Hodgkin-Huxley Neuron Research Articles

Memristive Hodgkin-Huxley Spiking Neuron Model for Reproducing Neuron Behaviors.

The Hodgkin-Huxley (HH) spiking neuron model reproduces the dynamic characteristics of the neuron by mimicking the action potential, ionic channels, and spiking behaviors. The memristor is a nonlinear device with variable resistance. In this paper, the memristor is introduced to the HH spiking model, and the memristive Hodgkin-Huxley spiking neuron model (MHH) is presented. We experimentally compare the HH spiking model and the MHH spiking model by applying different stimuli. First, the individual current pulse is injected into the HH and MHH spiking models. The comparison between action potentials, current densities, and conductances is carried out. Second, the reverse single pulse stimulus and a series of pulse stimuli are applied to the two models. The effects of current density and action time on the production of the action potential are analyzed. Finally, the sinusoidal current stimulus acts on the two models. The various spiking behaviors are realized by adjusting the frequency of the sinusoidal stimulus. We experimentally demonstrate that the MHH spiking model generates more action potential than the HH spiking model and takes a short time to change the memductance. The reverse stimulus cannot activate the action potential in both models. The MHH spiking model performs smoother waveforms and a faster speed to return to the resting potential. The larger the external stimulus, the faster action potential generated, and the more noticeable change in conductances. Meanwhile, the MHH spiking model shows the various spiking patterns of neurons.

Dynamic responses of neurons in different states under magnetic field stimulation.

Transcranial magnetic stimulation (TMS) is an effective method to treat neurophysiological disorders by modulating the electrical activities of neurons. Neurons can exhibit complex nonlinear behaviors underlying the external stimuli. Currently, we do not know how stimulation interacts with endogenous neural activity. In this paper, the effects of magnetic field on spiking neuron, bursting neuron and bistable neuron are studied based on the Hodgkin-Huxley (HH) neuron model. The results show that the neurons in three different states can exhibit different dynamic responses under magnetic field stimulation. The magnetic field stimulation could increase or decrease the firing frequencies of spiking neuron, bursting neuron and bistable neuron. The transitions between different firing patterns of neurons can be promoted by changing the parameters of the magnetic field. Magnetic field stimulation has a minimal impact on the firing temporal sequence sequences in bursting neuron than that in spiking neuron and bistable neuron. These results provided an insight into the impact of neuronal states on neuronal dynamic responses under brain stimulation and show that subtle changes in external conditions and stimuli can cause complex neuronal responses. This study can help us understand the state-dependent coding mechanism of neurons under electromagnetic stimulation.

The Hodgkin–Huxley neuron model for motion detection in image sequences

In this paper, we consider a biologically inspired spiking neural network model for motion detection. The proposed model simulates the neurons’ behavior in the cortical area MT to detect different kinds of motion in image sequences. We choose the conductance-based neuron model of the Hodgkin–Huxley to define MT cell responses. Based on the center-surround antagonism of MT receptive fields, we model the area MT by its great proportion of cells with directional selective responses. The network’s spiking output corresponds to an MT neuron population’s firing rates and enables to extract motion boundaries. We conduct several experiments on real image sequences. The experimental results show the proposed network’s ability to segregate multiple moving objects from an image sequence and reproduce the MT cells’ responses. We perform a quantitative evaluation on the YouTube Motion Boundaries (YMB) dataset, and we compare the result to state-of-the-art methods for boundary detection in videos: boundary flow estimation (BF) and temporal boundary difference (BD). The proposed network model provides the best results on YMB compared to BF and BD methods.

Impedance Spectroscopy Dynamics of Biological Neural Elements: From Memristors to Neurons and Synapses.

