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12 pages, 2349 KiB

Open AccessArticle

Effects of NMDA Receptor Hypofunction on Inhibitory Control in a Two-Layer Neural Circuit Model

by Weijie Ye and Xiaoying Chen

Mathematics 2023, 11(19), 4063; https://doi.org/10.3390/math11194063 - 25 Sep 2023

Viewed by 592

Abstract

Inhibitory control plays an important role in controlling behaviors, and its impairment is a characteristic feature of schizophrenia. Such inhibitory control has been examined through the the stop-signal task, wherein participants are asked to suppress a planned movement when a stop signal appears. [...] Read more.

Inhibitory control plays an important role in controlling behaviors, and its impairment is a characteristic feature of schizophrenia. Such inhibitory control has been examined through the the stop-signal task, wherein participants are asked to suppress a planned movement when a stop signal appears. In this research, we constructed a two-layer spiking neural circuit model to study how N-methyl-D-aspartate receptor (NMDAR) hypofunction, a potential pathological mechanism in schizophrenia, impacts the inhibitory control ability in the stop-signal task. To find the possible NMDAR hypofunction effects in schizophrenia, all NMDA-mediated synapses in the model were set to be NMDAR hypofunction at different levels. Our findings revealed that the performances of the stop-signal task were close to the experimental results in schizophrenia when NMDAR hypofunction was present in the neurons of two populations that controlled the “go” process and the “stop” process of the stop-signal task, implying that the execution and inhibition of behaviors were both impaired in schizophrenia. Under a certain degree of NMDAR hypofunction, the circuit model is able to replicate the stop-signal task performances observed in individuals with schizophrenia. In addition, we have observed a predictable outcome indicating that NMDAR hypofunction can lower the saccadic threshold in the stop-signal task. These results provide a mechanical explanation for the impairment of inhibitory control in schizophrenia. Full article

(This article belongs to the Special Issue Mathematical and Computational Neuroscience)

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25 pages, 1707 KiB

Open AccessArticle

Deep Diffusion Kalman Filter Combining Large-Scale Neuronal Networks Simulation with Multimodal Neuroimaging Data

by Wenyong Zhang and Wenlian Lu

Mathematics 2023, 11(12), 2716; https://doi.org/10.3390/math11122716 - 15 Jun 2023

Cited by 1 | Viewed by 1322

Abstract

Using computers to numerically simulate large-scale neuronal networks has become a common method for studying the mechanism of the human brain, and neuroimaging has brought forth multimodal brain data. Determining how to fully consider these multimodal data in the process of brain modeling [...] Read more.

Using computers to numerically simulate large-scale neuronal networks has become a common method for studying the mechanism of the human brain, and neuroimaging has brought forth multimodal brain data. Determining how to fully consider these multimodal data in the process of brain modeling has become a crucial issue. Data assimilation is an efficient method for combining the dynamic system with the observation data, and many related algorithms have been developed. In this paper, we utilize data assimilation to perform brain state variables estimation, put forward a general form of a diffusion Kalman filter named the deep diffusion Kalman filter, and provide a specific algorithm that is combined with data assimilation. Then, we theoretically demonstrate the deep diffusion Kalman filter’s effectiveness and further validate it by using an experiment in the toy model. Finally, according to the resting state functional magnetic resonance imaging signals, we assimilate a cortex networks model with the resting state brain, where the correlation is as high as 98.42%. Full article

(This article belongs to the Special Issue Mathematical and Computational Neuroscience)

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28 pages, 2879 KiB

Open AccessArticle

A New Spike Membership Function for the Recognition and Processing of Spatiotemporal Spike Patterns: Syllable-Based Speech Recognition Application

by Abigail María Elena Ramírez-Mendoza, Wen Yu and Xiaoou Li

Mathematics 2023, 11(11), 2525; https://doi.org/10.3390/math11112525 - 31 May 2023

Cited by 1 | Viewed by 1330

Abstract

This paper introduces a new spike activation function (SPKAF) or spike membership function for fuzzy adaptive neurons (FAN), developed for decoding spatiotemporal information with spikes, optimizing digital signal processing. A solution with the adaptive network-based fuzzy inference system (ANFIS) method is proposed and [...] Read more.

This paper introduces a new spike activation function (SPKAF) or spike membership function for fuzzy adaptive neurons (FAN), developed for decoding spatiotemporal information with spikes, optimizing digital signal processing. A solution with the adaptive network-based fuzzy inference system (ANFIS) method is proposed and compared with that of the FAN-SPKAF model, obtaining very precise simulation results. Stability analysis of systems models is presented. An application to voice recognition using solfeggio syllables in Spanish is performed experimentally, comparing the methods of FAN-step activation function (STEPAF)-SPKAF, Augmented Spiking Neuron Model, and Augmented FAN-STEPAF-SPKAF, achieving very good results. Full article

(This article belongs to the Special Issue Mathematical and Computational Neuroscience)

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24 pages, 6895 KiB

Open AccessArticle

Robust Evaluation and Comparison of EEG Source Localization Algorithms for Accurate Reconstruction of Deep Cortical Activity

by Hao Shen and Yuguo Yu

Mathematics 2023, 11(11), 2450; https://doi.org/10.3390/math11112450 - 25 May 2023

Cited by 2 | Viewed by 2533

Abstract

Accurately reconstructing deep cortical source activity from EEG recordings is essential for understanding cognitive processes. However, currently, there is a lack of reliable methods for assessing the performance of EEG source localization algorithms. This study establishes an algorithm evaluation framework, utilizing realistic human [...] Read more.

