Journal of Mathematical Neuroscience最新文献_第8页

Wilson-Cowan Equations for Neocortical Dynamics. 新皮质动力学的Wilson-Cowan方程。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2016-12-01 Epub Date: 2016-01-04 DOI: 10.1186/s13408-015-0034-5

Jack D Cowan, Jeremy Neuman, Wim van Drongelen

{"title":"Wilson-Cowan Equations for Neocortical Dynamics.","authors":"Jack D Cowan, Jeremy Neuman, Wim van Drongelen","doi":"10.1186/s13408-015-0034-5","DOIUrl":"10.1186/s13408-015-0034-5","url":null,"abstract":"In 1972-1973 Wilson and Cowan introduced a mathematical model of the population dynamics of synaptically coupled excitatory and inhibitory neurons in the neocortex. The model dealt only with the mean numbers of activated and quiescent excitatory and inhibitory neurons, and said nothing about fluctuations and correlations of such activity. However, in 1997 Ohira and Cowan, and then in 2007-2009 Buice and Cowan introduced Markov models of such activity that included fluctuation and correlation effects. Here we show how both models can be used to provide a quantitative account of the population dynamics of neocortical activity.We first describe how the Markov models account for many recent measurements of the resting or spontaneous activity of the neocortex. In particular we show that the power spectrum of large-scale neocortical activity has a Brownian motion baseline, and that the statistical structure of the random bursts of spiking activity found near the resting state indicates that such a state can be represented as a percolation process on a random graph, called directed percolation.Other data indicate that resting cortex exhibits pair correlations between neighboring populations of cells, the amplitudes of which decay slowly with distance, whereas stimulated cortex exhibits pair correlations which decay rapidly with distance. Here we show how the Markov model can account for the behavior of the pair correlations.Finally we show how the 1972-1973 Wilson-Cowan equations can account for recent data which indicates that there are at least two distinct modes of cortical responses to stimuli. In mode 1 a low intensity stimulus triggers a wave that propagates at a velocity of about 0.3 m/s, with an amplitude that decays exponentially. In mode 2 a high intensity stimulus triggers a larger response that remains local and does not propagate to neighboring regions. ","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-015-0034-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65847611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 81

Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience. 神经科学中振荡网络动力学的数学框架。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2016-12-01 Epub Date: 2016-01-06 DOI: 10.1186/s13408-015-0033-6

Peter Ashwin, Stephen Coombes, Rachel Nicks

引用次数: 0

Entrainment Ranges for Chains of Forced Neural and Phase Oscillators. 强迫神经和相位振荡器链的夹带范围。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2016-12-01 Epub Date: 2016-04-18 DOI: 10.1186/s13408-016-0038-9

Nicole Massarelli, Geoffrey Clapp, Kathleen Hoffman, Tim Kiemel

{"title":"Entrainment Ranges for Chains of Forced Neural and Phase Oscillators.","authors":"Nicole Massarelli, Geoffrey Clapp, Kathleen Hoffman, Tim Kiemel","doi":"10.1186/s13408-016-0038-9","DOIUrl":"https://doi.org/10.1186/s13408-016-0038-9","url":null,"abstract":"Sensory input to the lamprey central pattern generator (CPG) for locomotion is known to have a significant role in modulating lamprey swimming. Lamprey CPGs are known to have the ability to entrain to a bending stimulus, that is, in the presence of a rhythmic signal, the CPG will change its frequency to match the stimulus frequency. Bending experiments in which the lamprey spinal cord has been removed and mechanically bent back and forth at a single point have been used to determine the range of frequencies that can entrain the CPG rhythm. First, we model the lamprey locomotor CPG as a chain of neural oscillators with three classes of neurons and sinusoidal forcing representing edge cell input. We derive a phase model using the connections described in the neural model. This results in a simpler model yet maintains some properties of the neural model. For both the neural model and the derived phase model, entrainment ranges are computed for forcing at different points along the chain while varying both intersegmental coupling strength and the coupling strength between the forcer and chain. Entrainment ranges for chains with nonuniform intersegmental coupling asymmetry are larger when forcing is applied to the middle of the chain than when it is applied to either end, a result that is qualitatively similar to the experimental results. In the limit of weak coupling in the chain, the entrainment results of the neural model approach the entrainment results for the derived phase model. Both biological experiments and the robustness of non-monotonic entrainment ranges as a function of the forcing position across different classes of CPG models with nonuniform asymmetric coupling suggest that a specific property of the intersegmental coupling of the CPG is key to entrainment. ","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-016-0038-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34414173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 9

Wave Generation in Unidirectional Chains of Idealized Neural Oscillators. 理想神经振荡器单向链中的波产生。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2016-12-01 Epub Date: 2016-04-08 DOI: 10.1186/s13408-016-0037-x

Bastien Fernandez, Stanislav M Mintchev

引用次数: 2

Responses of Leaky Integrate-and-Fire Neurons to a Plurality of Stimuli in Their Receptive Fields. 漏性整合-放电神经元对其感受野中多种刺激的反应。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2016-12-01 Epub Date: 2016-05-23 DOI: 10.1186/s13408-016-0040-2

