Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series

The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state [Physiol. Rev. 9, 399-431 (1929)]. However, recent studies [Phys. Rev. Lett. 70, 1343-1346 (1993); Fractals in Biology and Medicine (Birkhauser-Verlag, Basel, 1994), pp. 55-65] reveal that under normal conditions, beat-to-beat fluctuations in heart rate display the kind of long-range correlations typically exhibited by dynamical systems far from equilibrium [Phys. Rev. Lett. 59, 381-384 (1987)]. In contrast, heart rate time series from patients with severe congestive heart failure show a breakdown of this long-range correlation behavior. We describe a new method--detrended fluctuation analysis (DFA)--for quantifying this correlation property in non-stationary physiological time series. Application of this technique shows evidence for a crossover phenomenon associated with a change in short and long-range scaling exponents. This method may be of use in distinguishing healthy from pathologic data sets based on differences in these scaling properties.     

Forecasting with imperfect models, dynamically constrained inverse problems, and gradient descent algorithms

This paper is part of a larger study investigating the meaning of, and appropriate procedures for, forecasting with imperfect models. (In the author’s opinion there is currently no satisfactory general theory and practice for doing so with complex nonlinear systems.) The focus of this paper is on initialisation of the forecast. At the heart of every forecasting scheme there is an inverse problem that translates observations of reality into an initial state, or ensemble of states, of the model. Inverse problems are divided into two classes depending on whether the underlying model of reality is that of a stochastic process or a (deterministic) dynamical process. The two classes have quite different formulations of their inverse problems and consequent solutions methods. This paper considers dynamical process models and their inverse problems, which will be referred to as the dynamically constrained inverse problem (DCIP) line. The interpretation and solutions of the DCIP line are investigated and new algorithms for solving them are presented. The new algorithms are modifications of classical gradient descent algorithms. The new algorithms are applied to a low-dimensional chaotic system and a high-dimensional operational weather forecasting model. Our examination of DCIP shows that gradient descent algorithms are an effective way of solving the inverse problem for complex nonlinear system given an imperfect dynamical model.     

基于Poincaré差值散点图的心率变异性分析方法研究

在心率变异性的非线性分析中, Poincaré散点图分析是一种重要手段.本文基于Poincaré差值散点图(modified Poincaré plot)提出了两个参数——区域分布熵和区域分布系数, 用于定量描述所考察区域内散点的分布趋势, 并提出对散点在4个象限中的分布进行分别计算.通过对MIT-BIH数据库中健康年轻人、健康老年人和充血性心力衰竭患者样本数据的分析, 发现两参数值均呈现显著的组间差异;同时, 不同象限的分析结果显示了四个象限具有不同的区分敏感性, 而其中尤以第一象限的区分度为最高, 反映出充血性心力衰竭患者相对健康人迷走神经调控功能的改变最为显著, 与以往的生理学研究结论相符.经验证, 该方法可用于短时数据, 更易于扩展至临床应用.     

Scale-independent measures and pathologic cardiac dynamics.

We study several scale-independent measures of cardiac interbeat interval dynamics defined through the application of the wavelet transform. We test their performance in detecting heart disease using a database consisting of records of interbeat intervals for a group of healthy individuals and subjects with congestive heart failure. We find that scale-independent measures effectively distinguish healthy from pathologic behavior and propose a new two-variable scale-independent measure that could be clinically useful. We compare the performance of a recently proposed scale-dependent measure and find that the results depend on the database analyzed and on the analyzing wavelet.     

