Reinforcement Learning-Based Low-Energy Control of Cardiac Spiral Waves: A Unified Nonlinear Dynamical Framework Integrating Hopf Bifurcation, Stochastic Ion Channel Kinetics, and Phase-Guided Defibrillation

Abstract

Chur Chin

Background: Cardiac arrhythmias, particularly ventricular fibrillation (VF) and atrial fibrillation (AF), remain leading causes of sudden cardiac death worldwide. Current therapeutic approaches including high- energy defibrillation carry significant risks of myocardial damage and patient discomfort. The underlying electrophysiological dynamics of these arrhythmias are fundamentally chaotic, governed by nonlinear spiral wave reentry in cardiac tissue.

Objective: This study presents a unified theoretical and computational framework that integrates Hopf bifurcation theory, stochastic Hodgkin-Huxley (HH) ion channel kinetics, calcium clock coupling, Lyapunov-based chaos quantification, and Proximal Policy Optimization (PPO)- based reinforcement learning (RL) for adaptive low-energy cardiac spiral wave suppression.

Methods: A two-dimensional FitzHugh-Nagumo reaction-diffusion model was employed as the substrate for spiral wave generation and propagation. Phase maps derived from topological winding numbers were used to identify spiral cores (phase singularities). Lyapunov exponents and multiscale entropy measures quantified the degree of spatiotemporal chaos. A PPO-based RL agent was trained to deliver spatiotemporally optimized stimuli to suppress spiral waves with minimal energy expenditure.

Results: Simulations demonstrated that pacemaker activity originates from a Hopf bifurcation in a nonlinear coupled oscillator system. The PPO agent successfully learned to suppress spiral wave reentry by targeting phase singularities with low-energy perturbations, achieving chaos suppression with energy requirements approximately 85% lower than conventional global shock defibrillation. Phase response curve analysis confirmed that stimulation timed to the optimal phase of the cardiac cycle maximizes defibrillation efficacy.

Conclusion: This unified framework demonstrates that cardiac arrhythmia dynamics can be understood and controlled as a spatiotemporal chaos control problem. Reinforcement learning-guided phase-targeted stimulation offers a promising avenue toward next-generation low-energy defibrillation strategies.

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