A data-driven framework for neural field modeling

Abstract

This paper presents a framework for creating neural field models from electrophysiological data. The Wilson and Cowan or Amari style neural field equations are used to form a parametric model, where the parameters are estimated from data. To illustrate the estimation framework, data is generated using the neural field equations incorporating modeled sensors enabling a comparison between the estimated and true parameters. To facilitate state and parameter estimation, we introduce a method to reduce the continuum neural field model using a basis function decomposition to form a finite-dimensional state-space model. Spatial frequency analysis methods are introduced that systematically specify the basis function configuration required to capture the dominant characteristics of the neural field. The estimation procedure consists of a two-stage iterative algorithm incorporating the unscented Rauch-Tung-Striebel smoother for state estimation and a least squares algorithm for parameter estimation. The results show that it is theoretically possible to reconstruct the neural field and estimate intracortical connectivity structure and synaptic dynamics with the proposed framework.

Spatiotemporal multi-resolution approximation of the Amari type neural field model

“…Wizard hat (Laplacian shape within layer) as depicted in Fig The stochastic IDE form of the Amari neural field formulation Amari (1977) is given by (see Freestone et al (2011) for a full derivation)…”

“…adjacent sensors was 0.05 mm, resulting into n y = 161 observations. The choice of B-spline function to model the observation kernel is justified by the experiment performed in Freestone et al (2011). The spacing and bandwidth of the sensors allowed the full spatial bandwidth of the field to be observed.…”

“…The problem of representing a continuous field with a finite number of states is solved by the basis function decomposition. An alternative to using the B-spline wavelets are Gaussian basis functions, which were adopted by Freestone et al (2011) field when it saturates. This may be beneficial to model neurological disorders such as epilepsy.…”

“…However, this is not the case when using B-spline scaling and wavelet functions due to their semi-orthogonality property. Freestone et al (2011) showed experimentally that Gaussian functions are a suitable choice for modeling the observation kernel when intracranial measurements are considered. B-splines converge to Gaussian functions as the order of the B-spline, m, tends to infinity.…”

“…Following this work, data-driven modeling was extended to continuum field equations that explained the richer dynamics of spatiotemporal neural fields (Galka et al, 2008;Schiff and Sauer, 2008;Daunizeau et al, 2009;Pinotsis et al, 2012). Most recently, a framework was developed where a finite-element model of the neural field (via a dynamic Galerkin projection) was formed, using a basis function decomposition, to transform the PDE neural field equations into a finite-dimensional system to facilitate efficient state and parameter estimation (Freestone et al, 2011). This paper is an extension to the aforementioned study, where we derive a neural field state-space model that accounts for the multi-resolution architecture and spatial dynamics of the human cortex.…”