Estimation of respiratory rate from photoplethysmogram data using time-frequency spectral estimation.

We present a new method that uses the pulse oximeter signal to estimate the respiratory rate. The method uses a recently developed time-frequency spectral estimation method, variable-frequency complex demodulation (VFCDM), to identify frequency modulation (FM) of the photoplethysmogram waveform. This FM has a measurable periodicity, which provides an estimate of the respiration period. We compared the performance of VFCDM to the continuous wavelet transform (CWT) and autoregressive (AR) model approaches. The CWT method also utilizes the respiratory sinus arrhythmia effect as represented by either FM or AM to estimate respiratory rates. Both CWT and AR model methods have been previously shown to provide reasonably good estimates of breathing rates that are in the normal range (12-26 breaths/min). However, to our knowledge, breathing rates higher than 26 breaths/min and the real-time performance of these algorithms are yet to be tested. Our analysis based on 15 healthy subjects reveals that the VFCDM method provides the best results in terms of accuracy (smaller median error), consistency (smaller interquartile range of the median value), and computational efficiency (less than 0.3 s on 1 min of data using a MATLAB implementation) to extract breathing rates that varied from 12-36 breaths/min.

Statistical approach to quantify the presence of phase coupling using the bispectrum.

The bispectrum is a method to detect the presence of phase coupling between different components in a signal. The traditional way to quantify phase coupling is by means of the bicoherence index, which is essentially a normalized bispectrum. The major drawback of the bicoherence index (BCI) is that determination of significant phase coupling becomes compromised with noise and low coupling strength. To overcome this limitation, a statistical approach that combines the bispectrum with a surrogate data method to determine the statistical significance of the phase coupling is introduced. Our method does not rely on the use of the BCI, where the normalization procedure of the BCI is the major culprit in its poor specificity. We demonstrate the accuracy of the proposed approach using simulation examples that are designed to test its robustness against noise contamination as well as varying levels of phase coupling. Our results show that the proposed approach outperforms the bicoherence index in both sensitivity and specificity and provides an unbiased and statistical approach to determining the presence of quadratic phase coupling. Application of this new method to renal hemodynamic data was applied to renal stop flow pressure data obtained from normotensive (N = 7) and hypertensive (N = 7) rats. We found significant nonlinear interactions in both strains of rats with a greater magnitude of coupling and smaller number of interaction peaks in normotensive rats than hypertensive rats.

Can photoplethysmography variability serve as an alternative approach to obtain heart rate variability information?

Heart rate variability (HRV), extracted from an electrocardiogram, is known to be a noninvasive indicator reflecting the dynamic interplay between perturbations to cardiovascular function and the dynamic response of the cardiovascular regulatory system. Photoplethysmography (PPG) is a noninvasive method to monitor arterial oxygen saturation on a continuous basis. Given the rich cardiovascular information in the PPG signal, and the ubiquity and simplicity of pulse oximetry, we are investigating the feasibility of acquiring dynamics pertaining to the autonomic nervous system from PPG waveforms. To do this, we are quantifying PPG variability (PPGV). Detailed algorithmic approaches for extracting accurate PPGV signals are presented. We compare PPGV to HRV by computing time and frequency domain parameters often associated with HRV measurements, as well as approximate entropy calculations. Our results demonstrate that the parameters of PPGV are highly correlated with the parameters of HRV. Thus, our results indicate that PPGV could be used as an alternative measurement of HRV.

Autonomic nervous nonlinear interactions lead to frequency modulation between low- and high-frequency bands of the heart rate variability spectrum.

Cardiac sympathetic and parasympathetic neural activities have been found to interact with each other to efficiently regulate the heart rate and maintain homeostasis. Quantitative and noninvasive methods used to detect the presence of interactions have been lacking, however. This may be because interactions among autonomic nervous systems are nonlinear and nonstationary. The goal of this work was to identify nonlinear interactions between the sympathetic and parasympathetic nervous systems in the form of frequency and amplitude modulations in human heart rate data. To this end, wavelet analysis was performed, followed by frequency analysis of the resultant wavelet decomposed signals in several frequency brackets defined as very low frequency (f < 0.04 Hz), low frequency (LF; 0.04-0.15 Hz), and high frequency (HF; 0.15-0.4 Hz). Our analysis suggests that the HF band is significantly modulated by the LF band in the heart rate data obtained in both supine and upright body positions. The strength of modulations is stronger in the upright than supine position, which is consistent with elevated sympathetic nervous activities in the upright position. Furthermore, significantly stronger frequency modulation than in the control condition was also observed with the cold pressor test. The results with the cold pressor test, as well as the body position experiments, further demonstrate that the frequency modulation between LF and HF is most likely due to sympathetic and parasympathetic nervous interactions during sympathetic activations. The modulation phenomenon suggests that the parasympathetic nervous system is frequency modulated by the sympathetic nervous system. In this study, there was no evidence of amplitude modulation among these frequencies.

