Dimitris A. Pinotsis

Neural masses and fields in dynamic causal modeling

Dynamic causal modeling (DCM) provides a framework for the analysis of effective connectivity among neuronal subpopulations that subtend invasive (electrocorticograms and local field potentials) and non-invasive (electroencephalography and magnetoencephalography) electrophysiological responses. This paper reviews the suite of neuronal population models including neural masses, fields and conductance-based models that are used in DCM. These models are expressed in terms of sets of differential equations that allow one to model the synaptic underpinnings of connectivity. We describe early developments using neural mass models, where convolution-based dynamics are used to generate responses in laminar-specific populations of excitatory and inhibitory cells. We show that these models, though resting on only two simple transforms, can recapitulate the characteristics of both evoked and spectral responses observed empirically. Using an identical neuronal architecture, we show that a set of conductance based models—that consider the dynamics of specific ion-channels—present a richer space of responses; owing to non-linear interactions between conductances and membrane potentials. We propose that conductance-based models may be more appropriate when spectra present with multiple resonances. Finally, we outline a third class of models, where each neuronal subpopulation is treated as a field; in other words, as a manifold on the cortical surface. By explicitly accounting for the spatial propagation of cortical activity through partial differential equations (PDEs), we show that the topology of connectivity—through local lateral interactions among cortical layers—may be inferred, even in the absence of spatially resolved data. We also show that these models allow for a detailed analysis of structure–function relationships in the cortex. Our review highlights the relationship among these models and how the hypothesis asked of empirical data suggests an appropriate model class.

LFP and oscillations-what do they tell us?

Highlights • A brief treatment of dynamic coordination in terms of predictive coding.• Understanding synchronous message passing in terms of hierarchical predictive coding.• Characterising cortical gain control with the dynamic causal modelling of neural fields.• Characterising pathophysiological oscillations with dynamic causal modelling of neural masses.

Dynamic causal modeling with neural fields

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.

Dynamic causal modelling of lateral interactions in the visual cortex

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.

Contrast gain control and horizontal interactions in V1: a DCM study

Using high-density electrocorticographic recordings – from awake-behaving monkeys – and dynamic causal modelling, we characterised contrast dependent gain control in visual cortex, in terms of synaptic rate constants and intrinsic connectivity. Specifically, we used neural field models to quantify the balance of excitatory and inhibitory influences; both in terms of the strength and spatial dispersion of horizontal intrinsic connections. Our results allow us to infer that increasing contrast increases the sensitivity or gain of superficial pyramidal cells to inputs from spiny stellate populations. Furthermore, changes in the effective spatial extent of horizontal coupling nuance the spatiotemporal filtering properties of cortical laminae in V1 — effectively preserving higher spatial frequencies. These results are consistent with recent non-invasive human studies of contrast dependent changes in the gain of pyramidal cells elaborating forward connections — studies designed to test specific hypotheses about precision and gain control based on predictive coding. Furthermore, they are consistent with established results showing that the receptive fields of V1 units shrink with increasing visual contrast.

Anatomical connectivity and the resting state activity of large cortical networks

This paper uses mathematical modelling and simulations to explore the dynamics that emerge in large scale cortical networks, with a particular focus on the topological properties of the structural connectivity and its relationship to functional connectivity. We exploit realistic anatomical connectivity matrices (from diffusion spectrum imaging) and investigate their capacity to generate various types of resting state activity. In particular, we study emergent patterns of activity for realistic connectivity configurations together with approximations formulated in terms of neural mass or field models. We find that homogenous connectivity matrices, of the sort of assumed in certain neural field models give rise to damped spatially periodic modes, while more localised modes reflect heterogeneous coupling topologies. When simulating resting state fluctuations under realistic connectivity, we find no evidence for a spectrum of spatially periodic patterns, even when grouping together cortical nodes into communities, using graph theory. We conclude that neural field models with translationally invariant connectivity may be best applied at the mesoscopic scale and that more general models of cortical networks that embed local neural fields, may provide appropriate models of macroscopic cortical dynamics over the whole brain.

