Altered Functional Connectivity and Small-World in Mesial Temporal Lobe Epilepsy

Background

The functional architecture of the human brain has been extensively described in terms of functional connectivity networks, detected from the low–frequency coherent neuronal fluctuations that can be observed in a resting state condition. Little is known, so far, about the changes in functional connectivity and in the topological properties of functional networks, associated with different brain diseases.

Methodology/Principal Findings

In this study, we investigated alterations related to mesial temporal lobe epilepsy (mTLE), using resting state functional magnetic resonance imaging on 18 mTLE patients and 27 healthy controls. Functional connectivity among 90 cortical and subcortical regions was measured by temporal correlation. The related values were analyzed to construct a set of undirected graphs. Compared to controls, mTLE patients showed significantly increased connectivity within the medial temporal lobes, but also significantly decreased connectivity within the frontal and parietal lobes, and between frontal and parietal lobes. Our findings demonstrated that a large number of areas in the default-mode network of mTLE patients showed a significantly decreased number of connections to other regions. Furthermore, we observed altered small-world properties in patients, along with smaller degree of connectivity, increased n-to-1 connectivity, smaller absolute clustering coefficients and shorter absolute path length.

Conclusions/Significance

We suggest that the mTLE alterations observed in functional connectivity and topological properties may be used to define tentative disease markers.     

How Does Connectivity Between Cortical Areas Depend on Brain Size? Implications for Efficient Computation

A formula for an average connectivity between cortical areas in mammals is derived. Based on comparative neuroanatomical data, it is found, surprisingly, that this connectivity is either only weakly dependent or independent of brain size. It is discussed how this formula can be used to estimate the average length of axons in white matter. Other allometric relations, such as cortical patches and area sizes vs. brain size, are also provided. Finally, some functional implications, with an emphasis on efficient cortical computation, are discussed as well.     

Mirrored STDP Implements Autoencoder Learning in a Network of Spiking Neurons

The autoencoder algorithm is a simple but powerful unsupervised method for training neural networks. Autoencoder networks can learn sparse distributed codes similar to those seen in cortical sensory areas such as visual area V1, but they can also be stacked to learn increasingly abstract representations. Several computational neuroscience models of sensory areas, including Olshausen & Field’s Sparse Coding algorithm, can be seen as autoencoder variants, and autoencoders have seen extensive use in the machine learning community. Despite their power and versatility, autoencoders have been difficult to implement in a biologically realistic fashion. The challenges include their need to calculate differences between two neuronal activities and their requirement for learning rules which lead to identical changes at feedforward and feedback connections. Here, we study a biologically realistic network of integrate-and-fire neurons with anatomical connectivity and synaptic plasticity that closely matches that observed in cortical sensory areas. Our choice of synaptic plasticity rules is inspired by recent experimental and theoretical results suggesting that learning at feedback connections may have a different form from learning at feedforward connections, and our results depend critically on this novel choice of plasticity rules. Specifically, we propose that plasticity rules at feedforward versus feedback connections are temporally opposed versions of spike-timing dependent plasticity (STDP), leading to a symmetric combined rule we call Mirrored STDP (mSTDP). We show that with mSTDP, our network follows a learning rule that approximately minimizes an autoencoder loss function. When trained with whitened natural image patches, the learned synaptic weights resemble the receptive fields seen in V1. Our results use realistic synaptic plasticity rules to show that the powerful autoencoder learning algorithm could be within the reach of real biological networks.     

Columnar Connectivity and Laminar Processing in Cat Primary Auditory Cortex

Background

Radial intra- and interlaminar connections form a basic microcircuit in primary auditory cortex (AI) that extracts acoustic information and distributes it to cortical and subcortical networks. Though the structure of this microcircuit is known, we do not know how the functional connectivity between layers relates to laminar processing.

Methodology/Principal Findings

We studied the relationships between functional connectivity and receptive field properties in this columnar microcircuit by simultaneously recording from single neurons in cat AI in response to broadband dynamic moving ripple stimuli. We used spectrotemporal receptive fields (STRFs) to estimate the relationship between receptive field parameters and the functional connectivity between pairs of neurons. Interlaminar connectivity obtained through cross-covariance analysis reflected a consistent pattern of information flow from thalamic input layers to cortical output layers. Connection strength and STRF similarity were greatest for intralaminar neuron pairs and in supragranular layers and weaker for interlaminar projections. Interlaminar connection strength co-varied with several STRF parameters: feature selectivity, phase locking to the stimulus envelope, best temporal modulation frequency, and best spectral modulation frequency. Connectivity properties and receptive field relationships differed for vertical and horizontal connections.