Accurately reconstructing deep cortical source activity from EEG recordings is essential for understanding cognitive processes. However, currently, there is a lack of reliable methods for assessing the performance of EEG source localization algorithms. This study establishes an algorithm evaluation framework, utilizing realistic human head models and simulated EEG source signals with spatial propagations. We compare the performance of several newly proposed Bayesian algorithms, including full Dugh, thin Dugh, and Mackay, against classical methods such as MN and eLORETA. Our results, which are based on 630 Monte Carlo simulations, demonstrate that thin Dugh and Mackay are mathematically sound and perform significantly better in spatial and temporal source reconstruction than classical algorithms. Mackay is less robust spatially, while thin Dugh performs best overall. Conversely, we show that full Dugh has significant theoretical flaws that negatively impact localization accuracy. This research highlights the advantages and limitations of various source localization algorithms, providing valuable insights for future development and refinement in EEG source localization methods. Full article

(This article belongs to the Special Issue Mathematical and Computational Neuroscience)

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23 pages, 10815 KiB

Open AccessArticle

A Connectome-Based Digital Twin Caenorhabditis elegans Capable of Intelligent Sensorimotor Behavior

by Zhongyu Chen, Yuguo Yu and Xiangyang Xue

Mathematics 2023, 11(11), 2442; https://doi.org/10.3390/math11112442 - 25 May 2023

Viewed by 2361

Abstract

Despite possessing a simple nervous system, the Caenorhabditis elegans exhibits remarkably intelligent behavior. However, the underlying mechanisms involved in sensory processing and decision making, which contribute to locomotion behaviors, remain unclear. In order to investigate the coordinated function of neurons in achieving chemotaxis [...] Read more.

Despite possessing a simple nervous system, the Caenorhabditis elegans exhibits remarkably intelligent behavior. However, the underlying mechanisms involved in sensory processing and decision making, which contribute to locomotion behaviors, remain unclear. In order to investigate the coordinated function of neurons in achieving chemotaxis behavior, we have developed a digital twin of the C. elegans that combines a connectome-based neural network model with a realistic digital worm body. Through training the digital worm using offline chemotaxis behavioral data generated with a PID controller, we have successfully replicated faithful sinusoidal crawling and intelligent chemotaxis behavior, similar to real worms. By ablating individual neurons, we have examined their roles in modulating or contributing to the regulation of behavior. Our findings highlight the critical involvement of 119 neurons in sinusoidal crawling, including B-type, A-type, D-type, and PDB motor neurons, as well as AVB and AVA interneurons, which was experimentally demonstrated. We have also predicted the involvement of DD04 and DD05 neurons and the lack of relevance of DD02 and DD03 neurons in crawling, which have been confirmed through experimentation. Additionally, head motor neurons, sublateral motor neurons, layer 1 interneurons, and layer 1 and layer 5 sensory neurons are expected to play a role in crawling. In summary, we present a novel methodological framework that enables the establishment of an animal model capable of closed-loop control, faithfully replicating realistic animal behavior. This framework holds potential for examining the neural mechanisms of behaviors in other species. Full article

(This article belongs to the Special Issue Mathematical and Computational Neuroscience)

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15 pages, 3470 KiB

Open AccessArticle

Synchronization Analysis of Linearly Coupled Systems with Signal-Dependent Noises

by Yanhao Ren, Qiang Luo and Wenlian Lu

Mathematics 2023, 11(10), 2328; https://doi.org/10.3390/math11102328 - 16 May 2023

Viewed by 946

Abstract

In this paper, we propose methods for analyzing the synchronization stability of stochastic linearly coupled differential equation systems, with signal-dependent noise perturbation. We consider signal-dependent noise, which is common in many fields, to discuss the stability of the synchronization manifold of multiagent systems [...] Read more.

In this paper, we propose methods for analyzing the synchronization stability of stochastic linearly coupled differential equation systems, with signal-dependent noise perturbation. We consider signal-dependent noise, which is common in many fields, to discuss the stability of the synchronization manifold of multiagent systems and linearly coupled nonlinear dynamical systems under sufficient conditions. Numerical simulations are performed in the paper, and the results show the effectiveness of our theorems. Full article

(This article belongs to the Special Issue Mathematical and Computational Neuroscience)

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15 pages, 2474 KiB

Open AccessArticle

A Comparative Analysis of Numerical Methods for Solving the Leaky Integrate and Fire Neuron Model

by Ghinwa El Masri, Asma Ali, Waad H. Abuwatfa, Maruf Mortula and Ghaleb A. Husseini

Mathematics 2023, 11(3), 714; https://doi.org/10.3390/math11030714 - 31 Jan 2023

Viewed by 2353

Abstract

The human nervous system is one of the most complex systems of the human body. Understanding its behavior is crucial in drug discovery and developing medical devices. One approach to understanding such a system is to model its most basic unit, neurons. The [...] Read more.

