A neurophysiologically-based mathematical model of flash visual evoked potentials

Adaptive fuzzy iterative learning control based neurostimulation system and in-silico evaluation

Closed-loop neural stimulation has been an effective treatment for epilepsy patients. Currently, most closed-loop neural stimulation strategies are designed based on accurate neural models. However, the uncertainty and complexity of the neural system make it difficult to build an accurate neural model, which poses a significant challenge to the design of the controller. This paper proposes an Adaptive Fuzzy Iterative Learning Control (AFILC) framework for closed-loop neural stimulation, which can realize neuromodulation with no model or model uncertainty. Recognizing the periodic characteristics of neural stimulation and neuronal firing, Iterative Learning Control (ILC) is employed as the primary controller. Furthermore, a fuzzy optimization module is established to update the internal parameters of the ILC controller in real-time. This module enhances the anti-interference ability of the control system and reduces the influence of initial controller parameters on the control process. The efficacy of this strategy is evaluated using a neural computational model. The simulation results validate the capability of the AFILC strategy to suppress epileptic states. Compared with ILC-based closed-loop neurostimulation schemes, the AFILC-based neurostimulation strategy has faster convergence speed and stronger anti-interference ability. Moreover, the control algorithm is implemented based on a digital signal processor, and the hardware-in-the-loop experimental platform is implemented. The experimental results show that the control method has good control performance and computational efficiency, which provides the possibility for future application in clinical research.

Recent Progress in Brain Network Models for Medical Applications: A Review

Importance: Pathological perturbations of the brain often spread via connectome to fundamentally alter functional consequences. By integrating multimodal neuroimaging data with mathematical neural mass modeling, brain network models (BNMs) enable to quantitatively characterize aberrant network dynamics underlying multiple neurological and psychiatric disorders. We delved into the advancements of BNM-based medical applications, discussed the prevalent challenges within this field, and provided possible solutions and future directions. Highlights: This paper reviewed the theoretical foundations and current medical applications of computational BNMs. Composed of neural mass models, the BNM framework allows to investigate large-scale brain dynamics behind brain diseases by linking the simulated functional signals to the empirical neurophysiological data, and has shown promise in exploring neuropathological mechanisms, elucidating therapeutic effects, and predicting disease outcome. Despite that several limitations existed, one promising trend of this research field is to precisely guide clinical neuromodulation treatment based on individual BNM simulation. Conclusion: BNM carries the potential to help understand the mechanism underlying how neuropathology affects brain network dynamics, further contributing to decision-making in clinical diagnosis and treatment. Several constraints must be addressed and surmounted to pave the way for its utilization in the clinic.

Criticality and partial synchronization analysis in Wilson-Cowan and Jansen-Rit neural mass models

Synchronization is a phenomenon observed in neuronal networks involved in diverse brain activities. Neural mass models such as Wilson-Cowan (WC) and Jansen-Rit (JR) manifest synchronized states. Despite extensive research on these models over the past several decades, their potential of manifesting second-order phase transitions (SOPT) and criticality has not been sufficiently acknowledged. In this study, two networks of coupled WC and JR nodes with small-world topologies were constructed and Kuramoto order parameter (KOP) was used to quantify the amount of synchronization. In addition, we investigated the presence of SOPT using the synchronization coefficient of variation. Both networks reached high synchrony by changing the coupling weight between their nodes. Moreover, they exhibited abrupt changes in the synchronization at certain values of the control parameter not necessarily related to a phase transition. While SOPT was observed only in JR model, neither WC nor JR model showed power-law behavior. Our study further investigated the global synchronization phenomenon that is known to exist in pathological brain states, such as seizure. JR model showed global synchronization, while WC model seemed to be more suitable in producing partially synchronized patterns.

Simulated dynamical transitions in a heterogeneous marmoset pFC cluster

Network analysis of the marmoset cortical connectivity data indicates a significant 3D cluster in and around the pre-frontal cortex. A multi-node, heterogeneous neural mass model of this six-node cluster was constructed. Its parameters were informed by available experimental and simulation data so that each neural mass oscillated in a characteristic frequency band. Nodes were connected with directed, weighted links derived from the marmoset structural connectivity data. Heterogeneity arose from the different link weights and model parameters for each node. Stimulation of the cluster with an incident pulse train modulated in the standard frequency bands induced a variety of dynamical state transitions that lasted in the range of 5-10 s, suggestive of timescales relevant to short-term memory. A short gamma burst rapidly reset the beta-induced transition. The theta-induced transition state showed a spontaneous, delayed reset to the resting state. An additional, continuous gamma wave stimulus induced a new beating oscillatory state. Longer or repeated gamma bursts were phase-aligned with the beta oscillation, delivering increasing energy input and causing shorter transition times. The relevance of these results to working memory is yet to be established, but they suggest interesting opportunities.

EEG generation mechanism of lower limb active movement intention and its virtual reality induction enhancement: a preliminary study

Introduction

Active rehabilitation requires active neurological participation when users use rehabilitation equipment. A brain-computer interface (BCI) is a direct communication channel for detecting changes in the nervous system. Individuals with dyskinesia have unclear intentions to initiate movement due to physical or psychological factors, which is not conducive to detection. Virtual reality (VR) technology can be a potential tool to enhance the movement intention from pre-movement neural signals in clinical exercise therapy. However, its effect on electroencephalogram (EEG) signals is not yet known. Therefore, the objective of this paper is to construct a model of the EEG signal generation mechanism of lower limb active movement intention and then investigate whether VR induction could improve movement intention detection based on EEG.

Methods

Firstly, a neural dynamic model of lower limb active movement intention generation was established from the perspective of signal transmission and information processing. Secondly, the movement-related EEG signal was calculated based on the model, and the effect of VR induction was simulated. Movement-related cortical potential (MRCP) and event-related desynchronization (ERD) features were extracted to analyze the enhancement of movement intention. Finally, we recorded EEG signals of 12 subjects in normal and VR environments to verify the effectiveness and feasibility of the above model and VR induction enhancement of lower limb active movement intention for individuals with dyskinesia.

Results

Simulation and experimental results show that VR induction can effectively enhance the EEG features of subjects and improve the detectability of movement intention.

Discussion

The proposed model can simulate the EEG signal of lower limb active movement intention, and VR induction can enhance the early and accurate detectability of lower limb active movement intention. It lays the foundation for further robot control based on the actual needs of users.

Addressing Global Environmental Challenges to Mental Health Using Population Neuroscience: A Review

Importance

Climate change, pollution, urbanization, socioeconomic inequality, and psychosocial effects of the COVID-19 pandemic have caused massive changes in environmental conditions that affect brain health during the life span, both on a population level as well as on the level of the individual. How these environmental factors influence the brain, behavior, and mental illness is not well known.

Observations

A research strategy enabling population neuroscience to contribute to identify brain mechanisms underlying environment-related mental illness by leveraging innovative enrichment tools for data federation, geospatial observation, climate and pollution measures, digital health, and novel data integration techniques is described. This strategy can inform innovative treatments that target causal cognitive and molecular mechanisms of mental illness related to the environment. An example is presented of the environMENTAL Project that is leveraging federated cohort data of over 1.5 million European citizens and patients enriched with deep phenotyping data from large-scale behavioral neuroimaging cohorts to identify brain mechanisms related to environmental adversity underlying symptoms of depression, anxiety, stress, and substance misuse.

