Complete Neuron-Astrocyte Interaction Model: Digital Multiplierless Design and Networking Mechanism

High-Matching and Low-Cost Realization of the FHN Neuron Model on Reconfigurable FPGA Board

The main objectives of neuromorphic engineering are the research, modeling, and implementation of neural functioning in the human brain. We provide a hardware solution that can replicate such a nature-inspired system by merging multiple scientific domains and is based on neural cell processes. This work provides a modified version of the original Fitz-Hugh Nagumo (FHN) neuron using a simple 2V term called Hybrid Piece-Wised Base-2 Model (HPWBM), which accurately reproduces numerous patterns of the original neuron model. With reduced terms, we suggest modifying the original nonlinear term to achieve high matching accuracy and little computing error. Time domain and phase portraits are used to validate the proposed model, which shows that it can reproduce all of the FHN model's properties with high accuracy and little mistake. We provide an effective digital hardware approach for large-scale neuron implementations based on resource-sharing and pipelining strategies. The Hardware Description Language (HDL) is used to construct the hardware on an FPGA as a proof of concept. The recommended model hardly uses 0.48 percent of the resources on a Virtex 4 FPGA board, according to the results of the hardware implementation. The circuit can run at a maximum frequency of 448.236 MHz, according to the static timing study.

Analysis of Network Models with Neuron-Astrocyte Interactions

Neural networks, composed of many neurons and governed by complex interactions between them, are a widely accepted formalism for modeling and exploring global dynamics and emergent properties in brain systems. In the past decades, experimental evidence of computationally relevant neuron-astrocyte interactions, as well as the astrocytic modulation of global neural dynamics, have accumulated. These findings motivated advances in computational glioscience and inspired several models integrating mechanisms of neuron-astrocyte interactions into the standard neural network formalism. These models were developed to study, for example, synchronization, information transfer, synaptic plasticity, and hyperexcitability, as well as classification tasks and hardware implementations. We here focus on network models of at least two neurons interacting bidirectionally with at least two astrocytes that include explicitly modeled astrocytic calcium dynamics. In this study, we analyze the evolution of these models and the biophysical, biochemical, cellular, and network mechanisms used to construct them. Based on our analysis, we propose how to systematically describe and categorize interaction schemes between cells in neuron-astrocyte networks. We additionally study the models in view of the existing experimental data and present future perspectives. Our analysis is an important first step towards understanding astrocytic contribution to brain functions. However, more advances are needed to collect comprehensive data about astrocyte morphology and physiology in vivo and to better integrate them in data-driven computational models. Broadening the discussion about theoretical approaches and expanding the computational tools is necessary to better understand astrocytes' roles in brain functions.

Investigation on the Wilson Neuronal Model: Optimized Approximation and Digital Multiplierless Implementation

Neuromorphic engineering is an essential science field which incorporates the basic aspects of issues together such as: physics, mathematics, electronics, etc. The primary block in the Central Nervous System (CNS) is neurons that have functional roles such as: receiving, processing, and transmitting data in the brain. This paper presents Wilson Multiplierless Neuron (WMN) model which is a modified version of the original model. This model uses power-2 based functions, Look-Up Table (LUT) approach and shifters to apply a multiplierless digital realization leads to overhead costs reduction and increases in the final system frequency. The proposed model specifically follows the original neuron model in case of spiking patterns and also dynamical pathways. To validate the proposed model in digital hardware implementation, the FPGA board (Xilinx Virtex II XC2VP30) can be used. Hardware results show the increasing in the system frequency compared with the original model and other similar papers. Numerical results demonstrate that the proposed system speed-up is 210 MHz that is higher than the original one, 85 MHz. Additionally, the overall saving in FPGA resources for the proposed model is 96.86 % that is more than the original model, 95.13 %. From case study viewpoint for CNS consideration, a network consisting of Wilson neurons, synapses, and astrocytes have been considered to test the controlling effects on LTP and LTD processes for investigating the neuronal diseases (medical approaches) such as Epilepsy.

