Integral Pulse Frequency Modulation Model Research Articles

Modeling peripheral arterial and venous pressure signals with integral pulse frequency modulation

This paper proposes a novel mathematical modeling framework for peripheral arterial and peripheral venous blood pressure signals from porcine experiments. Peripheral blood pressure signals can be acquired using regular catheters during standard patient treatment. The minimally invasive nature and ubiquitous availability of catheters render it an ideal candidate for various applications. However, there is no analytical model for peripheral blood pressure signals in the literature. We address this issue by proposing a model for these signals under the integral pulse frequency modulation (IPFM) framework. The model incorporates the impacts of physiological phenomena, such as the heartbeat pulse shape variation, heart rate variability, respiratory rate, etc. The model parameters are obtained by applying the IPFM model to experimental data collected from four pigs under different anesthetic dosages. The proposed model can fit the experimental data with Pearson correlation coefficients greater than 0.99 and 0.90 for arterial and venous blood pressure signals, respectively. The performance of model-synthesized data on the classification of two different anesthesia is comparable with experimental data. Parameters like pulse shape and duration can also work as distinguishable features under different anesthesia. We also proposed a way to distinguish respiratory-induced heart rate variability from other causes. Increasing doses of vasodilating anesthesia is similar to going from dehydration to hydration. Thus the results obtained in this study can be extended in distinguishing hydrated and dehydrated subjects. This model can be extended to similar biomedical signals like photoplethysmography, cerebral blood flow velocity, and Doppler waveforms.

Spectral decomposition of heart rate variability using generalized harmonic analysis

In this paper, a method for decomposing harmonics in the spectrum of heart rate variability (HRV) using generalized harmonic analysis (GHA) is introduced. First, a simulated RR interval signal generated by an integral pulse frequency modulation model was decomposed spectra by GHA, Pisarenko harmonic decomposition (PHD), and autoregressive (AR) spectral decomposition model. The spectral profiles were obtained by the GHA, PHD, and AR methods for various numbers of extracted sinusoids and model orders from 1 to 48. The spectral profiles of GHA were the most stable. Of the power values of the sinusoids extracted by each method, it was clear that the power values estimated by GHA were approximately equal to the mean square value and closer than that obtained using the PHD or a fast Fourier transform (FFT). Second, a comparison of the power of the low-frequency (LF) and high-frequency (HF) band components reveals that the values obtained by GHA are similar to those obtained by FFT for the analysis using a real ECG signal. Third, Bland-Altman analysis reveals that LF and HF band power value calculated by the GHA are compatible with ones by the Lomb-Scargle periodogram using MIT-BIH normal sinus rhythm database from short term recordings of 30 min. These results suggest that GHA is a useful tool for calculating the power of a component in the spectral analysis of HRV. The limitations of spectral decomposition by GHA are still discussed.

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

Computational models that generate synthetic heart rate variability (HRV) series constitute important tools for the assessment of the effect of autonomic nervous system activity on cardiovascular control, and for the evaluation of novel algorithms using synthetic data. A widely used technique for synthetic HRV generation is the integral pulse frequency modulation (IPFM) model; however, IPFM relies on the HRV spectral paradigm, which cannot separate sympathetic and vagal oscillations that are overlapped in the low-frequency band (0.04–0.15 Hz). To overcome this limitation, a novel IPFM-inspired model driven by cardiac sympathetic and vagal dynamics estimated from HRV is proposed, where our recently developed sympathetic and parasympathetic activity indices that rely on orthonormal Laguerre expansions of the RR interval autoregressive kernels are exploited. The performance of the proposed model is evaluated by comparing the synthetic vs. real RR interval series in a simulation study involving postural changes, with real HRV data gathered from 10 healthy subjects. Moreover, the performance of the proposed model is compared with that of the standard IPFM to discern different autonomic control states associated with resting and postural changes. The results confirm that the proposed physiologically inspired model adequately predicts RR intervals during resting and postural changes. The proposed model clearly outperforms the standard IPFM method, considering both median error, and maximum error. The developed model provides valuable insights for a better understanding of the sympathovagal activity in the analysis of heartbeat dynamics.

