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Neurons in the brain as the elementary processing units and nervous system play a key role. If a neuron gets a proper stimulus, it produces action potentials (spikes) that are transferred along its axon. Reaching the end of the neuron, other neurons or muscle cells may be activated [1]. The effect of neural morphology along with thickness of dendrites and passive electrical parameters on the spikes width and amplitude can be investigated by analytical and numerical investigations of spiking models. The impact of mentioned proper stimulus may be degraded by passing time. In this paper, it is tried to add the effective parameter ’membrane resistance’ in well-known Hodgkin-Huxley model with four dimensions to compare several outputs due to changing resistance and various injected current. The goal of this paper has been to measure spikes changes or even how to determine current threshold when resistance is not constant (non-linear time dependant) result of different factors.

The partial phase synchronization (sometimes called cooperation) of neurons is fundamental for the understanding of the complex behavior of the brain. The lack or the excess of synchronization can generate brain disorders like Parkinson's disease and epilepsy. The phase synchronization phenomenon is strongly related to the regular or chaotic dynamics of individual neurons. The individual dynamics themselves are a function of the ion channel conductances, turning the conductances into important players in the process of neuron synchronized health depolarization/repolarization processes. It is well known that many diseases are related to alterations of the ion-channel conductance properties. To normalize their functioning, drugs are used to block or activate specific channels, changing their conductances. We investigate the synchronization process of a Hodgkin-Huxley-type neural network as a function of the values of the individual neuron conductances, showing the dynamics of the neurons must be taken into account in the synchronization process. Particular sets of conductances lead to non-chaotic individual neuron dynamics allowing synchronization states for very weak coupling and resulting in a non-monotonic transition to synchronized states, as the coupling strength among neurons is varied. On the other hand, a monotonic transition to synchronized states is observed for individual chaotic dynamics of the neurons. We conclude the analysis of the individual dynamics of isolated neurons allows the prediction of the synchronization process of the network. We provide alternative ways to achieve the desired network state (phase synchronized or desynchronized) without any changes in the synaptic current of neurons but making just small changes in the neuron ion-channel conductances. The mechanism behind the control is the close relation between ion-channel conductance and the regular or chaotic dynamics of neurons. Finally, we show that by changing at least two conductances simultaneously the control may be much more efficient since the second conductance makes the synchronization possible just by performing a small change in the first. The study presented here may have an impact on new drug development research.

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.

We construct an electronic circuit for mimicking a single neuron's behavior in connection with the dynamics of the Hodgkin–Huxley mathematical model. Our results show that the electronic neuron, even though it contains binary-state circuitry components, displays a timing interplay between the ion channels, which is consistent with the corresponding timing encountered in the model equations. This is at the core of the mechanism determining not only the creation of action potentials but also the neuronal firing rate output. This work is suitable for educational purposes in physics, mathematical modeling, electronics, and neurophysiology and can be extended for implementation in networked neurons for more advanced studies of neuronal behaviors.

The existence of electrical communication among pyramidal cells (PCs) in the adult cortex has been debated by neuroscientists for several decades. Gap junctions (GJs) among cortical interneurons have been well documented experimentally and their functional roles have been proposed by both computational neuroscientists and experimentalists alike. Experimental evidence for similar junctions among pyramidal cells in the cortex, however, has remained elusive due to the apparent rarity of these couplings among neurons. In this work, we develop a neuronal network model that includes observed probabilities and strengths of electrotonic coupling between PCs and gap-junction coupling among interneurons, in addition to realistic synaptic connectivity among both populations. We use this network model to investigate the effect of electrotonic coupling between PCs on network behavior with the goal of theoretically addressing this controversy of existence and purpose of electrotonically coupled PCs in the cortex.

Myelinated neurons are characterized by the presence of myelin, a multilaminated wrapping around the axons formed by specialized neuroglial cells. Myelin acts as an electrical insulator and therefore, in myelinated neurons, the action potentials do not propagate within the axons but happen only at the nodes of Ranvier which are gaps in the axonal myelination. Recent advancements in brain science have shown that the shapes, timings, and propagation speeds of these so-called saltatory action potentials are controlled by various biochemical interactions among neurons, glial cells and the extracellular space. Given the complexity of brain’s structure and processes, the work hypothesis made in this paper is that non-local effects are involved in the optimal propagation of action potentials. A non- local model of the action potentials propagation in myelinated neurons is proposed that involves spatial derivatives of fractional order. The effects of non- locality on the distribution of the membrane potential are investigated using numerical simulations.

Since more than a decade ago, three statements about spiking neuron (SN) implementations have been widely accepted: 1) Hodgkin and Huxley (HH) model is computationally prohibitive, 2) Izhikevich (IZH) artificial neuron is as efficient as Leaky Integrate-and-Fire (LIF) model, and 3) IZH model is more efficient than HH model ( Izhikevich, 2004 ). As suggested by Hodgkin and Huxley (1952) , their model operates in two modes: by using the α ’s and β ’s rate functions directly (HH model) and by storing them into tables (HHT model) for computational cost reduction. Recently, it has been stated that: 1) HHT model (HH using tables) is not prohibitive, 2) IZH model is not efficient, and 3) both HHT and IZH models are comparable in computational cost ( Skocik & Long, 2014 ). That controversy shows that there is no consensus concerning SN simulation capacities. Hence, in this work, we introduce a refined approach, based on the multiobjective optimization theory, describing the SN simulation capacities and ultimately choosing optimal simulation parameters. We have used normalized metrics to define the capacity levels of accuracy, computational cost, and efficiency. Normalized metrics allowed comparisons between SNs at the same level or scale. We conducted tests for balanced, lower, and upper boundary conditions under a regular spiking mode with constant and random current stimuli. We found optimal simulation parameters leading to a balance between computational cost and accuracy. Importantly, and, in general, we found that 1) HH model (without using tables) is the most accurate, computationally inexpensive, and efficient, 2) IZH model is the most expensive and inefficient, 3) both LIF and HHT models are the most inaccurate, 4) HHT model is more expensive and inaccurate than HH model due to α ’s and β ’s table discretization, and 5) HHT model is not comparable in computational cost to IZH model. These results refute the theory formulated over a decade ago ( Izhikevich, 2004 ) and go more in-depth in the statements formulated by Skocik and Long (2014) . Our statements imply that the number of dimensions or FLOPS in the SNs are theoretical but not practical indicators of the true computational cost. The metric we propose for the computational cost is more precise than FLOPS and was found to be invariant to computer architecture. Moreover, we found that the firing frequency used in previous works is a necessary but an insufficient metric to evaluate the simulation accuracy. We also show that our results are consistent with the theory of numerical methods and the theory of SN discontinuity. Discontinuous SNs, such LIF and IZH models, introduce a considerable error every time a spike is generated. In addition, compared to the constant input current, the random input current increases the computational cost and inaccuracy. Besides, we found that the search for optimal simulation parameters is problem-specific. That is important because most of the previous works have intended to find a general and unique optimal simulation. Here, we show that this solution could not exist because it is a multiobjective optimization problem that depends on several factors. This work sets up a renewed thesis concerning the SN simulation that is useful to several related research areas, including the emergent Deep Spiking Neural Networks.

