatosensory cortex (S1) and attenuates coherence between S1 and ventral posterolateral (VPL) thalamus. Here, we asked whether similar changes occur in anesthetized rats and whether pain modulates phase-amplitude coupling between VPL and S1. We also hypothesized that the suppression of burst firing in VPL using Z944, a novel T-type calcium channel blocker, restores S1 synchrony and thalamocortical connectivity. Local field potentials were recorded from S1 and VPL in anesthetized rats 7 days after sciatic chronic constriction injury (CCI). In rats with CCI, low-frequency (4-12 Hz) synchrony in S1 was enhanced, whereas VPL-S1 coherence and theta-gamma phase-amplitude coupling were attenuated. Moreover, Granger causality showed decreased informational flow from VPL to S1. Systemic or intrathalamic delivery of Z944 to rats with CCI normalized these changes. Systemic Z944 also reversed thermal hyperalgesia and conditioned place preference. These data suggest that pain-induced cortical synchrony and thalamocortical disconnectivity are directly related to burst firing in VPL.

Analysis of complex neural circuits with nonlinear multidimensional hidden state models

A universal need in understanding complex networks is the identification of individual information channels and their mutual interactions under different conditions. In neuroscience, our premier example, networks made up of billions of nodes dynamically interact to bring about thought and action. Granger causality is a powerful tool for identifying linear interactions, but handling nonlinear interactions remains an unmet challenge. We present a nonlinear multidimensional hidden state (NMHS) approach that achieves interaction strength analysis and decoding of networks with nonlinear interactions by including latent state variables for each node in the network. We compare NMHS to Granger causality in analyzing neural circuit recordings and simulations, improvised music, and sociodemographic data. We conclude that NMHS significantly extends the scope of analyses of multidimensional, nonlinear networks, notably in coping with the complexity of the brain.

Feed-Forward Propagation of Temporal and Rate Information between Cortical Populations during Coherent Activation in Engineered In Vitro Networks

Transient propagation of information across neuronal assembles is thought to underlie many cognitive processes. However, the nature of the neural code that is embedded within these transmissions remains uncertain. Much of our understanding of how information is transmitted among these assemblies has been derived from computational models. While these models have been instrumental in understanding these processes they often make simplifying assumptions about the biophysical properties of neurons that may influence the nature and properties expressed. To address this issue we created an in vitro analog of a feed-forward network composed of two small populations (also referred to as assemblies or layers) of living dissociated rat cortical neurons. The populations were separated by, and communicated through, a microelectromechanical systems (MEMS) device containing a strip of microscale tunnels. Delayed culturing of one population in the first layer followed by the second a few days later induced the unidirectional growth of axons through the microtunnels resulting in a primarily feed-forward communication between these two small neural populations. In this study we systematically manipulated the number of tunnels that connected each layer and hence, the number of axons providing communication between those populations. We then assess the effect of reducing the number of tunnels has upon the properties of between-layer communication capacity and fidelity of neural transmission among spike trains transmitted across and within layers. We show evidence based on Victor-Purpura's and van Rossum's spike train similarity metrics supporting the presence of both rate and temporal information embedded within these transmissions whose fidelity increased during communication both between and within layers when the number of tunnels are increased. We also provide evidence reinforcing the role of synchronized activity upon transmission fidelity during the spontaneous synchronized network burst events that propagated between layers and highlight the potential applications of these MEMs devices as a tool for further investigation of structure and functional dynamics among neural populations.

Structure, Function, and Propagation of Information across Living Two, Four, and Eight Node Degree Topologies

In this study, we created four network topologies composed of living cortical neurons and compared resultant structural-functional dynamics including the nature and quality of information transmission. Each living network was composed of living cortical neurons and were created using microstamping of adhesion promoting molecules and each was "designed" with different levels of convergence embedded within each structure. Networks were cultured over a grid of electrodes that permitted detailed measurements of neural activity at each node in the network. Of the topologies we tested, the "Random" networks in which neurons connect based on their own intrinsic properties transmitted information embedded within their spike trains with higher fidelity relative to any other topology we tested. Within our patterned topologies in which we explicitly manipulated structure, the effect of convergence on fidelity was dependent on both topology and time-scale (rate vs. temporal coding). A more detailed examination using tools from network analysis revealed that these changes in fidelity were also associated with a number of other structural properties including a node's degree, degree-degree correlations, path length, and clustering coefficients. Whereas information transmission was apparent among nodes with few connections, the greatest transmission fidelity was achieved among the few nodes possessing the highest number of connections (high degree nodes or putative hubs). These results provide a unique view into the relationship between structure and its affect on transmission fidelity, at least within these small neural populations with defined network topology. They also highlight the potential role of tools such as microstamp printing and microelectrode array recordings to construct and record from arbitrary network topologies to provide a new direction in which to advance the study of structure-function relationships.