Closed-loop nonlinear system identification via the vector optimal parameter search algorithm: application to heart rate baroreflex control.

The vector optimal parameter search (VOPS) and the constrained optimal parameter search (COPS) are recently developed algorithms for closed-loop linear system identification. We extend both algorithms to be applicable to a closed-loop nonlinear system, which is characterized by a vector nonlinear autoregressive model. Monte Carlo simulations of nonlinear closed-loop systems were performed to compare the performance of the VOPS to the widely utilized vector least squares (VLS), the COPS and the total least squares (TLS) approaches. The relative error and linear transfer functions are computed to determine the accuracy of each method. The comparative results show that both the VOPS and COPS algorithms provide far superior parameter estimates than does the VLS for all simulation examples considered. The TLS provides better estimates than the VOPS, COPS and VLS when there is only observation noise present in the data. However, the performance of the TLS degrades considerably when the data are corrupted by dynamic noise. The clinical applicability of the two extended methods is examined by applying them to a classical physiological closed-loop system, the heart rate baroreflex. It was found that while both control and blockade of parasympathetic system conditions are dominated by linear dynamics, more nonlinearity was observed in the latter. This observation is statistically supported by the calculation of the mutual information of the data and their surrogates.

A high resolution approach to estimating time-frequency spectra and their amplitudes.

A high resolution approach to estimating time-frequency spectra (TFS) and associated amplitudes via the use of variable frequency complex demodulation (VFCDM) is presented. This is a two-step procedure in which the previously developed time-varying optimal parameter search (TVOPS) technique is used to obtain TFS, followed by using the VFCDM to obtain even greater TFS resolution and instantaneous amplitudes associated with only the specific frequencies of interest. This combinational use of the TVOPS and the VFCDM is termed the TVOPS-VFCDM. Simulation examples are provided to demonstrate the performance of the TVOPS-VFCDM for high resolution TFS as well as instantaneous amplitude estimation. The simulation results show that the TVOPS-VFCDM approach provides the highest resolution and most accurate amplitude estimates when compared to the smoothed pseudo Wigner-Ville, continuous wavelet transform and Hilbert-Huang transform methods. Application of the TVOPS-VFCDM to renal blood flow data indicates some promise of a quantitative approach to understanding the dynamics of renal autoregulatory mechanisms as well as a possible approach to quantitatively discriminating between different strains of rats.

Estimation of time-varying coherence function using time-varying transfer functions.

We introduce a new method to estimate reliable time-varying coherence functions (TVCF) for causal systems. The technique is based on our previously developed method to estimate time-varying transfer functions (TVTF), known as the time-varying optimal parameter search algorithm [Zou, R., H. Wang, and K. H. Chon. A robust time-varying identification algorithm using basis functions. Ann. Biomed. Eng. 31: 840-853, 2003]. The TVCF is estimated by the multiplication of two TVTFs. The two TVTFs are obtained using signal x as the input and signal y as the output to produce the first TVTF, and signal y as the input and signal x as the output to produce the second TVTF. Demonstration of the feasibility and efficacy of the proposed approach is provided with both simulation examples and application to renal blood flow and pressure data. The proposed approach provides higher time-frequency resolution TVCF than afforded by the short time Fourier transform based TVCF.

A method for segmentation of switching dynamic modes in time series.

