Individual time-dependent spectral boundaries for improved accuracy in time-frequency analysis of heart rate variability

Heart rate variability (HRV) is a major noninvasive technique for evaluating the autonomic nervous system (ANS). Use of time-frequency approach to analyze HRV allows investigating the ANS behavior from the power integrals, as a function of time, in both steady-state and non steady-state. Power integrals are examined mainly in the low-frequency and the high-frequency bands. Traditionally, constant boundaries are chosen to determine the frequency bands of interest. However, these ranges are individual, and can be strongly affected by physiologic conditions (body position, breathing frequency). In order to determine the dynamic boundaries of the frequency bands more accurately, especially during autonomic challenges, we developed an algorithm for the detection of individual time-dependent spectral boundaries (ITSB). The ITSB was tested on recordings from a series of standard autonomic maneuvers with rest periods between them, and the response to stand was compared to the known physiological response. A major advantage of the ITSB is the ability to reliably define the mid-frequency range, which provides the potential to investigate the physiologic importance of this range.     

Artificial Neural Network Expert System for Integrated Heart Rate Variability

This paper describes the combination of an expert system for bio-information with smart devices using a wireless sensor network. A wireless bio-sensor module acquires physiological signals, including electrocardiogram, heart rate, heart rate variability (HRV) and autonomic nervous system activity. The smart device transmits the bio-information over a wireless network to a real-time expert consultation function for analysis, storage and decision making. An artificial neural network algorithm detects the HRV parameters and examines them for features of diabetes. A centralized internet information service platform can interrogate the remote client at any time for its bio-information. In addition, the system platform can compare data files. Bio-information and diabetes information can trigger timely alert messages. The system described in this paper could be the basis for a ubiquitous mobile physiological monitor.     

A new heart rate variability analysis method by means of quantifying the variation of nonlinear dynamic patterns

A new heart rate variability (HRV) analysis method, quantifying the variation of nonlinear dynamic pattern (VNDP) in heart rate series, is proposed and validated against the age stratified Fantasia database. The method is based on three processes: (1) a recurrence quantification analysis (RQA) to quantify the dynamic patterns, (2) the use of mutual information (MI) and the entropy (EN) to characterize the VNDP, and 3) linear discriminant analysis to exploit the associations within MI and EN measures. Practically, the VNDP method overcomes the nonstationarity problem and exploits the nonstationary properties in HRV analyses. Physiologically, the VNDP reflects the properties of the fundamental short-term HRV dynamic system and the external associations of the system within the autonomous nervous system (ANS). The characteristic probability density peaks portrayed by VNDP plots indicate the quantum-like heart dynamics, which may provide valuable insights into the control of the ANS. The discrimination results of the reduced pattern dynamic range due to aging, from a new perspective, display the reduction in HRV. The significantly improved discriminatory power, compared to conventional RQA analyses, shows that the VNDP analysis can practically quantify the nonstationary nonlinear dynamics for ANS assessments.     

Pole-tracking algorithms for the extraction of time-variant heartrate variability spectral parameters

Various algorithms of autoregressive (AR) recursive identification make it possible to evaluate power spectral distribution in correspondence with each sample of a time series, and time-variant spectral parameters can be calculated through the evaluation of the pole positions in the complex z-plane. In traditional analysis, the poles are obtained by zeroing the denominator of the model transfer function, expressed as a function of the AR coefficients. Here, two algorithms for the direct updating and tracking of movements of poles of an AR time-variant model on the basis of the innovation given to the coefficients are presented and investigated. The introduced algorithms are based upon (1) the classical linearization method and (2) a recursive method to compute the roots of a polynomial, respectively. Here, applications in the field of heart rate variability (HRV) signal analysis are presented and efficient tools are proposed for quantitative extraction of spectral parameters (power and frequency of the low-frequency (LF) and high-frequency (HF) components) for the monitoring of the action of the autonomic nervous system in transient pathophysiological events. These computational methods seem to be very attractive for HRV applications, as they inherit the peculiarity of recursive time-variant identification, and provide a more immediate comprehension of the spectral process characteristics when expressed in terms of poles and AR spectral components     

Evolutionary Maximum Entropy Spectral Estimation and Heart Rate Variability Analysis

