Kernel Reconstruction for Delayed Neural Field Equations.

IF 2.3 4区 医学 Q1 Neuroscience Journal of Mathematical Neuroscience Pub Date : 2018-02-05 DOI:10.1186/s13408-018-0058-8
Jehan Alswaihli, Roland Potthast, Ingo Bojak, Douglas Saddy, Axel Hutt
{"title":"Kernel Reconstruction for Delayed Neural Field Equations.","authors":"Jehan Alswaihli,&nbsp;Roland Potthast,&nbsp;Ingo Bojak,&nbsp;Douglas Saddy,&nbsp;Axel Hutt","doi":"10.1186/s13408-018-0058-8","DOIUrl":null,"url":null,"abstract":"<p><p>Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues.In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed-point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Fréchet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience.</p>","PeriodicalId":54271,"journal":{"name":"Journal of Mathematical Neuroscience","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2018-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13408-018-0058-8","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Neuroscience","FirstCategoryId":"3","ListUrlMain":"https://doi.org/10.1186/s13408-018-0058-8","RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Neuroscience","Score":null,"Total":0}
引用次数: 8

Abstract

Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues.In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed-point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Fréchet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience.

Abstract Image

Abstract Image

Abstract Image

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
延迟神经场方程的核重构。
了解现实生命系统的神经场活动是当代神经科学中的一项具有挑战性的任务。在过去的四十年里,神经领域的理论和数值研究都取得了相当大的成功。然而,为了有效地利用这些模型,我们需要在实际系统中确定它们的组成部分。这包括模型参数的确定,特别是生物组织中潜在有效连接的重建。在这项工作中,我们提供了一个积分方程的方法来重建神经连通性的情况下,神经活动是由一个延迟神经场方程。作为准备,我们研究了基于Banach不动点定理的直接问题的解。然后将反问题转化为一类积分方程。当几个神经活动轨迹作为反问题的输入时,这个方程将是向量值。我们采用谱正则化技术求解其稳定解。对正则化核重构对输入信号u的敏感性进行了分析,研究了核重构对信号的fr可微性。最后,我们用数值例子证明了该方法用于核重构的可行性,包括数值灵敏度测试,结果表明积分方程方法是一种非常稳定和有前途的实用计算神经科学方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Journal of Mathematical Neuroscience
Journal of Mathematical Neuroscience Neuroscience-Neuroscience (miscellaneous)
自引率
0.00%
发文量
0
审稿时长
13 weeks
期刊介绍: The Journal of Mathematical Neuroscience (JMN) publishes research articles on the mathematical modeling and analysis of all areas of neuroscience, i.e., the study of the nervous system and its dysfunctions. The focus is on using mathematics as the primary tool for elucidating the fundamental mechanisms responsible for experimentally observed behaviours in neuroscience at all relevant scales, from the molecular world to that of cognition. The aim is to publish work that uses advanced mathematical techniques to illuminate these questions. It publishes full length original papers, rapid communications and review articles. Papers that combine theoretical results supported by convincing numerical experiments are especially encouraged. Papers that introduce and help develop those new pieces of mathematical theory which are likely to be relevant to future studies of the nervous system in general and the human brain in particular are also welcome.
期刊最新文献
Canard solutions in neural mass models: consequences on critical regimes. Rendering neuronal state equations compatible with the principle of stationary action. Pattern formation in a 2-population homogenized neuronal network model. Auditory streaming emerges from fast excitation and slow delayed inhibition. A model of on/off transitions in neurons of the deep cerebellar nuclei: deciphering the underlying ionic mechanisms.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1