The Hodgkin-Huxley (HH) neuron is one of the most biophysically-meaningful models used in computational neuroscience today. Ironically, the model's high experimental value is offset by its disproportional computational complexity. To such an extent that neuroscientists have either resorted to simpler models, losing precious neuron detail, or to using high-performance computing systems, to gain acceleration, for complex models. However, multicore/multinode CPU-based systems have proven too slow while FPGA-based ones have proven too time-consuming to (re)deploy to. Clearly, a solution that bridges user friendliness and high speedups is necessary. This paper presents flexHH, a flexible FPGA library implementing five popular, highly parameterizable variants of the HH neuron model. flexHH is the first crucial step towards making FPGA-based simulations of compute-intensive neural models available to neuroscientists without the debilitating penalty of re-engineering and re-synthesis. Through flexHH, the user can instantiate custom models and immediately take advantage of the acceleration without the mediation of an engineer, which has proven to be a major inhibitor to full adoption of FPGAs in neuroscience labs. In terms of performance, flexHH achieves speedups between $8\times $ -$20\times $ compared to sequential-C implementations, while only a small drop in real-time capabilities is observed when compared to hardcoded FPGA-based versions of the models tested.

Spinal cord stimulation for chronic pain or deep brain stimulation for epilepsy, there are similar other techniques using micro stimulation of tissues in order to modulate neural activity for therapeutic purposes. In addition to experimental work, computational modeling is a powerful tool to obtain characteristics of either a cluster of cell bundle or a single unit by largely exploring every single parameter. This enables to predict precisely neural responses to electrical stimulation, which ultimately improves clinical outcomes. This work uses pyramidal cell with realistic morphology from fifth layer of somatosensory cortex constructed by Blue Brain project. The biophysical properties are defined by conductance based voltage gated channels. NEURON v8.0 is used to simulate intracellular stimulation. Single cell model's validation and spike activity show that axonal compartments are the most possible area to fire for step current stimulation. This work presents insights into better computational infrastructure for parameter optimization.

Objective: Parkinson’s disease (PD) is a degenerative disease of the nervous system that frequently occurs in the aged. Transcranial magnetoacoustic stimulation (TMAS) is a neuronal adjustment method that combines sound fields and magnetic fields. It has the characteristics of high spatial resolution and noninvasive deep brain focusing.Methods: This paper constructed a simulation model of TMAS based on volunteer’s skull computer tomography, phased controlled transducer and permanent magnet. It simulates a transcranial focused sound pressure field with the Westervelt equation and builds a basal ganglia and thalamus neural network model in the PD state based on the Hodgkin-Huxley model.Results: A biased sinusoidal pulsed ultrasonic TMAS induced current with 0.3 T static magnetic field induction and 0.2 W⋅cm–2 sound intensity can effectively modulate PD states with RI ≥ 0.633. The magnitude of magnetic induction strength was changed to 0.2 and 0.4 T. The induced current was the same when the sound intensity was 0.4 and 0.1 W⋅cm–2. And the sound pressure level is in the range of −1 dB (the induced current difference is less than or equal to 0.019 μA⋅cm–2). TMAS with a duty cycle of approximately 50% can effectively modulates the error firings in the PD neural network with a relay reliability not less than 0.633.Conclusion: TMAS can modulates the state of PD.

The influence of astrocytes on the signal transmission processes in the neural network is the aim of paper studies. The architecture of the neuron-astrocyte network in the form of interacting three rings, corresponding to experimental data on the organization of networks in the brain, was considered. The first ring of the system is an ensemble of excitatory neurons, each of which is stimulated by an uncorrelated Poisson process that simulates the effect of an external neural network. The second ring of the system is a network of inhibitory neurons that receive signals from excitatory neurons, and which are under the influence of astrocytes that form the third ring of the network under consideration. The generation of calcium impulses in astrocytes is induced by the activity of the first ring of the system. The effect of astrocytes is to a change in the amplitudes of the action of excitatory neurons on inhibitory ones, as well as to a change in the effective forces of connections in the second ring. The paper examines the collective dynamics of signaling of inhibitory neurons. In this work, it is shown that the astrocytic regulation of signal transmission between neurons affects the establishment of synchronization of the activity of the neural ensemble at the times of calcium dynamics in astrocytes. It was found that the influence of astrocytes can lead both to the expansion of the synchronization region and to the displacement of its boundaries.

