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Understanding sensory induced hallucinations: From neural fields to amplitude equations

Nicks, Rachel; Cocks, Abigail; Avitabile, Daniele; Johnston, Alan; Coombes, Stephen

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Authors

Abigail Cocks

Daniele Avitabile



Abstract

Explorations of visual hallucinations, and in particular those of Billock and Tsou [V. A. Billock and B. H. Tsou, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 8490-8495], show that annular rings with a background flicker can induce visual hallucinations in humans that take the form of radial fan shapes. The well-known retino-cortical map tells us that the corresponding patterns of neural activity in the primary visual cortex for rings and arms in the retina are orthogonal stripe patterns. The implication is that cortical forcing by spatially periodic input can excite orthogonal modes of neural activity. Here we show that a simple scalar neural field model of primary visual cortex with state-dependent spatial forcing is capable of modeling this phenomenon. Moreover, we show that this occurs most robustly when the spatial forcing has a 2:1 resonance with modes that would otherwise be excited by a Turing instability. By utilizing a weakly nonlinear multiple-scales analysis we determine the relevant amplitude equations for uncovering the parameter regimes which favor the excitation of patterns orthogonal to sensory drive. In combination with direct numerical simulations we use this approach to shed further light on the original psychophysical observations of Billock and Tsou.

Citation

Nicks, R., Cocks, A., Avitabile, D., Johnston, A., & Coombes, S. (2021). Understanding sensory induced hallucinations: From neural fields to amplitude equations. SIAM Journal on Applied Dynamical Systems, 20(4), 1683-1714. https://doi.org/10.1137/20M1366885

Journal Article Type Article
Acceptance Date Jun 20, 2021
Online Publication Date Oct 4, 2021
Publication Date 2021-01
Deposit Date Jul 1, 2021
Publicly Available Date Jul 22, 2021
Journal SIAM Journal on Applied Dynamical Systems
Print ISSN 1536-0040
Electronic ISSN 1536-0040
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 20
Issue 4
Pages 1683-1714
DOI https://doi.org/10.1137/20M1366885
Keywords Visual hallucinations; Neural field model; Spatially forced pattern forming system; Amplitude
Public URL https://nottingham-repository.worktribe.com/output/5750894
Publisher URL https://epubs.siam.org/doi/abs/10.1137/20M1366885
Additional Information Understanding Sensory Induced Hallucinations: From Neural Fields to Amplitude Equations, Rachel Nicks, Abigail Cocks, Daniele Avitabile, Alan Johnston, and Stephen Coombes, SIAM Journal on Applied Dynamical Systems 2021 20:4, 1683-1714

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