Conclusions and Relevance

This research will lead to the development of objective biomarkers and evidence-based interventions that will significantly improve outcomes of environment-related mental illness.

Model Parameter Estimation As Features to Predict the Duration of Epileptic Seizures From Onset

The durations of epileptic seizures are linked to severity and risk for patients. It is unclear if the spatiotemporal evolution of a seizure has any relationship with its duration. Understanding such mechanisms may help reveal treatments for reducing the duration of a seizure. Here, we present a novel method to predict whether a seizure is going to be short or long at its onset using features that can be interpreted in the parameter space of a brain model. The parameters of a Jansen-Rit neural mass model were tracked given intracranial electroencephalography (iEEG) signals, and were processed as time series features using MINIROCKET. By analysing 2954 seizures from 10 patients, patient-specific classifiers were built to predict if a seizure would be short or long given 7 s of iEEG at seizure onset. The method achieved an area under the receiver operating characteristic curve (AUC) greater than 0.6 for five of 10 patients. The behaviour in the parameter space has shown different mechanisms are associated with short/long seizures.Clinical relevance-This shows that it is possible to classify whether a seizure will be short or long based on its early characteristics. Timely interventions and treatments can be applied if the duration of the seizures can be predicted.

Electrophysiological and Behavioral Effects of Alpha-Band Sensory Entrainment: Neural Mechanisms and Clinical Applications

Alpha-band (7-13 Hz) activity has been linked to visuo-attentional performance in healthy participants and to impaired functionality of the visual system in a variety of clinical populations including patients with acquired posterior brain lesion and neurodevelopmental and psychiatric disorders. Crucially, several studies suggested that short uni- and multi-sensory rhythmic stimulation (i.e., visual, auditory and audio-visual) administered in the alpha-band effectively induces transient changes in alpha oscillatory activity and improvements in visuo-attentional performance by synchronizing the intrinsic brain oscillations to the external stimulation (neural entrainment). The present review aims to address the current state of the art on the alpha-band sensory entrainment, outlining its potential functional effects and current limitations. Indeed, the results of the alpha-band entrainment studies are currently mixed, possibly due to the different stimulation modalities, task features and behavioral and physiological measures employed in the various paradigms. Furthermore, it is still unknown whether prolonged alpha-band sensory entrainment might lead to long-lasting effects at a neural and behavioral level. Overall, despite the limitations emerging from the current literature, alpha-band sensory entrainment may represent a promising and valuable tool, inducing functionally relevant changes in oscillatory activity, with potential rehabilitative applications in individuals characterized by impaired alpha activity.

Accurate and Efficient Simulation of Very High-Dimensional Neural Mass Models with Distributed-Delay Connectome Tensors

This paper introduces methods and a novel toolbox that efficiently integrates high-dimensional Neural Mass Models (NMMs) specified by two essential components. The first is the set of nonlinear Random Differential Equations (RDEs) of the dynamics of each neural mass. The second is the highly sparse three-dimensional Connectome Tensor (CT) that encodes the strength of the connections and the delays of information transfer along the axons of each connection. To date, simplistic assumptions prevail about delays in the CT, often assumed to be Dirac-delta functions. In reality, delays are distributed due to heterogeneous conduction velocities of the axons connecting neural masses. These distributed-delay CTs are challenging to model. Our approach implements these models by leveraging several innovations. Semi-analytical integration of RDEs is done with the Local Linearization (LL) scheme for each neural mass model, ensuring dynamical fidelity to the original continuous-time nonlinear dynamic. This semi-analytic LL integration is highly computationally-efficient. In addition, a tensor representation of the CT facilitates parallel computation. It also seamlessly allows modeling distributed delays CT with any level of complexity or realism. This ease of implementation includes models with distributed-delay CTs. Consequently, our algorithm scales linearly with the number of neural masses and the number of equations they are represented with, contrasting with more traditional methods that scale quadratically at best. To illustrate the toolbox's usefulness, we simulate a single Zetterberg-Jansen-Rit (ZJR) cortical column, a single thalmo-cortical unit, and a toy example comprising 1000 interconnected ZJR columns. These simulations demonstrate the consequences of modifying the CT, especially by introducing distributed delays. The examples illustrate the complexity of explaining EEG oscillations, e.g., split alpha peaks, since they only appear for distinct neural masses. We provide an open-source Script for the toolbox.

A physical neural mass model framework for the analysis of oscillatory generators from laminar electrophysiological recordings

Cortical function emerges from the interactions of multi-scale networks that may be studied at a high level using neural mass models (NMM) that represent the mean activity of large numbers of neurons. Here, we provide first a new framework called laminar NMM, or LaNMM for short, where we combine conduction physics with NMMs to simulate electrophysiological measurements. Then, we employ this framework to infer the location of oscillatory generators from laminar-resolved data collected from the prefrontal cortex in the macaque monkey. We define a minimal model capable of generating coupled slow and fast oscillations, and we optimize LaNMM-specific parameters to fit multi-contact recordings. We rank the candidate models using an optimization function that evaluates the match between the functional connectivity (FC) of the model and data, where FC is defined by the covariance between bipolar voltage measurements at different cortical depths. The family of best solutions reproduces the FC of the observed electrophysiology by selecting locations of pyramidal cells and their synapses that result in the generation of fast activity at superficial layers and slow activity across most depths, in line with recent literature proposals. In closing, we discuss how this hybrid modeling framework can be more generally used to infer cortical circuitry.

Complex spatiotemporal oscillations emerge from transverse instabilities in large-scale brain networks

Spatiotemporal oscillations underlie all cognitive brain functions. Large-scale brain models, constrained by neuroimaging data, aim to trace the principles underlying such macroscopic neural activity from the intricate and multi-scale structure of the brain. Despite substantial progress in the field, many aspects about the mechanisms behind the onset of spatiotemporal neural dynamics are still unknown. In this work we establish a simple framework for the emergence of complex brain dynamics, including high-dimensional chaos and travelling waves. The model consists of a complex network of 90 brain regions, whose structural connectivity is obtained from tractography data. The activity of each brain area is governed by a Jansen neural mass model and we normalize the total input received by each node so it amounts the same across all brain areas. This assumption allows for the existence of an homogeneous invariant manifold, i.e., a set of different stationary and oscillatory states in which all nodes behave identically. Stability analysis of these homogeneous solutions unveils a transverse instability of the synchronized state, which gives rise to different types of spatiotemporal dynamics, such as chaotic alpha activity. Additionally, we illustrate the ubiquity of this route towards complex spatiotemporal activity in a network of next generation neural mass models. Altogehter, our results unveil the bifurcation landscape that underlies the emergence of function from structure in the brain.