Spectral analysis has been used extensively in heart rate variability (HRV) studies. The spectral content of HRV signals is useful in assessing the status of the autonomic nervous system. Although most of the HRV studies assume stationarity, the statistics of HRV signals change with time due to transients caused by physiological phenomena. Therefore, the use of time-frequency analysis to estimate the time-dependent spectrum of these non-stationary signals is of great importance. Recently, the spectrogram, the Wigner distribution, and the evolutionary periodogram have been used to analyze HRV signals. In this paper, we propose the application of the evolutionary maximum entropy (EME) spectral analysis to HRV signals. The EME spectral analysis is based on the maximum entropy method for stationary processes and the evolutionary spectral theory. It consists in finding an EME spectrum that matches the Fourier coefficients of the evolutionary spectrum. The spectral parameters are efficiently calculated by means of the Levinson algorithm. The EME spectral estimator provides very good time-frequency resolution, sidelobe reduction and parametric modeling of the evolutionary spectrum. With the help of real HRV signals we show the superior performance of the EME over the earlier methods.     

Improved heart rate variability signal analysis from the beat occurrence times according to the IPFM model

The heart rate variability (HRV) is an extended tool to analyze the mechanisms controlling the cardiovascular system. In this paper, the integral pulse frequency modulation model (IPFM) is assumed. It generates the beat occurrence times from a modulating signal. This signal is thought to represent the autonomic nervous system action, mostly studied in its frequency components. Different spectral estimation methods try to infer the modulating signal characteristics from the available beat timing on the electrocardiogram signal. These methods estimate the spectrum through the heart period (HP) or the heart rate (HR) signal. We introduce a new time domain HRV signal, the Heart Timing (HT) signal. We demonstrate that this HT signal, in contrast with the HR or HP, makes it possible to recover an unbiased estimation of the modulating signal spectra. In this estimation we avoid the spurious components and the low-pass filtering effect generated when analyzing HR or HP.     

Comparison of detrended fluctuation analysis and spectral analysis for heart rate variability in sleep and sleep apnea

Sleep has been regarded as a testing situation for the autonomic nervous system, because its activity is modulated by sleep stages. Sleep-related breathing disorders also influence the autonomic nervous system and can cause heart rate changes known as cyclical variation. We investigated the effect of sleep stages and sleep apnea on autonomic activity by analyzing heart rate variability (HRV). Since spectral analysis is suited for the identification of cyclical variations and detrended fluctuation analysis can analyze the scaling behavior and detect long-range correlations, we compared the results of both complementary techniques in 14 healthy subjects, 33 patients with moderate, and 31 patients with severe sleep apnea. The spectral parameters VLF, LF, HF, and LF/HF confirmed increasing parasympathetic activity from wakefulness and REM over light sleep to deep sleep, which is reduced in patients with sleep apnea. Discriminance analysis was used on a person and sleep stage basis to determine the best method for the separation of sleep stages and sleep apnea severity. Using spectral parameters 69.7% of the apnea severity assignments and 54.6% of the sleep stage assignments were correct, while using scaling analysis these numbers increased to 74.4% and 85.0%, respectively. We conclude that changes in HRV are better quantified by scaling analysis than by spectral analysis.     

Les fondements géométriques et algébriques de la fractalité 1

Major features of fractality are scale invariance and tree growing. Both features relate fractal as phenomena of boundary behavior. A mathematical analysis leads to the fact that all properties can be fitted using a universal algebraic property of nilpotence. It appears that the actual corpus of mathematical tools could be used to describe the fractality even if several tools require additional développements such as differential calculus on folded manifolds, parabolic and hyperbolic operators for contact structures,?). In addition, the mathematical analysis support the conjectures concerning the fine structure of the space time which must be applied in microphysics but also in macrophysics. Key words: Fractal system, Mathematics, Mathematical physics, Tree structure, Mathematical analysis, Conformal transformation, Analytical function.     

Spectral distortion properties of the integral pulse frequencymodulation model

The integral pulse frequency modulation (IPFM) model has been used for the following two purposes. First, it has been utilized to verify the correspondence between the spectral structure of autonomic input and the estimated spectrum of heart rate variability (HRV), relying mainly on the theoretical work of Bayly (1968). Second, the IPFM model provides a framework for evaluating how precisely the proposed method of HRV analysis could estimate the input spectral structure. However, the appropriateness of the IPFM model for both purposes has not been examined sufficiently in realistic situations. Here, the spectral structure of the pulse train generated by the IPFM model is theoretically derived for an input signal containing multiple frequency components. This is a more general condition than the single sinusoidal input signal used earlier. In accordance with the theoretical results, the magnitude of the spectral distortion is computed for a pair of varied frequencies, considering the corresponding coefficient of variation of interpulse intervals. Results show that the distortion could be nonnegligible under practical values of the coefficient of variation. Such distortion may well affect the spectral structure in the wide frequency range. This study suggests that the spectral structure of HRV should be interpreted carefully, taking the above distortion properties into account, even though the IPFM model appears to be established as a mechanism mediating between autonomic input and heart rate variability     

