Use of amplitude-modulated breathing for assessment ofcardiorespiratory frequency response within subrespiratory frequencies

Presents a new technique which uses amplitude-modulated breathing patterns to obtain estimates of frequency response between respiration and heart rate within subrespiratory frequencies. Frequency response between respiration and heart rate has been previously estimated using broadband respiration and metronomic breathing. However, the estimates obtained using these techniques show low coherence between respiration and heart rate within the subrespiratory frequencies (<0.12-0.15 Hz). The advantages of amplitude-modulated breathing are: enhancement in the degree of perturbation within subrespiratory frequencies as indicated by relatively higher coherencies between respiration and heart rate (≅0.7), and the subjects do not have to breathe at very low breathing frequencies or resort to breath holds. Use of a squared sine wave carrier modulated by sinusoidal functions enabled the authors to obtain energy distributions at subrespiratory frequencies without using demodulation. Results obtained at 8 subrespiratory frequencies from 10 subjects show that the new technique is easy to implement and produces relatively higher coherence between respiration and heart rate. The advantage of the new technique in terms of enhancing the level of perturbations within subrespiratory frequencies is particularly important, because it is in this frequency range that the interpretation of variability in heart rate in terms of autonomic origins is incompletely understood and is confounded by respiratory interactions     

Difference equation representation of chirp signals andinstantaneous frequency/amplitude estimation

We present a time-varying coefficient difference equation representation for sinusoidal signals with time-varying amplitudes and frequencies. We first obtain a recursive equation for a single chirp signal. Then, using this result, we obtain time-varying coefficient difference equation representations for signals composed of multiple chirp signals. We analyze these equations using the skew-shift operators. We show that the phases of the poles of the difference equations produce instantaneous frequencies (IF), and the magnitudes are proportional to the ratio of successive values of the instantaneous amplitudes (IA). Then algorithms are presented for the estimation of instantaneous frequencies and instantaneous amplitudes for multicomponent signals composed of chirps using the difference equation representation. The first algorithm we propose is based on the skew-shift operators. Next we derive the conditions under which we can use the so-called frozen-time approach. We propose an algorithm for IF and IA estimation based on the frozen-time approach. Then we propose an automatic signal separation method. Finally, we apply the proposed algorithms to single and multicomponent signals and compare the results with some existing methods     

A method for the analysis of respiratory sinus arrhythmia using continuous wavelet transforms

A continuous wavelet transform-based method is presented to study the nonstationary strength and phase delay of the respiratory sinus arrhythmia (RSA). The RSA is the cyclic variation of instantaneous heart rate at the breathing frequency. In studies of cardio-respiratory interaction during sleep, paced breathing or postural changes, low respiratory frequencies, and fast changes can occur. Comparison on synthetic data presented here shows that the proposed method outperforms traditional short-time Fourier-transform analysis in these conditions. On the one hand, wavelet analysis presents a sufficient frequency-resolution to handle low respiratory frequencies, for which time frames should be long in Fourier-based analysis. On the other hand, it is able to track fast variations of the signals in both amplitude and phase for which time frames should be short in Fourier-based analysis.     

Estimation of the heart respiratory motion with applications for cone beam computed tomography imaging: a simulation study

Computed tomography (CT) reconstruction methods assume imaging of static objects; object movement during projection data acquisition causes tomogram artifacts. The continuously moving heart, therefore, represents a complicated imaging case. The associated problems due to the heart beating can be overcome either by using very short projection acquisition times, during which the heart may be considered static, or by ECG-gated acquisition. In the latter case, however, the acquisition of a large number of projections may not be completed in a single breath hold, thus heart displacement occurs as an additional problem. This problem has been addressed by applying heart motion models in various respiratory motion compensation algorithms. Our paper focuses on cone beam computed tomography (CBCT), performed in conjunction with isocentric, fluoroscopic equipment, and continuous ECG and respiratory monitoring. Such equipment is used primarily for in-theater three-dimensional (3-D) imaging and benefits particularly from the recent developments in flat panel detector technologies. The objectives of this paper are: (i) to develop a model for the motion of the heart due to respiration during the respiratory cycle; (ii) to apply this model to the tomographic reconstruction algorithm, in order to account for heart movement due to respiration in the reconstruction; and (iii) to initially evaluate this method by means of simulation studies. Based on simulation studies, we were able to demonstrate that heart displacement due to respiration can be estimated from the same projection data, required for a CBCT reconstruction. Our paper includes semiautomatic segmentation of the heart on the X-ray projections and reconstruction of a convex 3-D-heart object that performs the same motion as the heart during respiration, and use of this information into the CBCT reconstruction algorithm. The results reveal significant image quality improvements in cardiac image reconstruction.     

A programmable clock generator that uses noise shaping and itsapplication in switched-capacitor filters

A programmable digital clock generator that produces a wide range of clock frequencies with fine resolution is described. The clock generator consists of a noise-shaping control loop and a number-controlled oscillator. The generated clock has a time-varying period. When this clock is used as the sampling clock in a switched-capacitor filter (SCF) to set its frequency response, the time-varying period causes nonuniform sampling, which is acceptable under certain conditions that are described. Measured performance of a 2-μm CMOS implementation of the clock generator is presented. Also, measured data for the clock generator driving two SCF's are reported     

A robust method for ECG-based estimation of the respiratory frequency during stress testing

A robust method is presented for electrocardiogram (ECG)-based estimation of the respiratory frequency during stress testing. Such ECGs contain highly nonstationary noise and exhibit changes in QRS morphology which, when combined with the dynamic nature of the respiratory frequency, make most existing methods break down. The present method exploits the oscillatory pattern of the rotation angles of the heart's electrical axis as induced by respiration. The series of rotation angles, obtained from least-squares loop alignment, is subject to power spectral analysis and estimation of the respiratory frequency. Robust techniques are introduced to handle the nonstationary properties of exercise ECGs. The method is evaluated by means of both simulated signals, and ECG/airflow signals recorded from 14 volunteers and 20 patients during stress testing. The resulting respiratory frequency estimation error is, for simulated signals, equal to 0.5% +/- 0.2%, mean +/- SD (0.002 +/- 0.001 Hz), whereas the error between respiratory frequencies of the ECG-derived method and the airflow signals is 5.9% +/- 4% (0.022 +/- 0.016Hz). The results suggest that the method is highly suitable for analysis of noisy ECG signals recorded during stress testing.     