Comparison between an exact and a heuristic neural mass model with second-order synapses

Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear transfer function (NMM1). However, a recent exact mean-field theory for quadratic integrate-and-fire (QIF) neurons challenges this view by showing that the mean firing rate is not a static function of the neuronal state but follows two coupled nonlinear differential equations (NMM2). Here we analyze and compare these two descriptions in the presence of second-order synaptic dynamics. First, we derive the mathematical equivalence between the two models in the infinitely slow synapse limit, i.e., we show that NMM1 is an approximation of NMM2 in this regime. Next, we evaluate the applicability of this limit in the context of realistic physiological parameter values by analyzing the dynamics of models with inhibitory or excitatory synapses. We show that NMM1 fails to reproduce important dynamical features of the exact model, such as the self-sustained oscillations of an inhibitory interneuron QIF network. Furthermore, in the exact model but not in the limit one, stimulation of a pyramidal cell population induces resonant oscillatory activity whose peak frequency and amplitude increase with the self-coupling gain and the external excitatory input. This may play a role in the enhanced response of densely connected networks to weak uniform inputs, such as the electric fields produced by noninvasive brain stimulation.

The distribution and heterogeneity of excitability in focal epileptic network potentially contribute to the seizure propagation

Introduction

Existing dynamical models can explain the transmigration mechanisms involved in seizures but are limited to a single modality. Combining models with networks can reproduce scaled epileptic dynamics. And the structure and coupling interactions of the network, as well as the heterogeneity of both the node and network activities, may influence the final state of the network model.

Methods

We built a fully connected network with focal nodes prominently interacting and established a timescale separated epileptic network model. The factors affecting epileptic network seizure were explored by varying the connectivity patterns of focal network nodes and modulating the distribution of network excitability.

Results

The whole brain network topology as the brain activity foundation affects the consistent delayed clustering seizure propagation. In addition, the network size and distribution heterogeneity of the focal excitatory nodes can influence seizure frequency. With the increasing of the network size and averaged excitability level of focal network, the seizure period decreases. In contrast, the larger heterogeneity of excitability for focal network nodes can lower the functional activity level (average degree) of focal network. There are also subtle effects of focal network topologies (connection patterns of excitatory nodes) that cannot be ignored along with non-focal nodes.

Discussion

Unraveling the role of excitatory factors in seizure onset and propagation can be used to understand the dynamic mechanisms and neuromodulation of epilepsy, with profound implications for the treatment of epilepsy and even for the understanding of the brain.

Control of epileptic activities in a cortex network of multiple coupled neural populations under electromagnetic induction

Epilepsy is believed to be associated with the abnormal synchronous neuronal activity in the brain, which results from large groups or circuits of neurons. In this paper, we choose to focus on the temporal lobe epilepsy, and establish a cortex network of multiple coupled neural populations to explore the epileptic activities under electromagnetic induction. We demonstrate that the epileptic activities can be controlled and modulated by electromagnetic induction and coupling among regions. In certain regions, these two types of control are observed to show exactly reverse effects. The results show that the strong electromagnetic induction is conducive to eliminating the epileptic seizures. The coupling among regions has a conduction effect that the previous normal background activity of the region gives way to the epileptic discharge, owing to coupling with spike wave discharge regions. Overall, these results highlight the role of electromagnetic induction and coupling among the regions in controlling and modulating epileptic activities, and might provide novel insights into the treatments of epilepsy.

Decreased coherence in the model of the dorsal visual pathway associated with Alzheimer's disease

Decreased coherence in electroencephalogram (EEG) has been reported in Alzheimer's disease (AD) experimentally, which could be considered as a typical electrophysiological characteristic in AD. This work aimed to investigate the effect of AD on coherence in the dorsal visual pathway by the technique of neurocomputation. Firstly, according to the hierarchical organization of the cerebral cortex and the information flows of the dorsal visual pathway, a more physiologically plausible neural mass model including cortical areas v1, v2, and v5 was established in the dorsal visual pathway. The three interconnected cortical areas were connected by ascending and descending projections. Next, the pathological condition of loss of long synaptic projections in AD was simulated by reducing the parameters of long synaptic projections in the model. Then, the loss of long synaptic projections on coherence among different visual cortex areas was explored by means of power spectral analysis and coherence function. The results demonstrate that the coherence between these interconnected cortical areas showed an obvious decline with the gradual decrease of long synaptic projections, i.e. decrease in descending projections from area v2 to v1 and v5 to v2 and ascending projection from area v2 to v5. Hopefully, the results of this study could provide theoretical guidance for understanding the dynamical mechanism of AD.

Whole-brain modeling explains the context-dependent effects of cholinergic neuromodulation

Integration and segregation are two fundamental principles of brain organization. The brain manages the transitions and balance between different functional segregated or integrated states through neuromodulatory systems. Recently, computational and experimental studies suggest a pro-segregation effect of cholinergic neuromodulation. Here, we studied the effects of the cholinergic system on brain functional connectivity using both empirical fMRI data and computational modeling. First, we analyzed the effects of nicotine on functional connectivity and network topology in healthy subjects during resting-state conditions and during an attentional task. Then, we employed a whole-brain neural mass model interconnected using a human connectome to simulate the effects of nicotine and investigate causal mechanisms for these changes. The drug effect was modeled decreasing both the global coupling and local feedback inhibition parameters, consistent with the known cellular effects of acetylcholine. We found that nicotine incremented functional segregation in both empirical and simulated data, and the effects are context-dependent: observed during the task, but not in the resting state. In-task performance correlates with functional segregation, establishing a link between functional network topology and behavior. Furthermore, we found in the empirical data that the regional density of the nicotinic acetylcholine α₄β₂ correlates with the decrease in functional nodal strength by nicotine during the task. Our results confirm that cholinergic neuromodulation promotes functional segregation in a context-dependent fashion, and suggest that this segregation is suited for simple visual-attentional tasks.

Development of Mechanistic Neural Mass (mNM) Models that Link Physiology to Mean-Field Dynamics

Brain rhythms emerge from the mean-field activity of networks of neurons. There have been many efforts to build mathematical and computational embodiments in the form of discrete cell-group activities-termed neural masses-to understand in particular the origins of evoked potentials, intrinsic patterns of activities such as theta, regulation of sleep, Parkinson's disease related dynamics, and mimic seizure dynamics. As originally utilized, standard neural masses convert input through a sigmoidal function to a firing rate, and firing rate through a synaptic alpha function to other masses. Here we define a process to build mechanistic neural masses (mNMs) as mean-field models of microscopic membrane-type (Hodgkin Huxley type) models of different neuron types that duplicate the stability, firing rate, and associated bifurcations as function of relevant slow variables - such as extracellular potassium - and synaptic current; and whose output is both firing rate and impact on the slow variables - such as transmembrane potassium flux. Small networks composed of just excitatory and inhibitory mNMs demonstrate expected dynamical states including firing, runaway excitation and depolarization block, and these transitions change in biologically observed ways with changes in extracellular potassium and excitatory-inhibitory balance.

Structure-function models of temporal, spatial, and spectral characteristics of non-invasive whole brain functional imaging

We review recent advances in using mathematical models of the relationship between the brain structure and function that capture features of brain dynamics. We argue the need for models that can jointly capture temporal, spatial, and spectral features of brain functional activity. We present recent work on spectral graph theory based models that can accurately capture spectral as well as spatial patterns across multiple frequencies in MEG reconstructions.