心率变异性基本尺度熵的多尺度化研究

将基本尺度熵的方法在时间上做多尺度化的扩展,并将其应用到心跳间隔序列的分析研究中.研究发现,健康人的心率变异性是小时间尺度下的模式特定性与大时间尺度下的模式丰富性相结合的,而充盈性心衰患者则正好相反.这说明充盈性心衰患者在小时间尺度下心脏动力系统的控制不力,导致随机性增加,而在大时间尺度下对外界环境变化反应又不够丰富,从而导致生命更容易受威胁.据此提出了以小时间尺度下的基本尺度熵值相对于大时间尺度下平台区基本尺度熵值的变异参数δ作为区分健康人和充盈性心衰患者的诊断依据.通过对72例健康人和44例充盈性心衰患者的计算,发现两组样本差异显著,证明了参数δ的有效性. 关键词： 多尺度化的基本尺度熵 心跳间隔序列 心率变异性 充盈性心衰     

Multifractal analysis of human synchronous 12-lead ECG signals using multiple scale factors

Life is one of the most complex nonlinear systems and heart is the core of this lifecycle system. Electrocardiogram (ECG) signals taken from healthy adult subjects have been found to characterize multifractality. In this paper, multiscale analysis method was introduced to find the most effective parameters for expressing the complex dynamic characteristics during heart electrical activities. We then investigated the multifractal singularity spectrum area of synchronous 12-lead ECG signals from healthy human subjects and those with different clinical syndromes. The spectrum areas have spatial distribution along with scale factors, which is higher in the middle and lower on both sides and is not related to data length. The statistical results suggest the arithmetical mean value of the area of the 12 leads ECG signals is obviously small for myocardial infarction (MI) sufferer and large for healthy young, while the dispersing degree of the area of the 12 leads ECG signals is apparently large for MI sufferer and small for healthy young. As for the other crowds (e.g., the ischemia sufferer), these two values are almost of middle magnitude. Through those individual discrepancies, we can find some effective approaches to distinguish among healthy persons and the heart diseased.     

Long-term invariant parameters obtained from 24-h Holter recordings: a comparison between different analysis techniques

Over the last two decades, a large number of different methods had been used to study the fractal-like behavior of the heart rate variability (HRV). In this paper some of the most used techniques were reviewed. In particular, the focus is set on those methods which characterize the long memory behavior of time series (in particular, periodogram, detrended fluctuation analysis, rescale range analysis, scaled window variance, Higuchi dimension, wavelet-transform modulus maxima, and generalized structure functions). The performances of the different techniques were tested on simulated self-similar noises (fBm and fGn) for values of alpha, the slope of the spectral density for very small frequency, ranging from -1 to 3 with a 0.05 step. The check was performed using the scaling relationships between the various indices. DFA and periodogram showed the smallest mean square error from the expected values in the range of interest for HRV. Building on the results obtained from these tests, the effective ability of the different methods in discriminating different populations of patients from RR series derived from Holter recordings, was assessed. To this extent, the Noltisalis database was used. It consists of a set of 30, 24-h Holter recordings collected from healthy subjects, patients suffering from congestive heart failure, and heart transplanted patients. All the methods, with the exception at most of rescale range analysis, were almost equivalent in distinguish between the three groups of patients. Finally, the scaling relationships, valid for fBm and fGn, when empirically used on HRV series, also approximately held.     

An efficient method of distinguishing chaos from noise

It is an important problem in chaos theory whether an observed irregular signal is deterministic chaotic or stochastic. We propose an efficient method for distinguishing deterministic chaotic from stochastic time series for short scalar time series. We first investigate, with the increase of the embedding dimension, the changing trend of the distance between two points which stay close in phase space. And then, we obtain the differences between Gaussian white noise and deterministic chaotic time series underlying this method. Finally, numerical experiments are presented to testify the validity and robustness of the method. Simulation results indicate that our method can distinguish deterministic chaotic from stochastic time series effectively even when the data are short and contaminated.     

A Novel Source-Filter Stochastic Model for Voice Production

The novel stochastic model to produce voiced sounds proposed in this paper uses the source-filter Fant theory to generate voice signals and, consequently, it does not consider the coupling between the vocal tract and the vocal folds. Two novelties are proposed in the paper. The first one is the new model obtained from the unification of two other deterministic one mass-spring-damper models obtained from the literature and the second one is to build a stochastic model which can generate and control the level of jitter resulting even in hoarse voice signals or with pathological characteristics but using a simpler model than those ones discussed in the literature. An inverse stochastic problem is then solved for two cases, considering a normal voice and other obtained from a case of paralysis on the vocal folds. The parameters of the model are identified in the two cases allowing the validation of the model.