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Background Pulsed transcranial ultrasound stimulation (pTUS) can modulate the neuronal activity of motor cortex and elicit muscle contractions. Cortico-muscular coupling (CMC) can serve as a tool to identify interaction between the oscillatory activity of the motor cortex and effector muscle. This research aims to explore the neuromodulatory effect of low-intensity, pTUS with different number of tone burst to neural circuit of motor-control system by analyzing the coupling relationship between motor cortex and tail muscle in mouse. The motor cortex of mice was stimulated by pulsed transcranial ultrasound with different number of tone bursts (NTB = 100 150 200 250 300). The local field potentials (LFPs) in tail motor cortex and electromyography (EMG) in tail muscles were recorded simultaneously during pTUS. The change of integral coupling strength between cortex and muscle was evaluated by mutual information (MI). The directional information interaction between them were analyzed by transfer entropy (TE). Results Almost all of the MI and TE values were significantly increased by pTUS. The results of MI showed that the CMC was significantly enhanced with the increase of NTB. The TE results showed the coupling strength of CMC in descending direction (from LFPs to EMG) was significantly higher than that in ascending direction (from EMG to LFPs) after stimulation. Furthermore, compared to NTB = 100, the CMC in ascending direction were significantly enhanced when NTB = 250, 300, and CMC in descending direction were significantly enhanced when NTB = 200, 250, 300. Conclusion These results confirm that the CMC between motor cortex and the tail muscles in mouse could be altered by pTUS. And by increasing the NTB (i.e. sonication duration), the coupling strength within the cortico-muscular circuit could be increased, which might further influence the motor function of mice. It demonstrates that, using MI and TE method, the CMC could be used for quantitatively evaluating the effect of pTUS with different NTBs, which might provide a new insight into the effect of pTUS neuromodulation in motor cortex.

Human brains possess sophisticated information processing capabilities, which rely on the coordinated interplay of billions of neurons. Despite recent advances in characterizing the collective neuronal dynamics, however, it remains a major challenge to understand the principles of how functional neuronal networks develop and maintain these processing capabilities. A popular hypothesis is that neuronal networks self-organize to a critical state [1-3], because in models, criticality maximizes information processing capacities [4-6]. This predicts that biological networks should develop towards a critical state during maturation, and at the same time processing capabilities should increase. We tested this hypothesis using multi-electrode spike recordings in mouse hippocampal and cortical neurons over the first four weeks in vitro. We showed that developing neuronal networks indeed increased their information processing capacities, as quantified by transfer entropy and active information storage [6-8]. The increase in processing capacity was tightly linked to decreasing the distance to criticality (correlation r = 0.68, p < 10; r = 0.55, p < 10 for transfer and storage, respectively). Thereby our results for the first time demonstrate experimentally that approaching criticality with maturation goes in hand with increasing processing capabilities.

Extracellular electrical potential oscillations recorded as local field potentials (LFPs) in the hippocampal formation are thought to be involved in cognitive processes such as working memory retention, memory consolidation and spatial navigation. Recent studies have shown that combining spikes with LFP phase can increase the information content of spikes [1,2] and thus suggest LFP oscillations have the capacity to convey information. LFP oscillations within specific frequency bands can interact, for example by phase-phase and phase-amplitude coupling. We hypothesise that these LFP interactions can transfer information between neural networks. To test this hypothesis, we analyse multi-channel recordings of simultaneous LFPs from hippocampal area CA1 and the subiculum of urethane-anaesthetised rodents. Anatomical connections between these two regions in the hippocampal formation predict information in this system flows in 'nested loops' along separate projections [3]. We use advanced neurocomputational methods to determine how information flows within the CA1-subicular circuit by interactions of LFP rhythms. The results of correlation and coherence analyses of LFPs recorded from multiple sites suggest that LFP rhythms can transmit information within and between area CA1 and the subiculum. However, these methods alone are not enough to determine the oscillatory activity in which region drives activity in other regions, that is in which direction information flows. We use transfer entropy [4], which is an information theoretic method that can capture directionality, to quantify information transfer between area CA1 and subiculum. We show that information flow within the CA1-subicular circuit is bi-directional and follows a pattern of feedforward and feedback loops. Our results suggest that LFP interactions can route information at millisecond timescales along the anatomical connections in the hippocampal formation to achieve cognitive processing.

