Brain-wave equation incorporating axodendritic connectivity

James Ross, Michelle Margetts, Ingo Bojak, Rachel Nicks, Daniele Avitabile, and Stephen Coombes

Phys. Rev. E 101, 022411 – Published 18 February 2020

Abstract

We introduce an integral model of a two-dimensional neural field that includes a third dimension representing space along a dendritic tree that can incorporate realistic patterns of axodendritic connectivity. For natural choices of this connectivity we show how to construct an equivalent brain-wave partial differential equation that allows for efficient numerical simulation of the model. This is used to highlight the effects that passive dendritic properties can have on the speed and shape of large scale traveling cortical waves.

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Received 6 November 2019
Accepted 28 January 2020

DOI:https://doi.org/10.1103/PhysRevE.101.022411

Physics Subject Headings (PhySH)

Neuroscience, neural computation & artificial intelligence

Physics of Living Systems

Authors & Affiliations

James Ross^1,*, Michelle Margetts ^1,†, Ingo Bojak ^2,‡, Rachel Nicks ^1,§, Daniele Avitabile ^3,4,¶, and Stephen Coombes ^1,**

¹Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
²School of Psychology and Clinical Language Sciences, University of Reading, Reading RG6 6AL, United Kingdom
³Department of Mathematics, Vrije Universiteit (VU University Amsterdam), Faculteit der Exacte Wetenschappen, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
⁴Mathneuro Team, Inria Sophia Antipolis, 2004 Rue des Lucioles, 06902 Sophia Antipolis, Cedex, France

^*james.ross1@nottingham.ac.uk
^†m_margetts@btinternet.com
^‡i.bojak@reading.ac.uk
^§rachel.nicks@nottingham.ac.uk
^¶d.avitabile@vu.nl
^**stephen.coombes@nottingham.ac.uk

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Issue

Vol. 101, Iss. 2 — February 2020

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics