Spectral analysis of heart rate variability using the integral pulse frequency modulation model.

Integral pulse frequency modulation model driven by sympathovagal dynamics: Synthetic vs. real heart rate variability

An integral pulse frequency modulation (IPFM) model is a pulse generation mechanism model for the nervous systems and is one of the models which connects heart rate variability to autonomic nervous system activity. There is a refractory period just after a heart beat impulse occurs, in which no heart beat impulses occur at any rate. The IPFM model does not take the refractory period into account. It would be good to consider the refractory periods in order to make the IPFM model realistic. In this paper, we are examining the effects of the absolute refractory period on the spectral distortion properties and the demodulation accuracy. Spurious components, (which are caused by mutual interference among the frequency components), decreased as the absolute refractory period increased, while the side-band distortion around the input frequency components increased. The direct FFT method impairs demodulation accuracy as the absolute refractory period increases. Even the integral function (IF) method without taking the absolute refractory period into account can reduce the distortion that is peculiar to the absolute refractory period. Moreover, the IF method which took the absolute refractory period into account has higher demodulation accuracy in spite of the absolute refractory period.

In this work, an integral pulse frequency modulation(IPFM) model for physiological systems is studied from the viewpoint of nonlinear dynamics. Rich dynamical structures were found from the model while some model parameters varied, and five features including fix points, periods, bifurcations, period-three windows and quasi-periodicity were observed in the study. Because period-three windows in nonlinear systems are associated with chaos, it is postulated that chaos may occur in this IPFM system at some values of model parameters. The IPFM model has been used for modeling some physiological phenomena, and the results of this work will be useful in understanding the mechanism of physiological rhythm and in explaining some dynamical diseases in the human body.

This paper introduces an efficient algorithm to reconstruct heart rate signal based on an integral pulse frequency modulation (IPFM) model. The heart rate signal was reconstructed by the summation of a set of sinc functions with different weights, whose value could be determined from the IPFM process. Simulation study demonstrated that the signal reconstructed by the proposed method would preserve high frequency component with less distortion than the popular derivative of cubic spline interpolation (DCSI) method. When applied to the spectral analysis of heart rate variability (HRV) of simulated heart rate signal, the proposed method achieved smaller bias than the DCSI method. Therefore, the proposed method would be beneficial for the reconstruction of heart rate signal and the relevant spectral analysis of HRV in the future.

The analysis and interpretation of heart rate variability (HRV) during exercise is challenging not only because of the nonstationary nature of exercise, the time-varying mean heart rate, and the fact that respiratory frequency exceeds 0.4 Hz, but there are also other factors, such as the component centered at the pedaling frequency observed in maximal cycling tests, which may confuse the interpretation of HRV analysis. The objectives of this study are to test the hypothesis that a component centered at the running stride frequency (SF) appears in the HRV of subjects during maximal treadmill exercise testing, and to study its influence in the interpretation of the low-frequency (LF) and high-frequency (HF) components of HRV during exercise. The HRV of 23 subjects during maximal treadmill exercise testing is analyzed. The instantaneous power of different HRV components is computed from the smoothed pseudo-Wigner-Ville distribution of the modulating signal assumed to carry information from the autonomic nervous system, which is estimated based on the time-varying integral pulse frequency modulation model. Besides the LF and HF components, the appearance is revealed of a component centered at the running SF as well as its aliases. The power associated with the SF component and its aliases represents 22±7% (median±median absolute deviation) of the total HRV power in all the subjects. Normalized LF power decreases as the exercise intensity increases, while normalized HF power increases. The power associated with the SF does not change significantly with exercise intensity. Consideration of the running SF component and its aliases is very important in HRV analysis since stride frequency aliases may overlap with LF and HF components.

A new method for real-time heart rate variability (HRV) detection from the R-wave signal, based on the integral pulse frequency modulation (IPFM) model and its similarity to pulse position modulation, is presented. The proposed method exerts low-pass filtering with a Kaiser window. It can also be used for off-line HRV analysis in both the time and frequency domains. Real-time bandpass filtering as a new HRV investigation method and as a by-product of the proposed algorithm is also introduced. Furthermore, the discrete time domain version of the French-Holden algorithm is developed, and it is thoroughly proved that low-pass filtering is an ideal method for detection of HRV.