Modeling of Heart Rate Variability Using Time-Frequency Representations

The heart rate variability signal is highly correlated with the respiration even at high workload exercise. It is also known that this phenomenon still exists during increasing exercise. In the current study, we managed to model this correlation during increasing exercise using the time varying integral pulse frequency modulation (TVIPFM) model that relates the mechanical modulation (MM) to the respiration and the cardiac rhythm. This modulation of the autonomic nervous system (ANS) is able to simultaneously decrease sympathetic and increase parasympathetic activity. The TVIPFM model takes into consideration the effect of the increasing exercise test, where the effect of a time-varying threshold on the heart period is studied. Our motivation is to analyze the heart rate variability (HRV) acquired by time varying integral pulse frequency modulation using time frequency representations. The estimated autonomic nervous system (ANS) modulating signal is filtered throughout the respiration using a time varying filtering, during exercise stress testing. And after summing power of the filtered signal, we compare the power of the filtered modulation of the ANS obtained with different time frequency representations: smoothed pseudo Wigner–Ville representation, spectrogram and their reassignments. After that, we used a student t-test to compare the power of heart rate variability in the frequency band of respiration and elsewhere.

Quantifying the lagged Poincaré plot geometry of ultrashort heart rate variability series: automatic recognition of odor hedonic tone.

The application of Poincaré plot analysis to characterize inter-beat interval dynamics has been successfully proposed in the scientific literature for the assessment of humans' physiological states and related aberrations. In this study, we proposed novel descriptors to trace the evolution of Poincaré plot shape over the lags. Their reliability in ultra-short cardiovascular series analysis was validated on synthetic inter-beat series generated through a physiologically plausible integral pulse frequency modulation model. Furthermore, we used the proposed approach for the investigation of the direct relationship between autonomic nervous system (ANS) dynamics and hedonic olfactory elicitation, in a group of 30 healthy subjects. Participants with a similar olfactory threshold were selected, and were asked to score 5-s stimuli in terms of arousal and valence levels according to the Russell's circumflex model of affect. Their ANS response was investigated in 35-s windows after the elicitation. Experimental results showed a gender-specific, high discriminant power of the proposed approach, discerning between pleasant and unpleasant odorants with an accuracy of 83.33% and 73.33% for men and for women, respectively. Graphical Abstract Olfaction plays a crucial role in our life and is strictly related to the Autonomic Nervous System (ANS) activity, which can be monitored studying Heart Rate Variability. We used the Lagged Poincare Plot approach to recognize gender-specific ANS response in 35-second windows after the elicitation through pleasant/unpleasant odorants.

Very‐large‐scale integration implementation of the integral pulse frequency modulation model for spectral estimation of heart rate variability

Heart rate variability (HRV) can be used to assess autonomic control activities. Among the HRV analysis methods, the integral pulse frequency modulation (IPFM) model demonstrates the functional mechanism for the cardiac pacemaker that can explain the generation of heartbeats. In this study, the IPFM model was implemented into a low-cost very-large-scale integration (VLSI) chip, and the active spectrum of HRV was then estimated by solving for the nerve-modulation signal in the model based on the compressed sensing (CS) method. The proposed IPFM chip utilised a time-sharing scheme for hardware resource sharing, a look-up table to calculate the sine and cosine operations, and multiplexers to control the data flow. Furthermore, based on the hardware resource sharing scheme, the proposed chip achieved a low-cost and high-speed design. Implemented with TSMC 90 nm CMOS technology, the proposed IPFM core had an operation frequency of 62.5 MHz with only 9.8 K gate counts. The spectrum of HRV could be effectively estimated through the VLSI implementation of IPFM based on CS.

Investigation of Lagged Poincaré Plot reliability in ultra-short synthetic and experimental Heart Rate Variability series.

