Distinguishing cardiac randomness from chaos

Characterizing heart rate variability by scale-dependent Lyapunov exponent

Previous studies on heart rate variability (HRV) 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 (SDLE), 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.

Chaotic signatures of heart rate variability and its power spectrum in health, aging and heart failure

A paradox regarding the classic power spectral analysis of heart rate variability (HRV) is whether the characteristic high- (HF) and low-frequency (LF) spectral peaks represent stochastic or chaotic phenomena. Resolution of this fundamental issue is key to unraveling the mechanisms of HRV, which is critical to its proper use as a noninvasive marker for cardiac mortality risk assessment and stratification in congestive heart failure (CHF) and other cardiac dysfunctions. However, conventional techniques of nonlinear time series analysis generally lack sufficient sensitivity, specificity and robustness to discriminate chaos from random noise, much less quantify the chaos level. Here, we apply a ‘litmus test’ for heartbeat chaos based on a novel noise titration assay which affords a robust, specific, time-resolved and quantitative measure of the relative chaos level. Noise titration of running short-segment Holter tachograms from healthy subjects revealed circadian-dependent (or sleep/wake-dependent) heartbeat chaos that was linked to the HF component (respiratory sinus arrhythmia). The relative ‘HF chaos’ levels were similar in young and elderly subjects despite proportional age-related decreases in HF and LF power. In contrast, the near-regular heartbeat in CHF patients was primarily nonchaotic except punctuated by undetected ectopic beats and other abnormal beats, causing transient chaos. Such profound circadian-, age- and CHF-dependent changes in the chaotic and spectral characteristics of HRV were accompanied by little changes in approximate entropy, a measure of signal irregularity. The salient chaotic signatures of HRV in these subject groups reveal distinct autonomic, cardiac, respiratory and circadian/sleep-wake mechanisms that distinguish health and aging from CHF.

A history of chaos theory

Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century, when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely, although they can be predicted to some extent, in line with the chaos theory. Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory. This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms.