Hilbert-Huang transform for analysis of heart rate variability in cardiac health

This paper introduces a modified technique based on Hilbert-Huang transform (HHT) to improve the spectrum estimates of heart rate variability (HRV). In order to make the beat-to-beat (RR) interval be a function of time and produce an evenly sampled time series, we first adopt a preprocessing method to interpolate and resample the original RR interval. Then, the HHT, which is based on the empirical mode decomposition (EMD) approach to decompose the HRV signal into several monocomponent signals that become analytic signals by means of Hilbert transform, is proposed to extract the features of preprocessed time series and to characterize the dynamic behaviors of parasympathetic and sympathetic nervous system of heart. At last, the frequency behaviors of the Hilbert spectrum and Hilbert marginal spectrum (HMS) are studied to estimate the spectral traits of HRV signals. In this paper, two kinds of experiment data are used to compare our method with the conventional power spectral density (PSD) estimation. The analysis results of the simulated HRV series show that interpolation and resampling are basic requirements for HRV data processing, and HMS is superior to PSD estimation. On the other hand, in order to further prove the superiority of our approach, real HRV signals are collected from seven young health subjects under the condition that autonomic nervous system (ANS) is blocked by certain acute selective blocking drugs: atropine and metoprolol. The high-frequency power/total power ratio and low-frequency power/high-frequency power ratio indicate that compared with the Fourier spectrum based on principal dynamic mode, our method is more sensitive and effective to identify the low-frequency and high-frequency bands of HRV.     

Separation of Respiratory Influences from the Tachogram: A Methodological Evaluation

The variability of the heart rate (HRV) is widely studied as it contains information about the activity of the autonomic nervous system (ANS). However, HRV is influenced by breathing, independently of ANS activity. It is therefore important to include respiratory information in HRV analyses in order to correctly interpret the results. In this paper, we propose to record respiratory activity and use this information to separate the tachogram in two components: one which is related to breathing and one which contains all heart rate variations that are unrelated to respiration. Several algorithms to achieve this have been suggested in the literature, but no comparison between the methods has been performed yet. In this paper, we conduct two studies to evaluate the methods'' performances to accurately decompose the tachogram in two components and to assess the robustness of the algorithms. The results show that orthogonal subspace projection and an ARMAX model yield the best performances over the two comparison studies. In addition, a real-life example of stress classification is presented to demonstrate that this approach to separate respiratory information in HRV studies can reveal changes in the heart rate variations that are otherwise masked by differing respiratory patterns.     

What options does the supine-standing-supine test offer to patients with hypertension? Demonstrations of examples

Aims: The purpose of the study was to demonstrate autonomic nervous system (ANS) changes associated with treatment in hypertensive patients and utilization of these measurements in practice. Methods: Hypertensive patients were examined before the start of treatment and after blood pressure compensation. The telemetric system VarCor PF 5 was used for non-invasive heart rate registration and automatic evaluation of heart rate variability (HRV) parameters. The supine-standing-supine test with ortho-clinostatic loading in standard conditions was used for HRV evaluation. Results: The influence of antihypertensive therapy on ANS was demonstrated in two cases. The first was a case of a responder to therapy and the second case was example of a non-responder to monotherapy regarding more therapeutic steps for blood pressure control. Different modes of results presentation are demonstrated: 3D graph, numeric form of standard parameters of HRV, computer interpretation of results by means of complex parameters and indices in numeric, graphic and verbal form with functional age calculation, cross graph of vagal activity index versus sympatho-vagal balance index was used for repeated measurements and follow-up. The increased spectral performance with augmented vagal activity and slope down of sympatho-vagal ratio are evident after blood pressure control achievement. Improvement of functional age parameter associated with blood pressure compensation is visible using a complex age-dependent parameters interpretation. Conclusions: HRV evaluation in hypertensive patients provides new parameters for patient's examination. These parameters are influenced by both the illness itself and by pharmacotherapy. Such an approach offers more complex information about patient.     