Conclusions/Significance

Thus, the mode of local processing in supragranular layers differs from that in infragranular layers. Therefore, specific connectivity patterns in the auditory cortex shape the flow of information and constrain how spectrotemporal processing transformations progress in the canonical columnar auditory microcircuit.     

Specificity and Plasticity of Thalamocortical Connections in Sema6A Mutant Mice

The establishment of connectivity between specific thalamic nuclei and cortical areas involves a dynamic interplay between the guidance of thalamocortical axons and the elaboration of cortical areas in response to appropriate innervation. We show here that Sema6A mutants provide a unique model to test current ideas on the interactions between subcortical and cortical guidance mechanisms and cortical regionalization. In these mutants, axons from the dorsal lateral geniculate nucleus (dLGN) are misrouted in the ventral telencephalon. This leads to invasion of presumptive visual cortex by somatosensory thalamic axons at embryonic stages. Remarkably, the misrouted dLGN axons are able to find their way to the visual cortex via alternate routes at postnatal stages and reestablish a normal pattern of thalamocortical connectivity. These findings emphasize the importance and specificity of cortical cues in establishing thalamocortical connectivity and the spectacular capacity of the early postnatal cortex for remapping initial sensory representations.     

Emergence of Metastable State Dynamics in Interconnected Cortical Networks with Propagation Delays

The importance of the large number of thin-diameter and unmyelinated axons that connect different cortical areas is unknown. The pronounced propagation delays in these axons may prevent synchronization of cortical networks and therefore hinder efficient information integration and processing. Yet, such global information integration across cortical areas is vital for higher cognitive function. We hypothesized that delays in communication between cortical areas can disrupt synchronization and therefore enhance the set of activity trajectories and computations interconnected networks can perform. To evaluate this hypothesis, we studied the effect of long-range cortical projections with propagation delays in interconnected large-scale cortical networks that exhibited spontaneous rhythmic activity. Long-range connections with delays caused the emergence of metastable, spatio-temporally distinct activity states between which the networks spontaneously transitioned. Interestingly, the observed activity patterns correspond to macroscopic network dynamics such as globally synchronized activity, propagating wave fronts, and spiral waves that have been previously observed in neurophysiological recordings from humans and animal models. Transient perturbations with simulated transcranial alternating current stimulation (tACS) confirmed the multistability of the interconnected networks by switching the networks between these metastable states. Our model thus proposes that slower long-range connections enrich the landscape of activity states and represent a parsimonious mechanism for the emergence of multistability in cortical networks. These results further provide a mechanistic link between the known deficits in connectivity and cortical state dynamics in neuropsychiatric illnesses such as schizophrenia and autism, as well as suggest non-invasive brain stimulation as an effective treatment for these illnesses.     

Hierarchical Alteration of Brain Structural and Functional Networks in Female Migraine Sufferers

Background

Little is known about the changes of brain structural and functional connectivity networks underlying the pathophysiology in migraine. We aimed to investigate how the cortical network reorganization is altered by frequent cortical overstimulation associated with migraine.

Methodology/Principal Findings

Gray matter volumes and resting-state functional magnetic resonance imaging signal correlations were employed to construct structural and functional networks between brain regions in 43 female patients with migraine (PM) and 43 gender-matched healthy controls (HC) by using graph theory-based approaches. Compared with the HC group, the patients showed abnormal global topology in both structural and functional networks, characterized by higher mean clustering coefficients without significant change in the shortest absolute path length, which indicated that the PM lost optimal topological organization in their cortical networks. Brain hubs related to pain-processing revealed abnormal nodal centrality in both structural and functional networks, including the precentral gyrus, orbital part of the inferior frontal gyrus, parahippocampal gyrus, anterior cingulate gyrus, thalamus, temporal pole of the middle temporal gyrus and the inferior parietal gyrus. Negative correlations were found between migraine duration and regions with abnormal centrality. Furthermore, the dysfunctional connections in patients'' cortical networks formed into a connected component and three dysregulated modules were identified involving pain-related information processing and motion-processing visual networks.

