1. Brain-wave equation incorporating axodendritic connectivity
- Author
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James Ross, Stephen Coombes, Rachel Nicks, Ingo Bojak, Daniele Avitabile, Michelle Margetts, Vrije Universiteit Amsterdam [Amsterdam] (VU), Mathématiques pour les Neurosciences (MATHNEURO), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Amsterdam Neuroscience - Systems & Network Neuroscience, and Mathematics
- Subjects
Partial differential equation ,Scale (ratio) ,Computer simulation ,Quantitative Biology::Neurons and Cognition ,Computer science ,[SDV]Life Sciences [q-bio] ,Probability and statistics ,Brain waves ,Space (mathematics) ,Topology ,01 natural sciences ,010305 fluids & plasmas ,Tree (data structure) ,Dimension (vector space) ,0103 physical sciences ,[MATH]Mathematics [math] ,010306 general physics - 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.
- Published
- 2020