Quantifying Chaotic Behavior in Noisy Dynamical Systems: A Study on Heartbeat Dynamics

Background: Heart rate variability (HRV) series reflects the dynamical variation of R-R intervals in time and is one of the outputs of the cardiovascular system. This system has been recognized for generating nonlinear and complex 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, i.e., a physiological noise, invalidated those conclusions. Aim: We introduce a novel methodological framework for quantifying the presence of regular or chaotic dynamics in noisy dynamical systems. We aim to perform a comprehensive characterization of the cardiovascular system dynamics, accounting for dynamical noise inputs. Methodology: The method relies on the estimation of asymptotic growth rate of noisy mean square displacement series in a two-dimensional phase space. Cardiac oscillatory components are modelled through an Inverse-Gaussian function. We validated the proposed method using synthetic series comprising well-known regular and chaotic maps. We applied the method to real HRV series from 23 healthy subjects, as well as 28 patients with atrial fibrillation and 34 congestive heart failure, gathered during unstructured long-term activity. Results: Results on synthetic data validate the correctness of the method. While cardiac pathology does not modulate chaotic behavior, atrial fibrillation induces higher sensitivity to input changes. Conclusion: The proposed methodological framework provides a quantitative means for characterizing physiological dynamics in terms of regular versus chaotic patterns. Our findings demonstrate that HRV series is the output of a non-chaotic (regular) system driven by dynamical noise.