Low Cost Digital Implementation of Hybrid FitzHugh Nagumo-Morris Lecar Neuron Model Considering Electromagnetic Flux Coupling

Digital realization of neuron models, especially implementation on a field programmable gate array (FPGA), is one of the key objectives of neuromorphic research, because the effective hardware realization of the biological neural networks plays a crucial role in implementing the behaviors of the brain for future applications. In this paper, a hybrid FitzHugh Nagumo-Morris Lecar (FNML) neuron model with electromagnetic flux coupling is considered, and two multiplierless piecewise linear (PWL) models, which have similar behaviors to the biological neuron, are presented. A comparison between digital implementation results of the original FNML and PWL models illustrates that, the PWL1 model provides a 65% speed-up with an overall saving (in FPGA resources) of 66.2%, and the PWL2 model yields a 71% speed-up with an overall saving of 78.2%.

An Optimization on the Neuronal Networks Based on the ADEX Biological Model in Terms of LUT-State Behaviors: Digital Design and Realization on FPGA Platforms

Design and implementation of biological neural networks is a vital research field in the neuromorphic engineering. This paper presents LUT-based modeling of the Adaptive Exponential integrate-and-fire (ADEX) model using Nyquist frequency method. In this approach, a continuous term is converted to a discrete term by sampling factor. This new modeling is called N-LUT-ADEX (Nyquist-Look Up Table-ADEX) and is based on accurate sampling of the original ADEX model. Since in this modeling, the high-accuracy matching is achieved, it can exactly reproduce the spiking patterns, which have the same behaviors of the original neuron model. To confirm the N-LUT-ADEX neuron, the proposed model is realized on Virtex-II Field-Programmable Gate Array (FPGA) board for validating the final hardware. Hardware implementation results show the high degree of similarity between the proposed and original models. Furthermore, low-cost and high-speed attributes of our proposed neuron model will be validated. Indeed, the proposed model is capable of reproducing the spiking patterns in terms of low overhead costs and higher frequencies in comparison with the original one. The properties of the proposed model cause can make it a suitable choice for neuromorphic network implementations with reduced-cost attributes.

Central Nervous System: Overall Considerations Based on Hardware Realization of Digital Spiking Silicon Neurons (DSSNs) and Synaptic Coupling

The Central Nervous System (CNS) is the part of the nervous system including the brain and spinal cord. The CNS is so named because the brain integrates the received information and influences the activity of different sections of the bodies. The basic elements of this important organ are: neurons, synapses, and glias. Neuronal modeling approach and hardware realization design for the nervous system of the brain is an important issue in the case of reproducing the same biological neuronal behaviors. This work applies a quadratic-based modeling called Digital Spiking Silicon Neuron (DSSN) to propose a modified version of the neuronal model which is capable of imitating the basic behaviors of the original model. The proposed neuron is modeled based on the primary hyperbolic functions, which can be realized in high correlation state with the main model (original one). Really, if the high-cost terms of the original model, and its functions were removed, a low-error and high-performance (in case of frequency and speed-up) new model will be extracted compared to the original model. For testing and validating the new model in hardware state, Xilinx Spartan-3 FPGA board has been considered and used. Hardware results show the high-degree of similarity between the original and proposed models (in terms of neuronal behaviors) and also higher frequency and low-cost condition have been achieved. The implementation results show that the overall saving is more than other papers and also the original model. Moreover, frequency of the proposed neuronal model is about 168 MHz, which is significantly higher than the original model frequency, 63 MHz.

An Investigation on Spiking Neural Networks Based on the Izhikevich Neuronal Model: Spiking Processing and Hardware Approach

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.

A Novel Nonlinear Function Evaluation Approach for Efficient FPGA Mapping of Neuron and Synaptic Plasticity Models

Efficient hardware realization of spiking neural networks is of great significance in a wide variety of applications, such as high-speed modeling and simulation of large-scale neural systems. Exploiting the key features of FPGAs, this paper presents a novel nonlinear function evaluation approach, based on an effective uniform piecewise linear segmentation method, to efficiently approximate the nonlinear terms of neuron and synaptic plasticity models targeting low-cost digital implementation. The proposed approach takes advantage of a high-speed and extremely simple segment address encoder unit regardless of the number of segments, and therefore is capable of accurately approximating a given nonlinear function with a large number of straight lines. In addition, this approach can be efficiently mapped into FPGAs with minimal hardware cost. To investigate the application of the proposed nonlinear function evaluation approach in low-cost neuromorphic circuit design, it is applied to four case studies: the Izhikevich and FitzHugh-Nagumo neuron models as 2-dimensional case studies, the Hindmarsh-Rose neuron model as a relatively complex 3-dimensional model containing two nonlinear terms, and a calcium-based synaptic plasticity model capable of producing various STDP curves. Simulation and FPGA synthesis results demonstrate that the hardware proposed for each case study is capable of producing various responses remarkably similar to the original model and significantly outperforms the previously published counterparts in terms of resource utilization and maximum clock frequency.