Information theory has been used in many ways to analyse the output of neurons and how it relates to the input. Mutual information is often used as a means to describe this relationship [1], but as it is symmetrical, it does not necessarily describe how much information is transferred specifically from input to output. An alternative method, transfer entropy [2], introduces directionality to the analysis of this problem. Transfer entropy allows one to study how the predictability of the output of the cell is affected by varying time windows of preceding input spike trains. In this work we are using two different extensions to transfer entropy that attempt to limit bias. The first method of estimating transfer entropy we are using is as described by Wibral et al [3], which places a restriction of a single time step on the length of the delay considered on the destination time series. This restriction is placed to avoid overestimating the information transferred from input to output by ensuring that the information provided by the history of the output has not been underestimated. The second approach, put forward by Gourevitch and Eggermont [4] creates a 'shuffled' transfer entropy value from the average transfer entropy, taken over many runs where the history of the input is randomly shuffled. The shuffled value can then be used to normalise the transfer entropy of the un-shuffled data. We are currently investigating the use of transfer entropy to study the output of an active Purkinje cell model [5,6] in response to a gamma-distributed input, while varying the location of the input site. Active channels in dendrites allow the effect of input to be location-independent, but using transfer entropy enables us to highlight differences in delay of information transfer based on the morphology of the cell.

Measuring the effective connectivity between the elements of a neuronal system promises to give conclusions about brain function and the principles of information processing in the brain. Transfer Entropy [1] (TE) and its extensions have recently become more and more popular for this task and have been applied to various types of neuronal data, such as from EEG, Calcium Imaging and Multi-electrode Array measurements [2]. Being based on information theory, TE can be interpreted as the predictive information transfer between two time series. TE is a model free measurement and quantifies even non-linear interactions and very importantly the directionality. However, due to its information-theoretic nature, TE doesn't distinguish between different types of interactions, for example whether a pre-synaptic neuron drives a post-synaptic neuron via an excitatory or an inhibitory synapse [3]. This distinction is crucial for the understanding of the network dynamics and the exact interplay of excitation and inhibition in neuronal networks plays an important role for network bursts and synchronization. The balance of excitation and inhibition is believed to play a role for the occurrence of epileptic seizures [4]. We propose a method complementary to the TE measurement, to not only measure the effective connectivity from neuronal network dynamics, but also to classify, whether the interactions are excitatory or inhibitory. We achieve this by introducing a new quantity, which is a linear combination of the individual terms that sum up to the Transfer Entropy. This quantity can be computed by applying a Principal Component Analysis (PCA) to the Transfer Entropy terms across different measurements. It assumes positive values for excitatory connections and negative values for inhibitory connections. To verify this method we apply it to the spike trains of noise-driven recurrent neuronal network motifs, simulated with an extended Fitzhugh-Nagumo model. We analyze all possible combinations of three neurons being coupled with either excitatory or inhibitory synapses, which add up to a total of 132 network motifs. The best performance of our reconstruction of these motifs, being measured by the area under the Receiver Operating Characteristic curve, exceeds values of 0.99. Together with the PCA analysis, we are not only able to reconstruct the motif topologies from the neuronal dynamics, but we are also able to distinguish between excitatory and inhibitory synapses.

