A Stochastic Nonlinear Autoregressive Algorithm Reflects Nonlinear Dynamics of Heart-Rate Fluctuations

Abstract

Current methods for detecting nonlinear determinism in a time series require long and stationary data records, as most of them assume that the observed dynamics arise only from the internal, deterministic workings of the system, and the stochastic portion of the signal (the noise component) is assumed to be negligible. To explicitly account for the stochastic portion of the data we recently developed a method based on a stochastic nonlinear autoregressive (SNAR) algorithm. The method iteratively estimates nonlinear autoregressive models for both the deterministic and stochastic portions of the signal. Subsequently, the Lyapunov exponents (LE) are calculated for the estimated models in order to examine if nonlinear determinism is present in the deterministic portion of the fitted model. To determine if nonlinear dynamic analysis of heart-rate fluctuations can be used to assess arrhythmia susceptibility by predicting the outcome of invasive cardiac electrophysiologic study (EPS), we applied the SNAR algorithm to noninvasively measured resting sinus-rhythm heart-rate signals obtained from 16 patients. Our analysis revealed that a positive LE was highly correlated to a patient with a positive outcome of EPS. We found that the statistical accuracy of the SNAR algorithm in predicting the outcome of EPS was 88% (sensitivity=100%, specificity=75%, positive predictive value=80%, negative predictive value=100%, p=0.0019). Our results suggest that the SNAR algorithm may serve as a noninvasive probe for screening high-risk populations for malignant cardiac arrhythmias.

Characterizing Nonlinear Heartbeat Dynamics Within a Point Process Framework

“…Specifically, complex dynamics have been observed in heartbeat interval series from healthy subjects [27], [46], and there have been growing interests in developing nonlinearity indexes able to characterize the irregularity of heartbeat dynamics in both healthy and pathological conditions [4], [30], [42]. Research effort has been largely devoted to characterizing such nonlinear behavior at different timescales using relatively short recordings [3]. In time-series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a nonstationary signal [41], [42].…”

Estimation of Instantaneous Complex Dynamics through Lyapunov Exponents: A Study on Heartbeat Dynamics

“…The proposed approach relies on the previous literature for the LEs mathematical definition [38], [39] and is embedded in a novel IG-based point-process nonlinear framework defined through a third-order Wiener-Volterra representation, thus advancing on the previous models [19]. As a consequence, the novel instantaneous LEs definition is able to provide a reliable complexity measure tool to examine the unevenly spaced events at very high temporal resolutions, without resorting to any interpolation method.…”

“…In our case, the matrix corresponds to the Jacobian of the -dimensional system of the NARL model parameters, where is the value of the largest model order [39]. Therefore, given the NARL model reported in eq.…”

“…In order to test the efficiency of the proposed cubic NARL model in tracking the complexity of a synthetic stochastic series through the IDLE index, we simulated a modified version of the well-known chaotic Hénon Map as suggested in [39]. Such a complex system, in which stochastic terms are also considered, is governed by the following differential equations: …”

“…Relying on the approach suggested by Chon et al [38] and, later, by Armoundas et al [39], we consider the cardiovascular system both chaotic and stochastic. This concept is in agreement with current physiological knowledge, since healthy HRV dynamics can be considered/modeled as the output of a nonlinear deterministic system (the pacemaker cells of sinus node) being forced by a high-dimensional input (the activity in the nerves innervating the sinus node).…”