Hodgkin-Huxley Model Research Articles

Block-based color image encryption algorithm by a novel memristor chaotic system and new RNA computation

The security of images is closely related to the protection of information privacy. We proposed a novel 5D memory resistive chaotic system (5D-MRCS), which exhibits good chaotic characteristics. Therefore, we employed it to design an image encryption algorithm aimed at ensuring secure image transmission. To further enhance the complexity of the algorithm and obtain more chaotic sequences, we combine the 5D-MRCS with the Hodgkin-Huxley (HH) model and use this combination in algorithm design. Initially, we combine the plain image with the hash function SHA-384 to devise and generate the secret key. Subsequently, the algorithm determines whether to pad the plain image based on different block size requirements. Then, we use multiple chaotic sequences generated by the 5D-MRCS and HH model to perform the global image permutation operation. Our designed permutation algorithm includes two parts: Block-based permutation and a new pixel-level permutation. Next, the scrambled image undergoes block-based random RNA diffusion, incorporating two newly proposed methods in the RNA operations, ultimately resulting in the ciphertext image. The algorithm’s NPCR, UACI, information entropy, and other security performance metrics are very close to the ideal values, and it possess characteristics such as resistance to differential, cutting, chosen plaintext, and noise attacks. Compared with other algorithms, it still has some advantages across multiple images and demonstrates excellent image encryption performance.

Dynamic entrainment: A deep learning and data-driven process approach for synchronization in the Hodgkin-Huxley model.

Resonance and synchronized rhythm are significant phenomena observed in dynamical systems in nature, particularly in biological contexts. These phenomena can either enhance or disrupt system functioning. Numerous examples illustrate the necessity for organs within the human body to maintain their rhythmic patterns for proper operation. For instance, in the brain, synchronized or desynchronized electrical activities can contribute to neurodegenerative conditions like Huntington's disease. In this paper, we utilize the well-established Hodgkin-Huxley (HH) model, which describes the propagation of action potentials in neurons through conductance-based mechanisms. Employing a "data-driven" approach alongside the outputs of the HH model, we introduce an innovative technique termed "dynamic entrainment." This technique leverages deep learning methodologies to dynamically sustain the system within its entrainment regime. Our findings show that the results of the dynamic entrainment technique match with the outputs of the mechanistic (HH) model.

Dynamic Effects Analysis in Fractional Memristor-Based Rulkov Neuron Model.

Mathematical models such as Fitzhugh-Nagoma and Hodgkin-Huxley models have been used to understand complex nervous systems. Still, due to their complexity, these models have made it challenging to analyze neural function. The discrete Rulkov model allows the analysis of neural function to facilitate the investigation of neuronal dynamics or others. This paper introduces a fractional memristor Rulkov neuron model and analyzes its dynamic effects, investigating how to improve neuron models by combining discrete memristors and fractional derivatives. These improvements include the more accurate generation of heritable properties compared to full-order models, the treatment of dynamic firing activity at multiple time scales for a single neuron, and the better performance of firing frequency responses in fractional designs compared to integer models. Initially, we combined a Rulkov neuron model with a memristor and evaluated all system parameters using bifurcation diagrams and the 0-1 chaos test. Subsequently, we applied a discrete fractional-order approach to the Rulkov memristor map. We investigated the impact of all parameters and the fractional order on the model and observed that the system exhibited various behaviors, including tonic firing, periodic firing, and chaotic firing. We also found that the more I tend towards the correct order, the more chaotic modes in the range of parameters. Following this, we coupled the proposed model with a similar one and assessed how the fractional order influences synchronization. Our results demonstrated that the fractional order significantly improves synchronization. The results of this research emphasize that the combination of memristor and discrete neurons provides an effective tool for modeling and estimating biophysical effects in neurons and artificial neural networks.

Closed-loop baroreflex model with biophysically detailed afferent pathway.

In this work, we couple a lumped-parameter closed-loop model of the cardiovascular system with a physiologically-detailed mathematical description of the baroreflex afferent pathway. The model features a classical Hodgkin-Huxley current-type model for the baroreflex afferent limb (primary neuron) and for the second-order neuron in the central nervous system. The pulsatile arterial wall distension triggers a frequency-modulated sequence of action potentials at the afferent neuron. This signal is then integrated at the brainstem neuron model. The efferent limb, representing the sympathetic and parasympathetic nervous system, is described as a transfer function acting on heart and blood vessel model parameters in order to control arterial pressure. Three in silico experiments are shown here: a step increase in the aortic pressure to evaluate the functionality of the reflex arch, a hemorrhagic episode and an infusion simulation. Through this model, it is possible to study the biophysical dynamics of the ionic currents proposed for the afferent limb components of the baroreflex during the cardiac cycle, and the way in which currents dynamics affect the cardiovascular function. Moreover, this system can be further developed to study in detail each baroreflex loop component, helping to unveil the mechanisms involved in the cardiovascular afferent information processing.