Understanding the operation of neurons and synapses is essential to reproducing biological computation. Building artificial neuromorphic networks opens the door to a new generation of faster and low-energy-consuming electronic circuits for computation. The main candidates to imitate the natural biocomputation processes, such as the generation of action potentials and spiking, are memristors. Generally, the study of the performance of material neuromorphic elements is done by the analysis of time transient signals. Here, we present an analysis of neural systems in the frequency domain by small-amplitude ac impedance spectroscopy. We start from the constitutive equations for the conductance and memory effect, and we derive and classify the impedance spectroscopy spectra. We first provide a general analysis of a memristor and demonstrate that this element can be expressed as a combination of simple parts. In particular, we derive a basic equivalent circuit where the memory effect is represented by an RL branch. We show that this ac model is quite general and describes the inductive/negative capacitance response in many systems such as halide perovskites and organic LEDs. Thereafter, we derive the impedance response of the integrate-and-fire exponential adaptative neuron model that introduces a negative differential resistance and a richer set of spectra. On the basis of these insights, we provide an interpretation of the varied spectra that appear in the more general Hodgkin-Huxley neuron model. Our work provides important criteria to determine the properties that must be found in material realizations of neuronal elements. This approach has the great advantage that the analysis of highly complex phenomena can be based purely on the shape of experimental impedance spectra, avoiding the need for specific modeling of rather involved material processes that produce the required response.

A strategy for mapping biophysical to abstract neuronal network models applied to primary visual cortex.

A fundamental challenge for the theoretical study of neuronal networks is to make the link between complex biophysical models based directly on experimental data, to progressively simpler mathematical models that allow the derivation of general operating principles. We present a strategy that successively maps a relatively detailed biophysical population model, comprising conductance-based Hodgkin-Huxley type neuron models with connectivity rules derived from anatomical data, to various representations with fewer parameters, finishing with a firing rate network model that permits analysis. We apply this methodology to primary visual cortex of higher mammals, focusing on the functional property of stimulus orientation selectivity of receptive fields of individual neurons. The mapping produces compact expressions for the parameters of the abstract model that clearly identify the impact of specific electrophysiological and anatomical parameters on the analytical results, in particular as manifested by specific functional signatures of visual cortex, including input-output sharpening, conductance invariance, virtual rotation and the tilt after effect. Importantly, qualitative differences between model behaviours point out consequences of various simplifications. The strategy may be applied to other neuronal systems with appropriate modifications.

Implementation of Hodgkin-Huxley Neuron Model With the Novel Memristive Oscillator

In this brief, in order to simplify the implementation of the classical Hodgkin-Huxley neuron (HH) model, a novel floating memristor emulator is introduced, which consists of four electronic components and can be considered the simplest implementation in the existing literature. Firstly, the schematic diagrams of the proposed novel HH neuron-based memristive oscillator is presented, and the working mechanism and the bursting phenomenon of which are analyzed. Then, the simulation model of the proposed memristive oscillator emulator is developed in MULTISIM using several off-the-shelf components, which is used to implement a HH neuron model. Moreover, the electrical characteristics of it are examined. In particular, the relationship between the ion channels concentration and the variable voltages of the neuron model is described in detail. Simulation results confirm that the proposed model demonstrates rich bursting oscillation behaviors which is more suitable for simulating the giant squid axon compared to the existing model in the literature, which can be utilized to transmit the neuron information and establish the neural network.

Chaotic Signal Induced Delay Decay in Hodgkin-Huxley Neuron

It is a well-known fact that there are chaotic behaviors of neurons in the brain. These chaotic behaviors may affect the membrane potential dynamics of neurons. In the current study, we present a new phenomenon, called as Chaos Delayed Decay (CDD), which emerges when the first spike latency of a periodically forced deterministic Hodgkin-Huxley neuron exhibits a prominent delay depending on the chaotic current intensity. First, we indicate that the firing rate of the Hodgkin-Huxley neuron exhibits resonance-like dependence on the intensity of chaotic current. Then, we demonstrate that the first spike latency and jitter exhibits a resoance-like dependence on the chaotic current intensity for frequencies separating subthreshold and suprathreshold frequency regions. Besides, the obtained results reveal that chaotic activity may have unfavorable effects on the response of Hodgkin-Huxley neuron in the region of supra-threshold frequencies where the lowest mean latency and jitter occur. In this region increasing chaotic activity has augmented the latency and jitter in contrast to sub-threshold frequency region in which the mean latency and jitter of Hodgkin-Huxley neuron reasonably decrease versus increasing chaotic current intensity. It is also shown that, in this regime, the mean latency and jitter are insensitive to changes in frequency for high chaotic current intensities. Lastly, we have analyzed the effects of the phase of the forcing signal on the latency and jitter of the neuron. For a forcing signal in the lower sub-threshold region and an optimal one in the supra-threshold region, it is observed that there is an optimal initial phase of the forcing signal for the best encoding of information by the neuron, whereas the mean latency and jitter are insensitive to changes in the initial phase of the forcing signal in the upper sub-threshold region with high frequencies.