Filtering of kinematic signals using the Hodrick-Prescott filter

The use of the Hodrick-Prescott (HP) filter is presented as an alternative to the traditional digital filtering and spline smoothing methods currently used in biomechanics. In econometrics, HP filtering is a standard tool used to decompose a macroeconomic time series into a nonstationary trend component and a stationary residual component. The use of the HP filter in the present work is based on reasonable assumptions about the jerk and noise components of the raw displacement signal. Its applicability was tested on 4 kinematic signals with different characteristics. Two are well known signals taken from the literature on biomechanical signal filtering, and the other two were acquired with our own motion capture system. The criterion for the selection of cutoff frequency was based on the power spectral density of the raw displacement signals. The results showed the technique to be well suited to filtering biomechanical displacement signals in order to obtain accurate higher derivatives in a simple and systematic way. Namely, the HP filter and the generalized cross-validated quintic spline (GCVSPL) produce similar RMS errors on the first (0.1063 vs. 0.1024 m/s2) and second (23.76 vs. 23.24 rad/s2) signals. The HP filter performs slightly better than GCVSPL on the third (0.209 vs. 0.236 m/s2) and fourth (1.596 vs. 2.315 m/s2) signals.     

不同去趋势方法对树轮气候信号识别的影响

树木生长受到气候因子、随年龄增长的内在生长趋势、环境干扰和其他扰动信号的影响。目前存在不同的去趋势方法对树木年轮进行去趋势以识别树木生长中的气候信号。以往的研究多基于单个方法识别树轮气候信号，而不同去趋势方法识别的树轮气候信号可能会有一定的差别。为了对比不同去趋势方法对树轮气候信号识别的影响，我们基于国际年轮数据库网站获取中国西部地区68个点的树轮宽度数据，采用最常用的"signal-free"方法（SsfCrn）、线性和负指数函数法（std）、67%样条函数法（spline）、firedman方法、以及基于经验模式分解去趋势方法（EEMD）5种去趋势方法分别建立树轮年表，并对比分析同一地点的不同年表对气候响应的异同。结果表明：不同去趋势方法得到的年表对温度、降水以及相对湿度等气候因素的响应具有明显差异。其中，SsfCrn去趋势方法建立的年表对温度（月平均温、月最低温、月平均最低温）响应中相关最高的样点在所有样点中占比最高；EEMD去趋势方法建立的年表对降水量、相对湿度和月最高温响应中相关最高的样点在所有样点中占比最高；firedman去趋势方法建立的年表对月平均最高温响应中相关最高的样点在所有样点中占比最高。研究结果表明SsfCrn，EEMD和firedman方法在识别树轮气候信号方法具有一定的优势。在不同研究区域中，不同去趋势方法建立的年表对不同气候条件响应有差异，因此选择不同的去趋势方法识别树木生长趋势，分析哪种方法可以更好的反应气候变化对树木生长的影响显得尤为重要。     

A new algorithm for wavelet-based heart rate variability analysis

One of the most promising non-invasive markers of the activity of the autonomic nervous system is heart rate variability (HRV). HRV analysis toolkits often provide spectral analysis techniques using the Fourier transform, which assumes that the heart rate series is stationary. To overcome this issue, the Short Time Fourier Transform (STFT) is often used. However, the wavelet transform is thought to be a more suitable tool for analyzing non-stationary signals than the STFT. Given the lack of support for wavelet-based analysis in HRV toolkits, such analysis must be implemented by the researcher. This has made this technique underutilized.This paper presents a new algorithm to perform HRV power spectrum analysis based on the Maximal Overlap Discrete Wavelet Packet Transform (MODWPT). The algorithm calculates the power in any spectral band with a given tolerance for the band's boundaries. The MODWPT decomposition tree is pruned to avoid calculating unnecessary wavelet coefficients, thereby optimizing execution time. The center of energy shift correction is applied to achieve optimum alignment of the wavelet coefficients. This algorithm has been implemented in RHRV, an open-source package for HRV analysis. To the best of our knowledge, RHRV is the first HRV toolkit with support for wavelet-based spectral analysis.     

