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Dynamic Causal Modelling of Lateral Interactions in the Visual Cortex

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Dynamic Causal Modelling of Lateral Interactions in the Visual Cortex

D A Pinotsis et al. Neuroimage.

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.

Keywords: Connectivity; Dynamic causal modelling; Electrophysiology; MEG; Neural field theory; Visual cortex.

Figures

Fig. 1
Fig. 1
The Canonical Microcircuit (CMC) neural mass model. This figure shows the evolution equations that specify a CMC mass model of a single source. This model contains four populations occupying different cortical layers: the pyramidal cell population of the JR model is here split into two subpopulations allowing a separation of the sources of forward and backward connections in cortical hierarchies. As with the JR model, second-order differential equations mediate a linear convolution of presynaptic activity to produce postsynaptic depolarisation. This depolarisation gives rise to firing rates within each sub-population that provide inputs to other populations.
Fig. 2
Fig. 2
Connectivity kernel. This kernel describes a combination of patchy but isotropic distributions by using connectivity kernels with non-central peaks. It models sparse intrinsic connections in cortical circuits that mediate both local (within macrocolumn) and non-local (between macrocolumn) interactions. In other words, neurons talk both to their immediate neighbours and receive input from remote populations who share the same functional selectivity; see Eq. (8). The insert is a modified from www.ini.uzh.ch/node/23776.
Fig. 3
Fig. 3
Three neighbouring macrocolumns. Each macrocolumn consists of the four subpopulations of Fig. 1 connected to each other with intralaminar (within macrocolumn) and interlaminar (between macrocolumns) connections. We later assume that the visual cortex is tiled with replications of this cortical circuitry and that individual differences in neuroanatomy are reflected in gamma frequency activity that can be attributed to a variable columnar size (the c parameter of Fig. 2).
Fig. 4
Fig. 4
Observed MEG spectra from a selection of subjects with different V1 surface area. Schwarzkopf et al., 2012 found a strong positive correlation between gamma peak frequency (marked with arrows) and V1 surface area. We used a biophysical model to investigate whether individual differences in macroscopic gamma frequency may reflect inter-individual variability in the architecture of visual cortex.
Fig. 5
Fig. 5
Example of DCM fits for a single participant. Real data (dashed line) and model predictions (full line) for spectra in the gamma band obtained from the human visual cortex during visual stimulation (Schwarzkopf et al., 2012). We observe that the fits of both the field and mass models are equally good with no manifest differences.
Fig. 6
Fig. 6
(Top panel) Bar chart of relative log evidence for neural mass and field models over subjects. The average relative log evidence was 2.37 in favour of the mass models, which is considered insufficient for disambiguating between models: only a relative evidence of three (dashed line) constitutes strong evidence a particular model offers a better explanation for the data. Note that in 6 out of 16 individuals evidence in favour of the mass model was greater than three. (Bottom panel) Left: Bar chart of posterior cross-correlations between columnar width and the connection strength between deep pyramidal cells and inhibitory interneurons. The average cross-correlation was − 0.176. Right: Mean over subjects of the posterior cross–correlation matrices for all parameters in our neural field model.
Fig. 7
Fig. 7
Contribution analysis of particular parameters. This figure shows changes in spectral responses elicited by varying the lateral extent of intrinsic connectivity and the strength of intrinsic connections between interneurons and deep pyramidal cells (over a log-scaling range).
Fig. 8
Fig. 8
(Top panel): We found a correlation between the log scaling of the posterior estimate of columnar width and peak gamma frequency (Pearson r = 0.271, p = 0.06, 30 d.f., one-tailed test). This suggests that increases in peak gamma frequency across subjects can be attributed to a greater columnar width. (Bottom panel) Correlation between the log scaling of the posterior estimate of columnar width and V1 surface (Pearson r = 0.36, p = 0.02, 30 d.f., one-tailed test). This result suggests that a larger V1 is constituted by bigger macrocolumns. This finding, together with that reported in the top panel, confirm our earlier empirical finding that gamma peak and V1 size are correlated. Furthermore, our use of an underlying generative (mechanistic) model, offers insight into local cortical microstructure that would be hard (or impossible) to disclose otherwise. Confidence intervals are plotted as dotted lines.
Fig. 9
Fig. 9
Correlation between the log scaling of the connectivity estimate between pyramidal cells and inhibitory interneurons for the neural field (Pearson r = − 0.37, p = 0.02, 30 d.f., two-tailed test) and the neural mass model (Pearson r = − 0.36, p = 0.04, 30 d.f., two-tailed test). Confidence intervals are plotted as dotted lines.
Fig. 10
Fig. 10
Model space for structural equation modelling. In the winning model — model 8 — the correlation between V1 size and peak gamma frequency is mediated by three links involving posterior estimates of columnar width and connection strength.

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