The Hodgkin-Huxley model, decades after its first presentation, is still a reference model in neuroscience as it has successfully reproduced the electrophysiological activity of many organisms. The primary signal in the model represents the membrane potential of a neuron. A parametric and simple representation of this signal is presented in this paper.The new proposal is an adapted Frequency Modulated Möbius multicomponent model defined as a flexible decomposition in waves that describe the signal morphology. A specific feature of the new model is that the parameters are subject to interpretable restrictions.A broad simulation experiment is conducted to show the new model accurately represents the simulated Hodgkin-Huxley signal. Moreover, the model potential to predict the neuron’s relevant characteristics, described with parameters of the Hodgkin Huxley model, is shown using different Machine Learning methods. The proposed model is also validated with real data from Squid Giant Axons. The comparison of the parameter configuration between the simulated and real data demonstrated the flexibility of the model as well as interesting differences.Author summaryAlejandro Rodríguez-Collado. I received the double degree in Statistics and Computer Engineering and the Master’s degree in Business Intelligence and Big Data from the Universidad de Valladolid in 2019 and 2020, respectively. I work as researcher and Professor for the Department of Statistics and Operational Research at the Universidad de Valladolid. My main research interests include oscillatory signal processing, neuroscience, multivariate data analysis and supervised learning.Cristina Rueda. I received the BS degree in mathematics from the Universidad de Valladolid in 1987 and the PhD degree in statistical science from the Universidad de Valladolid in 1989. I am currently Professor in the Department of Statistics and Operational Research at the Universidad de Valladolid. My main research interests include statistical inference methods under restrictions, circular data, computational biology, and statistical methods for signal analysis.

Background Electrical spinal cord stimulation (SCS) is an alternative to conventional medication for chronic pain relief. Several hypotheses exist concerning the neurophysiological, vascular, and neurochemical mechanism behind SCS. Methods The excitation and blockade effects of the three common SCS waveforms (tonic, burst, and high-frequency stimulation) on the nerve fibers bypassing the region of the electrodes are analyzed in a computational study. The simulations are based on the model of Hodgkin and Huxley which is fitted to spike durations of 1 ms. Results and conclusions SCS is FDA approved technique for pain relief but the mechanisms of action are still under investigation. The first element in the chain of mechanisms is the generation and the block of spikes in nerve fibers close to the stimulating electrode. For these 'primary fibers' computer simulations showed that conventional SCS generates sharply synchronized spikes whereas the spread of the spiking times by burst stimulation is expected to cause the suppression of paresthesia. This rather uniform spread of spiking times (in comparison to tonic stimulation) is a consequence of more pulses (5 vs. 1), longer pulses, and increasing intensities within each train of 5 pulses. High-frequency stimulation can block the conduction of spikes but the distance of the fiber to the lead is a critical factor.

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.

Brain tissue is a complex material made of interconnected neural, glial, and vascular networks. While the physics and biochemistry of brain’s cell types and their interactions within their networks have been studied extensively, only recently the interactions of and feedback among the networks have started to capture the attention of the research community. Thus, a good understanding of the coupled mechano-electrochemical processes that either provide or diminish brain’s functions is still lacking. One way to increase the knowledge on how the brain yields its functions is by developing a robust controlled feedback engineering system that uses fundamental science concepts to guide and interpret experiments investigating brain’s response to various stimuli, aging, trauma, diseases, treatment and recovery processes. Recently, a mathematical model for an implantable neuro-glial-vascular unit, named brain-on-a-chip, was proposed that can be optimized to perform some fundamental cellular processes that could facilitate monitoring and supporting brain’s functions, and highlight basic brain mechanisms. In this paper we use coupled elastic, viscoelastic and mass elements to model a brain-on-a-chip made of a neuron and its membrane, and astrocyte’s endfeet connected to an arteriole’s wall. We propose two constrained Lagrangian formulations that link the Hodgkin-Huxley model of the neuronal membrane, and the mechanics of the neuron, neuronal membrane, and the glia’s endfeet. The effects of the nitric oxide produced by neurons and endothelial cells on the proposed brain-on-a-chip are investigated through numerical simulations. Our numerical simulations suggest that a non-decaying synthesis of nitric oxide may contribute to the onset of a cerebral microaneurysm.

Hodgkin and Huxley showed that even if the filaments are dissolved, a neuron’s membrane alone can generate and transmit the nerve spike. Regulating the time gap between spikes is key to the brain’s cognitive function, however, the time modulation mechanism is still a mystery. By inserting a coaxial probe deep inside a neuron, we repeatedly show that the filaments transmit electromagnetic signals of ~200 μs before an ionic nerve spike sets in. To understand its origin, here, we mapped the electromagnetic vortex produced by a filamentary bundle deep inside a neuron, regulating the nerve spike’s electrical-ionic vortex. We used monochromatic polarized light to measure the transmitted signals beating from the internal components of a cultured neuron. A nerve spike is a 3D ring of the electric field encompassing the perimeter of a neural branch. Several such vortices flow sequentially to keep precise timing for the brain’s cognition. The filaments hold millisecond order time gaps between membrane spikes with microsecond order signaling of electromagnetic vortices. Dielectric resonance images revealed that ordered filaments inside neural branches instruct the ordered grid-like network of actin–beta-spectrin just below the membrane. That layer builds a pair of electric field vortices, which coherently activates all ion-channels in a circular area of the membrane lipid bilayer when a nerve spike propagates. When biomaterials vibrate resonantly with microwave and radio-wave, simultaneous quantum optics capture ultra-fast events in a non-demolition mode, revealing multiple correlated time-domain operations beyond the Hodgkin–Huxley paradigm. Neuron holograms pave the way to understanding the filamentary circuits of a neural network in addition to membrane circuits.

The purpose of this paper is to conduct an in-depth study based on the Hodgkin-Huxley model and to highlight that the sodium and potassium ion channels distributed along the entire length of the neural axons can be composed of two active memristors.

The motor threshold measurement is a standard in preintervention probing in TMS experiments. We aim to predict the motor threshold for near-rectangular stimuli to efficiently determine the motor threshold size before any experiments take place. Estimating the behavior of large-scale networks requires dynamically accurate and efficient modeling. We utilized a Hodgkin–Huxley (HH) type model to evaluate motor threshold values and computationally validated its function with known true threshold data from 50 participants trials from state-of-the-art published datasets. For monophasic, bidirectional, and unidirectional rectangular stimuli in posterior-anterior or anterior-posterior directions as generated by the cTMS device, computational modeling of the HH model captured the experimentally measured population-averaged motor threshold values at high precision (maximum error ≤ 8%). The convergence of our biophysically based modeling study with experimental data in humans reveals that the effect of the stimulus shape is strongly correlated with the activation kinetics of the voltage-gated ion channels. The proposed method can reliably predict motor threshold size using the conductance-based neuronal models and could therefore be embedded in new generation neurostimulators. Advancements in neural modeling will make it possible to enhance treatment procedures by reducing the number of delivered magnetic stimuli to participants.

