A numerical simulation of neural fields on curved geometries

Area of Science:

• Computational Neuroscience
• Neuroimaging Analysis
• Mathematical Biology

Background:

• Traditional neural field models simplify the cortex to a 2D plane, ignoring complex brain geometries.
• Realistic cortical structures derived from neuroimaging data present challenges for existing models.

Purpose of the Study:

• To develop and validate a novel approach for solving neural field equations on realistic cortical surfaces.
• To investigate the impact of cortical geometry on neural activity patterns.

Main Methods:

• Solving the integral form of neural field equations using collocation techniques.
• Employing efficient numerical methods to compute geodesic distances on complex surfaces.
• Testing the approach on a 2D periodic domain, a torus, and a rat brain's cortical surface.

Main Results:

• Collocation methods accurately replicate solutions on flat domains, irrespective of mesh irregularity.
• The approach successfully models neural activity patterns on realistic cortical geometries.
• Geodesic computation enables inclusion of physiologically relevant cortical architectures.

Conclusions:

• This method allows for the study of cortical geometry's influence on neural activity.
• The approach offers insights into neurological disorders (e.g., epilepsy) and cognitive functions (e.g., attention).
• It provides a framework for more biologically plausible neural field modeling.