Possible mechanism of action potential propagation mediated by static electric field: A novel assumption of understanding nerve interaction and ephaptic coupling

The generation and propagation of physical signals in living biosystems are continuous issues. Traditional Hodgkin-Huxley model based on ionic current conduction could not explain the fast transmission of action potential in myelinated axons and factors influencing action potential velocity. We propose that the ion flow induced by Nav channel generates near field quasi-static electric field at extracellular space, termed as an ephaptic field which is able to excite nearby passive axons. Our simulation indicates that the static electric field produced by sodium ion channels in one node of Ranvier is improbable to stimulate the ion channels in the adjacent neighboring node. However, the ion channel ring in one node of Ranvier could induce the shift of membrane potential (0.01 mV) on the node at nearby axons (100 μm) in a bundle of axon synchronously, suggesting zig-zag propagation of action potential. Together with the superposition effect of ephaptic feedback field generated by the synchronized movement of adjacent parallel axons stimulate the adjacent node of the original axon, strengthen the action potential to travel in a zig-zag pattern. Our model also provides an explanation for the rapid velocity of action potential propagation reported in experimental studies.

Thermal effects and ephaptic entrainment in Hodgkin–Huxley model

The brain is understood as an intricate biological system composed of numerous elements. It is susceptible to various physical and chemical influences, including temperature. The literature extensively explores the conditions that influence synapses in the context of cellular communication. However, the understanding of how the brain’s global physical conditions can modulate ephaptic communication remains limited due to the poorly understood nature of ephapticity. This study proposes an adaptation of the Hodgkin and Huxley (HH) model to investigate the effects of ephaptic entrainment in response to thermal changes (HH-E). The analysis focuses on two distinct neuronal regimes: subthreshold and suprathreshold. In the subthreshold regime, circular statistics are used to demonstrate the dependence of phase differences with temperature. In the suprathreshold regime, the Inter-Spike Interval are employed to estimate phase preferences and changes in the spiking pattern. Temperature influences the model’s ephaptic interactions and can modify its preferences for spiking frequency, with the direction of this change depending on specific model conditions and the temperature range under consideration. Furthermore, temperature enhance the anti-phase differences relationship between spikes and the external ephaptic signal. In the suprathreshold regime, ephaptic entrainment is also influenced by temperature, especially at low frequencies. This study reveals the susceptibility of ephaptic entrainment to temperature variations in both subthreshold and suprathreshold regimes and discusses the importance of ephaptic communication in the contexts where temperature may plays a significant role in neural physiology, such as inflammatory processes, fever, and epileptic seizures.

Nonlinearities and timescales in neural models of temporal interference stimulation.

In temporal interference (TI) stimulation, neuronal cells react to two interfering sinusoidal electric fields with a slightly different frequency ( , in the range of about 1-4 kHz, in the range of about 1-100 Hz). It has been previously observed that for the same input intensity, the neurons do not react to a purely sinusoidal signal at or . This study seeks a better understanding of the largely unknown mechanisms underlying TI neuromodulation. To this end, single-compartment models are used to simulate computationally the response of neurons to the sinusoidal and TI waveform. This study compares five different neuron models: Hodgkin-Huxley (HH), Frankenhaeuser-Huxley (FH), along with leaky, exponential, and adaptive-exponential integrate-and-fire (IF). It was found that IF models do not entirely reflect the experimental behavior while the HH and FH model did qualitatively replicate the observed neural responses. Changing the time constants and steady state values of the ion gates in the FH model alters the response to both the sinusoidal and TI signal, possibly reducing the firing threshold of the sinusoidal input below that of the TI input. The results show that in the modified (simplified) model, TI stimulation is not qualitatively impacted by nonlinearities in the current-voltage relation. In contrast, ion channels have a significant impact on the neuronal response. This paper offers insights into neuronal biophysics and computational models of TI stimulation.

Network model with internal complexity bridges artificial intelligence and neuroscience.