Efficient singular element for finite element analysis of quasi-TEMtransmission lines and waveguides with sharp metal edges

The FEM presents a slow rate of convergence when it is used in the analysis of quasi-TEM transmission lines or homogeneous waveguides with field singularities. In order to improve this drawback, mesh techniques or vector elements that cope with the singularities can be used. A different solution is to employ scalar singular elements although, most of those that have been used are only compatible with first-order ordinary elements or can only be used with field singularities of order O(r^-1/2) and O(r^-1/3). In this paper, we present an improvement on the rate of convergence of FEM by employing a scalar singular element, which can be utilized for any order of singularity, is compatible with quadratic or higher order standard elements and is also easy to implement in standard finite element codes. Several transmission lines and waveguides with sharp metal edges have been analysed with a reduced number of degrees of freedom that compares well with other FEM approaches. We also show that electromagnetic fields computed using the proposed singular element have very good agreement with the ones theoretically expected from the singular edge condition     

On singular equilibria of index-1 DAEs

Some qualitative properties of singular equilibria arising in semiexplicit index-1 differential-algebraic equations are discussed in this paper. We extend a taxonomy of singularities from index-0 problems to address situations not covered by the singularity induced bifurcation, singular flow, and associated theorems. Although some related phenomena may occur, different behavior can be expected when the assumptions supporting these results are not satisfied, as is illustrated by several examples. Special attention is paid to the effect that the singular nature of the underlying ordinary differential equation and, eventually, of the solution manifold, has on the behavior of the original singular index-1 problem.Supported by a graduate fellowship from Universidad Politécnica de Madrid. The work of this author was done while he was with the Department of Mathematics at North Carolina State University.Research supported in part by NSF Grants DMS-9714811 and DMS-9802259.     

基于LGF的海杂波中微弱目标检测方法

该文主要研究了海杂波的模糊分形特性以及模糊分形理论在海杂波微弱目标检测中的应用。模糊分形理论是在融合了模糊理论与分形理论的基础上提出来的,其两个重要概念是局部模糊分形维数与局部分形度。海杂波序列的分形程度可以构造为一种模糊属性,即模糊集,其具有良好的模糊理论中定义的 “度”的概念,且对海杂波与目标具有良好的区分能力。局部模糊分形维数与局部分形度是针对短时海杂波序列进行处理的,对长时间海杂波序列进行处理可以滑动处理单元实现。经X波段实测海杂波数据验证,该文所提方法具有良好的微弱目标检测能力。      

QT variability and HRV interactions in ECG: quantification and reliability

In this paper, a dynamic linear approach was used over QT and RR series measured by an automatic delineator, to explore the interactions between QT interval variability (QTV) and heart rate variability (HRV). A low-order linear autoregressive model allowed to separate and quantify the QTV fractions correlated and not correlated with HRV, estimating their power spectral density measures. Simulated series and artificial ECG signals were used to assess the performance of the methods, considering a respiratory-like electrical axis rotation effect and noise contamination with a signal-to-noise ratio (SNR) from 30 to 10 dB. The errors found in the estimation of the QTV fraction related to HRV showed a nonrelevant performance decrease from automatic delineation. The joint performance of delineation plus variability analysis achieved less than 20% error in over 75% of cases for records presenting SNRs higher than 15 dB and QT standard deviation higher than 10 ms. The methods were also applied to real ECG records from healthy subjects where it was found a relevant QTV fraction not correlated with HRV (over 40% in 19 out of 23 segments analyzed), indicating that an important part of QTV is not linearly driven by HRV and may contain complementary information.     