Kang Li, Claus Bundesen, Susanne Ditlevsen

引用次数: 3

Neural Field Models with Threshold Noise. 带有阈值噪声的神经场模型

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2016-12-01 Epub Date: 2016-03-02 DOI: 10.1186/s13408-016-0035-z

Rüdiger Thul, Stephen Coombes, Carlo R Laing

{"title":"Neural Field Models with Threshold Noise.","authors":"Rüdiger Thul, Stephen Coombes, Carlo R Laing","doi":"10.1186/s13408-016-0035-z","DOIUrl":"10.1186/s13408-016-0035-z","url":null,"abstract":"The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches. ","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4775726/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65848167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stochastic Network Models in Neuroscience: A Festschrift for Jack Cowan. Introduction to the Special Issue 神经科学中的随机网络模型:杰克·考恩的经典著作。特刊简介

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2016-04-04 DOI: 10.1186/s13408-016-0036-y

P. Bressloff, B. Ermentrout, O. Faugeras, P. Thomas

引用次数: 3

Shifting Spike Times or Adding and Deleting Spikes-How Different Types of Noise Shape Signal Transmission in Neural Populations. 移动尖峰时间或增加和删除尖峰——不同类型的噪声如何影响神经群体中的信号传输。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2015-12-01 Epub Date: 2015-01-12 DOI: 10.1186/2190-8567-5-1

Sergej O Voronenko, Wilhelm Stannat, Benjamin Lindner

{"title":"Shifting Spike Times or Adding and Deleting Spikes-How Different Types of Noise Shape Signal Transmission in Neural Populations.","authors":"Sergej O Voronenko, Wilhelm Stannat, Benjamin Lindner","doi":"10.1186/2190-8567-5-1","DOIUrl":"https://doi.org/10.1186/2190-8567-5-1","url":null,"abstract":"We study a population of spiking neurons which are subject to independent noise processes and a strong common time-dependent input. We show that the response of output spikes to independent noise shapes information transmission of such populations even when information transmission properties of single neurons are left unchanged. In particular, we consider two Poisson models in which independent noise either (i) adds and deletes spikes (AD model) or (ii) shifts spike times (STS model). We show that in both models suprathreshold stochastic resonance (SSR) can be observed, where the information transmitted by a neural population is increased with addition of independent noise. In the AD model, the presence of the SSR effect is robust and independent of the population size or the noise spectral statistics. In the STS model, the information transmission properties of the population are determined by the spectral statistics of the noise, leading to a strongly increased effect of SSR in some regimes, or an absence of SSR in others. Furthermore, we observe a high-pass filtering of information in the STS model that is absent in the AD model. We quantify information transmission by means of the lower bound on the mutual information rate and the spectral coherence function. To this end, we derive the signal-output cross-spectrum, the output power spectrum, and the cross-spectrum of two spike trains for both models analytically. ","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/2190-8567-5-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34079060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 13

Uncertainty Propagation in Nerve Impulses Through the Action Potential Mechanism. 通过动作电位机制的神经冲动不确定性传播。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2015-12-01 Epub Date: 2015-01-12 DOI: 10.1186/2190-8567-5-3

Aldemar Torres Valderrama, Jeroen Witteveen, Maria Navarro, Joke Blom

引用次数: 10

Stochastic Synchronization in Purkinje Cells with Feedforward Inhibition Could Be Studied with Equivalent Phase-Response Curves. 用等效相位响应曲线研究具有前馈抑制的浦肯野细胞的随机同步。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2015-12-01 Epub Date: 2015-06-19 DOI: 10.1186/s13408-015-0025-6

Sergio Verduzco-Flores

{"title":"Stochastic Synchronization in Purkinje Cells with Feedforward Inhibition Could Be Studied with Equivalent Phase-Response Curves.","authors":"Sergio Verduzco-Flores","doi":"10.1186/s13408-015-0025-6","DOIUrl":"https://doi.org/10.1186/s13408-015-0025-6","url":null,"abstract":"Simple-spike synchrony between Purkinje cells projecting to a common neuron in the deep cerebellar nucleus is emerging as an important factor in the encoding of output information from cerebellar cortex. A phenomenon known as stochastic synchronization happens when uncoupled oscillators synchronize due to correlated inputs. Stochastic synchronization is a viable mechanism through which simple-spike synchrony could be generated, but it has received scarce attention, perhaps because the presence of feedforward inhibition in the input to Purkinje cells makes insights difficult. This paper presents a method to account for feedforward inhibition so the usual mathematical approaches to stochastic synchronization can be applied. The method consists in finding a single Phase Response Curve, called the equivalent PRC, that accounts for the effects of both excitatory inputs and delayed feedforward inhibition from molecular layer interneurons. The results suggest that a theory of stochastic synchronization for the case of feedforward inhibition may not be necessary, since this case can be approximately reduced to the case of inputs characterized by a single PRC. Moreover, feedforward inhibition could in many situations increase the level of synchrony experienced by Purkinje cells. ","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-015-0025-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33271946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2