An in vitro method to manipulate the direction and functional strength between neural populations

We report the design and application of a Micro Electro Mechanical Systems (MEMs) device that permits investigators to create arbitrary network topologies. With this device investigators can manipulate the degree of functional connectivity among distinct neural populations by systematically altering their geometric connectivity in vitro. Each polydimethylsilxane (PDMS) device was cast from molds and consisted of two wells each containing a small neural population of dissociated rat cortical neurons. Wells were separated by a series of parallel micrometer scale tunnels that permitted passage of axonal processes but not somata; with the device placed over an 8 × 8 microelectrode array, action potentials from somata in wells and axons in microtunnels can be recorded and stimulated. In our earlier report we showed that a one week delay in plating of neurons from one well to the other led to a filling and blocking of the microtunnels by axons from the older well resulting in strong directionality (older to younger) of both axon action potentials in tunnels and longer duration and more slowly propagating bursts of action potentials between wells. Here we show that changing the number of tunnels, and hence the number of axons, connecting the two wells leads to changes in connectivity and propagation of bursting activity. More specifically, the greater the number of tunnels the stronger the connectivity, the greater the probability of bursting propagating between wells, and shorter peak-to-peak delays between bursts and time to first spike measured in the opposing well. We estimate that a minimum of 100 axons are needed to reliably initiate a burst in the opposing well. This device provides a tool for researchers interested in understanding network dynamics who will profit from having the ability to design both the degree and directionality connectivity among multiple small neural populations.

Neural Connectivity in Epilepsy as Measured by Granger Causality

Epilepsy is a chronic neurological disorder characterized by repeated seizures or excessive electrical discharges in a group of brain cells. Prevalence rates include about 50 million people worldwide and 10% of all people have at least one seizure at one time in their lives. Connectivity models of epilepsy serve to provide a deeper understanding of the processes that control and regulate seizure activity. These models have received initial support and have included measures of EEG, MEG, and MRI connectivity. Preliminary findings have shown regions of increased connectivity in the immediate regions surrounding the seizure foci and associated low connectivity in nearby regions and pathways. There is also early evidence to suggest that these patterns change during ictal events and that these changes may even by related to the occurrence or triggering of seizure events. We present data showing how Granger causality can be used with EEG data to measure connectivity across brain regions involved in ictal events and their resolution. We have provided two case examples as a demonstration of how to obtain and interpret such data. EEG data of ictal events are processed, converted to independent components and their dipole localizations, and these are used to measure causality and connectivity between these locations. Both examples have shown hypercoupling near the seizure foci and low causality across nearby and associated neuronal pathways. This technique also allows us to track how these measures change over time and during the ictal and post-ictal periods. Areas for further research into this technique, its application to epilepsy, and the formation of more effective therapeutic interventions are recommended.

Accurate Connection Strength Estimation Based on Variational Bayes for Detecting Synaptic Plasticity

Connection strength estimation is widely used in detecting the topology of neuronal networks and assessing their synaptic plasticity. A recently proposed model-based method using the leaky integrate-and-fire model neuron estimates membrane potential from spike trains by calculating the maximum a posteriori (MAP) path. We further enhance the MAP path method using variational Bayes and dynamic causal modeling. Several simulations demonstrate that the proposed method can accurately estimate connection strengths with an error ratio of less than 20%. The results suggest that the proposed method can be an effective tool for detecting network structure and synaptic plasticity.

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.

Scale-free and economical features of functional connectivity in neuronal networks

A form of activity that is highly studied in cultured cortical networks is the neuronal avalanche, characterized by bursts whose distribution follows a power law. While the statistics of neuronal avalanches are well characterized, much less is known about the neuronal interactions from which they arise. We examined statistical dependencies between pairs of cells in spontaneously active cultures of cortical neurons using an information measure of transfer entropy. We show that the distribution of transfer entropy follows a power law with a slope near 3/2. Using graph-theoretic approaches of weighted networks, we demonstrate that this power law maximizes a measure of global economy that accounts for both the efficiency of neuronal interactions as well as the overall traffic in the network. Finally, we describe a pairwise Poisson model that captures the statistics of information transfer in a population of spiking neurons. Using this model, we show that avalanches can occur in systems with weak pairwise interactions, and that strong pairwise interactions can arise without avalanches, suggesting that these two measures capture distinct properties of brain dynamics.

