Experimental study of electrical FitzHugh–Nagumo neurons with modified excitability

Characteristics analysis of a single electromechanical arm driven by a functional neural circuit

From a biological viewpoint, the muscle tissue produces efficient gait behavior that can be adjusted by neural signals. From the physical viewpoint, the limb movement can be simulated by applying a neural circuit to control the artificial electromechanical arm (EA). In this paper, a functional neural circuit is used to excite a single EA, the load circuit attached to the moving beam is driven by a neural circuit, and the Ampere force is activated by the load circuit to control the artificial EA. The dynamic equations of the neural circuit are derived using Kirchhoff's theorem, while the energy and motion equations of the beam are computed through the application of mechanics and related theoretical principles. Furthermore, the dynamic characteristics of the functional neural circuit forced EA are analyzed. The results indicate that the beam movement can be controlled by the electrical activity of this functional neural circuit. This work will provide theoretical guidance to build the electromechanical device for complex gait behaviors.

Analysis of electrical activities in a functional neuron with dual memristors

Neuron as a charged body, it is easily disturbed by the external electromagnetic field, which changes the electrical activities of the neurons. In fact, the interference of external electric or magnetic field is the process of energy injection of neurons, the injection of energy will redistribute the field energy inside the neurons, and the redistribution of energy will change the electrical activities of the neurons. Therefore, we design a neuron model with double memristors to explore the external electromagnetic field on the regulation of neural electrical activity. The dimensionless equations of the model with double memristors and its energy function are obtained based on the Kirchhoff's and the Helmholtz's theorems. The electrical activities of the neuron model under the external electromagnetic field distribution are researched by applying the nonlinear analysis methods, and the coherence resonance of the neuron is explored under the external noise electromagnetic field. The results indicate that the electrical activities of the model are controlled by the external electromagnetic field. This neuron model can be used to study the synchronization between magnetic field coupled or electric field coupled neurons.

A Josephson junction-coupled neuron with double capacitive membranes

The channel currents have distinct magnetic field effect and any changes of the electromagnetic field or electirc stimulus will change the membrane potential effectively. A feasible neuron model considers the distinct physical characteristic is more suitable to mimic the neural activities accompanying with shift in energy level. A Josephson junction (JJ) is connected to a neural circuit for estimating the effect of external magnetic field and two capacitors are connected via a linear resistor for mimicing the capacitive field beside two sides of the cell membrane. Its equivalent Hamilton energy is calculated to show the relation between firing mode and energy level. Noisy disturbance is imposed to predict the occurrence of coherence resonance, and the biophysical neuron is excited to present higher energy level. This new neuron model can address the field effect and the biophysical property of cell membrane considered as combination of capacitive fields in double capacitors. It can mimic the physical property of outer and inner membranes, and energy exchange across the double membranes explains the energy mechanism in neural activities. Time-varying energy diveristy between capacitive field is crucial for supporting continuous firing activities. The JJ channel discerns slight changes in external magnetic field and regularity is stabilized under coherence resonance in presence of noisy excitation on the membrane or ion channels.

Competitive Decomposition-Based Multiobjective Architecture Search for the Dendritic Neural Model

The dendritic neural model (DNM) is computationally faster than other machine-learning techniques, because its architecture can be implemented by using logic circuits and its calculations can be performed entirely in binary form. To further improve the computational speed, a straightforward approach is to generate a more concise architecture for the DNM. Actually, the architecture search is a large-scale multiobjective optimization problem (LSMOP), where a large number of parameters need to be set with the aim of optimizing accuracy and structural complexity simultaneously. However, the issues of irregular Pareto front, objective discontinuity, and population degeneration strongly limit the performances of conventional multiobjective evolutionary algorithms (MOEAs) on the specific problem. Therefore, a novel competitive decomposition-based MOEA is proposed in this study, which decomposes the original problem into several constrained subproblems, with neighboring subproblems sharing overlapping regions in the objective space. The solutions in the overlapping regions participate in environmental selection for the neighboring subproblems and then propagate the selection pressure throughout the entire population. Experimental results demonstrate that the proposed algorithm can possess a more powerful optimization ability than the state-of-the-art MOEAs. Furthermore, both the DNM itself and its hardware implementation can achieve very competitive classification performances when trained by the proposed algorithm, compared with numerous widely used machine-learning approaches.

Biorealistic Control of Hand Prosthesis Augments Functional Performance of Individuals With Amputation

