Hodgkin-Huxley Neuron Model Research Articles

Dynamics and stability of neural systems with indirect interactions involved energy levels

Dynamical modelling for neural systems with direct and indirect connections is to understand how these connections contribute to neural dynamics. Despite recent findings suggesting the existence of indirect connections in neural systems, their dynamical characteristics remain poorly understood. In this paper, we propose a simplified circuit model with indirect interactions inspired by the indirect connection between two neurons, from an energy perspective. Through bifurcation and dynamics analysis, we find that the presented model has a striking resemblance with the classical Hodgkin-Huxley neuronal model. Moreover, stability in a neural network coupled with energy is demonstrated by combining stability analysis and numerical simulation. Our analysis sheds light on the excitability dynamics and multi-stability that can emerge in biophysical systems with nonlinear interactions inspired by the neural systems and highlights the role of energy in propagating electrical activities.

From Finite Element Simulations to Equivalent Circuit Models of Extracellular Neuronal Recording Systems Based on Planar and Mushroom Electrodes.

define a new methodology to build multi-compartment lumped-elements equivalent circuit models for neuron/electrode systems. the equivalent circuit topology is derived by careful scrutiny of accurate and validated multiphysics finite-elements method (FEM) simulations that couple ion transport in the intra- and extracellular fluids, activation of the neuron membrane ion channels, and signal acquisition by the electronic readout. robust and accurate circuit models are systematically derived, suited to represent the dynamics of the sensed extracellular signals over a wide range of geometrical/physical parameters (neuron and electrode sizes, electrolytic cleft thicknesses, readout input impedance, non-uniform ion channel distributions). FEM simulations point out phenomena that escape an accurate description by equivalent circuits; notably: steric effects in the thin electrolytic cleft and the impact of extracellular ion transport on the reversal potentials of the Hodgkin-Huxley neuron model. our multi-compartment equivalent circuits match accurately the FEM simulations. They unveil the existence of an optimum number of compartments for accurate circuit simulation. FEM simulations suggest that while steric effects are in most instances negligible, the extracellular ion transport affects the reversal potentials and consequently the recorded signal if the electrolytic cleft becomes thinner than approximately 100 nm. the proposed methodology and circuit models improve upon the existing area and point contact models. The coupling between the extracellular concentrations and reversal potential highlighted by FEM simulations emerges as a challenge for future developments in lumped-element modeling of the neuron/sensor interface.

Digital Hardware Implementation of Morris-Lecar, Izhikevich, and Hodgkin-Huxley Neuron Models With High Accuracy and Low Resources

Digital Hardware Implementation of Morris-Lecar, Izhikevich, and Hodgkin-Huxley Neuron Models With High Accuracy and Low Resources

Iontronic Nanopore Model for Artificial Neurons: The Requisites of Spiking.

Brain-inspired neuromorphic computing is currently being investigated for effective artificial intelligence (AI) systems. The development of artificial neurons and synapses is imperative to creating efficient computational biomimetic networks. Here we propose the minimal configuration of an effective iontronic spiking neuron based on a conical nanofluidic pore ionic diode. The conductance is composed of a Boltzmann open channel probability and a blocking inactivation function, forming the structure of a memristor. The presence of a negative resistance and the combination of activation-deactivation dynamics cause a Hopf bifurcation. Using the characteristic frequencies of small perturbation impedance spectroscopy, we discuss the conditions of spiking, in which the system enters a limit cycle oscillation. We arrive at the conclusion that an excitable neuron-like system can be made with a single active channel instead of the more complex combination of multiple channels that occurs in the Hodgkin-Huxley neuron model.