A personalizable autonomous neural mass model of epileptic seizures

Work in the last two decades has shown that neural mass models (NMM) can realistically reproduce and explain epileptic seizure transitions as recorded by electrophysiological methods (EEG, SEEG). In previous work, advances were achieved by increasing excitation and heuristically varying network inhibitory coupling parameters in the models. Based on these early studies, we provide a laminar NMM capable of realistically reproducing the electrical activity recorded by SEEG in the epileptogenic zone during interictal to ictal states. With the exception of the external noise input into the pyramidal cell population, the model dynamics are autonomous. By setting the system at a point close to bifurcation, seizure-like transitions are generated, including pre-ictal spikes, low voltage fast activity, and ictal rhythmic activity. A novel element in the model is a physiologically motivated algorithm for chloride dynamics: the gain of GABAergic post-synaptic potentials is modulated by the pathological accumulation of chloride in pyramidal cells due to high inhibitory input and/or dysfunctional chloride transport. In addition, in order to simulate SEEG signals for comparison with real seizure recordings, the NMM is embedded first in a layered model of the neocortex and then in a realistic physical model. We compare modeling results with data from four epilepsy patient cases. By including key pathophysiological mechanisms, the proposed framework captures succinctly the electrophysiological phenomenology observed in ictal states, paving the way for robust personalization methods based on NMMs.

Intensity dependence of sub-harmonics in cortical response to photic stimulation

Objective. Periodic photic stimulation of human volunteers at 10 Hz is known to entrain their Electroencephalography (EEG) signals. This entrainment manifests as an increment in power at 10, 20, 30 Hz. We observed that this entrainment is accompanied by the emergence of sub-harmonics, but only at specific frequencies and higher intensities of the stimulating signal. Thereafter, we describe our results and explain them using the physiologically inspired Jansen and Rit Neural Mass Model (NMM).Approach. Four human volunteers were separately exposed to both high and low intensity 10 Hz and 6 Hz stimulation. A total of 4 experiments per subject were therefore performed. Simulations and bifurcation analysis of the NMM were carried out and compared with the experimental findings. <i> Main results. High intensity 10 Hz stimulation led to an increment in power at 5 Hz across all the 4 subjects. No increment of power was observed with low intensity stimulation. However, when the same protocol was repeated with a 6 Hz photic stimulation, neither high nor low intensity stimulation were found to cause a discernible change in power at 3 Hz. We found that the NMM was able to recapitulate these results. A further numerical analysis indicated that this arises from the underlying bifurcation structure of the NMM. <i> Significance. The excellent match between theory and experiment suggest that the bifurcation properties of the NMM are mirroring similar features possessed by the actual neural masses producing the EEG dynamics. Neural Mass Models could thus be valuable for understanding properties and pathologies of EEG dynamics, and may contribute to the engineering of brain-computer interface technologies.

Modelling neural entrainment and its persistence: influence of frequency of stimulation and phase at the stimulus offset

Neural entrainment, the synchronization of brain oscillations to the frequency of an external stimuli, is a key mechanism that shapes perceptual and cognitive processes.Objective.Using simulations, we investigated the dynamics of neural entrainment, particularly the period following the end of the stimulation, since the persistence (reverberation) of neural entrainment may condition future sensory representations based on predictions about stimulus rhythmicity.Methods.Neural entrainment was assessed using a modified Jansen-Rit neural mass model (NMM) of coupled cortical columns, in which the spectral features of the output resembled that of the electroencephalogram (EEG). We evaluated spectro-temporal features of entrainment as a function of the stimulation frequency, the resonant frequency of the neural populations comprising the NMM, and the coupling strength between cortical columns. Furthermore, we tested if the entrainment persistence depended on the phase of the EEG-like oscillation at the time the stimulus ended.Main Results.The entrainment of the column that received the stimulation was maximum when the frequency of the entrainer was within a narrow range around the resonant frequency of the column. When this occurred, entrainment persisted for several cycles after the stimulus terminated, and the propagation of the entrainment to other columns was facilitated. Propagation also depended on the resonant frequency of the second column, and the coupling strength between columns. The duration of the persistence of the entrainment depended on the phase of the neural oscillation at the time the entrainer terminated, such that falling phases (fromπ/2 to 3π/2 in a sine function) led to longer persistence than rising phases (from 0 toπ/2 and 3π/2 to 2π).Significance.The study bridges between models of neural oscillations and empirical electrophysiology, providing insights to the mechanisms underlying neural entrainment and the use of rhythmic sensory stimulation for neuroenhancement.

Brain simulation augments machine-learning-based classification of dementia

Introduction

Computational brain network modeling using The Virtual Brain (TVB) simulation platform acts synergistically with machine learning (ML) and multi-modal neuroimaging to reveal mechanisms and improve diagnostics in Alzheimer's disease (AD).

Methods

We enhance large-scale whole-brain simulation in TVB with a cause-and-effect model linking local amyloid beta (Aβ) positron emission tomography (PET) with altered excitability. We use PET and magnetic resonance imaging (MRI) data from 33 participants of the Alzheimer's Disease Neuroimaging Initiative (ADNI3) combined with frequency compositions of TVB-simulated local field potentials (LFP) for ML classification.

Results

The combination of empirical neuroimaging features and simulated LFPs significantly outperformed the classification accuracy of empirical data alone by about 10% (weighted F1-score empirical 64.34% vs. combined 74.28%). Informative features showed high biological plausibility regarding the AD-typical spatial distribution.

Discussion

The cause-and-effect implementation of local hyperexcitation caused by Aβ can improve the ML-driven classification of AD and demonstrates TVB's ability to decode information in empirical data using connectivity-based brain simulation.

Mechanism analysis for excitatory interneurons dominating poly-spike wave and optimization of electrical stimulation

In addition to inhibitory interneurons, there exist excitatory interneurons (EINs) in the cortex, which mainly have excitatory projections to pyramidal neurons. In this study, we improve a thalamocortical model by introducing EIN, investigate the dominant role of EIN in generating spike and slow wave discharges (SWDs), and consider a non-rectangular pulse to control absence seizures. First, we display here that the improved model can reproduce typical SWDs of absence seizures. Moreover, we focus on the function of EIN by means of bifurcation analysis and find that EIN can induce transition behaviors under Hopf-type and fold limit cycle bifurcations. Specifically, the system has three stable solutions composing a tri-stable region. In this region, there are three attraction basins, which hints that external stimulation can drive the system trajectory from one basin to another, thereby eliminating abnormal oscillations. Furthermore, we compare the increasing ramp with rectangular pulse and optimize stimulation waveforms from the perspective of electrical charges input. The controlling role of the single increasing ramp to absence seizures is remarkable and the optimal stimulus parameters have been found theoretically. This work provides a computational model containing EIN and a theoretical basis for future physiological experiments and clinical research studies.