Background Transfer entropy (TE) is a measure for the detection of directed interactions. Transfer entropy is an information theoretic implementation of Wiener's principle of observational causality. It offers an approach to the detection of neuronal interactions that is free of an explicit model of the interactions. Hence, it offers the power to analyze linear and nonlinear interactions alike. This allows for example the comprehensive analysis of directed interactions in neural networks at various levels of description. Here we present the open-source MATLAB toolbox TRENTOOL that allows the user to handle the considerable complexity of this measure and to validate the obtained results using non-parametrical statistical testing. We demonstrate the use of the toolbox and the performance of the algorithm on simulated data with nonlinear (quadratic) coupling and on local field potentials (LFP) recorded from the retina and the optic tectum of the turtle (Pseudemys scripta elegans) where a neuronal one-way connection is likely present. Results In simulated data TE detected information flow in the simulated direction reliably with false positives not exceeding the rates expected under the null hypothesis. In the LFP data we found directed interactions from the retina to the tectum, despite the complicated signal transformations between these stages. No false positive interactions in the reverse directions were detected. Conclusions TRENTOOL is an implementation of transfer entropy and mutual information analysis that aims to support the user in the application of this information theoretic measure. TRENTOOL is implemented as a MATLAB toolbox and available under an open source license (GPL v3). For the use with neural data TRENTOOL seamlessly integrates with the popular FieldTrip toolbox.

Calcium imaging has become a standard technique for the measurement of the activity of a population of cultured neurons. Typically these recordings are slow compared to the cell dynamics and display a low signal-to-noise ratio, but they allow for the simultaneous recording of hundreds of neurons. We are interested in reconstructing an approximation of the structural connectivity of a culture of neurons. This would allow for characterization of the bulk properties of these networks, such as the dependence of connection probability of two nodes on the distance between them, the degree distribution or the clustering coefficient, which are currently inaccessible with single-cell or even typical multi-electrode techniques. In order to benchmark our connectivity inference methods, we first study simulations of fluorescence signals and examine established methods of inferring the topology. It turns out that we can improve on these methods if we turn to measures from information theory, which do not rely on a linearity assumption. Because we are interested in directed networks, our measure of choice is Transfer Entropy [1,2]. It turns out that we can achieve a high quality of the reconstruction if we allow for novel extensions of this measure. Specifically, we need to take into account the ability of the network to display different dynamical states (fig. ​(fig.1).1). We need to focus on phases of activity where the dynamics in the network are dominated by direct monosynaptic interactions, and where therefore the effective connectivity corresponds closely to the structural connectivity. Additionally, we need to correct for the slow acquisition rate of the recording by allowing for instantaneous interactions between nodes in addition to interactions from different image frames. Figure 1 The averaged fluorescence signal of the nodes in our network (A) reveals the existence of quiet phases and network spikes, which is then represented in the histogram over time (B). The effective connectivity calculated from the data points when the averaged ... We demonstrate post-processing improvements of the reconstruction using the Data Processing Inequality that are only possible in the case of information theoretical measures. These methods, already applied with success in the reconstruction of gene regulatory networks [3], help to discriminate indirect from direct interactions. We then apply our algorithm to real data from large cultures of hippocampal neurons in vitro stained with Fluo-4 AM dye. We probe and quantify the distance-dependent probability of connection and other topological properties of the reconstructed network, finding deviations from a random topology. Finally we point out and quantify which experimental parameters would be most relevant for an improved reconstruction using our method.