Conclusions

Our results may reflect brain alteration dynamics resulting from migraine and suggest that long-term and high-frequency headache attacks may cause both structural and functional connectivity network reorganization. The disrupted information exchange between brain areas in migraine may be reshaped into a hierarchical modular structure progressively.     

Network structure implied by initial axon outgrowth in rodent cortex: empirical measurement and models

The developmental mechanisms by which the network organization of the adult cortex is established are incompletely understood. Here we report on empirical data on the development of connections in hamster isocortex and use these data to parameterize a network model of early cortical connectivity. Using anterograde tracers at a series of postnatal ages, we investigate the growth of connections in the early cortical sheet and systematically map initial axon extension from sites in anterior (motor), middle (somatosensory) and posterior (visual) cortex. As a general rule, developing axons extend from all sites to cover relatively large portions of the cortical field that include multiple cortical areas. From all sites, outgrowth is anisotropic, covering a greater distance along the medial/lateral axis than along the anterior/posterior axis. These observations are summarized as 2-dimensional probability distributions of axon terminal sites over the cortical sheet. Our network model consists of nodes, representing parcels of cortex, embedded in 2-dimensional space. Network nodes are connected via directed edges, representing axons, drawn according to the empirically derived anisotropic probability distribution. The networks generated are described by a number of graph theoretic measurements including graph efficiency, node betweenness centrality and average shortest path length. To determine if connectional anisotropy helps reduce the total volume occupied by axons, we define and measure a simple metric for the extra volume required by axons crossing. We investigate the impact of different levels of anisotropy on network structure and volume. The empirically observed level of anisotropy suggests a good trade-off between volume reduction and maintenance of both network efficiency and robustness. Future work will test the model's predictions for connectivity in larger cortices to gain insight into how the regulation of axonal outgrowth may have evolved to achieve efficient and economical connectivity in larger brains.     

Neural Plasticity in Human Brain Connectivity: The Effects of Long Term Deep Brain Stimulation of the Subthalamic Nucleus in Parkinson’s Disease

Background

Positive clinical outcomes are now well established for deep brain stimulation, but little is known about the effects of long-term deep brain stimulation on brain structural and functional connectivity. Here, we used the rare opportunity to acquire pre- and postoperative diffusion tensor imaging in a patient undergoing deep brain stimulation in bilateral subthalamic nuclei for Parkinson’s Disease. This allowed us to analyse the differences in structural connectivity before and after deep brain stimulation. Further, a computational model of spontaneous brain activity was used to estimate the changes in functional connectivity arising from the specific changes in structural connectivity.

Results

We found significant localised structural changes as a result of long-term deep brain stimulation. These changes were found in sensory-motor, prefrontal/limbic, and olfactory brain regions which are known to be affected in Parkinson’s Disease. The nature of these changes was an increase of nodal efficiency in most areas and a decrease of nodal efficiency in the precentral sensory-motor area. Importantly, the computational model clearly shows the impact of deep brain stimulation-induced structural alterations on functional brain changes, which is to shift the neural dynamics back towards a healthy regime. The results demonstrate that deep brain stimulation in Parkinson’s Disease leads to a topological reorganisation towards healthy bifurcation of the functional networks measured in controls, which suggests a potential neural mechanism for the alleviation of symptoms.

Conclusions

The findings suggest that long-term deep brain stimulation has not only restorative effects on the structural connectivity, but also affects the functional connectivity at a global level. Overall, our results support causal changes in human neural plasticity after long-term deep brain stimulation and may help to identify the underlying mechanisms of deep brain stimulation.     

Neural Substrates of Motor and Non-Motor Symptoms in Parkinson’s Disease: A Resting fMRI Study

Background

Recently, non-motor symptoms of Parkinson’s disease (PD) have been considered crucial factors in determining a patient’s quality of life and have been proposed as the predominant features of the premotor phase. Researchers have investigated the relationship between non-motor symptoms and the motor laterality; however, this relationship remains disputed. This study investigated the neural connectivity correlates of non-motor and motor symptoms of PD with respect to motor laterality.

