Heart Rate Variability Series is the Output of a non-Chaotic System driven by Dynamical Noise

Heart rate variability (HRV) series reflects the dynamical variation of heartbeat-to-heartbeat intervals in time and is one of the outputs of the cardiovascular system. Over the years, this system has been recognized for generating nonlinear and complex heartbeat dynamics, with the latter referring to a high sensitivity to small -- theoretically infinitesimal -- input changes. While early research associated chaotic behavior with the cardiovascular system, evidence of stochastic inputs to the system, i.e., a physiological noise, invalidated those conclusions. To date, a comprehensive characterization of the cardiovascular system dynamics, accounting for dynamical noise input, has not been undertaken. In this study, we propose a novel methodological framework for evaluating the presence of regular or chaotic dynamics in noisy dynamical systems. The method relies on the estimation of asymptotic growth rate of noisy mean square displacement series in a two-dimensional phase space. We validated the proposed method using synthetic series comprising well-known regular and chaotic maps. We applied the method to real HRV series from healthy subjects, as well as patients with atrial fibrillation and congestive heart failure, during unstructured long-term activity. Results indicate that HRV series are consistently generated by a regular system driven by dynamical noise.