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Estimating anisotropy directly via neural timeseries


Fagerholm, Erik D; Foulkes, W M C; Gallero-Salas, Yasir; Helmchen, Fritjof; Moran, Rosalyn J; Friston, Karl J; Leech, Robert (2022). Estimating anisotropy directly via neural timeseries. Journal of Computational Neuroscience, 50(2):241-249.

Abstract

An isotropic dynamical system is one that looks the same in every direction, i.e., if we imagine standing somewhere within an isotropic system, we would not be able to differentiate between different lines of sight. Conversely, anisotropy is a measure of the extent to which a system deviates from perfect isotropy, with larger values indicating greater discrepancies between the structure of the system along its axes. Here, we derive the form of a generalised scalable (mechanically similar) discretized field theoretic Lagrangian that allows for levels of anisotropy to be directly estimated via timeseries of arbitrary dimensionality. We generate synthetic data for both isotropic and anisotropic systems and, by using Bayesian model inversion and reduction, show that we can discriminate between the two datasets - thereby demonstrating proof of principle. We then apply this methodology to murine calcium imaging data collected in rest and task states, showing that anisotropy can be estimated directly from different brain states and cortical regions in an empirical in vivo biological setting. We hope that this theoretical foundation, together with the methodology and publicly available MATLAB code, will provide an accessible way for researchers to obtain new insight into the structural organization of neural systems in terms of how scalable neural regions grow - both ontogenetically during the development of an individual organism, as well as phylogenetically across species.

Keywords: Anisotropy; DCM; Data fitting; Field theory; Lagrangian; Neuroimaging

Abstract

An isotropic dynamical system is one that looks the same in every direction, i.e., if we imagine standing somewhere within an isotropic system, we would not be able to differentiate between different lines of sight. Conversely, anisotropy is a measure of the extent to which a system deviates from perfect isotropy, with larger values indicating greater discrepancies between the structure of the system along its axes. Here, we derive the form of a generalised scalable (mechanically similar) discretized field theoretic Lagrangian that allows for levels of anisotropy to be directly estimated via timeseries of arbitrary dimensionality. We generate synthetic data for both isotropic and anisotropic systems and, by using Bayesian model inversion and reduction, show that we can discriminate between the two datasets - thereby demonstrating proof of principle. We then apply this methodology to murine calcium imaging data collected in rest and task states, showing that anisotropy can be estimated directly from different brain states and cortical regions in an empirical in vivo biological setting. We hope that this theoretical foundation, together with the methodology and publicly available MATLAB code, will provide an accessible way for researchers to obtain new insight into the structural organization of neural systems in terms of how scalable neural regions grow - both ontogenetically during the development of an individual organism, as well as phylogenetically across species.

Keywords: Anisotropy; DCM; Data fitting; Field theory; Lagrangian; Neuroimaging

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Neuroscience Center Zurich
04 Faculty of Medicine > Brain Research Institute
Dewey Decimal Classification:570 Life sciences; biology
610 Medicine & health
Scopus Subject Areas:Life Sciences > Sensory Systems
Life Sciences > Cognitive Neuroscience
Life Sciences > Cellular and Molecular Neuroscience
Language:English
Date:May 2022
Deposited On:09 Jan 2023 14:17
Last Modified:19 Feb 2024 11:54
Publisher:Springer
ISSN:0929-5313
OA Status:Hybrid
Free access at:PubMed ID. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s10827-021-00810-8
PubMed ID:35182268
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)