A walk-sum framework of frequency-dependent brain communication architecture

Area of Science:

• Neuroscience
• Network Science
• Computational Biology

Background:

• Neural communication relies on brain oscillations, but the link between oscillation frequencies and spatial modes is unclear.
• The structural connectome's topology is hypothesized to influence neural communication patterns.

Purpose of the Study:

• To analytically derive the frequency-dependent architecture of brain communication from connectome topology.
• To validate the derived framework using empirical neuroimaging data.

Main Methods:

• Utilized walk-sum algebra of the structural connectome to define a frequency-dependent transfer function (resolvent).
• Predicted spatial structure and frequency crossover points from the bare resolvent.
• Validated predictions using source-reconstructed MEG data from 912 subjects and intracranial EEG data from 90 epilepsy patients.

Main Results:

• The bare resolvent, with no free parameters, accurately predicted a parcellation-invariant crossover near 12.6 Hz and showed high correlation (ρ = 0.965) with empirical data.
• Five spatial predictions were confirmed across independent datasets, ruling out volume conduction.
• A two-parameter dressed resolvent further improved prediction accuracy.
• Neural mass models failed to replicate findings, confirming the resolvent describes communication channels, not neural dynamics.

Conclusions:

• The study presents the first analytical derivation of brain communication architecture based on connectome topology.
• The framework explains frequency-band coupling and spatial organization of neural signals.
• Disruptions in this architecture are observed in propofol anesthesia (collapse of alpha channels) and schizophrenia (exposed structural scaffold).