Electrical stimulation of large neural networks is a key tool for understanding neural population dynamics and ultimately for developing clinical treatments.  However, computational models of cortical networks of spiking neurons are inherently hard to simulate and analyze. We present an efficient mean-field model of excitatory and inhibitory adaptive exponential integrate-and-fire (AdEx) neurons of which we analyse the dynamical properties and validate the results using detailed 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. In this dynamical landscape, electrical stimuli can cause state transitions, such as turning on and off oscillations  . Oscillatory input can frequency-entrain and phase-lock endogenous oscillations  . 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.
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.
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large neural networks
neural systems
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population
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Many applications of electrical stimulation affect large populations of neurons.
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cortical
large
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present an efficient
evaluate a reduced
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of which we analyse the dynamical properties and validate the results using detailed
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
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In this dynamical landscape, electrical stimuli can cause
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
A
of the population rate
A
. 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