Dynamic causal modeling with neural fields

Abstract

The aim of this paper is twofold: first, to introduce a neural field model motivated by a well-known neural mass model; second, to show how one can estimate model parameters pertaining to spatial (anatomical) properties of neuronal sources based on EEG or LFP spectra using Bayesian inference. Specifically, we consider neural field models of cortical activity as generative models in the context of dynamic causal modeling (DCM). This paper considers the simplest case of a single cortical source modeled by the spatiotemporal dynamics of hidden neuronal states on a bounded cortical surface or manifold. We build this model using multiple layers, corresponding to cortical lamina in the real cortical manifold. These layers correspond to the populations considered in classical (Jansen and Rit) neural mass models. This allows us to formulate a neural field model that can be reduced to a neural mass model using appropriate constraints on its spatial parameters. In turn, this enables one to compare and contrast the predicted responses from equivalent neural field and mass models respectively. We pursue this using empirical LFP data from a single electrode to show that the parameters controlling the spatial dynamics of cortical activity can be recovered, using DCM, even in the absence of explicit spatial information in observed data.

Intersubject variability and induced gamma in the visual cortex: DCM with empirical Bayes and neural fields

“…Our findings are also in accord with recent computational work modeling the emergence of gamma power peaks in the visual cortex based on an inhibition‐stabilized network [Jadi and Sejnowski, 2014a; Tsodyks et al, 1997], that exhibits an Andronov–Hopf bifurcation: see [Pinotsis et al, 2012] for more details. In this article, we used neural fields to model the dispersion of axonal connections and describe the effect of surround suppression on gamma responses, see also [Pinotsis et al, 2013, 2014].…”

“…Our hierarchical model treated intrinsic connectivity as a random (between‐subject) effect, which was modeled by adding random Gaussian effects to subject‐specific parameters as is standard in DCM models for Cross Spectral Densities [Moran et al, 2009; Pinotsis et al, 2012]. The intrinsic connectivity and other fixed effects (i.e., the remaining DCM parameters) then generate observed spectral density responses for each subject as described above.…”

“…This allows us to identify the key components of cortical microcircuitry that determine gamma responses in a particular individual. We use a combination of biophysical models (neural fields) with DCM [Friston et al, 2003; Pinotsis et al, 2012]. This form of DCM offers a mechanistic understanding of brain function and individual differences in cortical responses.…”

Causal Mathematical Logic as a guiding framework for the prediction of “Intelligence Signals” in brain simulations

“…A large body of work exists for Dynamic Causal Modeling (DCM) applied successfully to brain imaging which is a novel basis for establishing the brains "intelligence signals" and their primary subcomponents (Friston, Harrison and Penny, 2003;Stephan et al, 2007;Moran et al, 2009;Pinotsis, Moran, and Friston, 2012). For review see (Daunizeau, David, and Stephan, 2011).…”

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

“…This approach was extended to coupled neural masses through a Bayesian estimation scheme called dynamic causal modeling (DCM) (David and Friston, 2003). 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).…”