# Biophysically grounded mean-field models of neural populations under electrical stimulation

## TL;DR

This paper develops and validates a biophysically grounded mean-field model of neural populations that efficiently predicts responses to electrical stimulation, including oscillation modulation and state transitions, with implications for clinical treatments.

## Contribution

It introduces a reduced mean-field model coupled with realistic electric field effects, enabling efficient analysis of large neural populations under stimulation, which was previously computationally challenging.

## Key findings

- Weak electric fields (~1 V/m) can significantly influence neural network states.
- The model accurately predicts oscillation entrainment and phase-locking due to stimulation.
- Bifurcation analysis reveals diverse dynamical regimes including bistability and oscillations.

## Abstract

Electrical stimulation of neural systems is a key tool for understanding neural dynamics and ultimately for developing clinical treatments. Many applications of electrical stimulation affect large populations of neurons. However, computational models of large networks of spiking neurons are inherently hard to simulate and analyze. We evaluate a reduced mean-field model of excitatory and inhibitory adaptive exponential integrate-and-fire (AdEx) neurons which can be used to efficiently study the effects of electrical stimulation on large neural populations. The rich dynamical properties of this basic cortical model are described in detail and validated using large network simulations. Bifurcation diagrams reflecting the network's state reveal asynchronous up- and down-states, bistable regimes, and oscillatory regions corresponding to fast excitation-inhibition and slow excitation-adaptation feedback loops. The biophysical parameters of the AdEx neuron can be coupled to an electric field with realistic field strengths which then can be propagated up to the population description.We show how on the edge of bifurcation, direct electrical inputs cause network state transitions, such as turning on and off oscillations of the population rate. Oscillatory input can frequency-entrain and phase-lock endogenous oscillations. Relatively weak electric field strengths on the order of 1 V/m are able to produce these effects, indicating that field effects are strongly amplified in the network. The effects of time-varying external stimulation are well-predicted by the mean-field model, further underpinning the utility of low-dimensional neural mass models.