## A mean-field model for conductance-based networks of adaptive
exponential integrate-and-fire neurons.

#### Yann Zerlaut and Alain Destexhe

*arXiv preprint:*
http://https://arxiv.org/abs/1703.00698 (2017)

## Abstract:

Voltage-sensitive dye imaging (VSDi) has revealed fundamental
properties of neocortical processing at mesoscopic scales. Since
VSDi signals report the average membrane potential, it seems
natural to use a mean-field formalism to model such signals. Here,
we investigate a mean-field model of networks of Adaptive
Exponential (AdEx) integrate-and-fire neurons, with
conductance-based synaptic interactions. The AdEx model can capture
the spiking response of different cell types, such as
regular-spiking (RS) excitatory neurons and fast-spiking (FS)
inhibitory neurons. We use a Master Equation formalism, together
with a semi-analytic approach to the transfer function of AdEx
neurons. We compare the predictions of this mean-field model to
simulated networks of RS-FS cells, first at the level of the
spontaneous activity of the network, which is well predicted by the
mean-field model. Second, we investigate the response of the
network to time-varying external input, and show that the
mean-field model accurately predicts the response time course of
the population. One notable exception was that the "tail" of the
response at long times was not well predicted, because the
mean-field does not include adaptation mechanisms. We conclude that
the Master Equation formalism can yield mean-field models that
predict well the behavior of nonlinear networks with
conductance-based interactions and various electrophysiolgical
properties, and should be a good candidate to model VSDi signals
where both excitatory and inhibitory neurons contribute.

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