The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference

BACKGROUND

Wiener-Granger causality ("G-causality") is a statistical notion of causality applicable to time series data, whereby cause precedes, and helps predict, effect. It is defined in both time and frequency domains, and allows for the conditioning out of common causal influences. Originally developed in the context of econometric theory, it has since achieved broad application in the neurosciences and beyond. Prediction in the G-causality formalism is based on VAR (vector autoregressive) modelling.

NEW METHOD

The MVGC Matlab© Toolbox approach to G-causal inference is based on multiple equivalent representations of a VAR model by (i) regression parameters, (ii) the autocovariance sequence and (iii) the cross-power spectral density of the underlying process. It features a variety of algorithms for moving between these representations, enabling selection of the most suitable algorithms with regard to computational efficiency and numerical accuracy.

RESULTS

In this paper we explain the theoretical basis, computational strategy and application to empirical G-causal inference of the MVGC Toolbox. We also show via numerical simulations the advantages of our Toolbox over previous methods in terms of computational accuracy and statistical inference.

COMPARISON WITH EXISTING METHOD(S)

The standard method of computing G-causality involves estimation of parameters for both a full and a nested (reduced) VAR model. The MVGC approach, by contrast, avoids explicit estimation of the reduced model, thus eliminating a source of estimation error and improving statistical power, and in addition facilitates fast and accurate estimation of the computationally awkward case of conditional G-causality in the frequency domain.

CONCLUSIONS

The MVGC Toolbox implements a flexible, powerful and efficient approach to G-causal inference.

Estimating temporal causal interaction between spike trains with permutation and transfer entropy

Estimating the causal interaction between neurons is very important for better understanding the functional connectivity in neuronal networks. We propose a method called normalized permutation transfer entropy (NPTE) to evaluate the temporal causal interaction between spike trains, which quantifies the fraction of ordinal information in a neuron that has presented in another one. The performance of this method is evaluated with the spike trains generated by an Izhikevich’s neuronal model. Results show that the NPTE method can effectively estimate the causal interaction between two neurons without influence of data length. Considering both the precision of time delay estimated and the robustness of information flow estimated against neuronal firing rate, the NPTE method is superior to other information theoretic method including normalized transfer entropy, symbolic transfer entropy and permutation conditional mutual information. To test the performance of NPTE on analyzing simulated biophysically realistic synapses, an Izhikevich’s cortical network that based on the neuronal model is employed. It is found that the NPTE method is able to characterize mutual interactions and identify spurious causality in a network of three neurons exactly. We conclude that the proposed method can obtain more reliable comparison of interactions between different pairs of neurons and is a promising tool to uncover more details on the neural coding.

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.

To appreciate how neural circuits control behaviors, we must understand two things. First, how the neurons comprising the circuit are connected, and second, how neurons and their connections change after learning or in response to neuromodulators. Neuronal connectivity is difficult to determine experimentally, whereas neuronal activity can often be readily measured. We describe a statistical model to estimate circuit connectivity directly from measured activity patterns. We use the timing relationships between observed spikes to predict synaptic interactions between simultaneously observed neurons. The model estimate provides each predicted connection with a curve that represents how strongly, and at which temporal delays, one circuit element effectively influences another. These curves are analogous to synaptic interactions of the level of the membrane potential of biological neurons and share some of their features such as being inhibitory or excitatory. We test our method on recordings from the pyloric circuit in the crab stomatogastric ganglion, a small circuit whose connectivity is completely known beforehand, and find that the predicted circuit matches the biological one — a result other techniques failed to achieve. In addition, we show that drug manipulations impacting the circuit are revealed by this technique. These results illustrate the utility of our analysis approach for inferring connections from neural spiking activity.

Assessing thalamocortical functional connectivity with Granger causality

Assessment of network connectivity across multiple brain regions is critical to understanding the mechanisms underlying various neurological disorders. Conventional methods for assessing dynamic interactions include cross-correlation and coherence analysis. However, these methods do not reveal the direction of information flow, which is important for studying the highly directional neurological system. Granger causality (GC) analysis can characterize the directional influences between two systems. We tested GC analysis for its capability to capture directional interactions within both simulated and in vivo neural networks. The simulated networks consisted of Hindmarsh-Rose neurons; GC analysis was used to estimate the causal influences between two model networks. Our analysis successfully detected asymmetrical interactions between these networks ( , t -test). Next, we characterized the relationship between the "electrical synaptic strength" in the model networks and interactions estimated by GC analysis. We demonstrated the novel application of GC to monitor interactions between thalamic and cortical neurons following ischemia induced brain injury in a rat model of cardiac arrest (CA). We observed that during the post-CA acute period the GC interactions from the thalamus to the cortex were consistently higher than those from the cortex to the thalamus ( 1.983±0.278 times higher, p = 0.021). In addition, the dynamics of GC interactions between the thalamus and the cortex were frequency dependent. Our study demonstrated the feasibility of GC to monitor the dynamics of thalamocortical interactions after a global nervous system injury such as CA-induced ischemia, and offers preferred alternative applications in characterizing other inter-regional interactions in an injured brain.