Spectral decomposition of heart rate variability using generalized harmonic analysis

Low-pass filtering techniques have been suggested as a simple approach to recover the original input modulating information from an integral pulse frequency modulation (IPFM) process mimicking neural physiological encoding mechanisms. However, due to the non-linearity of the IPFM model and the difficulty in estimating the threshold value of neurons in vivo, it is practically implausible to recover precisely the input modulation amplitude or intensity information through simple low-pass filtering. Instead, it is found through a mathematical analysis that such demodulation is of special importance for studying the firing characteristics of neural and muscle cells. In this paper, with a single sinusoidal signal as the input modulation signal to the IPFM model, an expression for the relationship between the instantaneous firing rate and the intensity of input signals is derived. The results show that the firing rate function in terms of the modulating signal and the threshold can be reconstructed with reasonable accuracy by simple low-pass filtering.

ObjectiveCardiovascular diseases generate the highest mortality in the globe population, mainly due to coronary artery disease (CAD) like arrhythmia, myocardial infarction and heart failure. Therefore, an early identification of CAD and diagnosis is essential. For this, we have proposed a new approach to detect the CAD patients using heart rate variability (HRV) signals. This approach is based on subspaces decomposition of HRV signals using multiscale wavelet packet (MSWP) transform and entropy features extracted from decomposed HRV signals. The detection performance was analyzed using Fisher ranking method, generalized discriminant analysis (GDA) and binary classifier as extreme learning machine (ELM). The ranking strategies designate rank to the available features extracted by entropy methods from decomposed heart rate variability (HRV) signals and organize them according to their clinical importance. The GDA diminishes the dimension of ranked features. In addition, it can enhance the classification accuracy by picking the best discerning of ranked features. The main advantage of ELM is that the hidden layer does not require tuning and it also has a fast rate of detection.MethodologyFor the detection of CAD patients, the HRV data of healthy normal sinus rhythm (NSR) and CAD patients were obtained from a standard database. Self recorded data as normal sinus rhythm (Self_NSR) of healthy subjects were also used in this work. Initially, the HRV time-series was decomposed to 4 levels using MSWP transform. Sixty two features were extracted from decomposed HRV signals by non-linear methods for HRV analysis, fuzzy entropy (FZE) and Kraskov nearest neighbour entropy (K-NNE). Out of sixty-two features, 31 entropy features were extracted by FZE and 31 entropy features were extracted by K-NNE method. These features were selected since every feature has a different physical premise and in this manner concentrates and uses HRV signals information in an assorted technique. Out of 62 features, top ten features were selected, ranked by a ranking method called as Fisher score. The top ten features were applied to the proposed model, GDA with Gaussian or RBF kernal + ELM having hidden node as sigmoid or multiquadric. The GDA method transforms top ten features to only one feature and ELM has been used for classification.ResultsNumerical experimentations were performed on the combination of datasets as NSR-CAD and Self_NSR- CAD subjects. The proposed approach has shown better performance using top ten ranked entropy features. The GDA with RBF kernel + ELM having hidden node as multiquadric method and GDA with Gaussian kernel + ELM having hidden node as sigmoid or multiquadric method achieved an approximate detection accuracy of 100% compared to ELM and linear discriminant analysis (LDA)+ELM for both datasets. The subspaces level-4 and level-3 decomposition of HRV signals by MSWP transform can be used for detection and analysis of CAD patients.