Systolic Peak Detection in Acceleration Photoplethysmograms Measured from Emergency Responders in Tropical Conditions

Photoplethysmogram (PPG) monitoring is not only essential for critically ill patients in hospitals or at home, but also for those undergoing exercise testing. However, processing PPG signals measured after exercise is challenging, especially if the environment is hot and humid. In this paper, we propose a novel algorithm that can detect systolic peaks under challenging conditions, as in the case of emergency responders in tropical conditions. Accurate systolic-peak detection is an important first step for the analysis of heart rate variability. Algorithms based on local maxima-minima, first-derivative, and slope sum are evaluated, and a new algorithm is introduced to improve the detection rate. With 40 healthy subjects, the new algorithm demonstrates the highest overall detection accuracy (99.84% sensitivity, 99.89% positive predictivity). Existing algorithms, such as Billauer''s, Li''s and Zong''s, have comparable although lower accuracy. However, the proposed algorithm presents an advantage for real-time applications by avoiding human intervention in threshold determination. For best performance, we show that a combination of two event-related moving averages with an offset threshold has an advantage in detecting systolic peaks, even in heat-stressed PPG signals.     

解除模拟失重后清醒大鼠血压信号的谱分析

本文旨在观察模拟失重28 d大鼠解除尾部悬吊前、后(2 h内),清醒自由活动状态下动脉收缩压(systolic bloodpressure,SBP)、舒张压(diastolic blood pressure,DBP)和心率(heart rate,HR)的变化.采用自回归模型法对不同时间点的收缩压变异性(SBP variability,SBPV)和心率变异性(HR variability,HRV)进行自谱与互谱分析,并比较自回归法与周期图法的自谱分析结果:由传递函数分析得到反映压力感受器-心率反射敏感性(baroreceptor-heart rate reflex sensitivity,BRS)变化的有关数据.结果显示,用自回归模型法对清醒大鼠血压信号进行短时程谱分析可得到较为平滑、谱峰清楚的谱估计曲线.28 d模拟失重大鼠解除尾部悬吊前、后,SBP、DBP和HR及其主要谱指标,以及高、低频段传递函数的平均增益均无显著性变化,不同时间点的谱指标也无显著差别;但模拟失重组的SBP、DBP和HR却显著高于对照组.上述结果提示,中期模拟失重大鼠恢复正常体位后,其清醒状态的BPV与HR均处于升高状态,但其短时程BPV与HRV谱及BRS均无显著变化,与最近报道的航天员HRV与BRS无显著改变一致.     

A Measurement of Electrocardiography and Photoplethesmography in Obese Children

The purpose of this study was to establish heart rate variability normative data on obese children and to comparing the accuracy of two medical technologies photoplethesmography (PPG) with electrocardiography (ECG) while measuring heart rate variability (HRV). PPG is a relatively new technique that holds promise for health care practitioners as an evaluative tool and biofeedback instrument due to its cost and easy administration. This study involved ten children who were recruited for an after-school program designed to reduce obesity. Three-five-minute recordings of HRV were collected while the children were lying in the supine position on a therapy bed. PPG was measured from a thumb sensor and ECG from sensors placed under wristbands on both wrists. The results indicate that PPG is as effective as ECG in measuring the eleven parameters of heart rate variability.     

Development of tree-ring maximum latewood density chronologies for the western Tien Shan Mountains,China: Influence of detrending method and climate response

Three tree-ring maximum latewood density chronologies were developed from high elevation Picea schrenkiana sites in the western Tien Shan Mountains using different detrending methods. The new chronologies extend back to the early 16th and late 17th centuries, and contain significant late spring and summer temperature signals, respectively. An assessment of varying detrending methods and band-pass filtering the chronologies revealed only slightly differing low frequency trends retained in the maximum latewood densities. The distance between sampling sites and the varying seasonality of limiting climatic factors are identified as key drivers affecting the correlation among the maximum latewood density records in the study region. The new chronologies represent reliable proxies of high elevation late spring and summer temperature variability in an area underrepresented by such data, and are ready-to-use for network analyses addressing longer-term climate variations in eastern central Asia.     