This study reports on the reliability of Lagged Poincaré Plot (LPP) parameters calculated from ultra-short cardiovascular time series (from 30 to 180 seconds). ity (HRV) signals, whereas a few studies have studied nonlinear approaches. Particularly, methods derived from the phase-space theory, especially the ones employing multi-lag analyses, are usually considered to be inaccurate with a low number of samples. Here we propose a comprehensive study about LPP, using both synthetic and real RR series. Specifically, we considered 109 5-minutes HRV series: 60 synthetic series generated through the Integral Pulse Frequency Modulation (IPFM) model and 49 experimental series acquired from healthy subjects during resting-state. Three parameters have been extracted through the ellipse-fitting method, SD1, SD2 and S, using ten values of lag. All LPP parameters were estimated by averaging estimates gathered from segments of 30, 120 and 180 seconds, and compared with the once from 5-minute series. Results showed Spearman's correlation coefficients higher than 0.9 in both synthetic and real series. In conclusion, SD1 gave promising results in terms of percentage absolute error, when it was extracted from series with a duration less than three minutes.

심박변이도 해석을 위한 가상 심장박동 발진기의 카오스-임계치 모델 성능 평가

The well-known Integral Pulse Frequency Modulation (IPFM) cardiac oscillator has been used to generate the heart beat fluctuations as a representation of the modulatory autonomic nervous activity in terms of sympathetic and parasympathetic state. The IPFM model produces heartbeats by integrating the modulated sinusoid signals and applying the threshold of unity or chaotic threshold levels. This study aims at evaluating the performance of IPFM model by analyzing the influence of the threshold level with comparatively applying preset threshold of unity and Logistic-map and Henon-map chaotic-threshold. Based on our simulated results with interpreting the spectral features of Heart Rate Variability (HRV), we can conclude that the IPFM model with preset threshold level of unity can generate the optimal heartbeat variations int the sense of clinically valid heartbeats.

Spectral Heart Rate Variability analysis using the heart timing signal for the screening of the Sleep Apnea–Hypopnea Syndrome

Some approaches have been published in the past using Heart Rate Variability (HRV) spectral features for the screening of Sleep Apnea–Hypopnea Syndrome (SAHS) patients. However there is a big variability among these methods regarding the selection of the source signal and the specific spectral components relevant to the analysis. In this study we investigate the use of the Heart Timing (HT) as the source signal in comparison to the classical approaches of Heart Rate (HR) and Heart Period (HP). This signal has the theoretical advantage of being optimal under the Integral Pulse Frequency Modulation (IPFM) model assumption. Only spectral bands defined as standard for the study of HRV are considered, and for each method the so-called LF/HF and VLFn features are derived. A comparative statistical analysis between the different resulting methods is performed, and subject classification is investigated by means of ROC analysis and a Naïve-Bayes classifier. The standard Apnea-ECG database is used for validation purposes. Our results show statistical differences between SAHS patients and controls for all the derived features. In the subject classification task the best performance in the testing set was obtained using the LF/HF ratio derived from the HR signal (Area under ROC curve=0.88). Only slight differences are obtained due to the effect of changing the source signal. The impact of using the HT signal in this domain is therefore limited, and has not shown relevant differences with respect to the use of the classical approaches of HR or HP.

IPFM 모델의 해석을 통한 심박변이도 해석

This study aims at the new analysis of heart beat fluctuations by applying physiological Heart Rate Variability Model with representing the cardiac control system in sympathetic and parasympathetic-coupling oscillator constants, Cs and C p. To find the effects of coupling constants on the beat-to-beat fluctuations, Integral Pulse Frequency Modulation (IPFM) model is adopted to generate the time series data of ECG R-peaks and represent them by poincare scattergram plot in the time domain and HRV in the frequency domain, respectively. The actual poincare plots and HRV spectrum are also analyzed by acquiring the experimental data from the subjects exposed to the emotional-stress invoking environment and the function of the coupling constants are verifi ed in terms of antagonism in sympathetic and parasympathetic activity.

A reweighted ℓ1-minimization based compressed sensing for the spectral estimation of heart rate variability using the unevenly sampled data.