A method to identify switching dynamics in time series, based on Annealed Competition of Experts algorithm (ACE), has been developed by Kohlmorgen et al. Incorrect selection of embedding dimension and time delay of the signal significantly affect the performance of the ACE method, however. In this paper, we utilize systematic approaches based on mutual information and false nearest neighbor to determine appropriate embedding dimension and time delay. Moreover, we obtained further improvements to the original ACE method by incorporating a deterministic annealing approach as well as phase space closeness measure. Using these improved implementations, we have enhanced the performance of the ACE algorithm in determining the location of the switching of dynamic modes in the time series. The application of the improved ACE method to heart rate data obtained from rats during control and administration of double autonomic blockade conditions indicate that the improved ACE algorithm is able to segment dynamic mode changes with pinpoint accuracy and that its performance is superior to the original ACE algorithm.

Identification of transient renal autoregulatory mechanisms using time-frequency spectral techniques.

Identification of the two principal mediators of renal autoregulation from time-series data is difficult, as both the tubuloglomerular feedback (TGF) and myogenic (MYO) mechanisms interact and share a common effector, the afferent arteriole. Moreover, although both mechanisms can exhibit oscillations in well-characterized frequency bands, these systems often operate in nonoscillatory states not detectable by frequency-domain analysis. To overcome these difficulties, we have developed a new approach to the characterization of the TGF and MYO systems. A laser Doppler probe is used to measure fluctuations in local cortical blood flow (CBF) in response to spontaneous changes in blood pressure (BP) and to large imposed perturbations in BP, which elicit strong, simultaneous, transient, oscillatory blood flow responses. These transient responses are identified by high-resolution time-frequency spectral analysis of the time-series data. In this report, we compare four different time-frequency spectral techniques (the short-time Fourier transform (STFT), smoothed pseudo Wigner-Ville, and two recently developed methods: the Hilbert-Huang transform and time varying optimal parameter search (TVOPS)) to determine which of these four methods is best suited for the identification of transient oscillations in renal autoregulatory mechanisms. We found that TVOPS consistently provided the best performance in both simulation examples and identification of the two autoregulatory mechanisms in actual data. While the STFT suffers in time and frequency resolution as compared to the other three methods, it was able to identify the two autoregulatory mechanisms. Taken together, our experience suggests a two level approach to the analysis of renal blood flow (RBF) data: STFT to obtain a low-resolution time-frequency spectrogram, followed by the use of a higher resolution technique, such as the TVOPS, if even higher time-frequency resolution of the transient responses is required.

Multiple time-varying dynamic analysis using multiple sets of basis functions.

We extend a recently developed algorithm that expands the time-varying parameters onto a single set of basis functions, to multiple sets of basis functions. This feature allows the capability to capture many different dynamics that may be inherent in the system. A single set of basis functions that has its own unique characteristics can best capture dynamics of the system that have similar features. Therefore, for systems that have multiple dynamics, the use of a single set of basis functions may not be adequate. Computer simulation examples do indeed show the benefit of using multiple sets of basis functions over the single set of basis functions for cases with many switching dynamics. Moreover, the proposed method remains accurate even under significant noise contamination. Application of the proposed approach to blood pressure data likewise indicate better tracking capability of the two sets of basis function than the recursive least squares or a single set of basis functions.

A new approach to closed-loop linear system identification via a vector autoregressive model.

A new vector autoregressive (VAR) model algorithm is developed for closed-loop identification. The new VAR approach is an extension of a recently developed algorithm, named the optimal parameter search (OPS), thus, we call the new technique VOPS, for vector OPS. Monte Carlo simulations of closed-loop systems were performed to compare the performance of VOPS to the widely utilized vector least squares (VLS) and vector fast orthogonal search (VFOS) approaches. In addition, we examined the effect on parameter estimates obtained via open-loop identification techniques, when using data from closed-loop systems. Comparative results show that both the VOPS and VFOS algorithms produce far more accurate parameter estimates than does the VLS. Furthermore, open-loop identification via univariate OPS and to a lesser extent univariate FOS for closed-loop systems, does not adversely affect the accuracy of the parameter estimates. An open-loop identification via the univariate least-squares method for closed-loop systems showed the most deleterious effect on the accuracy of the parameter estimates. In addition to developing the VOPS algorithm, we also developed approaches termed constrained OPS (COPS) and constrained FOS (CFOS). For closed-loop systems considered in this paper, both COPS and CFOS resulted in more accurate parameter estimates (less biased and more efficient) than did VLS, VFOS, and VOPS.

Blood pressure of endothelin-3 null (-/-) knockout mice and endothelin A receptor null (-/-) knockout mice under anaesthesia.

