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The implementation of biological neuron models plays an important role in understanding the functionality of the brain. Generally, analog and digital methods are preferred during implementation processes. The Raspberry Pi (RPi) microcontroller has the potential to be a new platform that can easily solve complex mathematical operations and does not have memory limitations, which will take advantage while realizing biological neuron models. In this paper, Hodgkin-Huxley (HH), FitzHugh-Nagumo (FHN), Morris-Lecar (ML), Hindmarsh-Rose (HR), and Izhikevich (IZ) neuron models have been implemented on a standard-equipped RPi. For the numerical solution of each neuron model, the one-step method (4th order Runge-Kutta (RK4), the new version of Runge-Kutta (RKN)), the multi-step method (Adams-Bashforth (AB), Adams-Moulton (AM)), and predictor-corrector method (Adams-Bashforth-Moulton (ABM)) are preferred to compare results. The implementation of HH, ML, FHN, HR, and IZ neuron models on RPi and the comparison of numerical models RK4, RKN, AB, AM, and ABM in the implementation of neuron models were made for the first time in this study. Firstly, MATLAB simulations of the various behaviors belonging to the HH, ML, FHN, HR, and IZ neuron models were completed. Then those models were realized on RPi and the outputs of the models are experimentally produced. The errors are also presented in the tables. The results show that RPi can be considered as a new alternative tool for making complex neuron models.

The implementation of biological neuron models plays an important role in understanding the functionality of the brain. Generally, analog and digital methods are preferred during implementation processes. The Raspberry Pi (RPi) microcontroller has the potential to be a new platform that can easily solve complex mathematical operations and does not have memory limitations, which will take advantage while realizing biological neuron models. In this paper, Hodgkin-Huxley (HH), FitzHugh-Nagumo (FHN), Morris-Lecar (ML), Hindmarsh-Rose (HR), and Izhikevich (IZ) neuron models have been implemented on a standard-equipped RPi. For the numerical solution of each neuron model, the one-step method (4th order Runge-Kutta (RK4), the new version of Runge-Kutta (RKN)), the multi-step method (Adams-Bashforth (AB), Adams-Moulton (AM)), and predictor-corrector method (Adams-Bashforth-Moulton (ABM)) are preferred to compare results. The implementation of HH, ML, FHN, HR, and IZ neuron models on RPi and the comparison of numerical models RK4, RKN, AB, AM, and ABM in the implementation of neuron models were made for the first time in this study. Firstly, MATLAB simulations of the various behaviors belonging to the HH, ML, FHN, HR, and IZ neuron models were completed. Then those models were realized on RPi and the outputs of the models are experimentally produced. The errors are also presented in the tables. The results show that RPi can be considered as a new alternative tool for making complex neuron models. [ABSTRACT FROM AUTHOR]

This paper proposes a new logic element model based on an Izhikevich (IZ) neuron and neural system that emulates two- and three-state logic behaviours. In a noise-free environment, with a periodic current of suitable amplitude and frequency, the IZ system is capable of performing logical AND and OR operations. Initially, a single IZ neuron demonstrates membrane dynamics in response to an input signal generated by combining two-state logic currents below the threshold. Subsequently, an IZ neural system model is introduced to enhance the reliability and resilience of the system. This model is characterised by electrical coupling with fast conduction and chemical coupling with a more adaptable structure. Each logic input independently influences each neuron within the system. Additionally, it has been observed that the reliability of the logic element is influenced by changes in synaptic strength, with a neural system lacking sufficient synaptic strength failing to generate logical output. Furthermore, the system displays a three-state logic behaviour under suitable forcing periodicity, thus enhancing the power efficiency of the logic element. The proposed IZ neuron and neural system are expected to significantly impact the development of brain-inspired logic elements.

The neuron is sometimes referred to as the “head” or “central” cell of the nervous system since it has the ability to communicate with other neurons or cells via electrical impulses. The hardware realization and simulation of these neurons are critical in neuromorphic engineering. In this paper, we made a device that generates 4 different spiking patterns of the nervous system as a Spike Generator (SG) using a hybrid approximation of the target model called the Piece-Wised Power-2 Based Izhikevich Model (PWP2BIM). This proposed model works in a low-cost state to achieve a correct digital implementation of the Izhikevich model, one of the main neuron models (i.e. decreasing hardware resources and enhancing speed and accuracy). The proposed model successfully reproduces the behavioral traits of the initial neuron model. To verify the results of the mathematical simulation, the proposed model was synthesized and implemented on the Zynq XC7Z010 (3CLG400) reconfigurable board (FPGA). The findings of hardware synthesis and applications of the suggested paradigm demonstrate that certain biological behaviors may be duplicated more effectively and at a significantly lower cost. The suggested model’s frequency can be increased using this technique (implemented on the Zynq board) at least by 3.6 times compared to the original model, and power consumption can be decreased by 28%. High-frequency design of neuronal models with low-cost attributes is required for application-based types of equipment in case of high-speed operations of these components. Thus, using our approach, the desired goals of application-based features are to be fulfilled. In addition, because the suggested model uses fewer hardware resources than the original model, it is feasible to construct a significantly higher number of neurons (approximately 5 times) on a single Zynq board.