Impaired prefrontal synaptic gain in people with psychosis and their relatives during the mismatch negativity

The mismatch negativity (MMN) evoked potential, a preattentive brain response to a discriminable change in auditory stimulation, is significantly reduced in psychosis. Glutamatergic theories of psychosis propose that hypofunction of NMDA receptors (on pyramidal cells and inhibitory interneurons) causes a loss of synaptic gain control. We measured changes in neuronal effective connectivity underlying the MMN using dynamic causal modeling (DCM), where the gain (excitability) of superficial pyramidal cells is explicitly parameterised. EEG data were obtained during a MMN task—for 24 patients with psychosis, 25 of their first‐degree unaffected relatives, and 35 controls—and DCM was used to estimate the excitability (modeled as self‐inhibition) of (source‐specific) superficial pyramidal populations. The MMN sources, based on previous research, included primary and secondary auditory cortices, and the right inferior frontal gyrus. Both patients with psychosis and unaffected relatives (to a lesser degree) showed increased excitability in right inferior frontal gyrus across task conditions, compared to controls. Furthermore, in the same region, both patients and their relatives showed a reversal of the normal response to deviant stimuli; that is, a decrease in excitability in comparison to standard conditions. Our results suggest that psychosis and genetic risk for the illness are associated with both context‐dependent (condition‐specific) and context‐independent abnormalities of the excitability of superficial pyramidal cell populations in the MMN paradigm. These abnormalities could relate to NMDA receptor hypofunction on both pyramidal cells and inhibitory interneurons, and appear to be linked to the genetic aetiology of the illness, thereby constituting potential endophenotypes for psychosis. Hum Brain Mapp 37:351–365, 2016.

Neural fields, spectral responses and lateral connections

This paper describes a neural field model for local (mesoscopic) dynamics on the cortical surface. Our focus is on sparse intrinsic connections that are characteristic of real cortical microcircuits. This sparsity is modelled with radial connectivity functions or kernels with non-central peaks. The ensuing analysis allows one to generate or predict spectral responses to known exogenous input or random fluctuations. Here, we characterise the effect of different connectivity architectures (the range, dispersion and propagation speed of intrinsic or lateral connections) and synaptic gains on spatiotemporal dynamics. Specifically, we look at spectral responses to random fluctuations and examine the ability of synaptic gain and connectivity parameters to induce Turing instabilities. We find that although the spatial deployment and speed of lateral connections can have a profound affect on the behaviour of spatial modes over different scales, only synaptic gain is capable of producing phase-transitions. We discuss the implications of these findings for the use of neural fields as generative models in dynamic causal modeling (DCM).

On conductance-based neural field models.

This technical note introduces a conductance-based neural field model that combines biologically realistic synaptic dynamics—based on transmembrane currents—with neural field equations, describing the propagation of spikes over the cortical surface. This model allows for fairly realistic inter-and intra-laminar intrinsic connections that underlie spatiotemporal neuronal dynamics. We focus on the response functions of expected neuronal states (such as depolarization) that generate observed electrophysiological signals (like LFP recordings and EEG). These response functions characterize the models transfer functions and implicit spectral responses to (uncorrelated) input. Our main finding is that both the evoked responses (impulse response functions) and induced responses (transfer functions) show qualitative differences depending upon whether one uses a neural mass or field model. Furthermore, there are differences between the equivalent convolution and conductance models. Overall, all models reproduce a characteristic increase in frequency, when inhibition was increased by increasing the rate constants of inhibitory populations. However, convolution and conductance-based models showed qualitatively different changes in power, with convolution models showing decreases with increasing inhibition, while conductance models show the opposite effect. These differences suggest that conductance based field models may be important in empirical studies of cortical gain control or pharmacological manipulations.

Neural masses and fields: modeling the dynamics of brain activity.

This technical note introduces a conductance-based neural field model that combines biologically realistic synaptic dynamics—based on transmembrane currents—with neural field equations, describing the propagation of spikes over the cortical surface. This model allows for fairly realistic inter-and intra-laminar intrinsic connections that underlie spatiotemporal neuronal dynamics. We focus on the response functions of expected neuronal states (such as depolarization) that generate observed electrophysiological signals (like LFP recordings and EEG). These response functions characterize the models transfer functions and implicit spectral responses to (uncorrelated) input. Our main finding is that both the evoked responses (impulse response functions) and induced responses (transfer functions) show qualitative differences depending upon whether one uses a neural mass or field model. Furthermore, there are differences between the equivalent convolution and conductance models. Overall, all models reproduce a characteristic increase in frequency, when inhibition was increased by increasing the rate constants of inhibitory populations. However, convolution and conductance-based models showed qualitatively different changes in power, with convolution models showing decreases with increasing inhibition, while conductance models show the opposite effect. These differences suggest that conductance based field models may be important in empirical studies of cortical gain control or pharmacological manipulations.