It is known that visual attention can modulate firing patterns of neurons in visual cortexes and play important functional roles in visual information processes. Despite of several decades of studies, mechanisms of visual attention still remain unclear. Recent neurophysiological studies reported that attention could increase NMDA and AMPA synaptic strength. To understand how neuronal activity is modulated by attention at the synaptic level, we proposed a three-layer neural network in this study. Each neuron receives AMPA and NMDA currents and also GABA currents. In the synapse between every two neurons, neurotransmitters are stochastically bound with receptors in post-synaptic membranes. In the model, it is hypothesized that attention could make the binding process less stochastic, and more neurotransmitters are bound with postsynaptic receptors. Our simulation showed that attention resulted neurons in the model had stronger firing rates and less response variability. We also found that attention had stronger modulation of neuronal activity in higher layers than in lower layers. Inhibitory neurons had stronger attention effects than did excitatory neurons. Overall, our results demonstrated that attention may modulate neuronal activity by controlling the stochastic binding process.

In this chapter, we analyze the phenomenon of frequency clusters in a population of coupled Hodgkin–Huxley neurons with spike timing-dependent plasticity. We show their persistence against external noise and introduce a phenomenological phase oscillator model to understand their emergence. We observe that the splitting of a neural population to a few clusters that are synchronized at different frequencies may lead to a slow waxing and waning of the mean field amplitude and might relate to low-frequency modulation found in brain signals like local field potentials (LFP) or electroencephalographic (EEG) signals.

General anesthesia has revolutionized healthcare over the past 200 years and continues to show advancements. However, many phenomena induced by general anesthetics including paradoxical excitation are still poorly understood. Voltage-gated sodium channels (NaV) were believed to be one of the proteins targeted during general anesthesia. Based on electrophysiological measurements before and after propofol treatments of different concentrations, we mathematically modified the Hodgkin–Huxley sodium channel formulations and constructed a thalamocortical model to investigate the potential roles of NaV. The ion channels of individual neurons were modeled using the Hodgkin–Huxley type equations. The enhancement of propofol-induced GABAa current was simulated by increasing the maximal conductance and the time-constant of decay. Electroencephalogram (EEG) was evaluated as the post-synaptic potential from pyramidal (PY) cells. We found that a left shift in activation of NaV was induced primarily by a low concentration of propofol (0.3–10 μM), while a left shift in inactivation of NaV was induced by an increasing concentration (0.3–30 μM). Mathematical simulation indicated that a left shift of NaV activation produced a Hopf bifurcation, leading to cell oscillations. Left shift of NaV activation around a value of 5.5 mV in the thalamocortical models suppressed normal bursting of thalamocortical (TC) cells by triggering its chaotic oscillations. This led to irregular spiking of PY cells and an increased frequency in EEG readings. This observation suggests a mechanism leading to paradoxical excitation during general anesthesia. While a left shift in inactivation led to light hyperpolarization in individual cells, it inhibited the activity of the thalamocortical model after a certain depth of anesthesia. This finding implies that high doses of propofol inhibit the network partly by accelerating NaV toward inactivation. Additionally, this result explains why the application of sodium channel blockers decreases the requirement for general anesthetics. Our study provides an insight into the roles that NaV plays in the mechanism of general anesthesia. Since the activation and inactivation of NaV are structurally independent, it should be possible to avoid side effects by state-dependent binding to the NaV to achieve precision medicine in the future.

Studies have shown that neurons exposed to two or more signals with different frequencies can fire at frequencies other than these. This phenomenon is known as Ghost Resonance (GR). In this study, GR phenomenon was investigated in a two-layer feed forward loop (FFL) network consisting of Hodgkin-Huxley (H-H) neurons. Periodic signals with different frequencies were applied to each of the two neurons in the first layer of the FFL network. The firing behavior of the neuron in the second layer of the FFL network has been studied. The results show that the third neuron in the FLL network fires at a frequency that is the absolute value of the difference between the frequencies of the signals applied to the first and second neurons. These results reveal the presence of GR phenomenon in H-H neurons.

Optogenetics has a lot of potential to become an effective neuromodulative therapy for clinical application. Selecting the correct opsin is crucial to have an optimal optogenetic tool. With computational modeling, the neuronal response to the current dynamics of an opsin can be extensively and systematically tested. Unlike electrical stimulation where the effect is directly defined by the applied field, the stimulation in optogenetics is indirect, depending on the selected opsin’s non-linear kinetics. With the continuous expansion of opsin possibilities, computational studies are difficult due to the need for an accurate model of the selected opsin first. To this end, we propose a Hodgkin-and-Huxley based model (22HH) as alternative to the conventional three and four state Markov models used for opsin modeling. Furthermore, we provide a fitting procedure, which allows for nearly automatic model fitting starting from a vast parameter space. With this procedure, we successfully fitted two distinctive opsins ChR2(H134R) and MerMAID. Both models are able to represent the experimental data with great accuracy and were obtained within an acceptable time frame. This is due to the absence of differential equations in the fitting procedure, with an enormous reduction in computational cost as result. The performance of the proposed model with a fit to ChR2(H134R) was tested, by comparing the neural response in a regular spiking neuron to the response obtained with the non-instantaneous, four state Markov model (4SB), derived by Williams et al. (2013) [1]. Finally, a computational speed gain was observed with the 22HH model in a regular spiking and sparse Pyramidal-Interneuron-Network-Gamma (sPING) network simulation with respect to the 4SB-model, due to the former having two differential equations less. Consequently, the proposed model allows for computationally efficient optogenetic neurostimulation and with the proposed fitting procedure will be valuable for further research in the field of optogenetics.