Recent years have witnessed relevant advancements in the quality of life of persons with lower limb amputations thanks to the technological developments in prosthetics. However, prostheses that provide information about the foot–ground interaction, and in particular about terrain irregularities, are still missing on the market. The lack of tactile feedback from the foot sole might lead subjects to step on uneven terrains, causing an increase in the risk of falling. To address this issue, a biomimetic vibrotactile feedback system that conveys information about gait and terrain features sensed by a dedicated insole has been assessed with intact subjects. After having shortly experienced both even and uneven terrains, the recruited subjects discriminated them with an accuracy of 87.5%, solely relying on the replay of the vibrotactile feedback. With the objective of exploring the human decoding mechanism of the feedback startegy, a KNN classifier was trained to recognize the uneven terrains. The outcome suggested that the subjects achieved such performance with a temporal dynamics of 45 ms. This work is a leap forward to assist lower-limb amputees to appreciate the floor conditions while walking, adapt their gait and promote a more confident use of their artificial limb. [ABSTRACT FROM AUTHOR]

The main required organ of the biological system is the Central Nervous System (CNS), which can influence the other basic organs in the human body. The basic elements of this important organ are neurons, synapses, and glias (such as astrocytes, which are the highest percentage of glias in the human brain). Investigating, modeling, simulation, and hardware implementation (realization) of different parts of the CNS are important in case of achieving a comprehensive neuronal system that is capable of emulating all aspects of the real nervous system. This paper uses a basic neuron model called the Izhikevich neuronal model to achieve a high copy of the primary nervous block, which is capable of regenerating the behaviors of the human brain. The proposed approach can regenerate all aspects of the Izhikevich neuron in high similarity degree and performances. The new model is based on Look-Up Table (LUT) modeling of the mathematical neuromorphic systems, which can be realized in a high degree of correlation with the original model. The proposed procedure is considered in three cases: 100 points LUT modeling, 1000 points LUT modeling, and 10,000 points LUT modeling. Indeed, by removing the high-cost functions in the original model, the presented model can be implemented in a low-error, high-speed, and low-area resources state in comparison with the original system. To test and validate the proposed final hardware, a digital FPGA board (Xilinx Virtex-II FPGA board) is used. Digital hardware synthesis illustrates that our presented approach can follow the Izhikevich neuron in a high-speed state (more than the original model), increase efficiency, and also reduce overhead costs. Implementation results show the overall saving of 84.30% in FPGA and also the higher frequency of the proposed model of about 264 MHz, which is significantly higher than the original model, 28 MHz.

Neural networks are applied in various scientific fields such as medicine, engineering, pharmacology, etc. Investigating operations of neural networks refers to estimating the relationship among single neurons and their contributions to the network as well. Hence, studying a single neuron is an essential process to solve complex brain problems. Mathematical models that simulate neurons and the way they transmit information are proven to be an indispensable tool for neuroscientists. Constructing appropriate mathematical models to simulate information transmission of a biological neural network is a challenge for researchers, as in the real world, identical neurons in terms of their electrophysiological characteristics in different brain regions do not contribute in the same way to information transmission within a neural network due to the intrinsic characteristics. This review highlights four mathematical, single-compartment models: Hodgkin-Huxley, Izhikevich, Leaky Integrate, and Fire and Morris-Lecar, and discusses comparison among them in terms of their biological plausibility, computational complexity, and applications, according to modern literature., (© 2023. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