Analysis of information transfer between variables in brain images is currently a popular topic, e.g. [1]. Such work typically focuses on average information transfer (i.e. transfer entropy[2]), yet the dynamics of transfer from a source to a destination can also be quantified at individual time points using the local transfer entropy (TE) [3]. This local perspective is known to reveal dynamical structure that the average cannot. We present a method to quantify local TE values in time between source and destination regions of variables in brain-imaging data, combining: a. computation of inter-regional transfer between two regions of variables (e.g. voxels) [1], with b. the local perspective of the dynamics of such transfer in time [3]. Transfer is computed over samples from all variables – there is no training in or subset selection of variables to use. We apply this method to a set of fMRI measurements where we could expect to see differences in local information transfer between two conditions at specific time steps. The fMRI data set analyzed (from [4]) contains brain activity recorded from 7 localized regions while 12 subjects (who gave informed written consent) were asked to freely decide whether to push one of two buttons (with left or right index finger), whenever they felt the urge to do so, and to press the button immediately on deciding . To our knowledge, this is the first analysis of transfer entropy on a local temporal scale in brain-imaging data (at specific time points rather than via sliding windows). Significant differences in the local TE between left and right button presses are revealed in a significant number of subjects (7) by: a. examining the difference in local TE from a single source region (e.g. pre-SMA) into left and right motor cortex respectively (e.g. see Figure ​Figure11 for subject 1); and Figure 1 Difference in TE(pre-SMA → left motor) and TE(pre-SMA → right motor) versus time after button press for subject 1. Error bars are std. err. over presses. Significant difference between left and right button press indicated by · ... b. aggregating local TE differences across 2 to 3 consecutive time steps (e.g. t=2,4 and 6 sec. after button press). Additionally, thresholding of these TE differences can decode the button push with a (statistically significant) mean of 65% accuracy across subjects. These measurements of local TE correlate well with the role of these regions in executing the motor response here [4]. We confirm that local TE can be used to reveal differences in task-based dynamical information transfer, with potential for the technique to be improved in the future.

Networks of cortical neurons are essentially non-random [1]. Although it is known that such networks show interesting structure at multiple temporal and spatial scales [2], almost no experimental work has been done to reveal how structures at these different scales relate to each other. This study aimed to clarify important relations between non-randomness in groups of 3-6 neurons (clusters) and non-randomness in groups of 50-100 neurons (communities) through five steps. First, we recorded spontaneous activity of up to 500 neurons from rodent somatosensory cortex using a 512ch. multi-electrode system over one hour [3]. Second, we reconstructed effective connectivity using transfer entropy [4]. Third, we compared topologies of effective networks at the 3-6 neuron scale (clusters including motifs [Figure1-B]) with topologies of synaptic connections measured from 12 neuron simultaneous patch clamp experiments [5,6]. Fourth, we constructed community or modular structures representing non-randomness from larger groups of neurons. Fifth, we evaluated the extent to which structure at each of these scales was robust. We did this by swapping connections from high degree nodes (hubs) with those from low degree nodes (non-hubs). Figure 1 (A) An example of spatial distribution of neurons and effective connections. Different markers indicate different communities. The biggest two communities are covered by blue and red regions. Upper-right yellow region is an example cluster of 6 neurons. ... We found three things. First, the degree-distribution followed a power-law This demonstrated that hubs could not have been the result of random sampling from a Gaussian distribution. Second, effective networks consisting of hundreds of cortical neurons have distinctive non-random structures of connectivity at two different scales. Third, structure at the cluster level was relatively more fragile than structure at the community level. The difference between non-randomness evaluated by cluster and community will become the important first step to understand multiple different scales of cortical neuronal networks.

The use of in vitro neuronal systems and computational models has strongly contributed to the better understanding of relevant neurophysiological principles. Taking advantages form these approaches, here we propose a revised method of partial correlation analysis to investigate functional connectivity in neuronal networks. The main goal of this work is to estimate the functional connectivity, by means of correlation and information theory-based methods, from the spontaneous activity of dissociated cortical neurons developing in vitro and coupled to micro-electrode arrays (MEAs). In particular we focused here on the Partial Correlation (PC) method [1] compared to Transfer Entropy [2] and Cross Correlation (CC) [3] algorithms. We first evaluated the methods’ performances applying the algorithms to a neural network model made up of 60 spatially distributed and synaptically connected Izhikevich neurons [4]. Using receiver operating characteristic (ROC) curves, calculating the values of the areas under these curves (AUC) and varying the average degree of each cell, we observed that Partial Correlation presented the best performances (see Figure ​Figure1)1) for all the tested average synaptic connectivity degree (from 5 to 55 connections for each neuron). Figure 1 AUC values: Comparison among the three algorithms (PC, CC and TE). Second we assessed the statistical significance of connections extracted through the aforementioned algorithms from electrophysiological data. Using “shuffling” techniques devised in [5], we implemented a reliable threshold-independent test, model free and not linked to any particular initial assumptions (i.e., choice of data distribution). Finally, applying the validated methods, we obtained functional mapping of biological in vitro models of cortical networks and we extracted relevant topological features.