Understanding the human brain is the biggest challenge for scientists in the twenty-first century. The Hodgkin-Huxley (HH) model is one of the most successful mathematical models for bio-realistic simulations of the brain. However, the simulation of HH neurons involves complex computation, which makes the implementation of large-scale brain networks difficult. In this paper, we propose a hardware architecture that efficiently computes a large-scale network of HH neurons. This architecture is based on the neuron machine hardware architecture, which has the limitation of speed as it has only one computation node. The proposed architecture is essentially a non-Von Neumann synchronous system with multiple computation nodes, called hardware neurons, to achieve linear speedup. In this paper, the design of a digital circuit that computes large-scale networks of HH neurons is presented as an example to provide a detailed description of the proposed architecture. This design supports axonal conduction delay of spikes and short- and long-term plasticity synapses, along with floating-point precision HH neurons. The design is implemented on a field-programmable gate array (FPGA) chip and computes a network of one million HH neurons in near real time. The implemented system can compute a network with up to 12 million HH neurons and 600 million synapses. The proposed design method can facilitate the design of systems supporting complex neuron models and their flexible implementation on reconfigurable FPGA chips., Comment: 8 pages, 14 figures, submitted to ICONS conference

The Hodgkin–Huxley (HH) model can simulate the process of neuron pulse delivery, and can reasonably explain each step in the process. In this study, we use a microcontroller based on the Advanced RISC Machines (ARM) core to implement the Hodgkin-Huxley model, and use four microcontrollers to implement three ion channels and an external current channel. The hardware experimental results and MATLAB simulation results are exactly the same. Studies have shown that the dynamic characteristics of the neuron model implemented on a microcontroller based on the ARM Cortex-M4 core can meet real-time computing requirements. In addition, due to the different conditions of patients, its external stimulation current and the reversal potential of each ion channel has a significant effect on the neuron release process. By changing the parameters on a single microcontroller, we adjusted and tested it on the hardware platform to show the experimental results more clearly and conveniently. The results show that changes in the stimulation current will affect the firing state of the neurons, and changes in the reversal potential of each ion channel will affect the firing frequency of the HH neuron model.

Brain is a highly complex non-linear system, made up of neurons which communicate with each other through neurotransmission. The focus here is to understand and simulate the signal transduction in one of the most important sensory bipolar neurons called olfactory receptor neurons (ORN). The first site of odorant transduction-cilia, house the G-protein signaling cascade that has components that interact with each other to produce the cell output. The work involves modelling of cilia, dendrite and axon of ORN, wherein axon has been modelled using the most biologically plausible Hodgkin and Huxley equations. These ORN outputs are in turn used to drive the next layer of neurons which are connected in Freeman’s topology in an attempt to create a small world network. The complete modelling was done in ‘NEURON’ tool.

The main cause of Parkinson's disease is that the loss of dopamine makes the direct and indirect pathways of striatum lose their original balance, which eventually leads to abnormality of basal ganglia network. At the same time, various structures of the basal ganglia network show abnormal synchronous discharge. Thalamus also can't respond to cortex normally, making Parkinson's patients tremble abnormally. As the key structure of basal ganglia network, striatum has been always put much attention in the research. However, due to the complexity of the two pathways, a simplified method was always used in the research. Namely, The input of the striatum is set as a constant and the input current of the two pathways is analyzed individually. However, it's obvious that the simplified method can't truly reflect the influence of the two pathways on the basal ganglia network. In this paper, we will use the modified Hodgkin-Huxley model to simulate the influence of the direct path and the indirect path on the network. Corresponding parameters are adjusted in normal state. Then sensitivity characteristics of the two pathways on the network were observed by analyzing the relay ability of thalamus to the signals from the cerebral cortex, which will have much significance in diagnosis in Parkinson's disease.

In many tasks related to realistic neurons and neural network simulation, the performance of desktop computers is nowhere near enough. To overcome this obstacle, researchers are developing FPGA-based simulators that naturally use fixed-point arithmetic. In these implementations, little attention is usually paid to the choice of numerical method for the discretization of the continuous neuron model. In our study, the implementation accuracy of a neuron described by simplified Hodgkin&ndash, Huxley equations in fixed-point arithmetic is under investigation. The principle of constructing a fixed-point neuron model with various numerical methods is described. Interspike diagrams and refractory period analysis are used for the experimental study of the synthesized discrete maps of the simplified Hodgkin&ndash, Huxley neuron model. We show that the explicit midpoint method is much better suited to simulate the neuron dynamics on an FPGA than the explicit Euler method which is in common use.

All cells in life systems are capable of communication between cells by the use of signaling molecules such as hormones. The speed of this form of communication is limited by diffusion rates. Multicellular animals early in evolution took advantage of the much faster internal electric signaling to coordinate their activities. Neurons are the specialized cells for this purpose. For quick analysis of inputs, using short connections, a concentrated network of neurons becames ganglions, and then brains. A brain consists of a set of interconnected neurons, each acting to process a set of inputs to produce one output. As such, a set of interconnected electronic gates is capable of acting as a brain (Turing’s lemma), and is the basis of modern-day computers. We can envision even more powerful computers using quantum coherent states, but our own brain seems to be acting classically, with ‘free-will’ coming from the complexity in the brain and the almost chaotic nature of its inputs.

In this chapter, we discuss elementary concepts from neurophysiology. We treat the generation of the membrane potential, the role and dynamics of voltage-gated channels and the Hodgkin-Huxley equations. We present experimental techniques, in particular the voltage and patch-clamp technique, that have been essential in elucidating fundamental processes of neuronal dynamics. Several concepts are illustrated with clinical examples. At the end of this chapter, you will understand the critical role of ion concentration gradients for establishing the resting membrane potential and the role of the voltage-gated sodium and potassium channels in the generation of action potentials. You understand how Hodgkin and Huxley were able to formulate the Hodgkin-Huxley equations and you can perform essential simulations using these equations to explore the effects of changes in ion homeostasis or abnormal channel gating.

The effects of channel blocks on the spontaneous spiking activity and neuron networks pattern selection are investigated by using an improved Hodgkin–Huxley (HH) model in which the electromagnetic induction is considered and the magnetic flux is used to describe the influence of electromagnetic field. The discharge behavior of neurons induced by potassium ion and sodium ion channel blocks was analyzed by numerical simulation in the improved HH model. The results suggest that changes in the maximum conductance of potassium channels can cause spontaneous discharge behavior of neurons. The poisoning of potassium ion can be weakened by the electromagnetic radiation in the neural network, and the neural network presents a state of spatial order in the case of spiral waves. It is interesting that the ordered waveform is generated by no-flux boundary condition when the initial states are selected as wedge-shaped type in the network. In addition, potassium channel blocks can promote the discharge of neurons and facilitate the formation of spiral waves in the neural network. By contrast, the electrical activity of neurons is inhibited by sodium channel blocks. The influence of membrane patch size on the electrical activity of single neuron is greater than that on the collective behavior of neural network. This research will enhance understanding of the role of toxins in neuronal firing and collective behavior of real neural systems.