Methods

Eight-seven patients with PD were recruited and classified into left-more-affected PD (n = 44) and right-more affected PD (n = 37) based on their MDS-UPDRS (Movement Disorder Society-sponsored revision of the Unified Parkinson’s Disease Rating Scale) motor examination scores. The patients underwent MRI scanning, which included resting fMRI. Brain regions were labeled as ipsilateral and contralateral to the more-affected body side. Correlation analysis between the functional connectivity across brain regions and the scores of various symptoms was performed to identify the neural connectivity correlates of each symptom.

Results

The resting functional connectivity centered on the ipsilateral inferior orbito-frontal area was negatively correlated with the severity of non-motor symptoms, and the connectivity of the contralateral inferior parietal area was positively correlated with the severity of motor symptoms (p < 0.001, |r| > 0.3).

Conclusions

These results suggest that the inferior orbito-frontal area may play a crucial role in non-motor dysfunctions, and that the connectivity information may be utilized as a neuroimaging biomarker for the early diagnosis of PD.     

Regional Brain Atrophy and Functional Disconnection in Broca’s Area in Individuals at Ultra-High Risk for Psychosis and Schizophrenia

Background

Abnormalities in cognitive abilities such as verbal fluency and in cognitive-related brain regions, particularly Broca’s area, have been reported in patients with schizophrenia. Additionally, previous studies have demonstrated that structural and functional abnormalities in Broca’s area were associated with clinical symptoms and cognitive deficits in patients with schizophrenia, suggesting that deficits in this area may reflect the core pathology of schizophrenia. Thus, it is important to understand how the structural volume and functional connectivity in this area changes at rest according to the course of the illness.

Methods/Principal Findings

We used magnetic resonance imaging (MRI) to measure the structural volume of Broca’s area as a region of interest in 16 schizophrenia, 16 ultra-high risk (UHR), and 23 healthy matched controls. We also assessed verbal fluency and analyzed differences across groups in the functional connectivity patterns using resting-state functional MRI. The UHR group showed significantly reduced structural volume in Broca’s area and significantly reduced functional connectivity between Broca’s area and the lateral and medial frontal cortex as well as decreased cognitive performance. Altered functional connectivity in patients was correlated with their positive symptoms.

Conclusions/Significance

Our results suggest the existence of functional disconnections in Broca’s area, even during resting-states, among those with schizophrenia as well as those at UHR for this disorder. These alterations may contribute to their clinical symptoms, suggesting that this is one of the key regions involved in the pathophysiology of schizophrenia.     

Reduced Structural Connectivity between Sensorimotor and Language Areas in Rolandic Epilepsy

Introduction

Rolandic epilepsy (RE) is a childhood epilepsy with centrotemporal (rolandic) spikes, that is increasingly associated with language impairment. In this study, we tested for a white matter (connectivity) correlate, employing diffusion weighted MRI and language testing.

Methods

Twenty-three children with RE and 23 matched controls (age: 8–14 years) underwent structural (T1-weighted) and diffusion-weighted MRI (b = 1200 s/mm², 66 gradient directions) at 3T, as well as neuropsychological language testing. Combining tractography and a cortical segmentation derived from the T1-scan, the rolandic tract were reconstructed (pre- and postcentral gyri), and tract fractional anisotropy (FA) values were compared between patients and controls. Aberrant tracts were tested for correlations with language performance.

Results

Several reductions of tract FA were found in patients compared to controls, mostly in the left hemisphere; the most significant effects involved the left inferior frontal (p = 0.005) and supramarginal (p = 0.004) gyrus. In the patient group, lower tract FA values were correlated with lower language performance, among others for the connection between the left postcentral and inferior frontal gyrus (p = 0.043, R = 0.43).

Conclusion

In RE, structural connectivity is reduced for several connections involving the rolandic regions, from which the epileptiform activity originates. Most of these aberrant tracts involve the left (typically language mediating) hemisphere, notably the pars opercularis of the inferior frontal gyrus (Broca’s area) and the supramarginal gyrus (Wernicke’s area). For the former, reduced language performance for lower tract FA was found in the patients. These findings provide a first microstructural white matter correlate for language impairment in RE.     