The human hand has compliant properties arising from muscle biomechanics and neural reflexes, which are absent in conventional prosthetic hands. We recently proved the feasibility to restore neuromuscular reflex control (NRC) to prosthetic hands using real-time computing neuromorphic chips. Here we show that restored NRC augments the ability of individuals with forearm amputation to complete grasping tasks, including standard Box and Blocks Test (BBT), Golf Balls Test (GBT), and Potato Chips Test (PCT). The latter two were more challenging, but novel to prosthesis tests. Performance of a biorealistic controller (BC) with restored NRC was compared to that of a proportional linear feedback (PLF) controller. Eleven individuals with forearm amputation were divided into two groups: one with experience of myocontrol of a prosthetic hand and another without any. Controller performances were evaluated by success rate, failure (drop/break) rate in each grasping task. In controller property tests, biorealistic control achieved a better compliant property with a 23.2% wider range of stiffness adjustment than that of PLF control. In functional grasping tests, participants could control prosthetic hands more rapidly and steadily with neuromuscular reflex. For participants with myocontrol experience, biorealistic control yielded 20.4, 39.4, and 195.2% improvements in BBT, GBT, and PCT, respectively, compared to PLF control. Interestingly, greater improvements were achieved by participants without any myocontrol experience for BBT, GBT, and PCT at 27.4, 48.9, and 344.3%, respectively. The functional gain of biorealistic control over conventional control was more dramatic in more difficult grasp tasks of GBT and PCT, demonstrating the advantage of NRC. Results support the hypothesis that restoring neuromuscular reflex in hand prosthesis can improve neural motor compatibility to human sensorimotor system, hence enabling individuals with amputation to perform delicate grasps that are not tested with conventional prosthetic hands.

Exponential distribution of lifetimes for transient bursting states in coupled noisy excitable systems

The phenomenon of transient bursting, caused by additive noise in a set of two coupled FitzHugh-Nagumo oscillators, is studied by direct numerical integration and by measurements in the analog electronic circuit. In the parameter region where the unique global attractor of the deterministic system is the state of rest, introduction of low or moderate intensity fluctuations into the voltage dynamics results in the onset of a transient bursting state: sequences of intermittent bursts (patches of spikes), followed by ultimate relaxation to the equilibrium. Like genuine deterministic bursting, this behavior has its origin in the slow-fast character of the underlying dynamics. Trajectories that in the deterministic variant would converge to the state of rest can, under the action of noise, escape the local basin of attraction of the equilibrium and experience a bursting episode, before being dynamically reinjected into the region around the equilibrium. Under frozen parameter values and fixed noise intensity, the number of bursts preceding the ultimate decay strongly varies for different realizations of the additive random signal. The average duration of the transient bursting stage, bounded for weak noise, diverges when the intensity of fluctuations is raised. For sufficiently large ensembles of realizations, the lifetimes of transient bursting states, both in simulations and in the analog circuit, obey the exponential distribution. We relate this distribution to the probability for a stochastic trajectory to temporarily escape from the local basin of attraction of the equilibrium.

Stochastic Memristive Interface for Neural Signal Processing

We propose a memristive interface consisting of two FitzHugh–Nagumo electronic neurons connected via a metal–oxide (Au/Zr/ZrO₂(Y)/TiN/Ti) memristive synaptic device. We create a hardware–software complex based on a commercial data acquisition system, which records a signal generated by a presynaptic electronic neuron and transmits it to a postsynaptic neuron through the memristive device. We demonstrate, numerically and experimentally, complex dynamics, including chaos and different types of neural synchronization. The main advantages of our system over similar devices are its simplicity and real-time performance. A change in the amplitude of the presynaptic neurogenerator leads to the potentiation of the memristive device due to the self-tuning of its parameters. This provides an adaptive modulation of the postsynaptic neuron output. The developed memristive interface, due to its stochastic nature, simulates a real synaptic connection, which is very promising for neuroprosthetic applications.

A model integrating multiple processes of synchronization and coherence for information instantiation within a cortical area

What is the form of dynamic, e.g., sensory, information in the mammalian cortex? Information in the cortex is modeled as a coherence map of a mixed chimera state of synchronous, phasic, and disordered minicolumns. The theoretical model is built on neurophysiological evidence. Complex spatiotemporal information is instantiated through a system of interacting biological processes that generate a synchronized cortical area, a coherent aperture. Minicolumn elements are grouped in macrocolumns in an array analogous to a phased-array radar, modeled as an aperture, a "hole through which radiant energy flows." Coherence maps in a cortical area transform inputs from multiple sources into outputs to multiple targets, while reducing complexity and entropy. Coherent apertures can assume extremely large numbers of different information states as coherence maps, which can be communicated among apertures with corresponding very large bandwidths. The coherent aperture model incorporates considerable reported research, integrating five conceptually and mathematically independent processes: 1) a damped Kuramoto network model, 2) a pumped area field potential, 3) the gating of nearly coincident spikes, 4) the coherence of activity across cortical lamina, and 5) complex information formed through functions in macrocolumns. Biological processes and their interactions are described in equations and a functional circuit such that the mathematical pieces can be assembled the same way the neurophysiological ones are. The model can be conceptually convolved over the specifics of local cortical areas within and across species. A coherent aperture becomes a node in a graph of cortical areas with a corresponding distribution of information.

Plasticity and Adaptation in Neuromorphic Biohybrid Systems

Neuromorphic systems take inspiration from the principles of biological information processing to form hardware platforms that enable the large-scale implementation of neural networks. The recent years have seen both advances in the theoretical aspects of spiking neural networks for their use in classification and control tasks and a progress in electrophysiological methods that is pushing the frontiers of intelligent neural interfacing and signal processing technologies. At the forefront of these new technologies, artificial and biological neural networks are tightly coupled, offering a novel "biohybrid" experimental framework for engineers and neurophysiologists. Indeed, biohybrid systems can constitute a new class of neuroprostheses opening important perspectives in the treatment of neurological disorders. Moreover, the use of biologically plausible learning rules allows forming an overall fault-tolerant system of co-developing subsystems. To identify opportunities and challenges in neuromorphic biohybrid systems, we discuss the field from the perspectives of neurobiology, computational neuroscience, and neuromorphic engineering.

