Spherical-harmonics mode decomposition of neural field equations

Area of Science:

• Computational neuroscience
• Mathematical modeling of neural systems

Background:

• Large-scale neural networks are modeled by neural field equations.
• Translational variant connectivity in brain networks creates computational challenges for simulations.

Purpose of the Study:

• To reduce the computational burden of simulating large-scale brain networks.
• To develop a low-dimensional representation of neural field dynamics.

Main Methods:

• Studied neural field dynamics using a delayed integrodifferential equation.
• Decomposed connectivity into spatially variant and invariant contributions.
• Mapped neural fields onto a spherical surface and used spherical harmonic basis functions for mode decomposition.

Main Results:

• Spatial truncation of leading orders at low wave numbers captured large-scale pattern formation.
• Achieved a low-dimensional representation of neural field dynamics.
• Demonstrated potential for orders-of-magnitude acceleration in numerical simulations.

Conclusions:

• The proposed method offers a computationally efficient approach for simulating large-scale brain network dynamics.
• This technique holds promise for accelerating neuroscience research through faster simulations.
• The findings align with observed large-scale patterns in brain imaging data.