Abstract: Artificial neural networks increasingly involve spiking dynamics to permit greater computational efficiency. This becomes especially attractive for on-chip implementation using dedicated neuromorphic hardware. However, both spiking neural networks and neuromorphic hardware have historically found difficulties in implementing efficient, effective learning rules. The best-known spiking neural network learning paradigm is Spike Timing Dependent Plasticity (STDP) which adjusts the strength of a connection in response to the time difference between the pre- and post-synaptic spikes. Approaches that relate learning features to the membrane potential of the post-synaptic neuron have emerged as possible alternatives to the more common STDP rule, with various implementations and approximations. Here we use a new type of neuromorphic hardware, SpiNNaker, which represents the flexible “neuromimetic” architecture, to demonstrate a new approach to this problem. Based on the standard STDP algorithm with modifications and approximations, a new rule, called STDP TTS (Time-To-Spike) relates the membrane potential with the Long Term Potentiation (LTP) part of the basic STDP rule. Meanwhile, we use the standard STDP rule for the Long Term Depression (LTD) part of the algorithm. We show that on the basis of the membrane potential it is possible to make a statistical prediction of the time needed by the neuron to reach the threshold, and therefore the LTP part of the STDP algorithm can be triggered when the neuron receives a spike. In our system these approximations allow efficient memory access, reducing the overall computational time and the memory bandwidth required. The improvements here presented are significant for real-time applications such as the ones for which the SpiNNaker system has been designed. We present simulation results that show the efficacy of this algorithm using one or more input patterns repeated over the whole time of the simulation. On-chip results show that the STDP TTS algorithm allows the neural network to adapt and detect the incoming pattern with improvements both in the reliability of, and the time required for, consistent output. Through the approximations we suggest in this paper, we introduce a learning rule that is easy to implement both in event-driven simulators and in dedicated hardware, reducing computational complexity relative to the standard STDP rule. Such a rule offers a promising solution, complementary to standard STDP evaluation algorithms, for real-time learning using spiking neural networks in time-critical applications. [Copyright &y& Elsevier]

Spiking neural network simulations incorporating variable transmission delays require synaptic events to be scheduled prior to delivery. Conventional methods have memory requirements that scale with the total number of synapses in a network. We introduce novel scheduling algorithms for both discrete and continuous event delivery, where the memory requirement scales instead with the number of neurons. Superior algorithmic performance is demonstrated using large-scale, benchmarking network simulations. [ABSTRACT FROM AUTHOR]

The main required organ of the biological system is the Central Nervous System (CNS), which can influence the other basic organs in the human body. The basic elements of this important organ are neurons, synapses, and glias (such as astrocytes, which are the highest percentage of glias in the human brain). Investigating, modeling, simulation, and hardware implementation (realization) of different parts of the CNS are important in case of achieving a comprehensive neuronal system that is capable of emulating all aspects of the real nervous system. This paper uses a basic neuron model called the Izhikevich neuronal model to achieve a high copy of the primary nervous block, which is capable of regenerating the behaviors of the human brain. The proposed approach can regenerate all aspects of the Izhikevich neuron in high similarity degree and performances. The new model is based on Look-Up Table (LUT) modeling of the mathematical neuromorphic systems, which can be realized in a high degree of correlation with the original model. The proposed procedure is considered in three cases: 100 points LUT modeling, 1000 points LUT modeling, and 10,000 points LUT modeling. Indeed, by removing the high-cost functions in the original model, the presented model can be implemented in a low-error, high-speed, and low-area resources state in comparison with the original system. To test and validate the proposed final hardware, a digital FPGA board (Xilinx Virtex-II FPGA board) is used. Digital hardware synthesis illustrates that our presented approach can follow the Izhikevich neuron in a high-speed state (more than the original model), increase efficiency, and also reduce overhead costs. Implementation results show the overall saving of 84.30 % in FPGA and also the higher frequency of the proposed model of about 264 MHz, which is significantly higher than the original model, 28 MHz. [ABSTRACT FROM AUTHOR]

Aim: In this paper, using a mathematical model, we will show that for special exchanged photons, the Hamiltonian of a collection of neurons tends to a constant number and all activities is stopped. These photons could be called as the dead photons. To this aim, we use concepts of Bio-BIon in Izhikevich Neuron model., Methods: In a neuron, there is a page of Dendrite, a page of axon's terminals and a tube of Schwann cells, axon and Myelin Sheath that connects them. These two pages and tube form a Bio-Bion. In a Bio-Bion, exchanging photons and some charged particles between terminals of dendrite and terminals of axon leads to the oscillation of neurons and transferring information. This Bion produces the Hamiltonian, wave equation and action potential of Izhikevich Neuron model. Also, this Bion determines the type of dependency of parameters of Izhikevich model on temperature and frequency and obtains the exact shape of membrane capacitance, resting membrane potential and instantaneous threshold potential., Results: Under some conditions, waves of neurons in this BIon join to each other and potential shrinks to a delta function. Consequently, total Hamiltonian of the system tends to a constant number and system of neuron act like a dead system. Finally, this model indicates that all neurons have the ability to produce similar waves and signals like waves of the mind., Conclusion: Generalizing this to biology, we can claim that neurons out of the brain can produce signals of minding and imaging and thus mind isn't confined to the brain., (Copyright: © 2019 Massimo Fioranelli, Alireza Sepehri, Maria Grazia Roccia, Chiara Rossi, Jacopo Lotti, Victoria Barygina, Petar Vojvodic, Aleksandra Vojvodic, Tatjana Vlaskovic-Jovicevic, Jovana Vojvodic, Sanja Dimitrijevic, Zorica Peric-Hajzler, Dusica Matovic, Goran Sijan, Uwe Wollina, Michael Tirant, Nguyen Van Thuong, Torello Lotti.)