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

Area of Science:

• Computational neuroscience
• Theoretical neuroscience
• Mathematical modeling of neural systems

Background:

• Neural mass models (NMMs) are crucial for understanding large-scale brain activity.
• A common NMM framework (NMM1) uses a static nonlinear transfer function for population firing rates.
• An exact mean-field theory for quadratic integrate-and-fire (QIF) neurons (NMM2) proposes a dynamic firing rate description.

Purpose of the Study:

• To mathematically compare two neural mass models: a static transfer function model (NMM1) and an exact mean-field model (NMM2).
• To investigate the validity of NMM1 as an approximation of NMM2 under realistic synaptic dynamics.
• To identify dynamical features captured by NMM2 but missed by NMM1.

Main Methods:

• Derivation of mathematical equivalence between NMM1 and NMM2 in the slow synapse limit.
• Analysis of model dynamics using inhibitory and excitatory synaptic parameters.
• Simulation and comparison of network responses to external stimulation in both models.

Main Results:

• NMM1 is mathematically equivalent to NMM2 only in the limit of infinitely slow synapses.
• NMM1 fails to reproduce self-sustained oscillations observed in NMM2 for inhibitory QIF networks.
• NMM2 predicts resonant oscillatory activity in pyramidal populations, dependent on self-coupling and input, a feature absent in NMM1.

Conclusions:

• The static transfer function approximation (NMM1) is insufficient for capturing essential neural population dynamics, especially oscillations.
• The exact mean-field model (NMM2) provides a more accurate representation of neural population behavior, including resonant responses.
• These findings have implications for understanding network sensitivity to weak inputs, relevant to noninvasive brain stimulation techniques.