Altered network communication following a neuroprotective drug treatment

Preconditioning is defined as a range of stimuli that allow cells to withstand subsequent anaerobic and other deleterious conditions. While cell protection under preconditioning is well established, this paper investigates the influence of neuroprotective preconditioning drugs, 4-aminopyridine and bicuculline (4-AP/bic), on synaptic communication across a broad network of in vitro rat cortical neurons. Using a permutation test, we evaluated cross-correlations of extracellular spiking activity across all pairs of recording electrodes on a 64-channel multielectrode array. The resulting functional connectivity maps were analyzed in terms of their graph-theoretic properties. A small-world effect was found, characterized by a functional network with high clustering coefficient and short average path length. Twenty-four hours after exposure to 4-AP/bic, small-world properties were comparable to control cultures that were not treated with the drug. Four hours following drug washout, however, the density of functional connections increased, while path length decreased and clustering coefficient increased. These alterations in functional connectivity were maintained at four days post-washout, suggesting that 4-AP/bic preconditioning leads to long-term effects on functional networks of cortical neurons. Because of their influence on communication efficiency in neuronal networks, alterations in small-world properties hold implications for information processing in brain systems. The observed relationship between density, path length, and clustering coefficient is captured by a phenomenological model where connections are added randomly within a spatially-embedded network. Taken together, results provide information regarding functional consequences of drug therapies that are overlooked in traditional viability studies and present the first investigation of functional networks under neuroprotective preconditioning.

Extracting functionally feedforward networks from a population of spiking neurons

Neuronal avalanches are a ubiquitous form of activity characterized by spontaneous bursts whose size distribution follows a power-law. Recent theoretical models have replicated power-law avalanches by assuming the presence of functionally feedforward connections (FFCs) in the underlying dynamics of the system. Accordingly, avalanches are generated by a feedforward chain of activation that persists despite being embedded in a larger, massively recurrent circuit. However, it is unclear to what extent networks of living neurons that exhibit power-law avalanches rely on FFCs. Here, we employed a computational approach to reconstruct the functional connectivity of cultured cortical neurons plated on multielectrode arrays (MEAs) and investigated whether pharmacologically induced alterations in avalanche dynamics are accompanied by changes in FFCs. This approach begins by extracting a functional network of directed links between pairs of neurons, and then evaluates the strength of FFCs using Schur decomposition. In a first step, we examined the ability of this approach to extract FFCs from simulated spiking neurons. The strength of FFCs obtained in strictly feedforward networks diminished monotonically as links were gradually rewired at random. Next, we estimated the FFCs of spontaneously active cortical neuron cultures in the presence of either a control medium, a GABA(A) receptor antagonist (PTX), or an AMPA receptor antagonist combined with an NMDA receptor antagonist (APV/DNQX). The distribution of avalanche sizes in these cultures was modulated by this pharmacology, with a shallower power-law under PTX (due to the prominence of larger avalanches) and a steeper power-law under APV/DNQX (due to avalanches recruiting fewer neurons) relative to control cultures. The strength of FFCs increased in networks after application of PTX, consistent with an amplification of feedforward activity during avalanches. Conversely, FFCs decreased after application of APV/DNQX, consistent with fading feedforward activation. The observed alterations in FFCs provide experimental support for recent theoretical work linking power-law avalanches to the feedforward organization of functional connections in local neuronal circuits.

In Vitro and In Vivo Recording of Local Field Potential Oscillations in Mouse Hippocampus

Oscillations in hippocampal local field potentials (LFP) reflect the coordinated, rhythmic activity of constituent interneuronal and principal cell populations. Quantifying changes in oscillatory patterns and power therefore provides a powerful metric through which to infer mechanisms and functions of hippocampal network activity at the mesoscopic level, bridging single-neuron studies to behavioral assays of hippocampal function. Here, complementary protocols that enable mechanistic analyses of oscillation generation in vitro (in slices and a whole hippocampal preparation) and functional analyses of hippocampal circuits in behaving mice are described. Used together, these protocols provide a comprehensive view of hippocampal phenotypes in mouse models, highlighting oscillatory biomarkers of hippocampal function and dysfunction. Curr. Protoc. Mouse Biol. 2:273-294 © 2012 by John Wiley & Sons, Inc.