In a succession of articles published over 65 years ago, Sir Alan Lloyd Hodgkin and Sir Andrew Fielding Huxley established what now forms our physical understanding of excitation in nerve, and how the axon conducts the action potential. They uniquely quantified the movement of ions in the nerve cell during the action potential, and demonstrated that the action potential is the result of a depolarizing event across the cell membrane. They confirmed that a complete depolarization event is followed by an abrupt increase in voltage that propagates longitudinally along the axon, accompanied by considerable increases in membrane conductance. In an elegant theoretical framework, they rigorously described fundamental properties of the Na+ and K+ conductances intrinsic to the action potential. Notwithstanding the elegance of Hodgkin and Huxley's incisive and explicative series of discoveries, their model is mathematically complex, relies on no small number of stochastic factors, and has no analytical solution. Solving for the membrane action potential and the ionic currents requires integrations approximated using numerical methods. In this article I present an analytical formalism of the nerve action potential, Vm and that of the accompanying cell membrane electric field, Em. To conclude, I present a novel description of Vm in terms of a single, nonlinear differential equation. This is an original stand-alone article: the major contribution is the latter, and how this description coincides with the cell membrane electric field. This work has necessitated unifying information from two preceding papers, each being concerned with the development of closed-form descriptions of the nerve action potential., 9 pages, 1 figure, 64 references

Recent studies have shown that the dynamics of action potential generation in neurons in vertebrates, in contrast to invertebrates, is significantly different from the slow exponential dynamics predicted by the Hodgkin–Huxley equations and is characterized by a sudden kink-like origin in the form of a steep linear increase. In this context, new and important aspects of studies of the links between the dynamics of action potential generation and the frequency coding abilities of neurons and neuronal networks have been found. This review addresses contemporary models describing the kink-type dynamics of action potential generation, including an alternative model of cooperative activation of potential-dependent sodium channels and the effects of the dynamics of action potential generation on the processing abilities of neural networks. The relevance of this direction comes from the fact that despite the rapid development of neuron simulation in recent years, generally accepted models of nerve cells cannot provide a realistic description of the complete dynamics of action potential generation in mammalian neurons or correct assessments of the ability of these cells to encode high-frequency signals. Contemporary experimental and theoretical analyses of action potential generation and neuronal encoding, as summarized in the present work, are highly significant for improving our understanding of nerve cell physiology and assisting the creation of more accurate and correct models of neurons.

The Hodgkin and Huxley model describes the electrophysiology of the membrane of the giant squid’s axon. This model was developed from measurements of passive and active electrical behavior of the nerve cell. The four-coupled nonlinear ordinary differential equations, which describe the model, are based on the behavior of sodium and potassium channels. The aim of this work is to study the dynamic behavior of a neuronal physiological system described by the Hodgkin-Huxley (H-H) model through the analysis and interpretation of numerical simulations.

Acid-sensing ion channels (ASICs) are H+-activated neuronal Na+ channels. They are involved in fear behavior, learning, neurodegeneration after ischemic stroke and in pain sensation. ASIC activation has so far been studied only with fast pH changes, although the pH changes associated with many roles of ASICs are slow. It is currently not known whether slow pH changes can open ASICs at all. Here, we investigated to which extent slow pH changes can activate ASIC1a channels and induce action potential signaling. To this end, ASIC1a current amplitudes and charge transport in transfected Chinese hamster ovary cells, and ASIC-mediated action potential signaling in cultured cortical neurons were measured in response to defined pH ramps of 1-40 s duration from pH 7.4 to pH 6.6 or 6.0. A kinetic model of the ASIC1a current was developed and integrated into the Hodgkin-Huxley action potential model. Interestingly, whereas the ASIC1a current amplitude decreased with slower pH ramps, action potential firing was higher upon intermediate than fast acidification in cortical neurons. Indeed, fast pH changes (10 s) did in many experiments not generate action potentials. Computer simulations corroborated these observations. We provide here the first description of ASIC function in response to defined slow pH changes. Our study shows that ASIC1a currents, and neuronal activity induced by ASIC1a currents, strongly depend on the speed of pH changes. Importantly, with pH changes that take >10 s to complete, ASIC1a activation is inefficient. Therefore, it is likely that currently unknown modulatory mechanisms allow ASIC activity in situations such as ischemia and inflammation.

While the nonlinearity and complexity of biological phenomena keeps much of the intricate details of science mysterious, computational modeling can help unveil the dynamics and functionalities of such complex phenomena by studying the various parts orchestrating the system and leading eventually to its overall behavior. In this work, we develop a dual-compartment conductance-based model to replicate the neurophysiological firing patterns and properties seen in cortical neurons of the zebra finch, which are responsible for the bird’s song. The model’s aim is to capture the timing of the action potentials in the spike train for various stimuli and the intricate details of spikes’ morphology.