Recent studies suggest that the functional organization of brain networks is altered in patients with severe disorders of consciousness (DOC), including coma [1]. A better characterization of these large-scale disturbances of brain function is fundamental for the understanding and eventual prediction of coma outcome. In this study we apply information theory tools and correlation measures to explore the brain functional connectivity (FC) in functional magnetic resonance imaging (fMRI) data from patients with DOC. In particular we are interested in the functional coherence within and between brain hemispheres as a measure of the integrity of brain function. The data analyzed comprises resting state fMRI data from 5 patients with traumatic DOC in two sessions, one early after the traumatic event and the second later in a stable clinical phase spanning several months. As a control we used similar data obtained from 17 healthy subjects. FC was assessed among time series of the blood oxygenated level dependent (BOLD) signal from 90 regions of interest (ROI) obtained using the Automated Anatomical Labelling (AAL) atlas [2]. These time series were used to estimate FC using two approaches: Partial Linear Correlation (PLC) and Transfer Entropy (TE) [3]. The major findings are summarized in Figure ​Figure1;1; the PLC analysis shows a significant reduction of the inter-hemispheric FC in DOC patients compared to controls. Regarding TE measures, we have found a strong reduction in the total TE of the DOC patients vs controls; mean values of 59.17 bits for DOC vs 123.97 bits for controls, whilst the two groups have a similar standard deviation (62.41 for DOC vs 76.69 for controls). Furthermore, the results based on TE seem to indicate that the inter-hemispheric FC asymmetry reported by the PLC in Figure ​Figure11 might be corresponded with an asymmetry between the TE travelling from "left to right" vs the one from "right to left" along the same ROI in the AAL. Notice that TE (but not PLC) is a non-symmetric measure. Interestingly, some of the DOC patients presented a FC pattern closer to the healthy subjects, for instance patient 3 who in the second session (i.e., 3' in Figure ​Figure1)1) was fully conscious. These findings might have clinical value for the diagnosis and design of recovery plans for patients with DOC. Figure 1 For each subject it is shown the PLC summed over the 45 regions of the left hemisphere (bottom graph), the right hemisphere (middle graph) or between all right-left homologous ROIs in the AAL (top graph). Numbers on x-axis are indicating the different ...

To investigate directed interactions in neural networks we often use Norbert Wiener's famous definition of observational causality. Wiener’s definition states that an improvement of the prediction of the future of a time series X from its own past by the incorporation of information from the past of a second time series Y is seen as an indication of a causal interaction from Y to X. Early implementations of Wiener's principle – such as Granger causality – modelled interacting systems by linear autoregressive processes and the interactions themselves were also assumed to be linear. However, in complex systems – such as the brain – nonlinear behaviour of its parts and nonlinear interactions between them have to be expected. In fact nonlinear power-to-power or phase-to-power interactions between frequencies are reported frequently. To cover all types of non-linear interactions in the brain, and thereby to fully chart the neural networks of interest, it is useful to implement Wiener's principle in a way that is free of a model of the interaction [1]. Indeed, it is possible to reformulate Wiener's principle based on information theoretic quantities to obtain the desired model-freeness. The resulting measure was originally formulated by Schreiber [2] and termed transfer entropy (TE). Shortly after its publication transfer entropy found applications to neurophysiological data. With the introduction of new, data efficient estimators (e.g. [3]) TE has experienced a rapid surge of interest (e.g. [4]). Applications of TE in neuroscience range from recordings in cultured neuronal populations to functional magnetic resonanace imaging (fMRI) signals. Despite widespread interest in TE, no publicly available toolbox exists that guides the user through the difficulties of this powerful technique. TRENTOOL (the TRansfer ENtropy TOOLbox) fills this gap for the neurosciences by bundling data efficient estimation algorithms with the necessary parameter estimation routines and nonparametric statistical testing procedures for comparison to surrogate data or between experimental conditions. TRENTOOL is an open source MATLAB toolbox based on the Fieldtrip data format. ...

