Unified Resonance Cascade Model: A Biophysical Theory of Brain–Heart Phase Coupling Derived from Oscillator Dynamics and Navier–Stokes Fluid Mechanics

This work presents a theoretical biophysical framework—the Unified Resonance Cascade Model (URCM)—which describes brain–heart interaction as a coupled dynamical system governed by phase synchronisation, stability theory, and viscous fluid mechanics. The model integrates two levels of description: (1) a nonlinear oscillator formulation in which EEG theta activity and cardiac variability are treated as weakly coupled oscillators, and (2) a Navier–Stokes–based field formulation in which blood and cerebrospinal fluid act as the physical medium transmitting resonance information. A central construct of the framework is the Resonance Coupling Invariant (R), a dimensionless quantity combining phase locking and Lyapunov‑derived stability margins. R reduces to classical coherence measures in the linear limit but diverges from them in the physiologically relevant nonlinear regime. The model further derives the Lorentzian HRV surrogate function from first principles as the resonance response of a damped harmonic oscillator, and identifies a predicted resonant spatial scale (~1.9 mm) consistent with cerebrovascular geometry. This is a theoretical model, grounded in established physics and existing physiological data, but not yet validated experimentally. It does not make clinical claims, diagnostic assertions, or interpretations of cognitive or emotional states. Instead, it provides a mathematically explicit structure that generates testable predictions regarding resonance bandwidth, stability thresholds, and fluid‑mechanical coupling. The purpose of this work is to offer a coherent, falsifiable framework that can be evaluated, challenged, or refined by experimental research. The authors explicitly invite empirical verification, replication attempts, and interdisciplinary critique. The URCM framework should be viewed as a hypothesis-generating theoretical construct, not as a substitute for clinical evidence.