Logistic stochastic resonance in the Hodgkin–Huxley neuronal system under electromagnetic induction

Hodgkin–Huxley neurons can be used as logic gates to perform reliable logic operations under an optimal noise intensity window. Fluctuations in ion concentrations inside and outside the neuron cell generate time-varying electromagnetic fields regulating neuronal dynamics. In this paper, a modified Hodgkin–Huxley neuron model is used to report the phenomenon of logical stochastic resonance under electromagnetic effects. The results show that electromagnetic induction affects the speed of neuronal response when switching to logic signals. Appropriately reducing the magnitude of the external bias current allows Hodgkin–Huxley neurons to perform reliable logic operations while consuming less energy. However, regulating the signal strength requires a trade-off between the reliability of logic operations and energy consumption. We further extend the logical stochastic resonance effect to neuronal networks. It is found that an appropriate increase in coupling strength has a favorable impact on system logic operations. The dynamical mechanism is explained in terms of bifurcation diagrams and phase space. Finally, we also compare the difference in the reliability of logical operations between small-world and scale-free networks. Small-world networks outperform scale-free networks for logical operations. Our results contribute to the study of neuronal simulation circuits with logic computation functions, and provides important clues for building new neuron-based logic devices with high energy efficiency.

High consistency VO2 memristor for artificial auditory neuron

With scalability and diverse device behavior, memristors present potential for executing neuromorphic computation with lower hardware cost and power consumption. However, Low consistency currently limited the application of memristors. Herein, we report a VO2-based memristor fabricated through magnetron sputtering and multiple annealing processes, exhibiting extremely low in both cycle-to-cycle (C2C) and device-to-device (D2D) variations. Further, a Hodgkin-Huxley model neuron circuit based on the extremely high consistency of the devices is established, which achieves auditory neuron perception simulation through spatiotemporal processing of spike signals, allowing for clear differentiation of sound source direction and displaying patterns akin to biological behavior. This easily implemented and highly consistent artificial neuron offers a promising approach for the development of next-generation artificial auditory systems.

A VO2 Neuristor Based on Microstrip Line Coupling.

The neuromorphic network based on artificial neurons and synapses can solve computational difficulties, and its energy efficiency is incomparable to the traditional von Neumann architecture. As a new type of circuit component, nonvolatile memristors are very similar to biological synapses in structure and function. Only one memristor can simulate the function of a synapse. Therefore, memristors provide a new way to build hardware-based artificial neural networks. To build such an artificial neural network, in addition to the artificial synapses, artificial neurons are also needed to realize the distribution of information and the adjustment of synaptic weights. As the VO2 volatile local active memristor is complementary to nonvolatile memristors, it can be used to simulate the function of neurons. However, determining how to better realize the function of neurons with simple circuits is one of the current key problems to be solved in this field. This paper considers the influence of distribution parameters on circuit performance under the action of high-frequency and high-speed signals. Two Mott VO2 memristor units are connected and coupled with microstrip lines to simulate the Hodgkin-Huxley neuron model. It is found that the proposed memristor neuron based on microstrip lines shows the characteristics of neuron action potential: amplification and threshold.

Mott Memristors and Neuronal Ion Channels: A Qualitative Analysis

Memristive devices have earned increased recognition over the past decade, owing to their application in memory and neuromorphic systems. Recently, memristive devices have found a propitious role in Spiking Neural Networks. This is partly attributed to an emerging family of memristive devices that are volatile. Volatile memristors, especially Mott memristors, have been used to implement Leaky Integrate and Fire neurons along with neuron circuits with richer dynamics, referred to as neuristors. The Mott memristor is often compared to voltage-gated ion channels in the Hodgkin-Huxley neuron model. However, voltage-gated ion channels in the Hodgkin-Huxley model do not exhibit voltage hysteresis in their quasi-static I-V characteristics, a critical property of Mott memristors. We discuss the association between Mott memristors based on joule heating and the Hodgkin-Huxley voltage-gated ion channels, and we prove that they are qualitatively dissimilar. Consequently, we propose a hypothetical potassium current-gated ion channel that exhibits voltage hysteresis. We simulate a Mott memristor Pearson-Anson oscillator and a current-gated ion channel oscillator. We use the nullcline plots and bifurcation diagrams of the circuits to demonstrate that both circuits are qualitatively similar. We further show that both circuits produce oscillations through a supercritical Andronov-Hopf bifurcation and have a similar oscillation-generation mechanism. We conclude that for the Mott memristor to share qualitative similarity to a neuronal ion channel, the channel must be current-gated rather than voltage-gated. Our aim is to supplement the understanding of how hardware neurons relate to their biological counterparts, which is a crucial first step towards implementing better brain-inspired systems.

