Cortical geometry as a determinant of brain activity eigenmodes: Neural field analysis

Area of Science:

• Computational neuroscience
• Theoretical neuroscience
• Mathematical modeling of brain activity

Background:

• Neural field theory describes brain activity as continuous fields.
• Cortical folding complicates the analysis of neural activity patterns.
• Previous numerical methods identified neural eigenmodes analogous to spherical harmonics.

Purpose of the Study:

• To derive spatial eigenmodes of neural activity on a cortical hemisphere using perturbation analysis.
• To compare these derived eigenmodes with previous numerical solutions.
• To investigate the influence of cortical folding on neural eigenmodes and their dynamics.

Main Methods:

• Perturbation analysis of neural field theory.
• Treating cortical folding as a first-order perturbation from spherical geometry.
• Deriving and comparing the first nine spatial eigenmodes with numerical solutions.

Main Results:

• The derived eigenmodes closely resemble spherical harmonics, consistent with numerical findings.
• Eigenvalues agree with previous numerical solutions within uncertainties.
• Spatial orientations are determined by gross cortical shape, while eigenvalues depend on finer folding details.

Conclusions:

• Perturbation theory and spherical harmonic analysis can effectively model low-order brain eigenmodes.
• Cortical folding influences neural dynamics, with finer details impacting eigenfrequencies.
• The findings support the use of these mathematical tools for understanding brain activity patterns and functional connectivity.