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.

Unraveling the general organizing principles of connectivity in neural circuits is a crucial step towards understanding brain function. However, even the simpler task of assessing the global excitatory connectivity of a culture in vitro, where neurons form self-organized networks in absence of external stimuli, remains challenging. Neuronal cultures undergo spontaneous switching between episodes of synchronous bursting and quieter inter-burst periods. We introduce here a novel algorithm which aims at inferring the connectivity of neuronal cultures from calcium fluorescence recordings of their network dynamics. To achieve this goal, we develop a suitable generalization of Transfer Entropy, an information-theoretic measure of causal influences between time series. Unlike previous algorithmic approaches to reconstruction, Transfer Entropy is data-driven and does not rely on specific assumptions about neuronal firing statistics or network topology. We generate simulated calcium signals from networks with controlled ground-truth topology and purely excitatory interactions and show that, by restricting the analysis to inter-bursts periods, Transfer Entropy robustly achieves a good reconstruction performance for disparate network connectivities. Finally, we apply our method to real data and find evidence of non-random features in cultured networks, such as the existence of highly connected hub excitatory neurons and of an elevated (but not extreme) level of clustering.

Identification of feedback loops in neural networks based on multi-step Granger causality

MOTIVATION

Feedback circuits are crucial network motifs, ubiquitously found in many intra- and inter-cellular regulatory networks, and also act as basic building blocks for inducing synchronized bursting behaviors in neural network dynamics. Therefore, the system-level identification of feedback circuits using time-series measurements is critical to understand the underlying regulatory mechanism of synchronized bursting behaviors.

RESULTS

Multi-Step Granger Causality Method (MSGCM) was developed to identify feedback loops embedded in biological networks using time-series experimental measurements. Based on multivariate time-series analysis, MSGCM used a modified Wald test to infer the existence of multi-step Granger causality between a pair of network nodes. A significant bi-directional multi-step Granger causality between two nodes indicated the existence of a feedback loop. This new identification method resolved the drawback of the previous non-causal impulse response component method which was only applicable to networks containing no co-regulatory forward path. MSGCM also significantly improved the ratio of correct identification of feedback loops. In this study, the MSGCM was testified using synthetic pulsed neural network models and also in vitro cultured rat neural networks using multi-electrode array. As a result, we found a large number of feedback loops in the in vitro cultured neural networks with apparent synchronized oscillation, indicating a close relationship between synchronized oscillatory bursting behavior and underlying feedback loops. The MSGCM is an efficient method to investigate feedback loops embedded in in vitro cultured neural networks. The identified feedback loop motifs are considered as an important design principle responsible for the synchronized bursting behavior in neural networks.

Extending transfer entropy improves identification of effective connectivity in a spiking cortical network model

Transfer entropy (TE) is an information-theoretic measure which has received recent attention in neuroscience for its potential to identify effective connectivity between neurons. Calculating TE for large ensembles of spiking neurons is computationally intensive, and has caused most investigators to probe neural interactions at only a single time delay and at a message length of only a single time bin. This is problematic, as synaptic delays between cortical neurons, for example, range from one to tens of milliseconds. In addition, neurons produce bursts of spikes spanning multiple time bins. To address these issues, here we introduce a free software package that allows TE to be measured at multiple delays and message lengths. To assess performance, we applied these extensions of TE to a spiking cortical network model (Izhikevich, 2006) with known connectivity and a range of synaptic delays. For comparison, we also investigated single-delay TE, at a message length of one bin (D1TE), and cross-correlation (CC) methods. We found that D1TE could identify 36% of true connections when evaluated at a false positive rate of 1%. For extended versions of TE, this dramatically improved to 73% of true connections. In addition, the connections correctly identified by extended versions of TE accounted for 85% of the total synaptic weight in the network. Cross correlation methods generally performed more poorly than extended TE, but were useful when data length was short. A computational performance analysis demonstrated that the algorithm for extended TE, when used on currently available desktop computers, could extract effective connectivity from 1 hr recordings containing 200 neurons in ∼5 min. We conclude that extending TE to multiple delays and message lengths improves its ability to assess effective connectivity between spiking neurons. These extensions to TE soon could become practical tools for experimentalists who record hundreds of spiking neurons.