Reducing neuronal size results in less cell membrane and therefore lower input conductance. Smaller neurons are thus more excitable as seen in their voltage responses to current injections in the soma. However, the impact of a neuron’s size and shape on its voltage responses to synaptic activation in dendrites is much less understood. Here we use analytical cable theory to predict voltage responses to distributed synaptic inputs and show that these are entirely independent of dendritic length. For a given synaptic density, a neuron’s response depends only on the average dendritic diameter and its intrinsic conductivity. These results remain true for the entire range of possible dendritic morphologies irrespective of any particular arborisation complexity. Also, spiking models result in morphology invariant numbers of action potentials that encode the percentage of active synapses. Interestingly, in contrast to spike rate, spike times do depend on dendrite morphology. In summary, a neuron’s excitability in response to synaptic inputs is not affected by total dendrite length. It rather provides a homeostatic input-output relation that specialised synapse distributions, local non-linearities in the dendrites and synaptic plasticity can modulate. Our work reveals a new fundamental principle of dendritic constancy that has consequences for the overall computation in neural circuits.In briefWe show that realistic neuron models essentially collapse to point neurons when stimulated by randomly distributed inputs instead of by single synapses or current injection in the soma.HighlightsA simple equation that predicts voltage in response to distributed synaptic inputs.Responses to distributed and clustered inputs are largely independent of dendritic length.Spike rates in various Hodgkin Huxley (HH) like or Leaky Integrate-and-Fire (LIF) models are largely independent of morphology.Precise spike timing (firing pattern) depends on dendritic morphology.NeuroMorpho.Org database-wide analysis of the relation between dendritic morphology and electrophysiology.Our equations set precise input-output relations in realistic dendrite models.

2019 Medical Technologies Congress, TIPTEKNO 2019 -- 3 October 2019 through 5 October 2019 -- -- 154293, It is known that activity is terminated abruptly as a result of strong synchronization in bistable neuron populations when there is sufficient current stimulation. The aim of this study is to investigate the effect of ion channel blocking on the phenomenon of spontaneous termination of ongoing activity in the bistable neural network connected by excitatory chemical synapses using stochastic Hodgkin-Huxley (H-H) equations. The obtained results show that significant changes in the dynamics of neurons occur due to the blocking of potassium ion channels at different rates depending on the coupling strength. As the coupling of synaptic interaction increases, the synchronization between neurons increases and the activity terminates. Simulation results showed that sodium ion channels are not effective on this phenomenon. © 2019 IEEE.

2019 Medical Technologies Congress, TIPTEKNO 2019 -- 3 October 2019 through 5 October 2019 -- -- 154293, Vital functions in living organisms occur through changes in electrical activity. These activities consist of brain rhythms with different frequencies that exhibit oscillatory behavior and can be monitored by local field potentials or EEG recordings. The synchronization of neural activity underlies the emergence of these rhythmic waves, which are of great importance in the nervous system. In this study, the effects of changes in intrinsic mechanisms and intercellular communication, that are constituting neural activity, on the synchronization of neuron pair which is composed of two nerve cells and connected with different types of synaptic junction were investigated in a biologically meaningful way. The obtained results showed that the excitability, synaptic and ionic conductivity levels are crucial for neurons to synchronize. It has also been found that the noise caused by the stochastic nature of the ion channels is an auxiliary biological component to achieve synchronization. © 2019 IEEE.

For the study of new computer architecture inspired by brain, implementing neuron function on hardware has become an emerging research direction. To study the feasibility of biological neuron implementation and acceleration characteristics on the hardware platform, the basic Hodgkin-Huxley (HH) neuron model and a small scale of synapse connection model is implemented on Xilinx Zynq7 Zedboard FPGA, high-level-synthesis method is used to reduce the burden of hardware design. The Hodgkin-Huxley model simulation result of FPGA are validated through high level software simulation tool in Brian2, furthermore, resource utilization and calculation time cost are provided in this paper, finally, a pipeline design of HH neuron model is used to accelerate calculations and reduce resource utilization, the result proves that this design is suitable for HH model simulation.

The ionic environment is vital to the excitability of neurons. Action of anticonvulsant drugs on the passage of ions through the cell membrane has been shown to be an important general mechanism by which many of these agents exert their seizure-suppressing effects. The importance of extracellular ions in regulation of excitable cells was discovered in the last century. However, modern thinking about the role played by ion channels crystallized from the elegant work of Hodgkin and Huxley in the 1950s. Ion channels are an important class of sites that a number of drugs affect, including agents that affect seizure susceptibility. Potassium channels are ubiquitous in eukaryotic cells and exhibit more diverse characteristics than channels for other ions. Calcium channels play a major role in neuronal function, in part, because of the important second messenger actions exerted by free intracellular Ca2+.

Computational modeling is essential to understand how the complex dendritic structure and membrane properties of a neuron process input signals to generate output signals. Compartmental models describe how inputs, such as synaptic currents, affect a neuron’s membrane potential and produce outputs, such as action potentials, by converting membrane properties into the components of an electrical circuit. The simplest such model consists of a single compartment with a leakage conductance which represents a neuron having spatially uniform membrane potential and a constant conductance summarizing the combined effect of every ion flowing across the neuron’s membrane. The Hodgkin-Huxley model introduces two additional active channels; the sodium channel and the delayed rectifier potassium channel whose associated conductances change depending on the membrane potential and that are described by an additional set of three nonlinear differential equations. Since its conception in 1952, many kinds of active channels have been discovered with a variety of characteristics that can successfully be modeled within the same framework. As the membrane potential varies spatially in a neuron, the next refinement consists in describing a neuron as an electric cable to account for membrane potential attenuation and signal propagation along dendritic or axonal processes. A discrete version of the cable equation results in compartments with possibly different properties, such as different types of ion channels or spatially varying maximum conductances to model changes in channel densities. Branching neural processes such as dendrites can be modeled with the cable equation by considering the junctions of cables with different radii and electrical properties. Single neuron computational models are used to investigate a variety of topics and reveal insights that cannot be evidenced directly by experimental observation. Studies on action potential initiation and on synaptic integration provide prototypical examples illustrating why computational models are essential. Modeling action potential initiation constrains the localization and density of channels required to reproduce experimental observations, while modeling synaptic integration sheds light on the interaction between the morphological and physiological characteristics of dendrites. Finally, reduced compartmental models demonstrate how a simplified morphological structure supplemented by a small number of ion channel-related variables can provide clear explanations about complex intracellular membrane potential dynamics.

The neuronal responses through excitatory and inhibitory synapses are implemented on a reconfigurable and programmable platform. The synaptic cleft between the pre synaptic and post synaptic neuron has been depicted as a ramp generator while the post synaptic potentials are observed from the transistor channel neuron model which emulates the ion channels in biological neurons. The synaptic strengths are tuned by modulating the charge on the floating gate devices on the hardware demonstrated through particular voltage levels and time constants. The models have been designed and built in such a way that the tools associated with the chip make it possible to build up and compile a bigger network of neurons and synapses. The experimental measurements are taken from the circuits compiled on a Field Programmable Analog Array fabricated on a 350nm process.