Artificial intelligence (AI) researchers currently believe that the main approach to building more general model problems is the big AI model, where existing neural networks are becoming deeper, larger and wider. We term this the big model with external complexity approach. In this work we argue that there is another approach called small model with internal complexity, which can be used to find a suitable path of incorporating rich properties into neurons to construct larger and more efficient AI models. We uncover that one has to increase the scale of the network externally to stimulate the same dynamical properties. To illustrate this, we build a Hodgkin-Huxley (HH) network with rich internal complexity, where each neuron is an HH model, and prove that the dynamical properties and performance of the HH network can be equivalent to a bigger leaky integrate-and-fire (LIF) network, where each neuron is a LIF neuron with simple internal complexity.

Utilising activity patterns of a complex biophysical network model to optimise intra-striatal deep brain stimulation

A large-scale biophysical network model for the isolated striatal body is developed to optimise potential intrastriatal deep brain stimulation applied to, e.g. obsessive-compulsive disorder. The model is based on modified Hodgkin–Huxley equations with small-world connectivity, while the spatial information about the positions of the neurons is taken from a detailed human atlas. The model produces neuronal spatiotemporal activity patterns segregating healthy from pathological conditions. Three biomarkers were used for the optimisation of stimulation protocols regarding stimulation frequency, amplitude and localisation: the mean activity of the entire network, the frequency spectrum of the entire network (rhythmicity) and a combination of the above two. By minimising the deviation of the aforementioned biomarkers from the normal state, we compute the optimal deep brain stimulation parameters, regarding position, amplitude and frequency. Our results suggest that in the DBS optimisation process, there is a clear trade-off between frequency synchronisation and overall network activity, which has also been observed during in vivo studies.

Interaction and adiabatic evolution of orthodromic and antidromic impulses in the axoplasmic fluid

Unlike expected from the Hodgkin-Huxley model predictions, in which there is annihilation once orthodromic and antidromic impulses collide, the Heimburg-Jackson model demonstrates that both impulses penetrate each other as it has been shown experimentally. These impulses can be depicted as low amplitude nonlinear excitations in a weakly dissipative soliton model described by the damped nonlinear Schrödinger equation. In view of the above, the Karpman-Maslov-Solov'ev perturbation theory turns out to be ideal to study the interaction and adiabatic evolution of orthodromic and antidromic impulses once axoplasmic fluid is present.

A Survey on Neuromorphic Architectures for Running Artificial Intelligence Algorithms

Neuromorphic computing, a brain-inspired non-Von Neumann computing system, addresses the challenges posed by the Moore’s law memory wall phenomenon. It has the capability to enhance performance while maintaining power efficiency. Neuromorphic chip architecture requirements vary depending on the application and optimising it for large-scale applications remains a challenge. Neuromorphic chips are programmed using spiking neural networks which provide them with important properties such as parallelism, asynchronism, and on-device learning. Widely used spiking neuron models include the Hodgkin–Huxley Model, Izhikevich model, integrate-and-fire model, and spike response model. Hardware implementation platforms of the chip follow three approaches: analogue, digital, or a combination of both. Each platform can be implemented using various memory topologies which interconnect with the learning mechanism. Current neuromorphic computing systems typically use the unsupervised learning spike timing-dependent plasticity algorithms. However, algorithms such as voltage-dependent synaptic plasticity have the potential to enhance performance. This review summarises the potential neuromorphic chip architecture specifications and highlights which applications they are suitable for.

Noise intensity of a Markov chain.

Stochastic transitions between discrete microscopic states play an important role in many physical and biological systems. Often these transitions lead to fluctuations on a macroscopic scale. A classic example from neuroscience is the stochastic opening and closing of ion channels and the resulting fluctuations in membrane current. When the microscopic transitions are fast, the macroscopic fluctuations are nearly uncorrelated and can be fully characterized by their mean and noise intensity. We show how, for an arbitrary Markov chain, the noise intensity can be determined from an algebraic equation, based on the transition rate matrix; these results are in agreement with earlier results from the theory of zero-frequency noise in quantum mechanical and classical systems. We demonstrate the validity of the theory using an analytically tractable two-state Markovian dichotomous noise, an eight-state model for a calcium channel subunit (De Young-Keizer model), and Markov models of the voltage-gated sodium and potassium channels as they appear in a stochastic version of the Hodgkin-Huxley model.