Offspring with a genetic predisposition to hypertension may have higher blood pressure (BP) at rest compared with those without a genetic predisposition to hypertension. They are also expected to have a higher sympathetic component in the heart rate variability (HRV) which could be computed with signal processing algorithms. The purpose of this study is to design a wavelet-based system to estimate the heart rate variability that can be used to detect early cardiovascular changes in offspring with a genetic predisposition to hypertension. Early detection will help in the treatment of those young people. In this work, the relation between the hypertension and the changes in HRV is investigated. The frequency domain and time domain analysis of heart rate variability (HRV) are studied to understand their relationship to the autonomic nervous system in offspring with and without a genetic predisposition to hypertension in Oman at resting state. The wavelet-based soft-decision algorithm is used as the spectral analysis tool to obtain different features from the HRV signal and to select the best performing features for detection of hypertension. The main task is to classify between three categories of subjects: 36 subjects with both normotensive parents (ONT), 22 subjects with single hypertensive parent (OHT1), and 11 subjects with both hypertensive parents (OHT2). The summation of the power of bands B4 and B5 of the 32 bands HRV wavelet-based spectrum, which is equivalent to the frequency range (0.046875 Hz-0.078125 Hz), is used as a classification factor among OHT2, OHT1, and ONT groups. The efficiency of classification between ONT and OHT2 is 85.10%, and between OHT1 and OHT2 is 81.81%. The result of classifying between (ONT and OHT1 as one group) and OHT2 is 85.50%. The work proves that the wavelet-based spectral analysis technique is a successful tool for classifying the three groups of subjects (ONT, OHT1, and OHT2) with different susceptibility for development of hypertension.

Digital spectral analysis of Heart Rate Variability (HRV) signals provides quantitative markers of the Autonomic Nervous System (ANS) activity, underpinning a variety of physiologic processes. In this investigation, a robust algorithm was developed to derive HRV signals, their FFT- or AR-based spectra and their standard spectral features from either electrocardiogram (ECG) or photoplethysmographic (PPG) signals. ECG/PPG signals were first interpolated to a common sampling rate and detrended using a first order DC-notch IIR high-pass filter to remove very low frequencies. Next, the undecimated Discrete Wavelet Transform (DWT) Daubechies-6 family of filters was used to selectively remove some of the high-frequency subbands from the signals. The filtered ECG/PPG signals were then squared to increase the dynamic range of the target dominant peaks from which accurate peak-to-peak intervals could be extracted. A smart peak-tracking and monitoring algorithm was used to detect the peaks while enforcing a valid trend of the instantaneous heart rate. Once the peak-to-peak intervals were obtained, the HRV signal was determined using cubic spline interpolation to create a signal at a very low sampling rate of 1-4 Hz. Standard Power Spectrum Estimation (PSD) of the HRV signal was then performed to generate normalized LF, HF and LF/HF spectral features to quantify parasympathetic influences and sympathovagal balance.

Many patients with severe obstructive sleep apnea (OSA) do not complain of excessive daytime sleepiness (EDS), possibly due to increased sympathetic nervous activity (SNA) and accompanying heightened alertness. We hypothesized that in patients with OSA, those without subjective EDS (Epworth Sleepiness Scale, ESS score < 11) would have higher very low frequency (VLF) heart rate variability (HRV) during sleep, reflecting greater sympathetic heart rate modulation than patients with an ESS score ≥ 11. Patients with severe OSA (AHI ≥ 30: 26 with and 65 without heart failure) were divided into those with and without EDS. Heart rate (HR) signals were acquired in stage 2 sleep during periods of recurrent apneas and hypopneas and submitted to coarse graining spectral analysis, which extracts harmonic, neurally mediated contributions to HRV from total spectral power. Because the apnea-hyperpnea cycle entrains muscle SNA at VLF (0 to 0.04 Hz), VLF power was our principal between-group comparison. Subjects without EDS had higher harmonic VLF power (944 ± 839 vs 447 ± 461 msec(2), p = 0.003) than those with EDS, irrespective of the presence or absence of heart failure (1218 ± 944 vs 426 ± 299 msec(2), p = 0.043, and 1029 ± 873 vs 503 ± 533 msec(2), p = 0.003, respectively). ESS scores correlated inversely with VLF power in all (r = -0.294, p = 0.005) and in heart failure subjects (r = -0.468, p = 0.016). Patients with severe OSA but without EDS have higher VLF-HRV than those with EDS. This finding suggests that patients with severe OSA but without EDS have greater sympathetic modulation of HRV than those with EDS that may reflect elevated adrenergically mediated alertness. Taranto Montemurro L; Floras JS; Picton P; Kasai T; Alshaer H; Gabriel JM; Bradley TD. Relationship of heart rate variability to sleepiness in patients with obstructive sleep apnea with and without heart failure.