Phase synchronization of neuronal oscillations has been suggested to underlie the coordination and integration of anatomically distributed processing [1,2]. To quantify "causal" or directional inter-areal phase-phase interactions, a phase-based measure of effective connectivity is needed. Methods for detecting effective connectivity can be divided into model-based (e.g., Dynamic Causal Modeling [3]) and model-free techniques (e.g., Granger Causality [4]). Transfer Entropy (TE) [5] is a model-free measure of effective connectivity based on information theory. Prior implementations of TE, however, focus on real-valued time series where the signal amplitude is a major bias and phase is only an implicit variable. Furthermore, the robustness of existing TE methods to narrow-band filtering, noise, and linear mixing between signals is limited. Finally, current approaches are dependent on accurate a priori estimation of several parameters, which is not feasible for connectomics approaches with all-to-all mappings of inter-areal interactions. Here we advance a novel measure, Phase Transfer Entropy (Phase TE), to estimate directional connectivity between complex phase time series of filtered signals. In this study, we first assess the reliability of Phase TE in quantifying directional connectivity. Second, we compare its performance to other TE implementations using real-valued narrowband and broadband signals. To quantify a unidirectional effect of signal 1 to signal 2, we define differential TE (dTE) as: dTE(1→2) = TE(1→2) - TE(2→1) and determine the sensitivity and specificity of our methods from the dTE distributions of uncoupled and coupled signals. We simulated ecologically valid neuronal-like oscillations with coupled Neural Mass Models [6] and estimated the phase time series with Morlet filtering. Phase TE increased monotonically with coupling strength and discriminated between coupled and non-coupled time series. Phase TE was robust to realistic amounts of noise and/or linear mixing. Effective connectivity even with small coupling values was reliably detected for moderate signal-to-noise ratios using an amount of data commonly acquired in neuroimaging experiments. We found that Phase dTE did not yield false positives in the presence of mixing and/or noise. Across a range of noise and mixing values, the sensitivity of Phase TE was comparable to or better than the sensitivities of prior TE implementations. Finally, Phase TE was computationally much faster than prior TE implementations. In conclusion, Phase TE is a computationally efficient method for detecting directed interactions between band-limited activities in neurophysiological time series. Phase TE works well with filtering and is robust against noise and linear mixing, which are the elementary confounders in electrophysiological data. Given that Phase TE is also essentially parameter free, we propose it to be an efficient and reliable method for assessing effective connectivity in connectomics analyses.

The mixing problem of electroencephalography (EEG) in the presence of common source could affect directed functional connectivity measures, resulting in an incorrect directionality of information flow between two signals. Here we introduce directed Weighted Phase Lag Index (dWPLI), a signed version of Weighted Phase Lag Index (WPLI) and compare this measure to Granger Causality (GC), Symbolic Transfer Entropy (STE), Phase Slope Index (PSI), and directed Phase Lag Index (dPLI) under common source effects. Robustness of the measures was tested in both analytic and simulating ways. For the simulated time series, signals were generated from unidirectionally coupled autoregressive model and linearly mixed to achieve volume conduction and common noise effects. As expected from the analytic calculation, dPLI and dWPLI were unaffected by the volume conduction while PSI, GC and STE were largely affected. (Figure ​(Figure1A).1A). The mean percentages of false identification were 14.00±7.66, 22.35±4.78, 27.38±7.04, 1.99±1.36, and 1.63±1.28, for the GC, STE, PSI, dPLI, and dWPLI, respectively. Figure 1 A. Directionalities of five directed connectivity measures under the volume conduction effect. Positive Directionality Index (DI) implies correct directionality of information flow. As M (mixing ratio) increases, the DIs of GC, STE and PSI decrease. However, ... For the common noise case, only dPLI and dWPLI had their signs preserved. (Figure ​(Figure1B).1B). The mean percentages of false identification were 30.14 ± 16.86, 49.74 ± 16.63, 34.72 ±10.23, 2.68 ± 1.90, and 2.34 ± 1.55. Furthermore, the dWPLI outperformed dPLI for the common noise case (p

