Comparison between an exact and a heuristic neural mass model with second order synapses

TL;DR

This paper compares an exact neural mass model based on mean-field theory with a heuristic approximation, analyzing their differences in dynamic behavior especially with second-order synapses, revealing limitations of the heuristic model.

Contribution

The study derives the mathematical equivalence between the models in slow synapse limits and evaluates their differences under realistic parameters, highlighting the heuristic model's shortcomings.

Findings

NMM1 is an approximation of NMM2 in the slow synapse limit.

NMM1 fails to reproduce key dynamical features like self-sustained oscillations.

Resonant oscillatory activity is observed in the exact model but not in the heuristic approximation.

Abstract

Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear transfer function (NMM1). However, a recent exact mean-field theory for quadratic integrate-and-fire (QIF) neurons challenges this view by showing that the mean firing rate is not a static function of the neuronal state but follows two coupled nonlinear differential equations (NMM2). Here we analyze and compare these two descriptions in the presence of second-order synaptic dynamics. First, we derive the mathematical equivalence between the two models in the infinitely slow synapse limit, i.e., we show that NMM1 is an approximation of NMM2 in this regime. Next, we evaluate the applicability of this limit in the context of realistic physiological parameter values by analyzing the dynamics of models with inhibitory or excitatory synapses. We show that NMM1 fails to reproduce important dynamical features of the exact model, such as the self-sustained oscillations of an inhibitory interneuron QIF network. Furthermore, in the exact model but not in the limit one, stimulation of a pyramidal cell population induces resonant oscillatory activity whose peak frequency and amplitude increase with the self-coupling gain and the external excitatory input. This may play a role in the enhanced response of densely connected networks to weak uniform inputs, such as the electric fields produced by non-invasive brain stimulation.