Proteome changes in methylmercury-exposed mouse primary cerebellar granule neurons and astrocytes

Methylmercury (MeHg) is a neurotoxicant, with the cerebellum as the main target of toxicity; however, the toxic effects of MeHg on specific cell types remain unclear. Here, primary cerebellar granule neurons (CGNs) and cerebellar astrocytes were isolated and analyzed for total mercury accumulation, cellular reactive oxygen species (ROS) production, and whole-cell proteome expression after exposure to 0-10 μM MeHg for 24 h. Intracellular mercury and ROS levels showed dose-dependent increases. Mercury accumulation was greater in CGNs than astrocytes. The proteomic analysis identified a total of 1966 and 3214 proteins in CGNs and astrocytes, among which 183 and 262 proteins were differentially expressed after mercury exposure, respectively. Enrichment analysis revealed mitochondrial-associated organelles as the main targets of MeHg in both cell types. Whereas multiple functions/pathways were affected in CGNs, the oxidation-reduction process was the most significantly changed function/pathway in astrocytes. CGNs were more sensitive to MeHg-mediated neurotoxicity than astrocytes. The two cell types showed distinct mechanistic responses to MeHg. In astrocytes, the mitochondrion was the primary target of toxicity, resulting in increases in oxidation-reduction process responses. In CGNs, the neurotrophin signaling pathway, cytoskeleton, cAMP signaling pathway, and thyroid hormone signaling pathway were affected.

Multiplierless Implementation of Noisy Izhikevich Neuron With Low-Cost Digital Design

Fast speed and a high accuracy implementation of biological plausible neural networks are vital key objectives to achieve new solutions to model, simulate and cure the brain diseases. Efficient hardware implementation of spiking neural networks is a significant approach in biological neural networks. This paper presents a multiplierless noisy Izhikevich neuron (MNIN) model, which is used for the digital implementation of biological neural networks in large scale. Simulation results show that the MNIN model reproduces the same operations of the original noisy Izhikevich neuron. The proposed model has a low-cost hardware implementation property compared with the original neuron model. The field-programmable gate array realization results demonstrated that the MNIN model follows the different spiking patterns appropriately.

Computational Models for Calcium-Mediated Astrocyte Functions

The computational neuroscience field has heavily concentrated on the modeling of neuronal functions, largely ignoring other brain cells, including one type of glial cell, the astrocytes. Despite the short history of modeling astrocytic functions, we were delighted about the hundreds of models developed so far to study the role of astrocytes, most often in calcium dynamics, synchronization, information transfer, and plasticity in vitro, but also in vascular events, hyperexcitability, and homeostasis. Our goal here is to present the state-of-the-art in computational modeling of astrocytes in order to facilitate better understanding of the functions and dynamics of astrocytes in the brain. Due to the large number of models, we concentrated on a hundred models that include biophysical descriptions for calcium signaling and dynamics in astrocytes. We categorized the models into four groups: single astrocyte models, astrocyte network models, neuron-astrocyte synapse models, and neuron-astrocyte network models to ease their use in future modeling projects. We characterized the models based on which earlier models were used for building the models and which type of biological entities were described in the astrocyte models. Features of the models were compared and contrasted so that similarities and differences were more readily apparent. We discovered that most of the models were basically generated from a small set of previously published models with small variations. However, neither citations to all the previous models with similar core structure nor explanations of what was built on top of the previous models were provided, which made it possible, in some cases, to have the same models published several times without an explicit intention to make new predictions about the roles of astrocytes in brain functions. Furthermore, only a few of the models are available online which makes it difficult to reproduce the simulation results and further develop the models. Thus, we would like to emphasize that only via reproducible research are we able to build better computational models for astrocytes, which truly advance science. Our study is the first to characterize in detail the biophysical and biochemical mechanisms that have been modeled for astrocytes.