Neurological diseases can be studied by performing bio-hybrid experiments using a real-time biomimetic Spiking Neural Network (SNN) platform. The Hodgkin-Huxley model offers a set of equations including biophysical parameters which can serve as a base to represent different classes of neurons and affected cells. Also, connecting the artificial neurons to the biological cells would allow us to understand the effect of the SNN stimulation using different parameters on nerve cells. Thus, designing a real-time SNN could useful for the study of simulations of some part of the brain. Here, we present a different approach to optimize the Hodgkin-Huxley equations adapted for Field Programmable Gate Array (FPGA) implementation. The equations of the conductance have been unified to allow the use of same functions with different parameters for all ionic channels. The low resources and high-speed implementation also include features, such as synaptic noise using the Ornstein–Uhlenbeck process and different synapse receptors including AMPA, GABAa, GABAb, and NMDA receptors. The platform allows real-time modification of the neuron parameters and can output different cortical neuron families like Fast Spiking (FS), Regular Spiking (RS), Intrinsically Bursting (IB), and Low Threshold Spiking (LTS) neurons using a Digital to Analog Converter (DAC). Gaussian distribution of the synaptic noise highlights similarities with the biological noise. Also, cross-correlation between the implementation and the model shows strong correlations, and bifurcation analysis reproduces similar behavior compared to the original Hodgkin-Huxley model. The implementation of one core of calculation uses 3% of resources of the FPGA and computes in real-time 500 neurons with 25,000 synapses and synaptic noise which can be scaled up to 15,000 using all resources. This is the first step toward neuromorphic system which can be used for the simulation of bio-hybridization and for the study of neurological disorders or the advanced research on neuroprosthesis to regain lost function.

Voltage-gated sodium channels (Nav) that initiate electrical signals in excitable nerve and muscle cells are molecular targets for drugs and acquire disease mutations. These ion channels were first discovered in 1952 by researchers Hodgkin and Huxley who published landmark papers in The Journal of Physiology. The three key features of sodium channels discovered were voltage-dependent activation, rapid inactivation, and selective ion conductance. Since that time, a total of nine sodium channels have been discovered. The Nav isoforms of most interest as analgesic targets are Nav 1.3, Nav 1.7, Nav 1.8, and Nav 1.9 as they play specific roles in the neurobiology of pain and serve as potential analgesic targets. Knowledge of these channels’ structure and function, as well as their alterations in chronic pain, are vital to understanding how current sodium channel antagonists work but also for future drug developments. Currently, sodium channel antagonists fall into four pharmacological classes including anti-arrhythmics, anticonvulsants, local anesthetics, and antidepressants (discussed in another chapter). The sodium channel antagonists discussed in this chapter are considered nonselective.

The Hodgkin-Huxley (HH) model is a widely used biophysically meaningful model that can simulate the action potentials in the nerve axons. It is mainly used to simulate the type 2 behavior of the axon firing. However other types of neuron spiking and bursting have been observed in the literature. This work demonstrates the novelty of showing the optimization of the HH model parameters to simulate neuron bursting behavior. The results of the study demonstrates that it is possible to extend the HH model beyond its intended type 2 behavior and can be modified to simulate more complex neuron firing patterns including neuron bursting. The optimized HH model was able to generate bursting patterns corresponding to the two target bursting patterns used in this study with error values $ < 18\%$ for Phasic bursting and $ < 6\%$ for Tonic bursting. This work shows by expanding the range of gating variables ($\mathrm {m}, \mathrm {n}$ and h) beyond the original model range of 0 to 1 can improve the HH model to simulate neuron bursting.

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.

Inhibitory effect often suppresses electronic activities of the nervous system. In this paper, the inhibitory autapse is identified to enhance the degree of coherence resonance (CR) induced by noise in the Hodgkin–Huxley (HH) model with Hopf bifurcation from resting state to spiking with nearly fixed period [Formula: see text]. Without noise, the inhibitory autapse can induce a post inhibitory rebound (PIR) spike from the resting state at time delay approximating [Formula: see text] and can inhibit a spike of spiking at time delay approximating [Formula: see text]. In the presence of noise, CR characterized by maximal value of power spectrum of spike trains appears in a wide range of both time delay and conductance of autapse. With increasing autaptic conductance, CR degree becomes stronger for time delay approximating [Formula: see text] plus integer (from 0) multiples of [Formula: see text], because the inhibitory autaptic current pulses can induce more PIR spikes. The decrease of CR degree at time delay approximating integer (from 1) multiples of [Formula: see text] can be explained by the inhibition effect. The promotion of coherence resonance degree and the underlying PIR mechanism induced by inhibitory self-feedback extends the paradoxical phenomenon of inhibitory autapse to stochastic system and presents potential measures to modulate CR degree and information processing.

The Hodgkin-Huxley model is the first successful mathematical model for explaining the initiation and propagation of an action potential in a neuron cell. In this paper we reinvestigated the Hodgkin-Huxley model through computer simulation and determined the threshold potentials by applying different types of stimulating input signals. To implement the work, a computer programme of the Hodgkin-Huxley model was written in MATLAB programming language. The action potentials of neuron cells were checked and the threshold potentials of the neuron cell for specific types of stimulating input signals were tabulated with an aim to utilize these values to do experiment on neuron cell in future.Dhaka Univ. J. Sci. 64(1): 15-20, 2016 (January)

In this paper, we study the effects of spike timing-dependent plasticity on synchronisation in a network of Hodgkin–Huxley neurons. Neuron plasticity is a flexible property of a neuron and its network to change temporarily or permanently their biochemical, physiological, and morphological characteristics, in order to adapt to the environment. Regarding the plasticity, we consider Hebbian rules, specifically for spike timing-dependent plasticity (STDP), and with regard to network, we consider that the connections are randomly distributed. We analyse the synchronisation and desynchronisation according to an input level and probability of connections. Moreover, we verify that the transition for synchronisation depends on the neuronal network architecture, and the external perturbation level.