Mathematical Modeling of Neuron Using Hodgkin-Huxley Model

The growing rate of mental illnesses has brought the idea to cure anxiety disorders through altering heart rate variability using sympathetic and parasympathetic stimulations. The parasympathetic activity in the sinoatrial node being responsible for arrythmia has been considered in the already existing cardiovascular model. This study presents a mathematical model of a single neuron and simulated its activity for a single burst to be amalgamated in a closed-loop system of the heart and uses heart rate variability as a control variable to treat anxiety disorders and decrease the rate of increasing mental disorders in the world population. The proposed study shows the results that rises from 7mV and goes up to 107mV and then again falls back to 7mV depicting a single burst. These results is being validated by comparing the model of neuron presented in classical Hodgkin-Huxley model using MATLAB.

Characterizing parameters and incorporating action potentials via the Hodgkin-Huxley model in a novel electric model for living cells

ABSTRACT To enhance our understanding of electroporation and optimize the pulses used within the frequency range of 1 kHz to 100 MHz, with the aim of minimizing side effects such as muscle contraction, we introduce a novel electrical model, structured as a 2D representation employing exclusively lumped elements. This model adeptly encapsulates the intricate dynamics of living cells’ impedance variation. A distinguishing attribute of the proposed model lies in its capacity to decipher the distribution of transmembrane potential across various orientations within living cells. This aspect bears critical importance, particularly in contexts such as electroporation and cellular stimulation, where precise knowledge of potential gradients is pivotal. Furthermore, the augmentation of the proposed electrical model with the Hodgkin-Huxley (HH) model introduces an additional dimension. This integration augments the model’s capabilities, specifically enabling the exploration of muscle cell stimulation and the generation of action potentials. This broader scope enhances the model’s utility, facilitating comprehensive investigations into intricate cellular behaviors under the influence of external electric fields.

Model-based analysis of the acute effects of transcutaneous magnetic spinal cord stimulation on micturition after spinal cord injury in humans.

After spinal cord injuries (SCIs), patients may develop either detrusor-sphincter dyssynergia (DSD) or urinary incontinence, depending on the level of the spinal injury. DSD and incontinence reflect the loss of coordinated neural control among the detrusor muscle, which increases bladder pressure to facilitate urination, and urethral sphincters and pelvic floor muscles, which control the bladder outlet to restrict or permit bladder emptying. Transcutaneous magnetic stimulation (TMS) applied to the spinal cord after SCI reduced DSD and incontinence. We defined, within a mathematical model, the minimum neuronal elements necessary to replicate neurogenic dysfunction of the bladder after a SCI and incorporated into this model the minimum additional neurophysiological features sufficient to replicate the improvements in bladder function associated with lumbar TMS of the spine in patients with SCI. We created a computational model of the neural circuit of micturition based on Hodgkin-Huxley equations that replicated normal bladder function. We added interneurons and increased network complexity to reproduce dysfunctional micturition after SCI, and we increased the density and complexity of interactions of both inhibitory and excitatory lumbar spinal interneurons responsive to TMS to provide a more diverse set of spinal responses to intrinsic and extrinsic activation of spinal interneurons that remains after SCI. The model reproduced the re-emergence of a spinal voiding reflex after SCI. When we investigated the effect of monophasic and biphasic TMS at two frequencies applied at or below T10, the model replicated the improved coordination between detrusor and external urethral sphincter activity that has been observed clinically: low-frequency TMS (1 Hz) within the model normalized control of voiding after SCI, whereas high-frequency TMS (30 Hz) enhanced urine storage. Neuroplasticity and increased complexity of interactions among lumbar interneurons, beyond what is necessary to simulate normal bladder function, must be present in order to replicate the effects of SCI on control of micturition, and both neuronal and network modifications of lumbar interneurons are essential to understand the mechanisms whereby TMS reduced bladder dysfunction after SCI.

In Silico Electrophysiological Investigation of Transient Receptor Potential Melastatin-4 Ion Channel Biophysics to Study Detrusor Overactivity.

Enhanced electrical activity in detrusor smooth muscle (DSM) cells is a key factor in detrusor overactivity which causes overactive bladder pathological disorders. Transient receptor potential melastatin-4 (TRPM4) channels, which are calcium-activated cation channels, play a role in regulating DSM electrical activities. These channels likely contribute to depolarizing the DSM cell membrane, leading to bladder overactivity. Our research focuses on understanding TRPM4 channel function in the DSM cells of mice, using computational modeling. We aimed to create a detailed computational model of the TRPM4 channel based on existing electrophysiological data. We employed a modified Hodgkin-Huxley model with an incorporated TRP-like current to simulate action potential firing in response to current and synaptic stimulus inputs. Validation against experimental data showed close agreement with our simulations. Our model is the first to analyze the TRPM4 channel's role in DSM electrical activity, potentially revealing insights into bladder overactivity. In conclusion, TRPM4 channels are pivotal in regulating human DSM function, and TRPM4 channel inhibitors could be promising targets for treating overactive bladder.

