Modeling Post-COVID Respiratory Rehabilitation with Nonlinear Dynamics and Fractal Metrics: Beyond Spirometry

COVID-19 frequently results in extended respiratory challenges that hinder daily activities and diminish quality of life. Standard pulmonary function tests (PFTs) offer significant, though partial, understanding of the intricate dynamics of post-COVID respiration. This study evaluates the integration of nonlinear dynamics and fractal analysis to characterize respiratory recovery and assess the effects of an 8-week rehabilitation program. We conducted a prospective investigation involving adults with persistent post-COVID respiratory symptoms alongside age-matched healthy controls. Respiratory function was evaluated using spirometry, thoracic impedance belts, and pulse-oximetry. Nonlinear analytical techniques - including phase-space attractor reconstruction and bifurcation analysis - were applied in combination with fractal metrics such as the Higuchi fractal dimension and box-counting. Standard clinical measures (FEV₁, FVC, DLCO, 6MWT, and dyspnea scores) were also recorded. All patients completed a structured three-phase rehabilitation program incorporating diaphragmatic breathing, HRV-based biofeedback, and progressive aerobic training. Nonlinear attractors displayed distinct morphologies: healthy individuals exhibited stable oscillations, post-COVID patients presented compressed, unstable cycles, and rehabilitation shifted trajectories towards normalization. Bifurcation diagrams illustrated essential compliance parameters that distinguish stability, collapse, and unstable respiration. The fractal dimension (FD) improved significantly from 1.08 ± 0.03 to 1.23 ± 0.03 after 8 weeks (p < 0.001), approaching reference values (FD > 1.20). Conventional indices improved concordantly: FEV1 went up by 17%, DLCO by 25%, the 6MWT by 80 meters, and ratings of dyspnea went down by 40%. Coupling nonlinear dynamics with fractal analysis provides higher-resolution assessment of respiratory recovery during post-COVID rehabilitation. Attractors, bifurcation thresholds, and fractal dimensions augment traditional metrics, capturing adaptability and stability that conventional metrics miss. These technologies can support individualized therapy progression and early identification of patients at risk for persistent dysfunction.