Obstructive sleep apnea (OSA) is a common disorder which can cause periodic fluctuations in heart rate. To diagnose sleep apnea, some studies analyze electrocardiogram (ECG) signals by adopting chaos-based analysis. This research is going to specifically focus on whether it is possible to use chaos-based analysis of heart rate variability (HRV) signals rather than using chaotic analysis of ECG signals to diagnose OSA. While conventional studies mostly use chaos-based analysis of ECG signals to detect OSA, here, we apply correlation dimension (CD) as a chaotic index to analyze HRV data in OSA patients. For this purpose, 17 patients with OSA and 9 healthy individuals referred to a sleep clinic in Isfahan/Iran are studied, and their HRV time series were extracted from 1-h ECG signals recorded overnight. The preliminary step to calculate CD is phase-space reconstruction of the system based on HRV time series. Corresponding parameters, including embedding dimension and lag time, are estimated optimally using enhanced related methods, and then CD is calculated using Grassberger–Procaccia algorithm. Moreover, to evaluate our results, detrended fluctuation analysis (DFA), one of the well-known nonlinear methods in HRV analysis to detect OSA, is also applied to our data and the result is compared with those obtained from CD analysis of HRV. CD index with P < 0.005 indicates a significant difference in nonlinear dynamics of HRV signals detected from OSA patients and healthy individuals.

Biological signals like Electroencephalography (EEG) and Electrocardiography (ECG) provide very useful information related to brain and heart condition. Spectral analysis of EEG frequency bands and analysis of Heart Rate Variability (HRV) of ECG signal are largely used as a biomarker in studying various pathological conditions. However, the studies on EEG and HRV frequency bands analysis have shown inconsistency in the size of segment length used to extract the features. In the power spectral analysis, the trade-off between time and frequency resolution remain unsolved issue. To increase a frequency resolution and reduced a spectral leakage, a long segment of input data is necessary. However, for a stationary consideration a short segment data is needed. Therefore, in this study we examine the effect of segmentation time window and overlapping in spectral analysis of EEG frequency bands and HRV. The EEG and ECG signals used in this study are collected from the healthy and sleep apnea patients. Five features (delta, theta, alpha, sigma and beta) are extracted from EEG frequency bands and three (LFnu,HFnu, LF/HF) from the HRV by using spectral analysis at various window size and overlapping percentage. The results show the optimum window size for EEG is achieved at 10 sec and 120 sec for HRV analysis.KeywordsEEGECGfrequency bandsHeart Rate Variability

Robots instead of humans work in unstructured environments, expanding the scope of human work. The interactions between humans and robots are indirect through operating terminals. The mental workloads of human increase with the lack of direct perception to the real scenes. Thus, mental workload assessment is important, which could effectively avoid serious accidents caused by mental overloading. In this paper, the operating object is a dual-arm robot. The classification of operator’s mental workload is studied by using the heart rate variability (HRV) signal. First, two kinds of electrocardiogram (ECG) signals are collected from six subjects who performed tasks or maintained a relaxed state. Then, HRV data is obtained from ECG signals and 20 kinds of HRV features are extracted. Last, six different classifications are used for mental workload classification. Using each subject’s HRV signal to train the model, the subject’s mental workload is classified. Average classification accuracy of 98.77% is obtained using the K-Nearest Neighbor (KNN) method. By using the HRV signal of five subjects for training and that of one subject for testing with the Gentle Boost (GB) method, the highest average classification accuracy (80.56%) is obtained. This study has implications for the analysis of HRV signals characteristic of mental workload in different subjects, which could improve operators’ well-being and safety in the human-robot interaction process.