Influence of recognition errors of computerised analysis of 24-hour electrocardiograms on the measurement of spectral components of heart rate variability

Spectral methods for the assessment of heart rate variability (HRV) in 24-h electrocardiogram (ECG) are believed to require visual verification and manual editing of the computerised recognition of the ECG. This study investigated the effect of the recognition errors of computerised ECG recognition on two methods providing spectral HRV indices: (a) Fast Fourier Transformation (FFT); and (b) peak-to-trough analysis (PTA). Both methods were used to measure HRV spectra in 24-h ECGs recorded in 557 survivors of acute myocardial infarction. Each ECG was analysed using the Marquette 8000 Holter system and spectral HRV analyses were performed both prior to and after manual verification of the automatic ECG analysis. The FFT and PTA methods were used to calculate the low (0.04-0.15 Hz), medium (0.15-0.40 Hz) and high (0.40-1.00 Hz) HRV spectral components. For each method and for each spectral component, the rank correlations between the results obtained from unedited and edited ECG recognition were calculated. The correlations between the corresponding spectral components provided by the FFT and PTA methods applied to the edited recognitions were also calculated. Both methods were substantially affected by recognition errors. The FFT method was more sensitive to the misrecognition than the PTA method. The inter-method correlations were higher for the high and medium spectral components than for the low spectral component. The study suggests that spectral HRV analysis should be performed only on carefully verified and manually corrected recognitions of long-term electrocardiograms.     

Spectral Analysis of Binary Time Series: Square Waves vs. Sinusoidal Functions

The analysis of signals consisting of discrete and irregular data causes methodological problems for the Fourier spectral Analysis: Since it is based on sinusoidal functions, rectangular signals with unequal periodicities cannot easily be replicated. The Walsh spectral Analysis is based on the so called "Walsh functions", a complete set of orthonormal, rectangular waves and thus seems to be the method of choice for analysing signals consisting of binary or ordinal data. The paper compares the Walsh spectral analysis and the Fourier spectral analysis on the basis of simulated and real binary data sets of various length. Simulated data were derived from signals with defined cyclic patterns that were noised by randomly generated signals of the same length. The Walsh and Fourier spectra of each set were determined and up to 25% of the periodogram coefficients were utilized as input for an inverse transform. Mean square approximation error (MSE) was calculated for each of the series in order to compare the goodness of fit between the original and the reconstructed signal. The same procedure was performed with real data derived from a behavioral observation in pigs. The comparison of the two methods revealed that, in the analysis of discrete and binary time series, Walsh spectral analysis is the more appropriate method, if the time series is rather short. If the length of the signal increases, the difference between the two methods is less substantial.     

Spectral Analysis of Binary Time Series: Square Waves vs. Sinusoidal Functions

The analysis of signals consisting of discrete and irregular data causes methodological problems for the Fourier spectral Analysis: Since it is based on sinusoidal functions, rectangular signals with unequal periodicities cannot easily be replicated. The Walsh spectral Analysis is based on the so called "Walsh functions", a complete set of orthonormal, rectangular waves and thus seems to be the method of choice for analysing signals consisting of binary or ordinal data. The paper compares the Walsh spectral analysis and the Fourier spectral analysis on the basis of simulated and real binary data sets of various length. Simulated data were derived from signals with defined cyclic patterns that were noised by randomly generated signals of the same length. The Walsh and Fourier spectra of each set were determined and up to 25% of the periodogram coefficients were utilized as input for an inverse transform. Mean square approximation error (MSE) was calculated for each of the series in order to compare the goodness of fit between the original and the reconstructed signal. The same procedure was performed with real data derived from a behavioral observation in pigs. The comparison of the two methods revealed that, in the analysis of discrete and binary time series, Walsh spectral analysis is the more appropriate method, if the time series is rather short. If the length of the signal increases, the difference between the two methods is less substantial.     