Using a new phase-locked visual feedback protocol to affirm simpler models for alpha dynamics

Alpha band oscillations are the most prominent rhythmic oscillations in EEG, which are related to various types of mental diseases, such as attention deficit hyperactivity disorder, anxiety, and depression. However, the dynamics of alpha oscillations, especially how the endogenous alpha oscillations be entrained by exogenous stimulus, are still unclear. Recently, a newly-developed phase-locked visual feedback (PLVF) protocol has shown effectiveness in modulating alpha rhythm, which provides empirical evidence for the further investigation of the neural mechanism of alpha dynamics. In this work, extensive numerical simulations based on four well-studied models were used to investigate the questions that (1) What kind of dynamic model exhibits a modulation phenomenon of PLVF? (2) What is the dynamic mechanism of PLVF for alpha modulation? (3) Which factors affect the modulation effects in PLVF? The result indicates that the dynamics of endogenous alpha oscillations are close to a simpler dynamic structure, like fixed-point attractor or limit-cycle attractor, which shows a global consistent dynamic behavior at different phases of the alpha oscillation. The further analysis explains the dynamic mechanism of PLVF for amplitude and frequency modulation of the alpha rhythm, as well as the influence of parameter settings in the modulation. All these findings provide a deeper understanding of the endogenous alpha oscillations entrained by exogenous phased locked visual stimulus and lead in turn to the refinement of a control strategy for alpha modulation, which could potentially be used in developing new neural modulation methods for cognitive enhancement and mental diseases treatment.

Realizing the Application of EEG Modeling in BCI Classification: Based on a Conditional GAN Converter

Electroencephalogram (EEG) modeling in brain-computer interface (BCI) provides a theoretical foundation for its development. However, limited by the lack of guidelines in model parameter selection and the inability to obtain personal tissue information in practice, EEG modeling in BCI is mainly focused on the theoretical qualitative level which shows a gap between the theory and its application. Based on such problems, this work combined the surface EEG simulation with a converter based on the generative adversarial network (GAN), to establish the connection from simulated EEG to its application in BCI classification. For the scalp EEGs modeling, a mathematical model was built according to the physics of surface EEG, which consisted of the parallel 3-population neural mass model, the equivalent dipole, and the forward computation. For application, a converter based on the conditional GAN was designed, to transfer the simulated theoretical-only EEG to its practical version, in the lack of individual bio-information. To verify the feasibility, based on the latest microexpression-assisted BCI paradigm proposed by our group, the converted simulated EEGs were used in the training of BCI classifiers. The results indicated that, compared with training with insufficient real data, by adding the simulated EEGs, the overall performance showed a significant improvement (P = 0.04 < 0.05), and the test performance can be improved by 2.17% ± 4.23, in which the largest increase was up to 12.60% ± 1.81. Through this work, the link from theoretical EEG simulation to BCI classification has been initially established, providing an enhanced novel solution for the application of EEG modeling in BCI.

Parcellation-induced variation of empirical and simulated brain connectomes at group and subject levels

Recent developments of whole-brain models have demonstrated their potential when investigating resting-state brain activity. However, it has not been systematically investigated how alternating derivations of the empirical structural and functional connectivity, serving as the model input, from MRI data influence modeling results. Here, we study the influence from one major element: the brain parcellation scheme that reduces the dimensionality of brain networks by grouping thousands of voxels into a few hundred brain regions. We show graph-theoretical statistics derived from the empirical data and modeling results exhibiting a high heterogeneity across parcellations. Furthermore, the network properties of empirical brain connectomes explain the lion’s share of the variance in the modeling results with respect to the parcellation variation. Such a clear-cut relationship is not observed at the subject-resolved level per parcellation. Finally, the graph-theoretical statistics of the simulated connectome correlate with those of the empirical functional connectivity across parcellations. However, this relation is not one-to-one, and its precision can vary between models. Our results imply that network properties of both empirical connectomes can explain the goodness-of-fit of whole-brain models to empirical data at a global group level but not at a single-subject level, which provides further insights into the personalization of whole-brain models.

The structural and functional connectivities of the brain, which reflect the anatomical connections of axonal bundles and the amount of coactivation between brain regions, respectively, only weakly correlate with each other. In order to enhance and investigate this relationship, large-scale whole-brain dynamical models were involved in this branch of research. However, how the definitions of the brain regions parcellated according to a so-called brain atlas influence these models has so far not been systematically assessed. In this article, we show that this influence can be large, and link group-averaged, atlas-induced deviations to network properties extracted from both types of connectivity. Additionally, we demonstrate that the same association does not apply to subject-specific variations. These results may contribute to the further personalization of the whole-brain models.

Synchronization of nonlinearly coupled networks based on circle criterion

The problem of synchronization in networks of linear systems with nonlinear diffusive coupling and a connected undirected graph is studied. By means of a coordinate transformation, the system is reduced to the form of mean-field dynamics and a synchronization-error system. The network synchronization conditions are established based on the stability conditions of the synchronization-error system obtained using the circle criterion, and the results are used to derive the condition for synchronization in a network of neural-mass-model populations with a connected undirected graph. Simulation examples are presented to illustrate the obtained results.

Delayed Feedback-Based Suppression of Pathological Oscillations in a Neural Mass Model

Suppression of excessively synchronous beta frequency (12-35 Hz) oscillatory activity in the basal ganglia is believed to correlate with the alleviation of hypokinetic motor symptoms of the Parkinson's disease. Delayed feedback is an effective strategy to interrupt the synchronization and has been used in the design of closed-loop neuromodulation methods computationally. Although tremendous efforts in this are being made by optimizing delayed feedback algorithm and stimulation waveforms, there are still remaining problems in the selection of effective parameters in the delayed feedback control schemes. In most delayed feedback neuromodulation strategies, the stimulation signal is obtained from the local field potential (LFP) of the excitatory subthalamic nucleus (STN) neurons and then is administered back to STN itself only. The inhibitory external globus pallidus (GPe) nucleus in the excitatory-inhibitory STN-GPe reciprocal network has not been involved in the design of the delayed feedback control strategies. Thus, considering the role of GPe, this paper proposes three schemes involving GPe in the design of the delayed feedback strategies and compared their effectiveness to the traditional paradigm using STN only. Based on a neural mass model of STN-GPe network having capability of simulating the LFP directly, the proposed stimulation strategies are tested and compared. Our simulation results show that the four types of delayed feedback control schemes are all effective, even if with a simple linear delayed feedback algorithm. But the three new control strategies we propose here further improve the control performance by enlarging the oscillatory suppression space and reducing the energy expenditure, suggesting that they may be more effective in applications. This paper may guide a new approach to optimize the closed-loop deep brain stimulation treatment to alleviate the Parkinsonian state by retargeting the measurement and stimulation nucleus.