The human nervous system is one of the most complex systems of the human body. Understanding its behavior is crucial in drug discovery and developing medical devices. One approach to understanding such a system is to model its most basic unit, neurons. The leaky integrate and fire (LIF) method models the neurons’ response to a stimulus. Given the fact that the model’s equation is a linear ordinary differential equation, the purpose of this research is to compare which numerical analysis method gives the best results for the simplified version of this model. Adams predictor and corrector (AB4-AM4) and Heun’s methods were then used to solve the equation. In addition, this study further researches the effects of different current input models on the LIF’s voltage output. In terms of the computational time, Heun’s method was 0.01191 s on average which is much less than that of the AB-AM4 method (0.057138) for a constant DC input. As for the root mean square error, the AB-AM4 method had a much lower value (0.0061) compared to that of Heun’s method (0.3272) for the same constant input. Therefore, our results show that Heun’s method is best suited for the simplified LIF model since it had the lowest computation time of 36 ms, was stable over a larger range, and had an accuracy of 72% for the varying sinusoidal current input model. Full article

(This article belongs to the Special Issue Mathematical and Computational Neuroscience)

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35 pages, 1515 KiB

Open AccessArticle

A Hierarchical Bayesian Model for Inferring and Decision Making in Multi-Dimensional Volatile Binary Environments

by Changbo Zhu, Ke Zhou, Fengzhen Tang, Yandong Tang, Xiaoli Li and Bailu Si

Mathematics 2022, 10(24), 4775; https://doi.org/10.3390/math10244775 - 15 Dec 2022

Viewed by 2291

Abstract

The ability to track the changes of the surrounding environment is critical for humans and animals to adapt their behaviors. In high-dimensional environments, the interactions between each dimension need to be estimated for better perception and decision making, for example in volatile or [...] Read more.

The ability to track the changes of the surrounding environment is critical for humans and animals to adapt their behaviors. In high-dimensional environments, the interactions between each dimension need to be estimated for better perception and decision making, for example in volatile or social cognition tasks. We develop a hierarchical Bayesian model for inferring and decision making in multi-dimensional volatile environments. The hierarchical Bayesian model is composed of a hierarchical perceptual model and a response model. Using the variational Bayes method, we derived closed-form update rules. These update rules also constitute a complete predictive coding scheme. To validate the effectiveness of the model in multi-dimensional volatile environments, we defined a probabilistic gambling task modified from a two-armed bandit. Simulation results demonstrated that an agent endowed with the proposed hierarchical Bayesian model is able to infer and to update its internal belief on the tendency and volatility of the sensory inputs. Based on the internal belief of the sensory inputs, the agent yielded near-optimal behavior following its response model. Our results pointed this model a viable framework to explain the temporal dynamics of human decision behavior in complex and high dimensional environments. Full article

(This article belongs to the Special Issue Mathematical and Computational Neuroscience)

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Review

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22 pages, 406 KiB

Open AccessReview

Canard Mechanism and Rhythm Dynamics of Neuron Models

by Feibiao Zhan, Yingteng Zhang, Jian Song and Shenquan Liu

Mathematics 2023, 11(13), 2874; https://doi.org/10.3390/math11132874 - 27 Jun 2023

Cited by 1 | Viewed by 885

Abstract

Canards are a type of transient dynamics that occur in singularly perturbed systems, and they are specific types of solutions with varied dynamic behaviours at the boundary region. This paper introduces the emergence and development of canard phenomena in a neuron model. The [...] Read more.

Canards are a type of transient dynamics that occur in singularly perturbed systems, and they are specific types of solutions with varied dynamic behaviours at the boundary region. This paper introduces the emergence and development of canard phenomena in a neuron model. The singular perturbation system of a general neuron model is investigated, and the link between the transient transition from a neuron model to a canard is summarised. First, the relationship between the folded saddle-type canard and the parabolic burster, as well as the firing-threshold manifold, is established. Moreover, the association between the mixed-mode oscillation and the folded node type is unique. Furthermore, the connection between the mixed-mode oscillation and the limit-cycle canard (singular Hopf bifurcation) is stated. In addition, the link between the torus canard and the transition from tonic spiking to bursting is illustrated. Finally, the specific manifestations of these canard phenomena in the neuron model are demonstrated, such as the singular Hopf bifurcation, the folded-node canard, the torus canard, and the “blue sky catastrophe”. The summary and outlook of this paper point to the realistic possibility of canards, which have not yet been discovered in the neuron model. Full article

(This article belongs to the Special Issue Mathematical and Computational Neuroscience)

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