A simulation study of transcranial magnetoacoustic stimulation of the basal ganglia thalamic neural network to improve pathological beta oscillations in Parkinson's disease

BackgroundParkinson's disease (PD) is a common neurodegenerative disease. Transcranial magnetoacoustic stimulation (TMAS) is a new therapy that combines a transcranial focused acoustic pressure field with a magnetic field to excite or inhibit neurons in targeted area, which suppresses the abnormally elevated beta band amplitude in PD states, with high spatial resolution and non-invasively. ObjectiveTo study the effective stimulation parameters of TMAS mononuclear and multinuclear stimulation for the treatment of PD with reduced beta band energy, improved abnormal synchronization, and no thermal damage. MethodsThe TMAS model is constructed based on the volunteer's computed tomography, 128 arrays of phase-controlled transducers, and permanent magnets. A basal ganglia-thalamic (BG-Th) neural network model of the PD state was constructed on the basis of the Izhikevich model and the acoustic model. An ultrasound stimulation neuron model is constructed based on the Hodgkin-Huxley model. Numerical simulations of transcranial focused acoustic pressure field, temperature field and induced electric field at single and dual targets were performed using the locations of STN, GPi, and GPe in the human brain as the main stimulation target areas. And the acoustic and electric parameters at the focus were extracted to stimulate mononuclear and multinuclear in the BG-Th neural network. ResultsWhen the stimulating effect of ultrasound is ignored, TMAS-STN simultaneously inhibits the beta-band amplitude of the GPi nucleus, whereas TMAS-GPi fails to simultaneously have an inhibitory effect on the STN. TMAS-STN&GPi can reduce the beta band amplitude. TMAS-STN&GPi&GPe suppressed the PD pathologic beta band amplitude of each nucleus to a greater extent. When considering the stimulatory effect of ultrasound, lower sound pressures of ultrasound do not affect the neuronal firing state, but higher sound pressures may promote or inhibit the stimulatory effect of induced currents. ConclusionsAt 9 T static magnetic field, 0.5–1.5 MPa and 1.5–2.0 MPa ultrasound had synergistic effects on individual STN and GPi neurons. TMAS multinuclear stimulation with appropriate ultrasound intensity was the most effective in suppressing the amplitude of pathological beta oscillations in PD and may be clinically useful.

Skin Comfort Sensation with Mechanical Stimulus from Electronic Skin.

The field of electronic skin has received considerable attention due to its extensive potential applications in areas including tactile sensing and health monitoring. With the development of electronic skin devices, electronic skin can be attached to the surface of human skin for long-term health monitoring, which makes comfort an essential factor that cannot be ignored in the design of electronic skin. Therefore, this paper proposes an assessment method for evaluating the comfort of electronic skin based on neurodynamic analysis. The holistic analysis framework encompasses the mechanical model of the skin, the modified Hodgkin-Huxley model for the transduction of stimuli, and the gate control theory for the modulation and perception of pain sensation. The complete process, from mechanical stimulus to the generation of pain perception, is demonstrated. Furthermore, the influence of different factors on pain perception is investigated. Sensation and comfort diagrams are provided to assess the mechanical comfort of electronic skin. The comfort assessment method proposed in this paper provides a theoretical basis when assessing the comfort of electronic skin.

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.

Analytical and numerical solutions to the Klein–Gordon model with cubic nonlinearity

In this paper, the nonlinear Klein–Gordon equation’s exact solutions are obtained through the application of an appropriate transformation based on He’s semi-inverse approach. This equation considered a generalization of other famous models in applied science, such as Phi-4 equation, Duffing equation, Fisher–Kolmogorov model through population dynamics and Hodgkin–Huxley equation that characterizes the propagation of electrical signals via nervous system. The suggested approach is simple, robust, and efficient, and its application in other partial differential equations in applied science seems promising. Numerical solution of the nonlinear Klein–Gordon equation is presented using finite difference method. The method’s accuracy is demonstrated by contrasting it with the exact solution that we obtained. The Von Neumann stability technique is applied to obtain the stability condition and a convergent test is presented Some 2D and 3D graphs matching to chosen solutions are simulated by taking into account appropriate values for the parameters.