Control of epileptic seizures by electrical stimulation: a model-based study

High frequency electrical stimulation of brain is commonly used in research experiments and clinical trials as a modern tool for control of epileptic seizures. However, the mechanistic basis by which periodic external stimuli alter the brain state is not well understood. This study provides a computational insight into the mechanism of seizure suppression by high frequency stimulation (HFS). In particular, a modified version of the Jansen-Rit neural mass model is employed, in which EEG signals can be considered as the input. The proposed model reproduces seizure-like activity in the output during the ictal period of the input signal. By applying a control signal to the model, a wide range of stimulation amplitudes and frequencies are systematically explored. Simulation results reveal that HFS can effectively suppress the seizure-like activity. Our results suggest that HFS has the ability of shifting the operating state of neural populations away from a critical condition. Furthermore, a closed-loop control strategy is proposed in this paper. The main objective has been to considerably reduce the control effort needed for blocking abnormal activity of the brain. Such an energy reduction could be of practical importance, to reduce possible side effects and increase battery life for implanted neurostimulators.

A Data Driven Experimental System for Individualized Brain Stimulation Design and Validation

Deep brain stimulation (DBS) is an effective clinical treatment for epilepsy. However, the individualized setting and adaptive adjustment of DBS parameters are still facing great challenges. This paper investigates a data-driven hardware-in-the-loop (HIL) experimental system for closed-loop brain stimulation system individualized design and validation. The unscented Kalman filter (UKF) is utilized to estimate critical parameters of neural mass model (NMM) from the electroencephalogram recordings to reconstruct individual neural activity. Based on the reconstructed NMM, we build a digital signal processor (DSP) based virtual brain platform with real time scale and biological signal level scale. Then, the corresponding hardware parts of signal amplification detection and closed-loop controller are designed to form the HIL experimental system. Based on the designed experimental system, the proportional-integral controller for different individual NMM is designed and validated, which proves the effectiveness of the experimental system. This experimental system provides a platform to explore neural activity under brain stimulation and the effects of various closed-loop stimulation paradigms.

Structural Features of the Human Connectome That Facilitate the Switching of Brain Dynamics via Noradrenergic Neuromodulation

The structural connectivity of human brain allows the coexistence of segregated and integrated states of activity. Neuromodulatory systems facilitate the transition between these functional states and recent computational studies have shown how an interplay between the noradrenergic and cholinergic systems define these transitions. However, there is still much to be known about the interaction between the structural connectivity and the effect of neuromodulation, and to what extent the connectome facilitates dynamic transitions. In this work, we use a whole brain model, based on the Jasen and Rit equations plus a human structural connectivity matrix, to find out which structural features of the human connectome network define the optimal neuromodulatory effects. We simulated the effect of the noradrenergic system as changes in filter gain, and studied its effects related to the global-, local-, and meso-scale features of the connectome. At the global-scale, we found that the ability of the network of transiting through a variety of dynamical states is disrupted by randomization of the connection weights. By simulating neuromodulation of partial subsets of nodes, we found that transitions between integrated and segregated states are more easily achieved when targeting nodes with greater connection strengths-local feature-or belonging to the rich club-meso-scale feature. Overall, our findings clarify how the network spatial features, at different levels, interact with neuromodulation to facilitate the switching between segregated and integrated brain states and to sustain a richer brain dynamics.

Computational Evidence for a Competitive Thalamocortical Model of Spikes and Spindle Activity in Rolandic Epilepsy

Rolandic epilepsy (RE) is the most common idiopathic focal childhood epilepsy syndrome, characterized by sleep-activated epileptiform spikes and seizures and cognitive deficits in school age children. Recent evidence suggests that this disease may be caused by disruptions to the Rolandic thalamocortical circuit, resulting in both an abundance of epileptiform spikes and a paucity of sleep spindles in the Rolandic cortex during non-rapid eye movement sleep (NREM); electrographic features linked to seizures and cognitive symptoms, respectively. The neuronal mechanisms that support the competitive shared thalamocortical circuitry between pathological epileptiform spikes and physiological sleep spindles are not well-understood. In this study we introduce a computational thalamocortical model for the sleep-activated epileptiform spikes observed in RE. The cellular and neuronal circuits of this model incorporate recent experimental observations in RE, and replicate the electrophysiological features of RE. Using this model, we demonstrate that: (1) epileptiform spikes can be triggered and promoted by either a reduced NMDA current or h-type current; and (2) changes in inhibitory transmission in the thalamic reticular nucleus mediates an antagonistic dynamic between epileptiform spikes and spindles. This work provides the first computational model that both recapitulates electrophysiological features and provides a mechanistic explanation for the thalamocortical switch between the pathological and physiological electrophysiological rhythms observed during NREM sleep in this common epileptic encephalopathy.

The Amygdala Responds Rapidly to Flashes Linked to Direct Retinal Innervation: A Flash-evoked Potential Study Across Cortical and Subcortical Visual Pathways

Rapid detection and response to visual threats are critical for survival in animals. The amygdala (AMY) is hypothesized to be involved in this process, but how it interacts with the visual system to do this remains unclear. By recording flash-evoked potentials simultaneously from the superior colliculus (SC), lateral posterior nucleus of the thalamus, AMY, lateral geniculate nucleus (LGN) and visual cortex, which belong to the cortical and subcortical pathways for visual fear processing, we investigated the temporal relationship between these regions in visual processing in rats. A quick flash-evoked potential (FEP) component was identified in the AMY. This emerged as early as in the LGN and was approximately 25 ms prior to the earliest component recorded in the SC, which was assumed to be an important area in visual fear. This quick P1 component in the AMY was not affected by restraint stress or corticosterone injection, but was diminished by RU38486, a glucocorticoid receptor blocker. By injecting a monosynaptic retrograde AAV tracer into the AMY, we found that it received a direct projection from the retina. These results confirm the existence of a direct connection from the retina to the AMY, that the latency in the AMY to flashes is equivalent to that in the sensory thalamus, and that the response is modulated by glucocorticoids.

NMMGenerator: an automatic neural mass model generator from population graphs

Neural mass models are among the most popular mathematical models of brain activity, since they enable the rapid simulation of large-scale networks involving different neural types at a spatial scale compatible with electrophysiological experiments (e.g. local field potentials). However, establishing neural mass model (NMM) equations associated with specific neuronal network architectures can be tedious and is an error-prone process, restricting their use to scientists who are familiar with mathematics. In order to overcome this challenge, we have developed a user-friendly software that enables a user to construct rapidly, under the form of a graph, a neuronal network with its populations and connectivity patterns. The resulting graph is then automatically translated into the corresponding set of differential equations, which can be solved and displayed within the same software environment. The software is proposed as open access, and should assist in offering the possibility for a wider audience of scientists to develop NMM corresponding to their specific neuroscience research questions.

Computational Models in Electroencephalography

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses in silico and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by “computational model” is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses in silico. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

Cholinergic neuromodulation of inhibitory interneurons facilitates functional integration in whole-brain models

Segregation and integration are two fundamental principles of brain structural and functional organization. Neuroimaging studies have shown that the brain transits between different functionally segregated and integrated states, and neuromodulatory systems have been proposed as key to facilitate these transitions. Although whole-brain computational models have reproduced this neuromodulatory effect, the role of local inhibitory circuits and their cholinergic modulation has not been studied. In this article, we consider a Jansen & Rit whole-brain model in a network interconnected using a human connectome, and study the influence of the cholinergic and noradrenergic neuromodulatory systems on the segregation/integration balance. In our model, we introduce a local inhibitory feedback as a plausible biophysical mechanism that enables the integration of whole-brain activity, and that interacts with the other neuromodulatory influences to facilitate the transition between different functional segregation/integration regimes in the brain.

