Probabilistic and State-Space Modeling of Autonomic Nervous System Dynamics from HRV Signals: A Complementary Probabilistic Framework for Sympathetic–Parasympathetic Characterization

Heart rate variability (HRV) reflects autonomic nervous system (ANS) regulation through beat-to-beat fluctuations in cardiac RR intervals. Conventional HRV analysis relies on deterministic features such as SDNN, RMSSD, HF power, and LF/HF ratio, which quantify autonomic activity but do not model the underlying sympathetic–parasympathetic dynamics. This study proposes a complementary probabilistic framework that treats HRV as the observable output of a latent ANS dynamical system. A linear state-space model with Kalman filtering estimates HRV-derived latent states, interpretable as proxies for sympathetic–parasympathetic balance under predefined physiological assumptions; an Ornstein–Uhlenbeck stochastic differential equation (OU-SDE) captures HRV variability and autonomic recovery; and a Hidden Markov Model (HMM) represents discrete autonomic regime transitions. Applied to ambulatory Holter electrocardiography (ECG) recordings from n = 20 healthy adults, the framework yields interpretable parameters—OU recovery rate θ = 0.533 ± 0.624 s−1, diffusion σ = 82.6.2 ± 105.6 ms·s−1/2—and confirms the algebraic self-consistency of the OU MLE (SDNN2 ≈ σ2/(2θ), r = 0.998; note: tautological by construction—both sides derive from the same RR series—and should not be interpreted as independent physiological validation). Each component addresses a distinct aspect of ANS dynamics—continuous-state trajectories, stochastic amplitude, and discrete-regime transitions—and together, they provide complementary layers of autonomic information. This formulation provides uncertainty-aware autonomic assessment suitable for wearable sensing and physiological computing. Note on generalizability: the framework was validated on N = 20 healthy ambulatory adults; findings should not be extrapolated to clinical populations, older cohorts, or individuals with cardiovascular or autonomic pathology without replication in larger, more diverse samples.