In this paper, a reweighted ℓ1-minimization based Compressed Sensing (CS) algorithm incorporating the Integral Pulse Frequency Modulation (IPFM) model for spectral estimation of HRV is introduced. Knowing as a novel sensing/sampling paradigm, the theory of CS asserts certain signals that are considered sparse or compressible can be possibly reconstructed from substantially fewer measurements than those required by traditional methods. Our study aims to employ a novel reweighted ℓ1-minimization CS method for deriving the spectrum of the modulating signal of IPFM model from incomplete RR measurements for HRV assessments. To evaluate the performance of HRV spectral estimation, a quantitative measure, referred to as the Percent Error Power (PEP) that measures the percentage of difference between the true spectrum and the spectrum derived from the incomplete RR dataset, was used. We studied the performance of spectral reconstruction from incomplete simulated and real HRV signals by experimentally truncating a number of RR data accordingly in the top portion, in the bottom portion, and in a random order from the original RR column vector. As a result, for up to 20% data truncation/loss the proposed reweighted ℓ1-minimization CS method produced, on average, 2.34%, 2.27%, and 4.55% PEP in the top, bottom, and random data-truncation cases, respectively, on Autoregressive (AR) model derived simulated HRV signals. Similarly, for up to 20% data loss the proposed method produced 5.15%, 4.33%, and 0.39% PEP in the top, bottom, and random data-truncation cases, respectively, on a real HRV database drawn from PhysioNet. Moreover, results generated by a number of intensive numerical experiments all indicated that the reweighted ℓ1-minimization CS method always achieved the most accurate and high-fidelity HRV spectral estimates in every aspect, compared with the ℓ1-minimization based method and Lomb's method used for estimating the spectrum of HRV from unevenly sampled RR data.

New Modeling for Generation of Normal and Abnormal Heart Rate Variability Signals

This research is performed based on the modeling of biological signals. We can produce Heart Rate (HR) and Heart Rate Variability (HRV) signals synthetically using the mathematical relationships which are used as input for the Integral Pulse Frequency Modulation (IPFM) model. Previous researches were proposed same methods such as one model of ECG signal synthetically based on RBF neural network, a model based on IPFM with random threshold, method was based on the estimation of produced signals which are dependent on autonomic nervous system using IPFM model with fixed threshold, a new method based on the theory of vector space that based on time-varying uses of IPMF model (TVTIPMF) and special functions, and two different methods for producing HRV signals with controlled characteristics and structure of time-frequency (TF) for using non-stationary HRV analysis. In this paper, several chaotic maps such as Logistic Map, Henon Map, Lorenz and Tent Map have been used. Also, effects of sympathetic and parasympathetic nervous system and an internal input to the SA node and their effects in HRV signals were evaluated. In the proposed method, output amount of integrator in IPFM model was compared with chaotic threshold level. Then, final output of IPFM model was characterized as the HR and HRV signal. So, from HR and HRV signals obtaining from this model, linear features such as Mean, Median, Variance, Standard Deviation, Maximum Range, Minimum Range, Mode, Amplitude Range and frequency spectrum, and non-linear features such as Lyapunov Exponent, Shanon Entropy, log Entropy, Threshold Entropy, sure Entropy and mode Entropy were extracted from artificial HRV and compared them with characteristics as extracted from natural HRV signal. Also, in this paper two patients that called high sympathetic Balance and Cardiovascular Autonomy Neuropathy (CAN) which is detected and evaluated by HRV signals were simulated. These signals by changing the values of the some coefficients of the normal simulated signal and with extracted frequency feature from these signals were simulated. For final generation of these abnormal signals, frequency features such as energy of low frequency band (EL), energy of high frequency band (HL), ratio of energy in low frequency band to the energy in high frequency band (EL/EH), ratio of energy in low frequency band to the energy in all frequency band (EL/ET) and ratio of energy in high frequency band to the energy in all frequency band (EH/ET) from abnormal signals were extracted and compared with these extracted values from normal signals. The results were closely correlated with the real data which confirm the effectiveness of the proposed model. Various signals derived from the output of this model can be used for final analysis of the HRV signals, such as arrhythmia detection and classification of ECG and HRV signals. One of the applications of the proposed model is the easy evaluation of diagnostic ECG signal processing devices. Such a model can also be used in signal compression and telemedicine application.

