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Uncertainty in Biology pp 367–391Cite as

Waves in Spatially-Disordered Neural Fields: A Case Study in Uncertainty Quantification

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Part of the book series: Studies in Mechanobiology, Tissue Engineering and Biomaterials ((SMTEB,volume 17))

Abstract

Neural field models have been used for many years to model a variety of macroscopic spatiotemporal patterns in the cortex. Most authors have considered homogeneous domains, resulting in equations that are translationally invariant. However, there is an obvious need to better understand the dynamics of such neural field models on heterogeneous domains. One way to include heterogeneity is through the introduction of randomly-chosen “frozen” spatial noise to the system. In this chapter we investigate the effects of including such noise on the speed of a moving “bump” of activity in a particular neural field model. The spatial noise is parameterised by a large but finite number of random variables, and the effects of including it can be determined in a computationally-efficient way using ideas from the field of Uncertainty Quantification. To determine the average speed of a bump in this type of heterogeneous domain involves evaluating a high-dimensional integral, and a variety of methods are compared for doing this. We find that including heterogeneity of this form in a variety of ways always slows down the moving bump.

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Authors and Affiliations

  1. Institute of Natural and Mathematical Sciences, Massey University, Private Bag, 102-904 NSMC, Auckland, New Zealand

    Carlo R. Laing

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  1. Carlo R. Laing
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Correspondence to Carlo R. Laing .

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Editors and Affiliations

  1. Biomechanics Research Unit, University of Liège, Liège 1, Belgium

    Liesbet Geris

  2. Center for Molecular Medicine, Karolinska University Hospital, Stockholm, Sweden

    David Gomez-Cabrero

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Laing, C.R. (2016). Waves in Spatially-Disordered Neural Fields: A Case Study in Uncertainty Quantification. In: Geris, L., Gomez-Cabrero, D. (eds) Uncertainty in Biology. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-21296-8_14

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  • DOI: https://doi.org/10.1007/978-3-319-21296-8_14

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  • Online ISBN: 978-3-319-21296-8

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