Sharp decrease in the Laplacian matrix rank of phase-space graphs: a potential biomarker in epilepsy

In this paper, phase space reconstruction from stereo-electroencephalography data of ten patients with focal epilepsy forms a series of graphs. Those obtained graphs reflect the transition characteristics of brain dynamical system from pre-seizure to seizure of epilepsy. Interestingly, it is found that the rank of Laplacian matrix of these graphs has a sharp decrease when a seizure is close to happen, which thus might be viewed as a new potential biomarker in epilepsy. In addition, the reliability of this method is numerically verified with a coupled mass neural model. In particular, our simulation suggests that this potential biomarker can play the roles of predictive effect or delayed awareness, depending on the bias current of the Gaussian noise. These results may give new insights into the seizure detection.

A state observer for the computational network model of neural populations

A state observer plays a vital role in the design of state feedback neuromodulation schemes used to prevent and treat neurological or psychiatric disorders. This paper aims to design a state observer to reconstruct all unmeasured states of the computational network model of neural populations that replicates patterns seen on the electroencephalogram by using the model inputs and outputs, as the theoretical basis for designing state feedback neuromodulation clinical schemes. The feasibility problem of linear matrix inequality conditions, which is the most important one for observer design of the computational network model of neural populations, is solved by using the input-output stability theory and the Lurie system theory. The observer matrices of the designed observer are formed by the optimal solution of the linear matrix inequality conditions. An illustrative example shows that the observer can simultaneously reproduce internal state variables of normal and lesion populations of the computational network model of neural populations under the background of focal origin brain dysfunction, and the designed observer has certain robustness toward input uncertainty and measurement noise. To the best of our knowledge, no observers have previously been designed for the computational network model of neural populations. The design of state feedback neuromodulation schemes based on the computational network model of neural populations is a new direction in the field of computational neuroscience.

A Connectome-Based, Corticothalamic Model of State- and Stimulation-Dependent Modulation of Rhythmic Neural Activity and Connectivity

Rhythmic activity in the brain fluctuates with behaviour and cognitive state, through a combination of coexisting and interacting frequencies. At large spatial scales such as those studied in human M/EEG, measured oscillatory dynamics are believed to arise primarily from a combination of cortical (intracolumnar) and corticothalamic rhythmogenic mechanisms. Whilst considerable progress has been made in characterizing these two types of neural circuit separately, relatively little work has been done that attempts to unify them into a single consistent picture. This is the aim of the present paper. We present and examine a whole-brain, connectome-based neural mass model with detailed long-range cortico-cortical connectivity and strong, recurrent corticothalamic circuitry. This system reproduces a variety of known features of human M/EEG recordings, including spectral peaks at canonical frequencies, and functional connectivity structure that is shaped by the underlying anatomical connectivity. Importantly, our model is able to capture state- (e.g., idling/active) dependent fluctuations in oscillatory activity and the coexistence of multiple oscillatory phenomena, as well as frequency-specific modulation of functional connectivity. We find that increasing the level of sensory drive to the thalamus triggers a suppression of the dominant low frequency rhythms generated by corticothalamic loops, and subsequent disinhibition of higher frequency endogenous rhythmic behaviour of intracolumnar microcircuits. These combine to yield simultaneous decreases in lower frequency and increases in higher frequency components of the M/EEG power spectrum during states of high sensory or cognitive drive. Building on this, we also explored the effect of pulsatile brain stimulation on ongoing oscillatory activity, and evaluated the impact of coexistent frequencies and state-dependent fluctuations on the response of cortical networks. Our results provide new insight into the role played by cortical and corticothalamic circuits in shaping intrinsic brain rhythms, and suggest new directions for brain stimulation therapies aimed at state-and frequency-specific control of oscillatory brain activity.

Thalamocortical inhibitory dynamics support conscious perception

Whether thalamocortical interactions play a decisive role in conscious perception remains an open question. We presented rapid red/green color flickering stimuli, which induced the mental perception of either an illusory orange color or non-fused red and green colors. Using magnetoencephalography, we observed 6-Hz thalamic activity associated with thalamocortical inhibitory coupling only during the conscious perception of the illusory orange color. This sustained thalamic disinhibition was temporally coupled with higher visual cortical activation during the conscious perception of the orange color, providing neurophysiological evidence of the role of thalamocortical synchronization in conscious awareness of mental representation. Bayesian model comparison consistently supported the thalamocortical model in conscious perception. Taken together, experimental and theoretical evidence established the thalamocortical inhibitory network as a gateway to conscious mental representations.

Model Predictive Control for Seizure Suppression Based on Nonlinear Auto-Regressive Moving-Average Volterra Model

This article investigates a closed-loop brain stimulation method based on model predictive control strategy to suppress epileptic seizures. A neural mass model (NMM), exhibiting the normal and various epileptic seizures by changing physiologically meaningful parameters, is used as a black-box model of the brain. Based on system identification, an auto-regressive moving-average Volterra model is established to reveal the relationship between stimulation and neuronal responses. Then, the model predictive control strategy is implemented based the Volterra model, which can generate an optimal stimulation waveform to eliminate epileptiform waves. The computational simulation results indicate the proposed closed-loop control strategy can optimize the stimulation waveform without particular knowledge of the physiological properties of the system. The robustness of the proposed control strategy to system disturbances makes it more appropriate for future clinical application.

A New Neural Mass Model Driven Method and Its Application in Early Epileptic Seizure Detection

OBJECTIVE

Despite numerous neural computational models proposed to explain physiological and pathological mechanisms of brain activity, a large gap remains between theory and application of the models. Building on the successful application of data-driven methods in epileptic seizure detection, we aim to build a bridge between data and models in this paper.

METHODS

We first propose a novel model-driven seizure detection method based on dynamic features in epileptic EEGs, where the rationale for dynamic features in epileptic EEGs can be clarified in theory by characterizing the variation of parameters of the model. Then we apply the proposed D&F-model-driven method to the problem of early epileptic seizure detection, where the evolution of model parameters selected and optimized by the proposed method is measured and used to detect the starting point of the seizure.

RESULTS

Numerical results on two open EEG databases demonstrate that our proposed method does a good job of early epileptic seizure detection. The average detection sensitivity, false positive rate and early detection period attain 100%, 0.1/h, and 7.1 s respectively.

CONCLUSION

This paper provides a strategy to characterize EEG signals using a NMM-related method and the model parameters optimized by real EEG may then serve as features in their own right for early seizure detection.

SIGNIFICANCE

An useful attempt to early detect epileptic seizures by combining the neural mass model with data analysis.