Influence of temperature and noise on the propagation of subthreshold signal in feedforward neural network

Temperature is an important environmental factor that all creatures depend on. Suitable temperature is essential for maintaining the normal physiological functions of nervous system. Subthreshold signal is generated by weak activities in the nervous system that is difficult to be detected. Based on an improved Hodgkin-Huxley (HH) neuron model considering temperature and noise, the ten-layers pure excitatory feedforward neural network and the ten-layers excitatory-inhibitory (EI) neural network are constructed to study the propagation of subthreshold excitatory postsynaptic current signal. It's found that increasing temperature can restrain the signal propagation, and raise the noises intensity threshold where the failed signal propagation can transform into succeed signal propagation. Under the large noise, the signal propagation in network of different temperatures exhibits different anti-noise capabilities. Moreover, temperature and noise can modulate the spontaneous activity of the EI neural network to transform between the synchronous regular (SR) state and the asynchronous irregular (AI) state. The EI network's spontaneous activity will completely cover subthreshold signal, and block the signal propagation under large noise. The jumping phenomenon in the value of fidelity, which measures the quality of signal propagation, appears in both pure excitatory network and EI network. This paper provides potential value for understanding the regulation of both temperature and noise in information propagation in neural network.

Generation and Transmission of Action Potential in Nerve Cells and Neuron Populations Based on the Realistic Hodgkin-Huxley Neuron Model

There are several types of nerve cells in the central nervous system. Thanks to the synaptic connections, these cells form large and complicated networks. However, these cells have a stereotypical electrical activity called action potential (AP) or spike. In this work, the mechanisms of formation of this typical electrical signal and the methods of transferring from one cell to another were investigated using Hodgkin-Huxley neuron model simulations. It has been seen that the formation of AP is based on the principle of "all or nothing" and that ion channel dynamics are critical in the typical form of AP. It has been shown that signal transduction between nerve cells is transmitted by post-synaptic potential and that these signals may be cell depolarizing or polarizing. Finally, it is discussed that these electrical activities are quantities that can be measured at micro and macro levels, and various methods are used for this purpose.

Creation of synaptic connection to memristive neurons under noise

Continuous pumping of intracellular and extracellular ions can induce distinct electromagnetic induction accompanied by the channel current. The external electric stimuli and electromagnetic radiation can change the inner field energy in biological neurons, and the firing mode is regulated to discern the energy information in the neurons. The involvement of memristive channel can estimate the effect of electromagnetic field of an isolated neuron, which is sensitive to discern and capture external field energy under electromagnetic field. When two or more neurons with energy diversity are clustered, the synaptic connection is awaken and created with increasing coupling intensity until reaching complete synchronization. In this paper, the memristive Hodgkin–Huxley neuron model is used to discuss the synchronization stability when two neurons with energy diversity are clustered, two identical neurons can be coupled adaptive for reaching complete synchronization and perfect energy balance. In case of electromagnetic radiation, synchronization stability is controlled with increasing the coupling intensity adaptively by imposing noisy disturbance on the magnetic flux variable, which is used to describe the effect of magnetic field. For non-identical neurons, the creation and enhancement of synaptic connection are also realized because of energy diversity between two neurons.

Estimation of the effect of magnetic field on a memristive neuron

A cell's action potential can be induced by rapid pumping and changes in intracellular and extracellular ions, and a magnetic field is generated to regulate neural activity effectively. Stochastic propagation and diffusion of ions across the cell membrane can break the balance of ion concentration. An appropriate external stimulus can speed up the exchange of ions and then different firing modes in the neuron can be induced for energy release. An improved neuron model is proposed and suggested to explore the effect of the magnetic field from the physical aspect, which a memristive channel with locally active feature is added to the known Hodgkin-Huxley (HH) neuron model by connecting a memristor in parallel with the HH neural circuit. That is, the memristive channel current is equivalent to the induction current, and an additive magnetic flux variable is introduced into the HH model, and its evolution is guided by the law of electromagnetic induction and energy conversion. The induction current can modulate the excitability and the threshold for inducing distinct action potentials. The transition from different-type firing patterns is induced by modulating the inductive current. In addition, an external magnetic field from two sources is applied to estimate the mode transition and firing patterns by regulating the magnetic flux, which induces further changes in the neural activity of the neuron. The neuron keeps quiescent when two identical magnetic field sources are emitted at high frequency. While the neuron can be activated to generate continuous firing patterns when the two applied magnetic field sources show certain diversity in the frequency. The potential mechanism is that the frequency synthesized by the two stimuli is close to the intrinsic frequency of the neuron, and then bursting can be induced effectively.

