Abstract
Measures of nonlinearity and complexity, and in particular the study of Lyapunov exponents, have been increasingly used to characterize dynamical properties of a wide range of biological nonlinear systems, including cardiovascular control. In this work, we present a novel methodology able to effectively estimate the Lyapunov spectrum of a series of stochastic events in an instantaneous fashion. The paradigm relies on a novel point-process high-order nonlinear model of the event series dynamics. The long-term information is taken into account by expanding the linear, quadratic, and cubic Wiener-Volterra kernels with the orthonormal Laguerre basis functions. Applications to synthetic data such as the Hénon map and Rössler attractor, as well as two experimental heartbeat interval datasets (i.e., healthy subjects undergoing postural changes and patients with severe cardiac heart failure), focus on estimation and tracking of the Instantaneous Dominant Lyapunov Exponent (IDLE). The novel cardiovascular assessment demonstrates that our method is able to effectively and instantaneously track the nonlinear autonomic control dynamics, allowing for complexity variability estimations.
Highlights
Hearth contractions are regarded by many scientists as the foremost example of a physiological system showing predominantly nonlinear behavior, mainly generated through integration of multiple neural signaling at the level of the sinoatrial node [1]
We present two applications on synthetic datasets and two experimental applications portraying the crucial role of the instantaneous Lyapunov Exponents in assessing autonomic changes in humans, focusing our attention on the Instantaneous Dominant Lyapunov Exponent (IDLE, l), which is the first exponent of the Lyapunov spectrum
The simulated time series along with the resulted IDLE series are shown in Fig. 1, whereas the corresponding box plots are shown in Fig. 3 in terms of IDLE median and its median absolute deviation slRR
Summary
Hearth contractions are regarded by many scientists as the foremost example of a physiological system showing predominantly nonlinear behavior, mainly generated through integration of multiple neural signaling at the level of the sinoatrial node [1]. Stationary aperiodic behavior, can arise in linear or nonlinear stochastic systems In light of these considerations, as this work deals with (instantaneous) LEs estimation with applications on heartbeat dynamics, we do not address the issue related to the chaotic behavior of heart rate variability (HRV). We present two applications on synthetic datasets (the Henon map and Rossler attractor) and two experimental applications portraying the crucial role of the instantaneous Lyapunov Exponents in assessing autonomic changes in humans (ten heathy subjects undergoing postural changes, and fourteen patients with severe heart failure), focusing our attention on the Instantaneous Dominant Lyapunov Exponent (IDLE, l), which is the first exponent of the Lyapunov spectrum. We start with a detailed, exhaustive presentation of our methodological framework through the following ‘‘Materials and Methods’’ section
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