FPGA Realization of Hodgkin-Huxley Neuronal Model

One of the appealing cases of the neuromorphic research area is the implementation of biological neural networks. The current study offers Multiplierless Hodgkin-Huxley Model (MHHM). This modified model may reproduce various spiking behaviors, like the biological HH neurons, with high accuracy. The presented modified model, in comparison to the original HH model, due to its exact similarity to the original model, has more top performances in the case of FPGA saving and more achievable frequency (speed-up). In this approach, the proposed model has a 69 % saving in FPGA resources and also the maximum frequency of 85 MHz that is more than other similar works. In this modification, all spiking behaviors of the original model have been generated with low error calculations. To validate the MHHM neuron, this proposed model has been implemented on digital hardware FPGA. This approach demonstrates that the original HH model and the proposed model have high similarity in terms of higher performance and digital hardware cost reduction.

Epileptic seizures in a heterogeneous excitatory network with short-term plasticity

Epilepsy involves a diverse group of abnormalities, including molecular and cellular disorders. These abnormalities prove to be associated with the changes in local excitability and synaptic dynamics. Correspondingly, the epileptic processes including onset, propagation and generalized seizure may be related with the alterations of excitability and synapse. In this paper, three regions, epileptogenic zone (EZ), propagation area and normal region, were defined and represented by neuronal population model with heterogeneous excitability, respectively. In order to describe the synaptic behavior that the strength was enhanced and maintained at a high level for a short term under a high frequency spike train, a novel activity-dependent short-term plasticity model was proposed. Bifurcation analysis showed that the presence of hyperexcitability could increase the seizure susceptibility of local area, leading to epileptic discharges first seen in the EZ. Meanwhile, recurrent epileptic activities might result in the transition of synaptic strength from weak state to high level, augmenting synaptic depolarizations in non-epileptic neurons as the experimental findings. Numerical simulation based on a full-connected weighted network could qualitatively demonstrate the epileptic process that the propagation area and normal region were successively recruited by the EZ. Furthermore, cross recurrence plot was used to explore the synchronization between neuronal populations, and the global synchronization index was introduced to measure the global synchronization. Results suggested that the synchronization between the EZ and other region was significantly enhanced with the occurrence of seizure. Interestingly, the desynchronization phenomenon was also observed during seizure initiation and propagation as reported before. Therefore, heterogeneous excitability and short-term plasticity are believed to play an important role in the epileptic process. This study may provide novel insights into the mechanism of epileptogenesis.

Controllability of Networks of Multiple Coupled Neural Populations: An Analytical Method for Neuromodulation's Feasibility

Neuromodulation plays a vital role in the prevention and treatment of neurological and psychiatric disorders. Neuromodulation's feasibility is a long-standing issue because it provides the necessity for neuromodulation to realize the desired purpose. A controllability analysis of neural dynamics is necessary to ensure neuromodulation's feasibility. Here, we present such a theoretical method by using the concept of controllability from the control theory that neuromodulation's feasibility can be studied smoothly. Firstly, networks of multiple coupled neural populations with different topologies are established to mathematically model complicated neural dynamics. Secondly, an analytical method composed of a linearization method, the Kalman controllable rank condition and a controllability index is applied to analyze the controllability of the established network models. Finally, the relationship between network dynamics or topological characteristic parameters and controllability is studied by using the analytical method. The proposed method provides a new idea for the study of neuromodulation's feasibility, and the results are expected to guide us to better modulate neurodynamics by optimizing network dynamics and network topology.

Effects of Cholinergic Neuromodulation on Thalamocortical Rhythms During NREM Sleep: A Model Study

It has been suggested that cholinergic neurons shape the oscillatory activity of the thalamocortical (TC) network in behavioral and electrophysiological experiments. However, theoretical modeling demonstrating how cholinergic neuromodulation of thalamocortical rhythms during non-rapid eye movement (NREM) sleep might occur has been lacking. In this paper, we first develop a novel computational model (TC-ACH) by incorporating a cholinergic neuron population (CH) into the classical thalamo-cortical circuitry, where connections between populations are modeled in accordance with existing knowledge. The neurotransmitter acetylcholine (ACH) released by neurons in CH, which is able to change the discharge activity of thalamocortical neurons, is the primary focus of our work. Simulation results with our TC-ACH model reveal that the cholinergic projection activity is a key factor in modulating oscillation patterns in three ways: (1) transitions between different patterns of thalamocortical oscillations are dramatically modulated through diverse projection pathways; (2) the model expresses a stable spindle oscillation state with certain parameter settings for the cholinergic projection from CH to thalamus, and more spindles appear when the strength of cholinergic input from CH to thalamocortical neurons increases; (3) the duration of oscillation patterns during NREM sleep including K-complexes, spindles, and slow oscillations is longer when cholinergic input from CH to thalamocortical neurons becomes stronger. Our modeling results provide insights into the mechanisms by which the sleep state is controlled, and provide a theoretical basis for future experimental and clinical studies.

Spectral density-based and measure-preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs

Approximate Bayesian computation (ABC) has become one of the major tools of likelihood-free statistical inference in complex mathematical models. Simultaneously, stochastic differential equations (SDEs) have developed to an established tool for modelling time-dependent, real-world phenomena with underlying random effects. When applying ABC to stochastic models, two major difficulties arise: First, the derivation of effective summary statistics and proper distances is particularly challenging, since simulations from the stochastic process under the same parameter configuration result in different trajectories. Second, exact simulation schemes to generate trajectories from the stochastic model are rarely available, requiring the derivation of suitable numerical methods for the synthetic data generation. To obtain summaries that are less sensitive to the intrinsic stochasticity of the model, we propose to build up the statistical method (e.g. the choice of the summary statistics) on the underlying structural properties of the model. Here, we focus on the existence of an invariant measure and we map the data to their estimated invariant density and invariant spectral density. Then, to ensure that these model properties are kept in the synthetic data generation, we adopt measure-preserving numerical splitting schemes. The derived property-based and measure-preserving ABC method is illustrated on the broad class of partially observed Hamiltonian type SDEs, both with simulated data and with real electroencephalography data. The derived summaries are particularly robust to the model simulation, and this fact, combined with the proposed reliable numerical scheme, yields accurate ABC inference. In contrast, the inference returned using standard numerical methods (Euler-Maruyama discretisation) fails. The proposed ingredients can be incorporated into any type of ABC algorithm and directly applied to all SDEs that are characterised by an invariant distribution and for which a measure-preserving numerical method can be derived.

PyRates-A Python framework for rate-based neural simulations

In neuroscience, computational modeling has become an important source of insight into brain states and dynamics. A basic requirement for computational modeling studies is the availability of efficient software for setting up models and performing numerical simulations. While many such tools exist for different families of neural models, there is a lack of tools allowing for both a generic model definition and efficiently parallelized simulations. In this work, we present PyRates, a Python framework that provides the means to build a large variety of rate-based neural models. PyRates provides intuitive access to and modification of all mathematical operators in a graph, thus allowing for a highly generic model definition. For computational efficiency and parallelization, the model is translated into a compute graph. Using the example of two different neural models belonging to the family of rate-based population models, we explain the mathematical formalism, software structure and user interfaces of PyRates. We show via numerical simulations that the behavior of the PyRates model implementations is consistent with the literature. Finally, we demonstrate the computational capacities and scalability of PyRates via a number of benchmark simulations of neural networks differing in size and connectivity.