Simulation of spiking activities neuron models using the Euler method

Simulation of neuron spiking activity models has been carried out using the Euler method. This study aims to simulate spiking activity in a neuron model. The neuron model used is the Hodgkin-Huxley neuron model, Integrate and Fire neuron model, Wilson neuron model, and Izhikevich neuron model. The research was conducted by implementing the mathematical equations of each neuron model used and then recording the membrane potential changes from time to time using the Euler method in MATLAB. The different forms of spiking activity were done by varying the variable’s value in each mathematical equation of a neuron model that describes the processing of action potentials (spikes) influenced by ion channel activity. The results showed that the Integrate and Fire neuron models produce regular spiking (RS), Hodgkin-Huxley neuron models have regular spiking (RS) forms, Wilson neuron models produce regular spiking (RS), fast-spiking (FS), and intrinsic bursting (IB), Izhikevich neuron model produces regular spiking (RS), fast-spiking (FS), intrinsic bursting (IB), chattering neurons (CH), and low threshold spiking (LTS). The complexity of the variables used and the spiking activity generated by each neuron model can provide an overview of computational efficiency and proximity to actual biological neurons.

A reliability assessment approach for a Hodgkin-Huxley neuron circuit

The performance of the Hodgkin-Huxley neuron circuits used in novel communication and computer systems depends on its capacitors. Thus, degradation of capacitors in neuron circuits may have significant impact on reliability of the neuron. In this paper, a simulation-based reliability assessment approach was developed for a Hodgkin-Huxley neuron circuit to consider the degradation of capacitors. SPICE simulation, neural information coding method, and degradation modelling of capacitors are integrated to assess impact of capacitors on the given neuron circuit. A MOS-based Hodgkin-Huxley neuron circuit is simulated to obtain output waveforms with degraded capacitors. It has been found that the output waveform of the selected neuron changes significantly with capacitors' degradation. In the total operation range of the neuron, degradation of capacitors may result in significant errors and loss of neural information. Capacitor's degradation elevates the duty ratio threshold for generating voltage spikes, and would lead to higher values of the inter-spike interval, regardless of variation of input period and duty cycle. However, by limitation of the input range and duty ration, information carried by S-Space code is transmitted correctly.

Visibility-graphlet approach to the output series of a Hodgkin–Huxley neuron

The output signals of neurons that are exposed to external stimuli are of great importance for brain functionality. Traditional time-series analysis methods have provided encouraging results; however, the associated patterns and their correlations in the output signals of neurons are masked by statistical procedures. Here, graphlets are employed to extract the local temporal patterns and the transitions between them from the output signals when neurons are exposed to external stimuli with selected stimulating periods. A transition network is defined where the node is the graphlet and the direct link is the transition between two successive graphlets. The transition-network structure is affected by the simulating periods. When the stimulating period moves close to an integer multiple of the neuronal intrinsic period, only the backbone or core survives, while the other linkages disappear. Interestingly, the size of the backbone (number of nodes) equals the multiple. The transition-network structure is conservative within each stimulating region, which is defined as the range between two successive integer multiples. Nevertheless, the backbone or detailed structure is significantly altered between different stimulating regions. This alternation is induced primarily from a total of 12 active linkages. Hence, the transition network shows the structure of cross correlations in the output time-series for a single neuron.

