Journal of Mathematical Neuroscience最新文献_第7页

The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions. 有界域上神经场的动力学:Dirichlet边界条件的界面方法。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-10-26 DOI: 10.1186/s13408-017-0054-4

Aytül Gökçe, Daniele Avitabile, Stephen Coombes

{"title":"The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions.","authors":"Aytül Gökçe, Daniele Avitabile, Stephen Coombes","doi":"10.1186/s13408-017-0054-4","DOIUrl":"https://doi.org/10.1186/s13408-017-0054-4","url":null,"abstract":"Continuum neural field equations model the large-scale spatio-temporal dynamics of interacting neurons on a cortical surface. They have been extensively studied, both analytically and numerically, on bounded as well as unbounded domains. Neural field models do not require the specification of boundary conditions. Relatively little attention has been paid to the imposition of neural activity on the boundary, or to its role in inducing patterned states. Here we redress this imbalance by studying neural field models of Amari type (posed on one- and two-dimensional bounded domains) with Dirichlet boundary conditions. The Amari model has a Heaviside nonlinearity that allows for a description of localised solutions of the neural field with an interface dynamics. We show how to generalise this reduced but exact description by deriving a normal velocity rule for an interface that encapsulates boundary effects. The linear stability analysis of localised states in the interface dynamics is used to understand how spatially extended patterns may develop in the absence and presence of boundary conditions. Theoretical results for pattern formation are shown to be in excellent agreement with simulations of the full neural field model. Furthermore, a numerical scheme for the interface dynamics is introduced and used to probe the way in which a Dirichlet boundary condition can limit the growth of labyrinthine structures.","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2017-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-017-0054-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35496165","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: 7

Fundamental Limits of Forced Asynchronous Spiking with Integrate and Fire Dynamics. 强制异步尖峰脉冲与积分和火焰动力学的基本极限。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-10-11 DOI: 10.1186/s13408-017-0053-5

Anirban Nandi, Heinz Schättler, Jason T Ritt, ShiNung Ching

引用次数: 0

Symmetries Constrain Dynamics in a Family of Balanced Neural Networks. 一类平衡神经网络的对称性约束动力学。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-10-10 DOI: 10.1186/s13408-017-0052-6

Andrea K Barreiro, J Nathan Kutz, Eli Shlizerman

引用次数: 2

An Analysis of Waves Underlying Grid Cell Firing in the Medial Enthorinal Cortex. 内皮层网格细胞放电的波分析。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-08-25 DOI: 10.1186/s13408-017-0051-7

Mayte Bonilla-Quintana, Kyle C A Wedgwood, Reuben D O'Dea, Stephen Coombes

{"title":"An Analysis of Waves Underlying Grid Cell Firing in the Medial Enthorinal Cortex.","authors":"Mayte Bonilla-Quintana, Kyle C A Wedgwood, Reuben D O'Dea, Stephen Coombes","doi":"10.1186/s13408-017-0051-7","DOIUrl":"https://doi.org/10.1186/s13408-017-0051-7","url":null,"abstract":"Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an [Formula: see text] current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo (Philos. Trans. R. Soc. Lond. B, Biol. Sci. 369:20120523, 2013) showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the [Formula: see text] current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in [Formula: see text] resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the [Formula: see text] current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions.","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2017-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-017-0051-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35347021","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

A Stochastic Version of the Jansen and Rit Neural Mass Model: Analysis and Numerics. Jansen和Rit神经质量模型的随机版本:分析和数值。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-08-08 DOI: 10.1186/s13408-017-0046-4

Markus Ableidinger, Evelyn Buckwar, Harald Hinterleitner

引用次数: 33

Emergent Dynamical Properties of the BCM Learning Rule BCM学习规则的涌现动态特性

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-02-20 DOI: 10.1186/s13408-017-0044-6

Lawrence C. Udeigwe, P. Munro, G. Ermentrout

引用次数: 14

Stable Control of Firing Rate Mean and Variance by Dual Homeostatic Mechanisms 用双稳态机制稳定控制射速均值和方差

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2017-01-17 DOI: 10.1186/s13408-017-0043-7

Jonathan J. Cannon, P. Miller

引用次数: 18

A Theoretical Study on the Role of Astrocytic Activity in Neuronal Hyperexcitability by a Novel Neuron-Glia Mass Model 星形胶质细胞活动在神经元高兴奋性中的作用的新神经元-胶质细胞质量模型的理论研究

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2016-12-21 DOI: 10.1186/s13408-016-0042-0

A. Garnier, A. Vidal, H. Benali

引用次数: 12

Ill-Posed Point Neuron Models. 不适定点神经元模型。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2016-12-01 Epub Date: 2016-04-30 DOI: 10.1186/s13408-016-0039-8

Bjørn Fredrik Nielsen, John Wyller

引用次数: 6

Analytic Modeling of Neural Tissue: I. A Spherical Bidomain. 神经组织的解析建模:I.球面双域。

IF 2.3 4区医学

Journal of Mathematical Neuroscience Pub Date : 2016-12-01 Epub Date: 2016-09-09 DOI: 10.1186/s13408-016-0041-1

Benjamin L Schwartz, Munish Chauhan, Rosalind J Sadleir

{"title":"Analytic Modeling of Neural Tissue: I. A Spherical Bidomain.","authors":"Benjamin L Schwartz, Munish Chauhan, Rosalind J Sadleir","doi":"10.1186/s13408-016-0041-1","DOIUrl":"https://doi.org/10.1186/s13408-016-0041-1","url":null,"abstract":"Presented here is a model of neural tissue in a conductive medium stimulated by externally injected currents. The tissue is described as a conductively isotropic bidomain, i.e. comprised of intra and extracellular regions that occupy the same space, as well as the membrane that divides them, and the injection currents are described as a pair of source and sink points. The problem is solved in three spatial dimensions and defined in spherical coordinates [Formula: see text]. The system of coupled partial differential equations is solved by recasting the problem to be in terms of the membrane and a monodomain, interpreted as a weighted average of the intra and extracellular domains. The membrane and monodomain are defined by the scalar Helmholtz and Laplace equations, respectively, which are both separable in spherical coordinates. Product solutions are thus assumed and given through certain transcendental functions. From these electrical potentials, analytic expressions for current density are derived and from those fields the magnetic flux density is calculated. Numerical examples are considered wherein the interstitial conductivity is varied, as well as the limiting case of the problem simplifying to two dimensions due to azimuthal independence. Finally, future modeling work is discussed. ","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/s13408-016-0041-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34377559","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: 3