Characterizing heart rate variability by scale-dependent Lyapunov exponent

Abstract

Hu, J; Gao, J.; and Tung, W., "Characterizing heart rate variability by scale-dependent Lyapunov exponent" (2009) Previous studies on heart rate variability ͑HRV͒ using chaos theory, fractal scaling analysis, and many other methods, while fruitful in many aspects, have produced much confusion in the literature. Especially the issue of whether normal HRV is chaotic or stochastic remains highly controversial. Here, we employ a new multiscale complexity measure, the scale-dependent Lyapunov exponent ͑SDLE͒, to characterize HRV. SDLE has been shown to readily characterize major models of complex time series including deterministic chaos, noisy chaos, stochastic oscillations, random 1 / f processes, random Levy processes, and complex time series with multiple scaling behaviors. Here we use SDLE to characterize the relative importance of nonlinear, chaotic, and stochastic dynamics in HRV of healthy, congestive heart failure, and atrial fibrillation subjects. We show that while HRV data of all these three types are mostly stochastic, the stochasticity is different among the three groups. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3152007͔Determining whether heartbeat dynamics is chaotic or stochastic is an important issue, both theoretically and clinically. The problem is difficult to solve neatly, however, since heart rate variability (HRV) may exhibit both nonlinear, and possibly chaotic, as well as stochastic behaviors. This motivates us to employ a recently developed multiscale complexity measure, the scale-dependent Lyapunov exponent (SDLE), to characterize HRV. SDLE cannot only unambiguously distinguish chaos from noise but also characterize various types of complex time series. Using SDLE, we are able to quantify the relative importance of nonlinear, chaotic, and stochastic dynamics in HRV of healthy, congestive heart failure, and atrial fibrillation subjects.

Complexity measures of brain wave dynamics

“…The periodic components only affect the behavior of SDLE near the characteristic scale, but not the fractal/chaotic scalings (Gao et al 2007;Hu et al 2009). At this point, we also like to note that when nonstationarity reveals itself as amplitude variations in the signal, then all the scaling laws expressed by Eqs.…”

“…SDLE is defined in a phase space through consideration of an ensemble of trajectories (Gao et al 2006a(Gao et al , 2007Hu et al 2009Hu et al , 2010. When one is only given a scalar time series, one can use the time delay embedding to reconstruct a suitable phase space, as explained before.…”

“…To understand the relations among the measures considered above, we now carry out a multiscale analysis of EEG by computing the scale-dependent Lyapunov exponent (SDLE) (Gao et al 2006a(Gao et al , 2007Hu et al 2009Hu et al , 2010.…”

On the dynamics of ocean ambient noise: Two decades later

“…13 Since then, SDLE is used in various fields of research for characterizing the dynamic complexity of the time series signals. [47][48][49][50][51][52][53] SDLE can efficiently characterize the embedded dynamics in complex time series by identifying chaos, noisy chaos, stochastic oscillations, random 1/f process, random levy process, and complex time series with multiple scaling behaviors. Moreover, it is robust to nonstationarity.…”

Reduced Data Dualscale Entropy Analysis of HRV Signals for Improved Congestive Heart Failure Detection

“…As Physiological systems are governed by mechanisms which are operating over multiple time scales, many methods, such as Scale dependent Lyapunov exponent(SDLE) [3,4], Multifractal Analysis (MFA) [5][6][7] and Entropy analysis [8,9] have been developed in the last few years for the analysis of these complex physiological signals. By analyzing the degree of complexity, a greater understanding can be achieved on the fundamental mechanisms and their underlying dynamics of physiological systems.…”