Dynamics of large-scale cortical interactions at high gamma frequencies during word production: event related causality (ERC) analysis of human electrocorticography (ECoG)

Intracranial EEG studies in humans have shown that functional brain activation in a variety of functional-anatomic domains of human cortex is associated with an increase in power at a broad range of high gamma (>60Hz) frequencies. Although these electrophysiological responses are highly specific for the location and timing of cortical processing and in animal recordings are highly correlated with increased population firing rates, there has been little direct empirical evidence for causal interactions between different recording sites at high gamma frequencies. Such causal interactions are hypothesized to occur during cognitive tasks that activate multiple brain regions. To determine whether such causal interactions occur at high gamma frequencies and to investigate their functional significance, we used event-related causality (ERC) analysis to estimate the dynamics, directionality, and magnitude of event-related causal interactions using subdural electrocorticography (ECoG) recorded during two word production tasks: picture naming and auditory word repetition. A clinical subject who had normal hearing but was skilled in American Signed Language (ASL) provided a unique opportunity to test our hypothesis with reference to a predictable pattern of causal interactions, i.e. that language cortex interacts with different areas of sensorimotor cortex during spoken vs. signed responses. Our ERC analyses confirmed this prediction. During word production with spoken responses, perisylvian language sites had prominent causal interactions with mouth/tongue areas of motor cortex, and when responses were gestured in sign language, the most prominent interactions involved hand and arm areas of motor cortex. Furthermore, we found that the sites from which the most numerous and prominent causal interactions originated, i.e. sites with a pattern of ERC "divergence", were also sites where high gamma power increases were most prominent and where electrocortical stimulation mapping interfered with word production. These findings suggest that the number, strength and directionality of event-related causal interactions may help identify network nodes that are not only activated by a task but are critical to its performance.

Functional connectivity in a rhythmic inhibitory circuit using Granger causality

Background

Understanding circuit function would be greatly facilitated by methods that allow the simultaneous estimation of the functional strengths of all of the synapses in the network during ongoing network activity. Towards that end, we used Granger causality analysis on electrical recordings from the pyloric network of the crab Cancer borealis, a small rhythmic circuit with known connectivity, and known neuronal intrinsic properties.

Results

Granger causality analysis reported a causal relationship where there is no anatomical correlate because of the strong oscillatory behavior of the pyloric circuit. Additionally, we failed to find a direct relationship between synaptic strength and Granger causality in a set of pyloric circuit models.

Conclusions

We conclude that the lack of a relationship between synaptic strength and functional connectivity occurs because Granger causality essentially collapses the direct contribution of the synapse with the intrinsic properties of the postsynaptic neuron. We suggest that the richness of the dynamical properties of most biological neurons complicates the simple interpretation of the results of functional connectivity analyses using Granger causality.

A new cross-correlation algorithm for the analysis of "in vitro" neuronal network activity aimed at pharmacological studies

Modern drug discovery for Central Nervous System pathologies has recently focused its attention to in vitro neuronal networks as models for the study of neuronal activities. Micro Electrode Arrays (MEAs), a widely recognized tool for pharmacological investigations, enable the simultaneous study of the spiking activity of discrete regions of a neuronal culture, providing an insight into the dynamics of networks. Taking advantage of MEAs features and making the most of the cross-correlation analysis to assess internal parameters of a neuronal system, we provide an efficient method for the evaluation of comprehensive neuronal network activity. We developed an intra network burst correlation algorithm, we evaluated its sensitivity and we explored its potential use in pharmacological studies. Our results demonstrate the high sensitivity of this algorithm and the efficacy of this methodology in pharmacological dose-response studies, with the advantage of analyzing the effect of drugs on the comprehensive correlative properties of integrated neuronal networks.

Assessing cortico-hippocampal functional connectivity under anesthesia and kainic acid using generalized partial directed coherence

A significant challenge in modern neuroscience lies in determining the functional connectivity between discrete populations of neurones and brain regions. In this study, a variation of partial directed coherence, the generalized partial directed coherence (gPDC), along with a newly proposed critical value for gPDC, were applied on recorded local field potentials (LFPs) and single-unit activity, in order to assess information flow between medial prefrontal cortex (mPFC) and hippocampus and within the hippocampus of the rat brain, under isoflurane anesthesia and kainic acid-induced enhanced neuronal activity. Our findings suggest that, under anesthesia, there exists a continuous information flow from hippocampus towards mPFC, reversed mostly during activity bursts occurring in the mPFC. Moreover, there was a clear directional connection from the lateral towards medial dorsal hippocampus, most prominent in the beta frequency band (10-30 Hz). Kainic acid resulted in partially disrupting the reciprocal cortico-hippocampal connectivity and reversing the intra-hippocampal one. The biological implications of these findings on the effects of anesthesia and kainic acid in brain connectivity, along with implementation issues of gPDC analysis on field potentials and spike trains, are extensively discussed.