Switch Elements with S-Shaped Current-Voltage Characteristic in Models of Neural Oscillators

In this paper, we present circuit solutions based on a switch element with the S-type I–V characteristic implemented using the classic FitzHugh–Nagumo and FitzHugh–Rinzel models. Using the proposed simplified electrical circuits allows the modeling of the integrate-and-fire neuron and burst oscillation modes with the emulation of the mammalian cold receptor patterns. The circuits were studied using the experimental I–V characteristic of an NbO2 switch with a stable section of negative differential resistance (NDR) and a VO2 switch with an unstable NDR, considering the temperature dependences of the threshold characteristics. The results are relevant for modern neuroelectronics and have practical significance for the introduction of the neurodynamic models in circuit design and the brain–machine interface. The proposed systems of differential equations with the piecewise linear approximation of the S-type I–V characteristic may be of scientific interest for further analytical and numerical research and development of neural networks with artificial intelligence.

Low-Voltage Low-Power Integrable CMOS Circuit Implementation of Integer- and Fractional-Order FitzHugh-Nagumo Neuron Model

The low-voltage low-power sinh-domain (SD) implementations of integer- and fractional-order FitzHugh-Nagumo (FHN) neuron model have been introduced in this paper. Besides, the effect of fractional-orders on the external excitation current and dynamics of the neuron has been examined in this paper. The proposed SD designs of FHN neuron model have the benefits of: 1) low-voltage operation; 2) integrability, due to resistor-less design and the employment of only grounded components; 3) electronic tunability of performance parameters; and 4) low-power implementation due to the inherent properties of SD technique. HSPICE simulator tool and Taiwan Semiconductor Manufacturing Company, Hsinchu, Taiwan 130-nm CMOS process was used to evaluate and verify the correct functioning of the model. In addition, to experimentally verify the operation of the proposed fractional-order FHN neuron model, field-programmable analog array (FPAA) implementation of the model has been presented, and the proper functioning of the model has been verified. To the best of the authors' knowledge, this is the first paper that describes the electronic realization of the fractional-order FHN neuron model. In addition, it is the first time that the FPAA implementation of any fractional-order neuron model has been presented.

Optimized Real-Time Biomimetic Neural Network on FPGA for Bio-hybridization

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.

Optoelectronic system for brain neuronal network stimulation

We propose an optoelectronic system for stimulation of living neurons. The system consists of an electronic circuit based on the FitzHugh–Nagumo model, an optical fiber, and a photoelectrical converter. We used this system for electrical stimulation of hippocampal living neurons in acute hippocampal brain slices (350-μm thick) obtained from a 20–28 days old C57BL/6 mouse or a Wistar rat. The main advantage of our system over other similar stimulators is that it contains an optical fiber for signal transmission instead of metallic wires. The fiber is placed between the electronic circuit and stimulated neurons and provides galvanic isolation from external electrical and magnetic fields. The use of the optical fiber allows avoiding electromagnetic noise and current flows which could affect metallic wires. Furthermore, it gives us the possibility to simulate “synaptic plasticity” by adaptive signal transfer through optical fiber. The proposed optoelectronic system (hybrid neural circuit) provides a very high efficiency in stimulating hippocampus neurons and can be used for restoring brain activity in particular regions or replacing brain parts (neuroprosthetics) damaged due to a trauma or neurodegenerative diseases.

Experimental implementation of a biometric laser synaptic sensor

We fabricate a biometric laser fiber synaptic sensor to transmit information from one neuron cell to the other by an optical way. The optical synapse is constructed on the base of an erbium-doped fiber laser, whose pumped diode current is driven by a pre-synaptic FitzHugh–Nagumo electronic neuron, and the laser output controls a post-synaptic FitzHugh–Nagumo electronic neuron. The implemented laser synapse displays very rich dynamics, including fixed points, periodic orbits with different frequency-locking ratios and chaos. These regimes can be beneficial for efficient biorobotics, where behavioral flexibility subserved by synaptic connectivity is a challenge.

Oscillatory threshold logic

In the 1940s, the first generation of modern computers used vacuum tube oscillators as their principle components, however, with the development of the transistor, such oscillator based computers quickly became obsolete. As the demand for faster and lower power computers continues, transistors are themselves approaching their theoretical limit and emerging technologies must eventually supersede them. With the development of optical oscillators and Josephson junction technology, we are again presented with the possibility of using oscillators as the basic components of computers, and it is possible that the next generation of computers will be composed almost entirely of oscillatory devices. Here, we demonstrate how coupled threshold oscillators may be used to perform binary logic in a manner entirely consistent with modern computer architectures. We describe a variety of computational circuitry and demonstrate working oscillator models of both computation and memory.