Dynamic causal modelling of lateral interactions in the visual cortex

D.S. Schwarzkopf,V. Litvak,G. Barnes,K.J. Friston,D.A. Pinotsis,G. Rees

doi:10.1016/j.neuroimage.2012.10.078

Abstract

This paper presents a dynamic causal model based upon neural field models of the Amari type. We consider the application of these models to non-invasive data, with a special focus on the mapping from source activity on the cortical surface to a single channel. We introduce a neural field model based upon the canonical microcircuit (CMC), in which neuronal populations are assigned to different cortical layers. We show that DCM can disambiguate between alternative (neural mass and field) models of cortical activity. However, unlike neural mass models, DCM with neural fields can address questions about neuronal microcircuitry and lateral interactions. This is because they are equipped with interlaminar connections and horizontal intra-laminar connections that are patchy in nature. These horizontal or lateral connections can be regarded as connecting macrocolumns with similar feature selectivity. Crucially, the spatial parameters governing horizontal connectivity determine the separation (width) of cortical macrocolumns. Thus we can estimate the width of macro columns, using non-invasive electromagnetic signals. We illustrate this estimation using dynamic causal models of steady-state or ongoing spectral activity measured using magnetoencephalography (MEG) in human visual cortex. Specifically, we revisit the hypothesis that the size of a macrocolumn is a key determinant of neuronal dynamics, particularly the peak gamma frequency. We are able to show a correlation, over subjects, between columnar size and peak gamma frequency — that fits comfortably with established correlations between peak gamma frequency and the size of visual cortex defined retinotopically. We also considered cortical excitability and assessed its relative influence on observed gamma activity. This example highlights the potential utility of dynamic causal modelling and neural fields in providing quantitative characterisations of spatially extended dynamics on the cortical surface — that are parameterised in terms of horizontal connections, implicit in the cortical micro-architecture and its synaptic parameters.

Highlights

This work combines neural field models — that model the activity of layers of cells in cortical patches — with a Bayesian framework for optimising model parameters — known as Dynamic Causal Modelling (DCM)
A full description of the paradigm, recording and processing can be found in Schwarzkopf et al (2012). We modelled these spectral data — using DCM — to address the following questions: (i) Are neural masses or fields more appropriate for explaining these data? (ii) Can differences in the width of cortical columns explain the intersubject differences in gamma frequency? (iii) How does cortical excitability relate to the peak gamma frequency? And (iv) what are the important determinants of spectral gamma activity? The first question illustrates the use of Bayesian model comparison to compare DCMs based on neural fields and neural masses
By exploiting a combination of neural field modelling and Bayesian inference, we have shown that dynamic causal modelling can answer the following sorts of questions: which is the best biophysical model for explaining electrophysiological data? What are the important determinants of gamma peak frequency — in terms of synaptic parameters and horizontal interactions? Can MEG beamformed data help us access local cortical microstructure? And how can we distinguish between competing hypotheses about structure-function relationships? We have focused on two classes of biophysical models of brain α 23

Summary

Dynamic causal modelling of lateral interactions in the visual cortex

The Wellcome Trust Centre for Neuroimaging, University College London, Queen Square, London WC1N 3BG, UK article info. Unlike neural mass models, DCM with neural fields can address questions about neuronal microcircuitry and lateral interactions This is because they are equipped with interlaminar connections and horizontal intra-laminar connections that are patchy in nature. We can estimate the width of macro columns, using non-invasive electromagnetic signals We illustrate this estimation using dynamic causal models of steady-state or ongoing spectral activity measured using magnetoencephalography (MEG) in human visual cortex. We considered cortical excitability and assessed its relative influence on observed gamma activity This example highlights the potential utility of dynamic causal modelling and neural fields in providing quantitative characterisations of spatially extended dynamics on the cortical surface — that are parameterised in terms of horizontal connections, implicit in the cortical micro-architecture and its synaptic parameters

Introduction

Spectral responses of neural fields

Lateral interactions and neural fields

The canonical microcircuit

Deep pyramidal

Intrinsic and extrinsic connectivity kernels

The second equality follows by substituting the transfer function

Model inversion and fitting

Empirical data and validation

Spectral density

Neural masses or fields?

Neural mass model