Quantifying auditory event-related responses in multichannel human intracranial recordings

Multichannel intracranial recordings are used increasingly to study the functional organization of human cortex. Intracranial recordings of event-related activity, or electrocorticography (ECoG), are based on high density electrode arrays implanted directly over cortex, combining good temporal and spatial resolution. Developing appropriate statistical methods for analyzing event-related responses in these high dimensional ECoG datasets remains a major challenge for clinical and systems neuroscience. We present a novel methodological framework that combines complementary, existing methods adapted for statistical analysis of auditory event-related responses in multichannel ECoG recordings. This analytic framework integrates single-channel (time-domain, time–frequency) and multichannel analyses of event-related ECoG activity to determine statistically significant evoked responses, induced spectral responses, and effective (causal) connectivity. Implementation of this quantitative approach is illustrated using multichannel ECoG data from recent studies of auditory processing in patients with epilepsy. Methods described include a time–frequency matching pursuit algorithm adapted for modeling brief, transient cortical spectral responses to sound, and a recently developed method for estimating effective connectivity using multivariate autoregressive modeling to measure brief event-related changes in multichannel functional interactions. A semi-automated spatial normalization method for comparing intracranial electrode locations across patients is also described. The individual methods presented are published and readily accessible. We discuss the benefits of integrating multiple complementary methods in a unified and comprehensive quantitative approach. Methodological considerations in the analysis of multichannel ECoG data, including corrections for multiple comparisons are discussed, as well as remaining challenges in the development of new statistical approaches.

On the use of dynamic Bayesian networks in reconstructing functional neuronal networks from spike train ensembles

Coordination among cortical neurons is believed to be a key element in mediating many high-level cortical processes such as perception, attention, learning, and memory formation. Inferring the structure of the neural circuitry underlying this coordination is important to characterize the highly nonlinear, time-varying interactions between cortical neurons in the presence of complex stimuli. In this work, we investigate the applicability of dynamic Bayesian networks (DBNs) in inferring the effective connectivity between spiking cortical neurons from their observed spike trains. We demonstrate that DBNs can infer the underlying nonlinear and time-varying causal interactions between these neurons and can discriminate between mono- and polysynaptic links between them under certain constraints governing their putative connectivity. We analyzed conditionally Poisson spike train data mimicking spiking activity of cortical networks of small and moderately large size. The performance was assessed and compared to other methods under systematic variations of the network structure to mimic a wide range of responses typically observed in the cortex. Results demonstrate the utility of DBN in inferring the effective connectivity in cortical networks.

Designing Neural Networks in Culture: Experiments are described for controlled growth, of nerve cells taken from rats, in predesigned geometrical patterns on laboratory culture dishes

Technology has advanced to where it is possible to design and grow-with predefined geometry and surprisingly good fidelity-living networks of neurons in culture dishes. Here we overview the elements of design, emphasizing the lithographic techniques that alter the cell culture surface which in turn influences the attachment and growth of the neural networks. Advanced capability in this area makes it possible to design networks of desired complexity. Other issues addressed include the influence of glial cells and media on activity and the potential for extending the designs into three dimensions. Investigators are advancing the art and science of analyzing and controlling through stimulation the function of the neural networks, including the ability to take advantage of their geometric form in order to influence functional properties.

Granger causality and transfer entropy are equivalent for Gaussian variables

Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. Developed originally in the field of econometrics, it has since found application in a broader arena, particularly in neuroscience. More recently transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, has gained traction in a similarly wide field. While it has been recognized that the two concepts must be related, the exact relationship has until now not been formally described. Here we show that for Gaussian variables, Granger causality and transfer entropy are entirely equivalent, thus bridging autoregressive and information-theoretic approaches to data-driven causal inference.