Structural and functional connectivity of macroscopic brain regions has been very widely researched [1] in the last decade, however very little work has been done on the effective connectivity between individual neurons, largely because of limitations on the simultaneous measurement of large numbers of neurons at high spatiotemporal resolution. We recorded spontaneous single neuron activity from 15 organotypic cultures (prepared from the mouse cortex), with a 512 channel micro-electrode array at a temporal resolution of less than 1 ms and a spatial resolution of 60 μm. The average number of recorded neurons was 347 ± 119. Effective connectivity matrices, both binary and weighted, were constructed from the spike trains using transfer entropy (TE) analysis to estimate directed neuronal interactions [2]. The strength of information flow from neuron i to j was quantified in terms of the TE value calculated from neuron i to j. We observed that only 20% of the recorded neurons accounted for 80% of the total information flow in these networks (see Figure 1A) which we define as the network’s set of rich nodes. The rich nodes were characterized by a higher firing rate, and graph theoretic analysis revealed their participation in a number of highly non-random network features. The networks were highly clustered with small average path

Functional connectivity of the brain describes the networkof correlated activities of different brain areas. However,correlation does not imply causality and most synchroni-zation measures do not distinguish causal and non-causalinteractions among remote brain areas, i.e. determine theeffective connectivity [1]. Identification of causal interac-tions in brain networks is fundamental to understandingthe processing of information. Attempts at unveiling signsof functional or effective connectivity from non-invasiveMagneto-/Electroencephalographic (M/EEG) recordingsat the sensor level are hampered by volume conductionleading to correlated sensor signals without the presenceof effective connectivity. Here, we make use of the transferentropy (TE) concept to establish effective connectivity.The formalism of TE has been proposed as a rigorousquantification of the information flow among systems ininteraction and is a natural generalization of mutualinformation [2]. In contrast to Granger causality, TE is anon-linear measure and not influenced by volume con-duction.We evaluate TE on MEG data recorded during a Simontask. Subjects were presented with a "L" or "R" letter ineither the left or the right side of a screen and had to pressa left-side key in response to the "L" letter and the right-side key in response to the "R" letter, independently of thespatial location of the stimulus. The sequential organiza-tion of this task allows us to infer gross effective connec-tivity: Visual input has to be processed and the letterrecognized before motor action can be planned. Hence,effective connectivity from visual cortices to frontal andmotor areas was expected. Our tasks directed visual inputeither to the left or right hemisphere in early visual cortexand required left or right hemispheric motor responses,presumably changing connectivity patterns.TE of channel pairs was computed with a Kozachenko-Leonenko estimator while the statistical significance ofthe causal interactions was determined by a non-paramet-ric permutation test. The flow of information revealedthat different neuronal circuits (including long-rangecausal influences like inter hemispheric temporal lobeinteractions) were recruited for the four different experi-mental conditions, in accordance to the physiologicalexpectation. The effective networks of Simon versus non-Simon effect conditions were also compared to explorethe use of effective connectivity as a tool to investigatecognitive processes.