Initial heart rate variability and radiosensitivity in rabbits

The goal of the work was to investigate the rabbits' radiosensitivity dependence on the initial functional state of the autonomous nervous system (ANS), as assessed by time-frequency parameters of the heart rate variability (HRV). Survival rate and rhythm-cardiologic correlates of the pathological processes following total X-irradiation, at doses of 2 and 12 Gy, were studied with an aid of modern computer technologies of measurement and data analysis. It has been found that the animals with initial prevailing of adrenergic influences on the HRV ("sympathicotonics") are significantly more sensitive to irradiation than those in which the parasympathetic prevalence was evident ("vagotonics"). The most characteristic and determining difference between these two groups of animals is initial level of the sum regulatory influences on the heart rhythm, which is manifested in value of total power of spectral density (TP) of HRV. In the sympathicotonics the TP is significantly lower than in the vagotonics. The primary HRV response to irradiation practically does not differ according to the dose and manifests in sharp suppression of the TP in both groups of the animals. At 12 Gy this process is irreversible. In the sympathicotonics it develops earlier and terminates with death much sooner than in the vagotonics. An average life-span of the rabbits, at this dose, is 18.8 +/- 2.6 days in vagotonics, and 10.3 +/- 1.3 days in sympathicotonics (p < 0.02). At 2 Gy initial sharp decrease of the TP in the vagotonics lasts one week only. Then the sum regulatory influence of the ANS on the heart rate increases (rebound) and this condition, which probably points at general resistance of the organism, could be seen within two months; at the end of third month it stabilizes at the initial level. In the sympathycotonics initial sharp decrease of the TP also occurred, however no rebound was observed. The results obtained show that low initial level of the TP of HRV is sufficiently correct marker for higher radiosensitivity in the sympathotonic rabbits against the vagotonic ones.     

Blind noise reduction for multisensory signals using ICA and subspace filtering, with application to EEG analysis

 In many applications of signal processing, especially in communications and biomedicine, preprocessing is necessary to remove noise from data recorded by multiple sensors. Typically, each sensor or electrode measures the noisy mixture of original source signals. In this paper a noise reduction technique using independent component analysis (ICA) and subspace filtering is presented. In this approach we apply subspace filtering not to the observed raw data but to a demixed version of these data obtained by ICA. Finite impulse response filters are employed whose vectors are parameters estimated based on signal subspace extraction. ICA allows us to filter independent components. After the noise is removed we reconstruct the enhanced independent components to obtain clean original signals; i.e., we project the data to sensor level. Simulations as well as real application results for EEG-signal noise elimination are included to show the validity and effectiveness of the proposed approach. Received: 6 November 2000 / Accepted in revised form: 12 November 2001     

Relationship between cortical electrical and cardiac autonomic activities in the awake lizard, Gallotia galloti

ECG and EEG signals were simultaneously recorded in lizards, Gallotia galloti, both in control conditions and under autonomic nervous system (ANS) blockade, in order to evaluate possible relationships between the ANS control of heart rate and the integrated central nervous system activity in reptiles. The ANS blockers used were prazosin, propranolol, and atropine. Time-domain summary statistics were derived from the series of consecutive R-R intervals (RRI) of the ECG to measure beat-to-beat heart rate variability (HRV), and spectral analysis techniques were applied to the EEG activity to assess its frequency content. Both prazosin and atropine did not alter the power spectral density (PSD) of the EEG low frequency (LF: 0.5-7.5 Hz) and high frequency (HF: 7.6-30 Hz) bands, whereas propranolol decreased the PSD in these bands. These findings suggest that central beta-adrenergic receptor mechanisms could mediate the reptilian waking EEG activity without taking part any alpha(1)-adrenergic and/or cholinergic receptor systems. In 55% of the lizards in control conditions, and in approximately 43% of the lizards under prazosin and atropine, a negative correlation between the coefficient of variation of the series of RRI value (CV(RRI)) and the mean power frequency (MPF) of the EEG spectra was found, but not under propranolol. Consequently, the lizards' HRV-EEG-activity relationship appears to be independent of alpha(1)-adrenergic and cholinergic receptor systems and mediated by beta-adrenergic receptor mechanisms.     

