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.
Highlights
Ever since Hans Berger made the first recording of the human electroencephalogram (EEG) in 1924 there has been a tremendous interest in understanding the physiological basis of brain rhythms [1]
The generalized model bridges multiple scales, combining local models of dendrites with global models of synaptic and firing rate activity with both distributed and space-dependent delays, emphasizing that dendritic response (Green’s) functions can lead to another form of distributed delay that shapes emerging spatiotemporal network patterns
As well as being relevant to EEG the finer detail of the local model makes it relevant to recorded potentials arising in electrocorticography (ECoG) and local field potential (LFP) recordings, with spatial resolution of 2–5 mm for ECoG and 0.1–1 mm for LFP, contrasting with the 20–30 mm of EEG
Summary
Ever since Hans Berger made the first recording of the human electroencephalogram (EEG) in 1924 there has been a tremendous interest in understanding the physiological basis of brain rhythms [1] This has included the development of so-called neural field models, recently reviewed in [2], for the forward generation of EEG signals as well as the use of techniques from spatiotemporal pattern formation [3], and nonequilibrium phase transitions [4] for their analysis. II we describe the formulation of the model in terms of a generalized neural field, prescribed by a given pattern of axodendritic connectivity This tissue model is a continuum description of cell bodies arranged in a surface with each point fibrated by a simple one-dimensional model of a dendritic tree. V we discuss natural extensions of the work in this paper
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