Reduced-Dimension, Biophysical Neuron Models Constructed From Observed Data

Using methods from nonlinear dynamics and interpolation techniques from applied mathematics, we show how to use data alone to construct discrete time dynamical rules that forecast observed neuron properties. These data may come from simulations of a Hodgkin-Huxley (HH) neuron model or from laboratory current clamp experiments. In each case, the reduced-dimension, data-driven forecasting (DDF) models are shown to predict accurately for times after the training period. When the available observations for neuron preparations are, for example, membrane voltage V(t) only, we use the technique of time delay embedding from nonlinear dynamics to generate an appropriate space in which the full dynamics can be realized. The DDF constructions are reduced-dimension models relative to HH models as they are built on and forecast only observables such as V(t). They do not require detailed specification of ion channels, their gating variables, and the many parameters that accompany an HH model for laboratory measurements, yet all of this important information is encoded in the DDF model. As the DDF models use and forecast only voltage data, they can be used in building networks with biophysical connections. Both gap junction connections and ligand gated synaptic connections among neurons involve presynaptic voltages and induce postsynaptic voltage response. Biophysically based DDF neuron models can replace other reduced-dimension neuron models, say, of the integrate-and-fire type, in developing and analyzing large networks of neurons. When one does have detailed HH model neurons for network components, a reduced-dimension DDF realization of the HH voltage dynamics may be used in network computations to achieve computational efficiency and the exploration of larger biological networks.

White-noise-induced double coherence resonances in reduced Hodgkin-Huxley neuron model near subcritical Hopf bifurcation.

Coherence resonance (CR) describes a counterintuitive phenomenon in which the optimal oscillatory responses in nonlinear systems are shaped by a suitable noise amplitude. This phenomenon has been observed in neural systems. In this research, the generation of double coherence resonances (DCRs) due to white noise is investigated in a three-dimensional reduced Hodgkin-Huxley neuron model with multiple-timescale feature. We show that additive white noise can induce DCRs from the resting state near a subcritical Hopf bifurcation. The appearance of DCRs is related to the changes of the firing pattern aroused by the increases of the noise amplitude. The underlying dynamical mechanisms for the appearance of the DCRs and the changes of the firing pattern are interpreted using the phase space analysis and the dynamics of the stable focus-node near the subcritical Hopf bifurcation. We find that the multiple-timescale dynamics is essential for generating the DCRs and different firing patterns. The results not only present a case in which noise can induce DCRs near a Hopf bifurcation but also provide its dynamical mechanism, which enriches the phenomena in nonlinear dynamics and provides further understanding on the roles of noise in neural systems with multiple-timescale feature.

Inhibitory autapse with time delay induces mixed-mode oscillations related to unstable dynamical behaviors near subcritical Hopf bifurcation

<abstract><p>Mixed-mode oscillations (MMOs) consisting of spikes alternating with a series of subthreshold oscillations have been observed in various neurons related to some physiological functions. In the present paper, inhibitory-autapse-induced MMOs are simulated by using the Hodgkin-Huxley neuron model, and the underlying dynamical mechanism is identified to be related to dynamics of unstable behaviors near subcritical Hopf bifurcation. For the monostable spiking, a delayed inhibitory current pulse activated by a spike can suppress the phase trajectory corresponding to depolarization phase of the next spike to the unstable focus nearby or the neighborhood outside of unstable limit cycle, respectively. Then the trajectory rotates multiple cycles away and converges to the stable limit cycle, resulting in an evolution process of membrane potential from small-amplitude subthreshold oscillations to a large-amplitude spike, i.e., MMOs. For the spiking coexisting with the resting state, inhibitory autapse induces MMOs and resting state from the spiking. The difference in the MMOs from those induced by the excitatory autapse is identified. The result presents the underlying nonlinear mechanisms of inhibitory autapse to suppress the neuronal firing and reveals the potential role to control the neuronal firing patterns near subcritical Hopf bifurcation.</p></abstract>

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.