Blood pressure (BP) and heart rate (HR) in endothelin-3 (ET-3) null (-/-) knockout mice and ET(A) receptor (-/-) mice were measured using the servo null pressure measuring technique under halothane anaesthesia. In infant ET-3 (-/-) mice (2-3 weeks old), mean BP and HR were 55+/-2 mmHg and 436+/-30 beats/min respectively. These values were not different from those in age-matched wild-type mice (53+/-3 mmHg and 430+/-18 beats/min respectively). Baroreflex sensitivity, which was calculated as the slope of the relationship between systolic BP and RR interval on an ECG, was also similar in ET-3 (-/-) mice (0.84+/-0.20 ms/mmHg) and wild-type mice (1.07+/-0.38 ms/mmHg). ET(A) receptor (-/-) mice were obtained by caesarean section on the expected day of delivery and tracheotomized, so that they would live for more than 24 h. Mean BP and HR in ET(A) receptor (-/-) mice were 15+/-1 mmHg and 333+/-6 beats/min respectively. These values were not different from those in age-matched, similarly treated wild-type mice (16+/-3 mmHg and 308+/-10 beats/min respectively). Baroreflex sensitivity in the newborn ET(A) receptor (-/-) mice (0.45+/-0.15 ms/mmHg) and wild-type mice (0.31+/-0.06 ms/mmHg) were very low compared with the values in infant wild-type mice, but not different between the mutant mice and their littermates. Moreover, HR in awake ET(A) receptor (-/-) mice (396+/-13 beats/min) was not different from that in wild-type mice (409+/-13 beats/min). These results show that the ET(A) receptor and ET-3 are not involved in cardiovascular regulation, at least during the very early life of the mice. A possible involvement of the ET(A) receptor in BP regulation, if any, seems to occur at later times and/or in some pathological settings.

Changes in blood pressure and heart rate by repetitive transcranial magnetic stimulation in rats.

We examined whether repetitive transcranial magnetic stimulation (rTMS) could influence blood pressure (BP) and heart rate (HR) in rats and the possible mechanisms involved. In urethane anesthetized Wistar-Kyoto rats, BP and HR were recorded from the femoral artery around the point of rTMS at a frequency of 10 Hz and an intensity of 1.88-2.44 Tesla. rTMS but not sham stimulation reduced BP and HR by approximately 20 mmHg and approximately 30 beats/min, respectively (n = 22). Pretreatment with an alpha-adrenoceptor antagonist, prazosin, or a beta-adrenoceptor antagonist, atenolol, significantly attenuated the response, whereas the muscarinic acetylcholine antagonist, atropine, had little effect. An inhibitory effect of prazosin on BP reduction by rTMS was also observed when basal BP was preserved by a combination of prazosin and a nitric oxide synthase inhibitor, N-monomethyl-L-arginine. These results suggest that rTMS reduces BP through the inhibition of the sympathetic nervous system but not through activation of the parasympathetic nervous system.

A stochastic nonlinear autoregressive algorithm reflects nonlinear dynamics of heart-rate fluctuations.

Current methods for detecting nonlinear determinism in a time series require long and stationary data records, as most of them assume that the observed dynamics arise only from the internal, deterministic workings of the system, and the stochastic portion of the signal (the noise component) is assumed to be negligible. To explicitly account for the stochastic portion of the data we recently developed a method based on a stochastic nonlinear autoregressive (SNAR) algorithm. The method iteratively estimates nonlinear autoregressive models for both the deterministic and stochastic portions of the signal. Subsequently, the Lyapunov exponents (LE) are calculated for the estimated models in order to examine if nonlinear determinism is present in the deterministic portion of the fitted model. To determine if nonlinear dynamic analysis of heart-rate fluctuations can be used to assess arrhythmia susceptibility by predicting the outcome of invasive cardiac electrophysiologic study (EPS), we applied the SNAR algorithm to noninvasively measured resting sinus-rhythm heart-rate signals obtained from 16 patients. Our analysis revealed that a positive LE was highly correlated to a patient with a positive outcome of EPS. We found that the statistical accuracy of the SNAR algorithm in predicting the outcome of EPS was 88% (sensitivity=100%, specificity=75%, positive predictive value=80%, negative predictive value=100%, p=0.0019). Our results suggest that the SNAR algorithm may serve as a noninvasive probe for screening high-risk populations for malignant cardiac arrhythmias.