Synchronization of interacted spiking neuronal networks with inhibitory coupling

• The synchronization index (SI) in two large interacted via inhibitory coupling networks oscillates periodically in time; the time intervals of high SI alternates with the time intervals of low SI. • The synchronization indexes in these networks exhibit either inphase or antiphase synchronization depending on the inhibitory coupling strength between them. We suppose that the underlying mechanism behind the antiphase dynamics lies in the cognitive resource redistribution between neuronal ensembles in the brain. • Excitatory coupling between the neurons inside the network affects the synchronization index. To maintain the neural network in the regimes of inphase or antiphase SI oscillations, we should keep a balance between excitatory and inhibitory connections. It suggests that the excitatory and the inhibitory currents should compensate each other. In other words, when one of them increases, the other must be increased too, and vice versa. • The coupling inside the input small network affects antiphase synchronization between two large networks. However, the scenario from positive and negative correlation and back between the large networks are only determined by inhibitory coupling between them. The development of mathematical models to describe neuronal interaction processes in the brain is a challenging task of nonlinear dynamics. Recent advances in biochemistry and neuroscience allow better understanding of biological mechanisms underlying the neuron functioning and synaptic connections between neurons. Moreover, significant progress in brain imaging sheds light on the structure of the brain network and certain aspects of neuronal dynamics. However, dynamical mechanisms leading to synchronization between different brain areas still remain unknown and require further investigation. To shed light on this issue, we consider two small-world networks of Hodgkin-Huxley neurons interacting via inhibitory coupling. We found that synchronization indices (SI) in both networks oscillate periodically in time, so that time intervals of high SI alternate with time intervals of low SI. Depending on the coupling strength, the two coupled networks can be in the regime of either in-phase or anti-phase synchronization. We suppose that the inherent mechanism behind such a behavior lies in the cognitive resource redistribution between neuronal ensembles of the brain.

A Compact Model of Ovonic Threshold Switch Combining Thermal Dissipation Effect.

Ovonic threshold switch (OTS) has received great attention in neuromorphic computing due to its support for high-density synapse array as a selector and leaky-integration-firing functions Hodgkin-Huxley neurons. However, there is no simple and complete model for device simulation and integrated circuit design, which hindered application until now. In this work, we developed a compact physical model of OTS based on the Poole-Frenkel effect accompanied by the thermal dissipation effect for the first time. The thermal dissipation effect describes the energy flow between the device and the environment so that the model is more practical. Compared with previous experiments, the numerical results fairly fitted the electrical characteristics, demonstrating the model validity. In addition, the relation of the device performance with material and structure was deduced, which can facilitate optimizing the OTS device. The model will be useful for device design and implemented with high speed for simplicity.

Short-term and spike-timing-dependent plasticity facilitate the formation of modular neural networks

The brain has the phenomenal ability to reorganise itself by forming new connections among neurons and by pruning others. The so-called neural or brain plasticity facilitates the modification of brain structure and function over different time scales. Plasticity might occur due to external stimuli received from the environment, during recovery from brain injury, or due to modifications within the body and brain itself. In this paper, we study the combined effect of short-term (STP) and spike-timing-dependent plasticity (STDP) on the synaptic strength of excitatory coupled Hodgkin-Huxley neurons and show that plasticity can facilitate the formation of modular neural networks with complex topologies that resemble those of networks with preferential attachment properties. In particular, we use an STDP rule that alters the synaptic coupling intensity based on time intervals between spikes of postsynaptic and presynaptic neurons. Previous work has shown that STDP may induce the emergence of directed connections from high to low frequency spiking neurons. On the other hand, STP is attributed to the release of neurotransmitters in the synaptic cleft of neurons that alter its synaptic efficiency. Our results suggest that the combined effect of STP and STDP with long recovery times facilitates the formation of connections among neurons with similar spike frequencies only, a kind of preferential attachment. We then pursue this further and show that, when starting with all-to-all neural configurations, depending on the STP recovery time and distribution of neural frequencies, modular neural networks can emerge as a direct result of the combined effect of STP and STDP.

FPGA-Based Real-Time Simulation Platform for Large-Scale STN-GPe Network.

The real-time simulation of large-scale subthalamic nucleus (STN)-external globus pallidus (GPe) network model is of great significance for the mechanism analysis and performance improvement of deep brain stimulation (DBS) for Parkinson's states. This paper implements the real-time simulation of a large-scale STN-GPe network containing 512 single-compartment Hodgkin-Huxley type neurons on the Altera Stratix IV field programmable gate array (FPGA) hardware platform. At the single neuron level, some resource optimization schemes such as multiplier substitution, fixed-point operation, nonlinear function approximation and function recombination are adopted, which consists the foundation of the large-scale network realization. At the network level, the simulation scale of network is expanded using module reuse method at the cost of simulation time. The correlation coefficient between the neuron firing waveform of the FPGA platform and the MATLAB software simulation waveform is 0.9756. Under the same physiological time, the simulation speed of FPGA platform is 75 times faster than the Intel Core i7-8700K 3.70 GHz CPU 32GB RAM computer simulation speed. In addition, the established platform is used to analyze the effects of temporal pattern DBS on network firing activities. The proposed large-scale STN-GPe network meets the need of real time simulation, which would be rather helpful in designing closed-loop DBS improvement strategies.

High Speed and Low Digital Resources Implementation of Hodgkin-Huxley Neuronal Model Using Base-2 Functions

Neurons are the basic blocks in the Central Nervous System (CNS). Simulation and hardware realization of these blocks are vital in neuromorphic engineering. This paper presents a set of multiplierless mathematical equations based on 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</sup> terms to achieve a low-cost, high-speed, and high-accuracy digital implementation of Hodgkin-Huxley (HH) neuron model. The HH model is the most complicated and high-accuracy among the mathematical neuron models. The proposed model can reproduce spiking behaviors of the original HH model with high precision. To validate the mathematical simulation results, the proposed model has been synthesized and implemented on Field-Programmable Gate Array (FPGA) development board. Hardware synthesis and physical implementations reveal that the biological behavior of different spiking patterns can be reproduced with higher performance and significantly lower implementation costs compared with the original HH model. Also, in this approach the maximum frequency of 200 MHz is achievable which is valuable in comparison with other similar works.

Synchronization and metabolic energy consumption in stochastic Hodgkin-Huxley neurons: Patch size and drug blockers

In this work, a stochastic Langevin approach is adopted to coupled Hodgkin-Huxley neuron system to elucidate the role of channel noise in the kinetics and energetics of spiking of action potential and the synchronization between neurons. The size of patch plays a pivotal role in synchronization and metabolic energy consumption. The behavior of postsynaptic neuron is explored by taking three different patch size ranges from noise enhanced phase to dead range state before reaching a deterministic limit. We also discuss the effect of sodium and potassium channel blockers on kinetic and energetic characteristics of synchronization and metabolic energy consumption rate.

SECONIC: Towards multi-compartmental models for ultrasonic brain stimulation by intramembrane cavitation * * This work was carried out using the Supercomputer Infrastructure (STEVIN) at Ghent University, funded by Ghent University, the Flemish Supercomputer Center (VSC), the Hercules Foundation and the Flemish Government department EWI.

Objective. To design a computationally efficient model for ultrasonic neuromodulation (UNMOD) of morphologically realistic multi-compartmental neurons based on intramembrane cavitation. Approach. A Spatially Extended Neuronal Intramembrane Cavitation model that accurately predicts observed fast Charge Oscillations (SECONIC) is designed. A regular spiking cortical Hodgkin-Huxley type nanoscale neuron model of the bilayer sonophore and surrounding proteins is used. The accuracy and computational efficiency of SECONIC is compared with the Neuronal Intramembrane Cavitation Excitation (NICE) and multiScale Optimized model of Neuronal Intramembrane Cavitation (SONIC). Main results. Membrane charge redistribution between different compartments should be taken into account via fourier series analysis in an accurate multi-compartmental UNMOD-model. Approximating charge and voltage traces with the harmonic term and first two overtones results in reasonable goodness-of-fit, except for high ultrasonic pressure (adjusted R-squared ≥0.61). Taking into account the first eight overtones results in a very good fourier series fit (adjusted R-squared ≥0.96) up to 600 kPa. Next, the dependency of effective voltage and rate parameters on charge oscillations is investigated. The two-tone SECONIC-model is one to two orders of magnitude faster than the NICE-model and demonstrates accurate results for ultrasonic pressure up to 100 kPa. Significance. Up to now, the underlying mechanism of UNMOD is not well understood. Here, the extension of the bilayer sonophore model to spatially extended neurons via the design of a multi-compartmental UNMOD-model, will result in more detailed predictions that can be used to validate or falsify this tentative mechanism. Furthermore, a multi-compartmental model for UNMOD is required for neural engineering studies that couple finite difference time domain simulations with neuronal models. Here, we propose the SECONIC-model, extending the SONIC-model by taking into account charge redistribution between compartments.