Multifractal ECG mapping of ventricular epicardium during regional ischemia in the pig

Myocardial ischemia creates abnormal electrophysiological substrates that can result in life-threatening ventricular arrhythmias. Early clinical identification of ischemia in patients is important to managing their condition. We analyzed electrograms from an ischemia-reperfusion animal model in order to investigate the relationship between myocardial ischemia and variability of electrocardiogram (ECG) multifractality. Ventricular epicardial electropotential maps from the anesthetized pig during LAD ischemia-reperfusion were analyzed using multifractal methods. A new parameter called the singularity spectrum area reference dispersion (SARD) is presented to represent the temporal evolution of multifractality. By contrasting the ventricular epicardial SARD and range of singularity strength (delta alpha) maps against activation-recovery interval (ARI) maps, we found that the dispersions of SARD and dleta alpha increased following the onset of ischemia and decreased with tissue recovery. In addition, steep spatial gradients of SARD and delta alpha corresponded to locations of ischemia, although the distribution of multifractality did not reflect the degree of myocardial ischemia. However, the multifractality of the ventricular epicardial electrograms was useful for classifying the recoverability of ischemic tissue. Myocardial ischemia significantly influenced the multifractality of ventricular electrical activity. Recoverability of ischemic myocardium can be classified using the multifractality of ventricular epicardial electrograms. The location and size of regions of severe ischemic myocardium with poor recoverability is detectable using these methods.     

Dynamic analysis of ventricular repolarization duration from24-hour Holter recordings

Evaluation of the influence of the autonomic nervous system on the ventricular repolarization duration was carried out using beat-to-beat analysis of the time intervals between the peaks of the R and T waves (RTm). After pre-processing of digitized Holter ECG's, auto and cross spectrum analyses were applied to heart rate and repolarization duration variability signals. Coherence analysis was used to assess the existence of common spectral contributions. The heart rate variability signal was used as reference of the sympatho-vagal balance at the sinus node. It was found that, in normal individuals, the autonomic nervous system directly influences the ventricular repolarization duration and that this influence is qualitatively very similar to the one that modulates the heart rate. Pathological alteration of these parallel autonomic activities to the heart (on the sinus node and on the ventricle) might cause uncoupling between depolarization and repolarization     

Threshold modeling of autonomic control of heart rate variability

Even in the absence of external perturbation to the human cardiovascular system, measures of cardiac function, such as heart rate, vary with time in normal physiology. The primary source of the variation is constant regulation by a complex control system which modulates cardiac function through the autonomic nervous system. Here, we present methods of characterizing the statistical properties of the underlying processes that result in variations in ECG R-wave event times within the framework of an integrate-and-fire model. We first present techniques for characterizing the noise processes that result in heart rate variability even in the absence of autonomic input. A relationship is derived that relates the spectrum of R-R intervals to the spectrum of the underlying noise process. We then develop a technique for the characterization of the dynamic nature of autonomically related variability resulting from exogenous inputs, such as respiratory-related modulation. A method is presented for the estimation of the transfer function that relates the respiratory-related input to the variations in R-wave event times. The result is a very direct analysis of autonomic control of heart rate variability through noninvasive measures, which provides a method for assessing autonomic function in normal and pathological states.     

The Measurement of Heart Rate Variability Spectra with the Help of a Personal Computer

The analysis of fluctuations in heart rate or heart rate variability (HRV) has found applications in, among others, the study of the neural cardiovascular system and ergonomic psychology. In particular, the study of the frequency components of HRV is becoming increasingly important. A method for the computation of HRV spectra directly from the heart beat event series as derived from the electrocardiogram has been developed. Because of the computational efficiency achieved, this method is implemented on a personal computer. Apart from an external QRS detector, a completely stand-alone system is realized. User interaction takes place on a menu card display basis. The system can operate at both real time and up to eightfold increased speed. The resultant spectra are displayed as histograms. Different ways of smoothing and segment averaging are possible.     

分数阶光敏神经元的动力学特性分析及其同步研究

神经元是神经系统的基本单位,神经元模型的准确性影响对其本质特征的分析和理解。该文研究了由分数阶电容和电感构成的分数阶光敏FitzHugh-Nagumo(FHN)神经元电路。利用分岔图、相轨迹图和时间序列图分析了分数阶光敏神经元模型的动力学特性。研究发现,随着分数阶阶次的降低,分数阶光敏神经元的活跃度增加。当选取不同参数时,神经元系统可以诱发不同的放电模式,如周期放电态、混沌放电态和尖峰放电态。此外,利用电突触耦合的方式连接两个分数阶光敏神经元。通过调整耦合强度,可以实现分数阶光敏神经元系统之间的相位同步和完全同步。最后,采用dSPACE验证了外部光信号对神经元兴奋性的调制作用。