Independently Outgrowing Neurons and Geometry-Based Synapse Formation Produce Networks with Realistic Synaptic Connectivity

Neuronal signal integration and information processing in cortical networks critically depend on the organization of synaptic connectivity. During development, neurons can form synaptic connections when their axonal and dendritic arborizations come within close proximity of each other. Although many signaling cues are thought to be involved in guiding neuronal extensions, the extent to which accidental appositions between axons and dendrites can already account for synaptic connectivity remains unclear. To investigate this, we generated a local network of cortical L2/3 neurons that grew out independently of each other and that were not guided by any extracellular cues. Synapses were formed when axonal and dendritic branches came by chance within a threshold distance of each other. Despite the absence of guidance cues, we found that the emerging synaptic connectivity showed a good agreement with available experimental data on spatial locations of synapses on dendrites and axons, number of synapses by which neurons are connected, connection probability between neurons, distance between connected neurons, and pattern of synaptic connectivity. The connectivity pattern had a small-world topology but was not scale free. Together, our results suggest that baseline synaptic connectivity in local cortical circuits may largely result from accidentally overlapping axonal and dendritic branches of independently outgrowing neurons.     

Cell Assembly Dynamics of Sparsely-Connected Inhibitory Networks: A Simple Model for the Collective Activity of Striatal Projection Neurons

Striatal projection neurons form a sparsely-connected inhibitory network, and this arrangement may be essential for the appropriate temporal organization of behavior. Here we show that a simplified, sparse inhibitory network of Leaky-Integrate-and-Fire neurons can reproduce some key features of striatal population activity, as observed in brain slices. In particular we develop a new metric to determine the conditions under which sparse inhibitory networks form anti-correlated cell assemblies with time-varying activity of individual cells. We find that under these conditions the network displays an input-specific sequence of cell assembly switching, that effectively discriminates similar inputs. Our results support the proposal that GABAergic connections between striatal projection neurons allow stimulus-selective, temporally-extended sequential activation of cell assemblies. Furthermore, we help to show how altered intrastriatal GABAergic signaling may produce aberrant network-level information processing in disorders such as Parkinson’s and Huntington’s diseases.     

Influence of Wiring Cost on the Large-Scale Architecture of Human Cortical Connectivity

In the past two decades some fundamental properties of cortical connectivity have been discovered: small-world structure, pronounced hierarchical and modular organisation, and strong core and rich-club structures. A common assumption when interpreting results of this kind is that the observed structural properties are present to enable the brain''s function. However, the brain is also embedded into the limited space of the skull and its wiring has associated developmental and metabolic costs. These basic physical and economic aspects place separate, often conflicting, constraints on the brain''s connectivity, which must be characterized in order to understand the true relationship between brain structure and function. To address this challenge, here we ask which, and to what extent, aspects of the structural organisation of the brain are conserved if we preserve specific spatial and topological properties of the brain but otherwise randomise its connectivity. We perform a comparative analysis of a connectivity map of the cortical connectome both on high- and low-resolutions utilising three different types of surrogate networks: spatially unconstrained (‘random’), connection length preserving (‘spatial’), and connection length optimised (‘reduced’) surrogates. We find that unconstrained randomisation markedly diminishes all investigated architectural properties of cortical connectivity. By contrast, spatial and reduced surrogates largely preserve most properties and, interestingly, often more so in the reduced surrogates. Specifically, our results suggest that the cortical network is less tightly integrated than its spatial constraints would allow, but more strongly segregated than its spatial constraints would necessitate. We additionally find that hierarchical organisation and rich-club structure of the cortical connectivity are largely preserved in spatial and reduced surrogates and hence may be partially attributable to cortical wiring constraints. In contrast, the high modularity and strong s-core of the high-resolution cortical network are significantly stronger than in the surrogates, underlining their potential functional relevance in the brain.     

Probabilistic Clustering of the Human Connectome Identifies Communities and Hubs

A fundamental assumption in neuroscience is that brain function is constrained by its structural properties. This motivates the idea that the brain can be parcellated into functionally coherent regions based on anatomical connectivity patterns that capture how different areas are interconnected. Several studies have successfully implemented this idea in humans using diffusion weighted MRI, allowing parcellation to be conducted in vivo. Two distinct approaches to connectivity-based parcellation can be identified. The first uses the connection profiles of brain regions as a feature vector, and groups brain regions with similar connection profiles together. Alternatively, one may adopt a network perspective that aims to identify clusters of brain regions that show dense within-cluster and sparse between-cluster connectivity. In this paper, we introduce a probabilistic model for connectivity-based parcellation that unifies both approaches. Using the model we are able to obtain a parcellation of the human brain whose clusters may adhere to either interpretation. We find that parts of the connectome consistently cluster as densely connected components, while other parts consistently result in clusters with similar connections. Interestingly, the densely connected components consist predominantly of major cortical areas, while the clusters with similar connection profiles consist of regions that have previously been identified as the ‘rich club’; regions known for their integrative role in connectivity. Furthermore, the probabilistic model allows quantification of the uncertainty in cluster assignments. We show that, while most clusters are clearly delineated, some regions are more difficult to assign. These results indicate that care should be taken when interpreting connectivity-based parcellations obtained using alternative deterministic procedures.     

Fronto-Parietal Connectivity Is a Non-Static Phenomenon with Characteristic Changes during Unconsciousness

Background

It has been previously shown that loss of consciousness is associated with a breakdown of dominating fronto-parietal feedback connectivity as assessed by electroencephalogram (EEG) recordings. Structure and strength of network connectivity may change over time. Aim of the current study is to investigate cortico-cortical connectivity at different time intervals during consciousness and unconsciousness. For this purpose, EEG symbolic transfer entropy (STEn) was calculated to indicate cortico-cortical information transfer at different transfer times.

Methods

The study was performed in 15 male volunteers. 29-channel EEG was recorded during consciousness and propofol-induced unconsciousness. EEG data were analyzed by STEn, which quantifies intensity and directionality of the mutual information flow between two EEG channels. STEn was computed over fronto-parietal channel pair combinations (10 s length, 0.5–45 Hz total bandwidth) to analyze changes of intercortical directional connectivity. Feedback (fronto → parietal) and feedforward (parieto → frontal) connectivity was calculated for transfer times from 25 ms to 250 ms in 5 ms steps. Transfer times leading to maximum directed interaction were identified to detect changes of cortical information transfer (directional connectivity) induced by unconsciousness (p<0.05).

Results

The current analyses show that fronto-parietal connectivity is a non-static phenomenon. Maximum detected interaction occurs at decreased transfer times during propofol-induced unconsciousness (feedback interaction: 60 ms to 40 ms, p = 0.002; feedforward interaction: 65 ms to 45 ms, p = 0.001). Strength of maximum feedback interaction decreases during unconsciousness (p = 0.026), while no effect of propofol was observed on feedforward interaction. During both consciousness and unconsciousness, intensity of fronto-parietal interaction fluctuates with increasing transfer times.

Conclusion

Non-stationarity of directional connectivity may play a functional role for cortical network communication as it shows characteristic changes during propofol-induced unconsciousness.     

LiCl-induced sickness modulates rat gustatory cortical responses

Gustatory cortex (GC), a structure deeply involved in the making of consumption decisions, presumably performs this function by integrating information about taste, experiences, and internal states related to the animal’s health, such as illness. Here, we investigated this assertion, examining whether illness is represented in GC activity, and how this representation impacts taste responses and behavior. We recorded GC single-neuron activity and local field potentials (LFPs) from healthy rats and rats made ill (via LiCl injection). We show (consistent with the extant literature) that the onset of illness-related behaviors arises contemporaneously with alterations in 7 to 12 Hz LFP power at approximately 12 min following injection. This process was accompanied by reductions in single-neuron taste response magnitudes and discriminability, and with enhancements in palatability-relatedness—a result reflecting the collapse of responses toward a simple “good-bad” code visible in the entire sample, but focused on a specific subset of GC neurons. Overall, our data show that a state (illness) that profoundly reduces consumption changes basic properties of the sensory cortical response to tastes, in a manner that can easily explain illness’ impact on consumption.

Sickness is an internal state that impacts consumption, and so could be expected to influence the neural processing of tastes. This study shows that onset of illness changes basic properties of gustatory cortical network processing and taste responses, such that activity comes more purely to reflect the "goodness" or "badness" of tastes.     

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.