Compressed Sensing Technology-Based Spectral Estimation of Heart Rate Variability Using the Integral Pulse Frequency Modulation Model

In this paper, a compressed sensing (CS)-based spectral estimation of heart rate variability (HRV) using the integral pulse frequency modulation (IPFM) model is introduced. Previous research in the literature indicated that the IPFM model is widely accepted as a functional description of the cardiac pacemaker, and thus, very useful in modeling the mechanism by which the autonomic nervous system modulates the heart rate (HR). On the other hand, recently CS becomes an emerging technology that has attracted great attention since it is capable of acquiring and reconstructing signals that are considered sparse or compressible, even when the number of measurements is small. Using the IPFM model, we here present a CS-based algorithm for deriving the amplitude spectrum of the modulating signal for HRV assessments. In fact, the application of the CS method into HRV spectral estimation is unprecedented. Numerical results produced by a real RR database of PhysioNet demonstrated that the proposed approach can robustly provide high-fidelity HRV spectral estimates, even under the situation of a degree of incompleteness in the RR data caused by ectopic or missing beats.

Influence of Running Stride Frequency in Heart Rate Variability Analysis During Treadmill Exercise Testing

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.

The Integral Pulse Frequency Modulation Model With Time-Varying Threshold: Application to Heart Rate Variability Analysis During Exercise Stress Testing

In this paper, an approach for heart rate variability analysis during exercise stress testing is proposed based on the integral pulse frequency modulation (IPFM) model, where a time-varying threshold is included to account for the nonstationary mean heart rate. The proposed technique allows the estimation of the autonomic nervous system (ANS) modulating signal using the methods derived for the IPFM model with constant threshold plus a correction, which is shown to be needed to take into account the time-varying mean heart rate. On simulations, this technique allows the estimation of the ANS modulation on the heart from the beat occurrence time series with lower errors than the IPFM model with constant threshold (1.1% ± 1.3% versus 15.0% ± 14.9%). On an exercise stress testing database, the ANS modulation estimated by the proposed technique is closer to physiology than that obtained from the IPFM model with constant threshold, which tends to overestimate the ANS modulation during the recovery and underestimate it during the initial rest.

Detection Performance and Risk Stratification Using a Model-Based Shape Index Characterizing Heart Rate Turbulence

A detection-theoretic approach to quantify heart rate turbulence (HRT) following a ventricular premature beat is proposed and validated using an extended integral pulse frequency modulation (IPFM) model which accounts for HRT. The modulating signal of the extended IPFM model is projected into a three-dimensional subspace spanned by the Karhunen-Loève basis functions, characterizing HRT shape. The presence or absence of HRT is decided by means of a likelihood ratio test, the Neyman-Pearson detector, resulting in a quadratic detection statistic. Using a labeled dataset built from different interbeat interval series, detection performance is assessed and found to outperform the two widely used indices: turbulence onset (TO) and turbulence slope (TS). The ability of the proposed method to predict the risk of cardiac death is evaluated in a population of patients (n = 90) with ischemic cardiomyopathy and mild-to-moderate congestive heart failure. While both TS and the novel HRT index differ significantly in survivors and cardiac death patients, mortality analysis shows that the latter index exhibits much stronger association with risk of cardiac death (hazard ratio = 2.8, CI = 1.32-5.97, p = 0.008). It is also shown that the model-based shape indices, but not TO and TS, remain predictive of cardiac death in our population when computed from 4-h instead of 24-h ambulatory ECGs.

