Intrinsic resonance depends on network size for coupled-delayed interacting oscillators

Area of Science:

• Neuroscience
• Computational Neuroscience
• Physics

Background:

• Network resonance, the collective frequency of synchronized neuronal populations, exhibits a systematic relationship with brain size.
• Larger brain networks oscillate slowly, while smaller, fixed-volume parcellations show faster rhythms.
• The underlying physical mechanism for this resonance-size scaling has remained elusive.

Purpose of the Study:

• To elucidate the physical mechanism behind size-dependent network resonance in neuronal populations.
• To derive an analytical framework explaining the relationship between brain size, propagation delays, and network resonance.
• To validate theoretical predictions with numerical simulations.

Main Methods:

• Utilized a Kuramoto model with heterogeneous delays, a standard model for coupled oscillators.
• Linearized the model around a near-synchronous solution to derive a closed-form approximation for resonance frequency.
• Performed numerical simulations with varying delay distributions and geometric scaling scenarios.

Main Results:

• Derived a generic scaling law: resonance frequency (Ω) is inversely proportional to the sum of coupling strengths and delays (Ω≈(∑_{j}c_{ij}τ)⁻¹).
• Demonstrated that resonance is delay-limited and systematically depends on geometric size or parcellation density.
• Validated the analytical prediction, showing that only geometry-consistent scaling satisfies the derived law.

Conclusions:

• Identified propagation delays in delay-coupled phase oscillators as the minimal physical mechanism for size-dependent cortical resonance.
• Provided an analytical framework that unifies outputs from numerical simulations of neural mass models.
• Established a direct link between physical size, signal propagation delays, and emergent network frequencies in the brain.