Differential Covariance: A New Method to Estimate Functional Connectivity in fMRI.

Measuring functional connectivity from fMRI recordings is important in understanding processing in cortical networks. However, because the brain's connection pattern is complex, currently used methods are prone to producing false functional connections. We introduce differential covariance analysis, a new method that uses derivatives of the signal for estimating functional connectivity. We generated neural activities from dynamical causal modeling and a neural network of Hodgkin-Huxley neurons and then converted them to hemodynamic signals using the forward balloon model. The simulated fMRI signals, together with the ground-truth connectivity pattern, were used to benchmark our method with other commonly used methods. Differential covariance achieved better results in complex network simulations. This new method opens an alternative way to estimate functional connectivity.

Memristive biophysical neuron models forming an excitatory–inhibitory neural network for modeling PING rhythm generation

SPICE models are constructed for memristive devices to form associated biophysical neuron circuit models such as the Hodgkin–Huxley (HH) type II excitability neuron circuit model, the HH type III excitability neuron circuit model, the simplified HH neuron circuit model, the Morris–Lecar neuron circuit model, and the memristive based direct-current (DC) circuit model. Rigorous nonlinear circuit-theoretic principles are also applied to analyze the different behaviors of the generic memristor Na $$^{+}$$ -ion, K $$^{+}$$ -ion, and Ca $$^{++}$$ -ion channels forming these biophysical neuron circuit models. Detailed explanations and clarifications are presented on the memristive HH type II and HH type III axonal excitabilities based on mathematical analysis as well as the circuit models. This is done from the perspective of the spike patterns generated by both of these biophysical neuron circuit models. Moreover, various experimental studies have revealed a synchronous brain state known as gamma rhythms that are responsible for sensory, memory, and motor processes. This suggests that understanding how the gamma oscillation (30–100 Hz) is generated in the brain will be extremely important to unravel the link between the activity of an individual neuron and the cognitive processing achieved by a population of networked neurons. We thus also study the dynamics of an interconnected excitatory–inhibitory (E–I) network population, which is ubiquitous in the brain. Utilizing biophysical models of the E–I network, we investigate the generation of pyramidal-interneuronal network gamma (PING) rhythms caused by the external input to the network and the connectivity heterogeneities. The results reveal that synchronous strong PING and sparsely firing weak PING rhythms are generated based on the network connectivities and external input heterogeneities in simulations of 100 memristive HH type II excitability neurons forming an E–I network.

Lévy noise-induced inverse stochastic resonance on Newman–Watts networks of Hodgkin–Huxley neurons

This paper primarily investigates the inverse stochastic resonance (ISR) of neuron network driven by Lévy noise with electrical autapse and chemical autapse, respectively. Firstly, the discharge of Hodgkin–Huxley (HH) neuron network under different noise parameters, autapse parameters and network coupling strength is shown. Then, the variation of average firing rate with Lévy noise in the case of electrical autapse and chemical autapse is presented. We find that there exists a minimum value of the average firing rate curve caused by stability index and noise intensity of Lévy noise across the whole network, which is the phenomenon of ISR. With the increase of autaptic intensity and coupling strength, the ISR inhibitory effect of neuron discharge is weakened. In addition, with the increase of coupling strength, the neuron discharge of neural network is more intense and regular. As a consequence, our work suggests that autaptic intensity and coupling efficient of neuronal network can regulate the neuronal firing activities and suppress the effect of ISR, and Lévy noise can induce ISR phenomenon in Newman–Watts neuronal network.