Model-Based Detection of Heart Rate Turbulence Using Mean Shape Information

A generalized likelihood ratio test (GLRT) statistic is proposed for detection of heart rate turbulence (HRT), where a set of Karhunen-LoEve basis functions models HRT. The detector structure is based on the extended integral pulse frequency modulation model that accounts for the presence of ectopic beats and HRT. This new test statistic takes a priori information regarding HRT shape into account, whereas our previously presented GLRT detector relied solely on the energy contained in the signal subspace. The spectral relationship between heart rate variability (HRV) and HRT is investigated for the purpose of modeling HRV "noise" present during the turbulence period, the results suggesting that the white noise assumption is feasible to pursue. The performance was studied for both simulated and real data, leading to results which show that the new GLRT detector is superior to the original one as well as to the commonly used parameter turbulence slope (TS) on both types of data. Averaging ten ventricular ectopic beats, the estimated detection probability of the new detector, the previous detector, and TS were found to be 0.83, 0.35, and 0.41, respectively, when the false alarm probability was held fixed at 0.1.

A comparison of two Hilbert spectral analyses of heart rate variability

The present paper compares the performance of two Hilbert spectral analyses when applied to a synthetic RR series from a nonstationary integral pulse frequency modulation model and to real RR series from a dataset of normal sinus arrhythmia. The Hilbert-Huang transformation based on empirical mode decomposition is compared to the presently introduced Hilbert-Olhede-Walden transformation based on stationary wavelet packet decomposition. The comparison gives consistent results pointing to a superior performance of the Hilbert-Olhede-Walden transformation showing 33-163 times smaller deviations when estimating the instantaneous frequency traces of the synthetic RR series. Artificial fluctuations caused by mode mixing in the Hilbert-Huang spectrum are seen in both the synthetic and real RR series. It can be concluded that the instantaneous frequencies and amplitudes estimated by the Hilbert-Huang transformation should be interpreted with caution when investigating heart rate variability.

Model-Based Detection of Heart Rate Turbulence

In this study, the integral pulse frequency modulation model is extended to account for the presence of ectopic beats and heart rate turbulence (HRT). Based on this model, a new statistical approach to the detection and characterization of HRT is presented. The detector structure involves a set of Karhunen-LoEve basis functions and a generalized likelihood ratio test statistic T(x) . The three most significant basis functions reflect the difference in heart rate prior to a ventricular ectopic beat (VEB) compared to after HRT, the "average" HRT, and a delayed contribution to HRT, respectively. Detector performance was studied on both simulated and ECG signals. Three different simulations were performed for the purpose of studying the influence of SNR, QRS jitter, and ECG sampling rate. The results show that the HRT test statistic T(x) performs better in all simulations than do the commonly used parameters known as turbulence onset (TO) and turbulence slope (TS). In order to attain the same performance as T(x), TS needs at least twice the amount of VEBs for averaging, and TO at least four times. The detector performance was also studied on ECGs acquired from eight patients who underwent hemodialysis treatment with the goal to discriminate between patients considered to be hypotension-resistant (HtR) and hypotension-prone (HtP). The results show that T(x) exhibits larger mean values in HtR patients than in HtP, suggesting that HRT is mostly present in HtR patients. The overlap between the two groups was larger for TO and TS than for T(x).

Spectrum of the nonstationary electromyographic signal modelled with integral pulse frequency modulation and its application to estimating neural drive information

The spectrum of nonstationary electromyographic signal (EMG) is investigated, from which the error for neural drive information estimation from nonstationary EMG is studied in terms of signal-to-noise ratio (SNR), in analytical, numerical simulation, and experimental work. The signal refers to the neural drive information embedded within the nonstationary EMG, and noise refers to other portions of EMG that induce error in the estimation. The analytical expressions for the SNRs of force-modulated EMG with both single and multiple motor units (MU) are derived based on a sinusoidal integral pulse frequency modulation (IPFM) model. It is shown that the previously developed SNR expressions for stationary (unmodulated) EMG are special cases of the formulas presented here. The SNR results obtained from numerical simulated EMG agree very well with the analytical result. Results from nonstationary (modulated) surface EMG obtained from seven subjects also match the analytical and simulation results reasonably well. The results obtained from this work establish an analytical framework in studying and estimating the neural drive information contained in the EMG in the context of anisotonic and isometric contractions. Through the analytical study, the effects of different physiological parameters are identified, thus providing theoretical guidelines for developing advanced signal processing methods for nonstationary EMG in applications such as prosthesis control.