A MATLAB toolbox for Granger causal connectivity analysis

Assessing directed functional connectivity from time series data is a key challenge in neuroscience. One approach to this problem leverages a combination of Granger causality analysis and network theory. This article describes a freely available MATLAB toolbox--'Granger causal connectivity analysis' (GCCA)--which provides a core set of methods for performing this analysis on a variety of neuroscience data types including neuroelectric, neuromagnetic, functional MRI, and other neural signals. The toolbox includes core functions for Granger causality analysis of multivariate steady-state and event-related data, functions to preprocess data, assess statistical significance and validate results, and to compute and display network-level indices of causal connectivity including 'causal density' and 'causal flow'. The toolbox is deliberately small, enabling its easy assimilation into the repertoire of researchers. It is however readily extensible given proficiency with the MATLAB language.

Morphine modulation of pain processing in medial and lateral pain pathways

Background

Despite the wide-spread use of morphine and related opioid agonists in clinic and their powerful analgesic effects, our understanding of the neural mechanisms underlying opioid analgesia at supraspinal levels is quite limited. The present study was designed to investigate the modulative effect of morphine on nociceptive processing in the medial and lateral pain pathways using a multiple single-unit recording technique. Pain evoked neuronal activities were simultaneously recorded from the primary somatosensory cortex (SI), ventral posterolateral thalamus (VPL), anterior cingulate cortex (ACC), and medial dorsal thalamus (MD) with eight-wire microelectrode arrays in awake rats.

Results

The results showed that the noxious heat evoked responses of single neurons in all of the four areas were depressed after systemic injection of 5 mg/kg morphine. The depressive effects of morphine included (i) decreasing the neuronal response magnitude; (ii) reducing the fraction of responding neurons, and (iii) shortening the response duration. In addition, the capability of cortical and thalamic neural ensembles to discriminate noxious from innocuous stimuli was decreased by morphine within both pain pathways. Meanwhile, morphine suppressed the pain-evoked changes in the information flow from medial to lateral pathway and from cortex to thalamus. These effects were completely blocked by pre-treatment with the opiate receptor antagonist naloxone.

Conclusion

These results suggest that morphine exerts analgesic effects through suppressing both sensory and affective dimensions of pain.

Evaluation of the performance of information theory-based methods and cross-correlation to estimate the functional connectivity in cortical networks

Functional connectivity of in vitro neuronal networks was estimated by applying different statistical algorithms on data collected by Micro-Electrode Arrays (MEAs). First we tested these "connectivity methods" on neuronal network models at an increasing level of complexity and evaluated the performance in terms of ROC (Receiver Operating Characteristic) and PPC (Positive Precision Curve), a new defined complementary method specifically developed for functional links identification. Then, the algorithms better estimated the actual connectivity of the network models, were used to extract functional connectivity from cultured cortical networks coupled to MEAs. Among the proposed approaches, Transfer Entropy and Joint-Entropy showed the best results suggesting those methods as good candidates to extract functional links in actual neuronal networks from multi-site recordings.

Causal pattern recovery from neural spike train data using the Snap Shot Score

We present a new approach to learning directed information flow networks from multi-channel spike train data. A novel scoring function, the Snap Shot Score, is used to assess potential networks with respect to their quality of causal explanation for the data. Additionally, we suggest a generic concept of plausibility in order to assess network learning techniques under partial observability conditions. Examples demonstrate the assessment of networks with the Snap Shot Score, and neural network simulations show its performance in complex situations with partial observability. We discuss the application of the new score to real data and indicate how it can be modified to suit other neural data types.

Directed Interactions Between Auditory and Superior Temporal Cortices and their Role in Sensory Integration

Recent studies using functional imaging and electrophysiology demonstrate that processes related to sensory integration are not restricted to higher association cortices but already occur in early sensory cortices, such as primary auditory cortex. While anatomical studies suggest the superior temporal sulcus (STS) as likely source of visual input to auditory cortex, little evidence exists to support this notion at the functional level. Here we tested this hypothesis by simultaneously recording from sites in auditory cortex and STS in alert animals stimulated with dynamic naturalistic audio–visual scenes. Using Granger causality and directed transfer functions we first quantified causal interactions at the level of field potentials, and subsequently determined those frequency bands that show effective interactions, i.e. interactions that are relevant for influencing neuronal firing at the target site. We found that effective interactions from auditory cortex to STS prevail below 20 Hz, while interactions from STS to auditory cortex prevail above 20 Hz. In addition, we found that directed interactions from STS to auditory cortex make a significant contribution to multisensory influences in auditory cortex: Sites in auditory cortex showing multisensory enhancement received stronger feed-back from STS during audio–visual than during auditory stimulation, while sites with multisensory suppression received weaker feed-back. These findings suggest that beta frequencies might be important for inter-areal coupling in the temporal lobe and demonstrate that superior temporal regions indeed provide one major source of visual influences to auditory cortex.