| Heart rate variability (HRV), as denoted by successive beat-to-beat fluctuation, is of critical importance to maintain homeostasis of human being. Since Akselrod and coworkers [1,2] showed that heart rate variability, when Fourier-transformed into the power spectrum, displayed characteristic high-frequency (HF,0.15-0.40 cycle/beat), low-frequency (LF,0.04-0.15 cycle/beat) and very-low-frequency (VLF,<0.04 cycle/beat) peaks that could be identified with neurohumoral influences, spectral analysis (or equivalent time-domain analysis) of HRV[3] or other cardiovascular variabilities has been widely adopted as a noninvasive probe of cardiac-autonomic function[4]. HRV has received much attention in the last decades. Recently, an average of 10 scintific articles on HRV is published on each week[5]. A lot of diseases, such as acute myocardiac infarction [6], hypertention[7], diabetes[8] and obstructive sleep apnea syndrome[9] were revealed to cause abnormal HRV. Such "a new field of impetuous research" has made an amazing achievement from physiological study to clinical applications.Among three main frequency bands, it was whilom accepted that the HF reflects parasympathetic activity of the autonomic nervous system, whereas the LF reflects both sympathetic and parasympathetic outflows [3]. Since spectral analysis has long been classified as a linear method [3], the interpretation of physiological mechanism underlying such presumably linear spectrum led to a notion of sympathovagal balance [10], which expresses sympathetic-parasympathetic interaction as a reciprocally push-pull activity. Nevertheless, disputes abound as to whether the spectral components, presented by either absolute or normalized unit, are really linear expressions of autonomic branches [11]. The current debate seems converging toward an emerging consensus that sympathovagal interaction probably represents a nonlinear phenomenon reflecting the dynamic fluctuations of cardiac-autonomic outflows about their means [12,13].The recent advances call for a paradigm shift from linear to nonlinear anaysis of HRV. However, whether HRV per se is chaotic or merely random has remained a controversial problem[14]. Parallel attempts over the past several decades to characterize HRV using traditional nonlinear or stochastic theory in lieu of spectral analysis have unfortunately yielded more contention than conclusion in the literatures. Prevailing tests of heartbeat chaos using myriad idealized measures of nonlinear dynamics, mono- or multifractality [15,16,17,18,19,20] or complexity (singly or with surrogate data) [21,22,23,24] are fraught with many limitations as these measures generally lack the sensitivity, specificity and robustness required to definitively prove the presence or absence of chaos and to characterize it in the face of random noise.In this thesis, Chapter 1 provides necessary background to understand the development of HRV study from physiological research to clinical applications and the main aspect of chaos theory. Two main debates, first in 2006 "Cardiovascular variability is/is not an index of autonomic control of circulation" and second in 2009 "Is the normal heart rate chaotic?", are briefly introduced.Chapter 2 reevaluates several prevailing nonlinear analyses. They are Lyapunove exponent with both equation-based and algorithm-based, monofractal of 1/f scale-invariant and detrended fluctuation analysis (DFA), entropic complexity with approximate entropy, sample entropy and multiscale entropy, surrogate data method, and Barahona-Poon nonlinear autoregressive model to detect nonlinearity and noise titration method base on above model. We demonstrated that the monofractal is in fact a linear, rather than nonlinear correlation of time series, although the 1/f scale-invariant is ubiquitous in natural world. Entropic complexity per se cannot discriminate nonlinearity from noise, except in combination with surrogeate data method. However, surrogate data itself should be tested its nonlinearity to avoid the parasitical artifact in generation like AAFT algorithm. Comparing above indices, the most reliable nonlinear index is noise limit in titration method, which distinguishes nonlinearity from linearity and noise.Chapter 3 presents the evidences and demonstration of HF chaos. We found that the circadian variation of HF power in spectral analysis is close correlated with nonlinear detection using Barahona-Poon nonlinear autoregressive model[25]. This interesting finding promoted us to propose a novel band-phase-randomized surrogate data method, in combination with titration, to detect the relative contribution of frequency band to overall nonlinearity. The laboratory experiment of control breathing also showed that respiratory sinus arrhythmia, which is in time domain a synonym of HF power, contributed most nonlinearity of HRV. Thus the spectral analysis is no longer a linear alias; rather the nonlinearity is hided in its phase structure.Chapter 4 suggests a sinus-atrial node (SAN) model under mediation of parasympathetic and sympathetic outflows based on Hodgkin-Huxley equations and Demir model [26]. The simulation of SAN model reproduced mimic fluctuations of action potential (AP) duration, which resemble HRV of healthy subject and congestive heart failure (CHF) patient both in spectrum and nonlinearity. The spike-like singular beat-to-beat AP duration, which was found in RR intervals of CHF patients to be responsive for hyper chaos[25], is owing to enhanced sympathetic stimulus to SAN.In summary, the surprising results in this thesis are:1. General accepted nonlinear monofractal analysis has only linear information;2. Spectrum involves ensential nonlinearity, either in total frequency band or in specific band, due to its phase structure;3. Barahona-Poon nonlinear autoregressive model provides a sensitive, robustic and specific method to detect nonlinear, and possibly chaotic, characteristics of time series, which is superior to most prevailing nonlinear analyses.4. Respiratory sinus arrhythmia is a main source of HRV nonlinearity. |
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