Understanding how information flowing in neuronal networks is encoded by populations of neurons is a fundamental problem in neuroscience. Brains and neuronal networks must at the same time store information about the world and react to information in the world. We used simulations of neocortical columns to measure how the activity of the network alters information flow and related this to experimental data from animal models of epilepsy and schizophrenia. In our simulations, we found that networks with greater internal connectivity reduced information flow from inputs to outputs, measured by normalized transfer entropy [1]. With no internal connectivity, the feed-forward network transformed inputs through nonlinear summation and thresholding. With greater connectivity strength, the recurrent network translated activity and information due to contribution of activity from intrinsic network dynamics. This dynamic contribution amounted to added information coming from the network. Gradual reduction in information flow-through with increased internal weight was asymptotic. At one extreme, the highly interconnected network was epileptic and any input ignited a seizure [2]. Such networks no longer accepted external information and no longer coordinated well with other brain areas. These types of networks also had more stereotyped activity patterns, with lesser information content present in the network and minimal information communicated from outside. EEG data from an animal model of epilepsy showed a similar reduction in entropy, which was also accompanied with a decrease in coordination between different brain areas. At a lower level of dynamic pathology, abnormalities in power and coordination in gamma bands were seen, as has been noted in schizophrenia [3-5]. In schizophrenia, the core cognitive deficit is believed to be a problem of coordinating external and internal states to provide a coherent view of the world, and the person's relation to the world [6]. This is most evident with hallucinations, a mistaken attribution of internal activity to the external world. EEG data from an animal model of schizophrenia showed increased correlation between the power of oscillations in the gamma and beta bands, suggesting an over-reliance on internal information. This is analogous to the over reliance on internal information in our simulations of networks with overly high internal connectivity. Our simulations provide a framework for relating aspects of epilepsy and schizophrenia to information processing. By quantifying the competing effects of internal and external information sources in simulation, we can suggest how symptoms of these disorders may be produced.

Effective connectivity analysis is a popular approach in computational neuroscience, whereby one seeks to infer a network of directed edges between neural variables (e.g. voxels or regions in fMRI, or reconstructed source time series in MEG data) which can explain their observed time-series dynamics. This is an important approach in understanding brain function, contrasting with functional connectivity analysis in being directed and dynamic, and with structural connectivity analysis in not requiring interventions and in being task-modulated. In particular, effective connectivity analysis seeks to find a minimal circuit model that can reconstruct the activity patterns contained in the given data. Ideally, such inference would be: made using model-free techniques; capture non-linear, multivariate, directional relationships; handle small amounts of data, and be statistically robust. The information-theoretic measure transfer entropy (TE) [1] (a non-linear Granger causality) is becoming

An approach to study the mechanism of information processing in a neural circuit is to identify synaptic connectivity between neurons. As recent advances in experimental techniques facilitate simultaneous recording of a large population of neurons, estimation of synaptic connectivity from multiple neural spike train data has become a major goal in computational neuroscience. Although it is important to develop an accurate method, it is difficult to validate a method on the basis of experimental data because of the lack of knowledge regarding synaptic connectivity. In this contribution, we have developed a method to estimate synaptic connection on the basis of a coupled escape rate model (CERM), which is an extension of the escape rate model [1]. The strength of the synaptic connection was determined by maximizing the likelihood function. We applied this method as well as model-free methods (transfer entropy and cross-correlation [2]) to synthetic spike train data. The synthetic data were generated by a cortical network model, which consisted of thousands of Hodgkin-Huxley type neurons [3]. These methods are applied to the spike data generated by the cortical network model with different topologies of synaptic connectivity (regular, small-world, and random). It should be noted that the true connectivity is known and the estimation performance can be evaluated by the receiver operating characteristic (ROC) analysis. Our results demonstrated that all methods gave better results for nonrandom (regular and small-world) networks than for random networks. Furthermore, CERM is considered to be the optimal method because it does not involve binning and requires smallest observation length. Therefore, despite high computational costs, CERM is a most suitable method to estimate synaptic connections from multiple spike train data.