Assessing temporal scales and patterns in time series: Comparing methods based on redundancy analysis

Time-series modelling techniques are powerful tools for studying temporal scaling structures and dynamics present in ecological and other complex systems and are gaining popularity for assessing resilience quantitatively. Among other methods, canonical ordinations based on redundancy analysis are increasingly used for determining temporal scaling patterns that are inherent in ecological data. However, modelling outcomes and thus inference about ecological dynamics and resilience may vary depending on the approaches used. In this study, we compare the statistical performance, logical consistency and information content of two approaches: (i) asymmetric eigenvector maps (AEM) that account for linear trends and (ii) symmetric distance-based Moran's eigenvector maps (MEM), which requires detrending of raw data to remove linear trends prior to analysis. Our comparison is done using long-term water quality data (25 years) from three Swedish lakes. This data set therefore provides the opportunity for assessing how the modelling approach used affects performance and inference in time series modelling. We found that AEM models had consistently more explanatory power than MEM, and in two out of three lakes AEM extracted one more temporal scale than MEM. The scale-specific patterns detected by AEM and MEM were uncorrelated. Also individual water quality variables explaining these patterns differed between methods, suggesting that inferences about systems dynamics are dependent on modelling approach. These findings suggest that AEM might be more suitable for assessing dynamics in time series analysis compared to MEM when temporal trends are relevant. The AEM approach is logically consistent with temporal autocorrelation where earlier conditions can influence later conditions but not vice versa. The symmetric MEM approach, which ignores the asymmetric nature of time, might be suitable for addressing specific questions about the importance of correlations in fluctuation patterns where there are no confounding elements of linear trends or a need to assess causality.     

Analysis of cardiac signals using spatial filling index and time-frequency domain

Background  

Analysis of heart rate variation (HRV) has become a popular noninvasive tool for assessing the activities of the autonomic nervous system (ANS). HRV analysis is based on the concept that fast fluctuations may specifically reflect changes of sympathetic and vagal activity. It shows that the structure generating the signal is not simply linear, but also involves nonlinear contributions. These signals are essentially non-stationary; may contain indicators of current disease, or even warnings about impending diseases. The indicators may be present at all times or may occur at random in the time scale. However, to study and pinpoint abnormalities in voluminous data collected over several hours is strenuous and time consuming.     

Heart rate analysis in normal subjects of various age groups

Background  

Analysis of heart rate variation (HRV) has become a popular noninvasive tool for assessing the activities of the autonomic nervous system (ANS). HRV analysis is based on the concept that fast fluctuations may specifically reflect changes of sympathetic and vagal activity. It shows that the structure generating the signal is not simply linear, but also involves nonlinear contributions. Linear parameters, Power spectral indice (LF/HF) is calculated with nonlinear indices Poincare plot geometry(SD1,SD2), Approximate Entropy (ApEn), Largest Lyapunov Exponent (LLE) and Detrended Fluctuation Analysis(DFA). The results show that, with aging the heart rate variability decreases. In this work, the ranges of all linear and nonlinear parameters for four age group normal subjects are presented with an accuracy of more than 89%.     

Synthesis of HRV signals characterized by predetermined time-frequency structure by means of time-varying ARMA models

In this paper we present two methodologies to generate heart rate variability (HRV) signals characterized by controlled and real-like time-frequency (TF) structure to be used to assess different methods of non-stationary HRV analysis. The synthesized signals are stochastic processes whose TF structure is predetermined by choosing either the time-course of the instantaneous frequencies and powers or the shape of the TF model function. They consist of three steps: (a) choice of the desired TF structure of the signals by choosing a set of design parameters; (b) automatic identification of the parameters of the corresponding models via simple closed-form expressions; (c) synthesis of the desired stochastic signals. Two measures to evaluate the goodness of the simulated signals are also given. Using this framework we were able to model the wide range of non-stationarities observed in heart rate modulation during exercise stress testing and experiments of music-induced emotions. We used the proposed methodology to assess the capability of the smoothed pseudo Wigner–Ville distribution (SPWVD) to quantify HRV patterns. We observed that the SPWVD followed the temporal evolution of the spectral components even when sudden and sharp transitions occur.