Exact mean-field models for spiking neural networks with adaptation

Area of Science:

• Computational Neuroscience
• Neural Dynamics
• Mathematical Biology

Background:

• Spiking neural networks with adaptation exhibit complex dynamics crucial for brain function and disorders.
• Exact mean-field models are vital for linking individual neuron behavior to macroscopic network activity.
• Previous models often relied on approximations for adaptation dynamics, limiting accuracy.

Purpose of the Study:

• To derive and analyze exact mean-field equations for spiking neural networks with spike frequency adaptation.
• To overcome limitations of previous models by accurately including adaptation dynamics.
• To provide a tractable tool for investigating neural network behavior.

Main Methods:

• Utilized a network of Izhikevich neurons, modeled by quadratic integrate-and-fire and adaptation equations.
• Employed a Lorentzian ansatz combined with moment closure for deriving mean-field equations in the thermodynamic limit.
• Extended the model to two-population networks and performed numerical bifurcation analysis.

Main Results:

• Developed a closed set of mean-field equations that accurately capture neural network dynamics, including transitions between asynchronous firing and synchronous bursting.
• Identified novel bifurcations and a new mechanism for the emergence of bursting.
• Demonstrated qualitative and quantitative agreement between the mean-field model and the spiking neural network.

Conclusions:

• The derived exact mean-field model provides a reliable tool for computational neuroscience research.
• The model accurately describes collective neural dynamics, offering insights into brain function and dysfunction.
• The approach successfully incorporates adaptation dynamics without approximations, enhancing model fidelity.