The effect of respiration-induced heart movements on the ECG

We present a model describing the rotation of the cardiac vector as a possible mechanism resulting in the presence of respiratory information in the ECG. The way in which this information is revealed is analyzed and the predictions subjected to qualitative experimental assessment via spectral analysis. The results show that respiratory frequencies occur in the ECG spectrum due to heart movement. By measuring on a patient wearing a pacemaker and ventilated to control respiratory rate we show that even in the absence of respiratory sinus arrhythmia (RSA) there is a baseband information in the ECG spectrum, attributable neither to electrode artifacts nor to emg, and sidebands from the respiratory cycle.     

Anharmonic frequency analysis: the complement to Fourier analysis

Fourier analysis of a finite time series allocates amplitudes and phases to a given set of frequencies which are integer multiples of a basic frequency determined by the length of the time series. Anharmonic frequency analysis (Afa)collects the spectral components between those frequencies and the results are the average amplitude and phase for each band defined by two consecutive frequencies. A repetition of the transform involved for a later reference time determines the effective frequency within each band by the time change of the phase. This process is by far superior to Fourier analysis especially if unknown discrete frequencies are present in the time series and those frequencies are not harmonics of one common basic frequency. The principles of this method, some of its properties and a few results are presented.     

A dynamical model for generating synthetic electrocardiogram signals

A dynamical model based on three coupled ordinary differential equations is introduced which is capable of generating realistic synthetic electrocardiogram (ECG) signals. The operator can specify the mean and standard deviation of the heart rate, the morphology of the PQRST cycle, and the power spectrum of the RR tachogram. In particular, both respiratory sinus arrhythmia at the high frequencies (HFs) and Mayer waves at the low frequencies (LFs) together with the LF/HF ratio are incorporated in the model. Much of the beat-to-beat variation in morphology and timing of the human ECG, including QT dispersion and R-peak amplitude modulation are shown to result. This model may be employed to assess biomedical signal processing techniques which are used to compute clinical statistics from the ECG.     

On the time-frequency analysis based filtering

Efficient processing of nonstationary signals requires time-varying approach. An interesting research area within this approach is time-varying filtering. Since there is a certain amount of freedom in the definition of time-varying spectra, several definitions and solutions for the time-varying filtering have been proposed so far. Here we will consider the Wigner distribution based time- varying filtering form defined by using the Weyl correspondence. Its slight modification will be proposed and justified in the processing of noisy frequency modulated signals based on a single signal realization. An algorithm for the efficient determination of the filters ’region of support in the time-frequency plane, in the case of noisy signals, will be presented. In the second part of the paper, the theory is applied on the filtering of multicomponent noisy signals. The S-method is used as a tool for the filters’region of support estimation in this case. This method, combined with the presented algorithm, enables very efficient time-varying filtering of the multicomponent noisy signals based on a single realization of the signal and noise. Theory is illustrated by examples.     

Nonholonomic control in quantum computers based on ions in a trap

Currently, the scheme of a quantum computer based on ions in traps is accepted as one of the most realistic schemes of a scaled quantum computer. In this article, we show application of the method of nonholonomic control over the quantum evolution to this scheme. We consider this to be the most universal and simplest control method for an arbitrary scheme of a quantum computer. In this case, for arbitrary controlled evolution of the quantum system, it is sufficient to have available two lasers operating at a combined frequency equal to a frequency of internal ion transitions and selected total vibrational mode of the system of ions in a trap with different amplitudes. For each laser, it is sufficient to control only the time of their alternate operation with a sufficient accuracy.     

Data-adaptive evolutionary spectral estimation

We present a novel data-adaptive estimator for the evolutionary spectrum of nonstationary signals. We model the signal at a frequency of interest as a sinusoid with a time-varying amplitude, which is accurately represented by an orthonormal basis expansion. We then compute a minimum mean-squared error estimate of this amplitude and use it to estimate the time-varying spectrum at that frequency, all while minimizing the interference from the signal components at other frequencies. Repeating the process over all frequencies, we obtain a power distribution that is consistent with the Wold-Cramer evolutionary spectrum and reduces to Capon's (1969) method for the stationary case. Our estimator possesses desirable properties in terms of time-frequency resolution and positivity and is robust in the spectral estimation of noisy nonstationary data. We also propose a new estimator for the autocorrelation of nonstationary signals. This autocorrelation estimate is needed in the data-adaptive spectral estimation. We illustrate the performance of our estimator using simulation examples and compare it with the recently presented evolutionary periodogram and the bilinear time-frequency distribution with exponential kernels     

Suppression of Time-varying Multi-tone Interference Based on Frequency Domain Interference Detection

Existing active multi-tone interference (MTI) suppression methods used in direct sequence spread spectrum (DSSS) consider the interference to be time-invariant. However, in most practical scenarios, the interference is time-varying. These conventional analytic models cannot be directly applied to current realistic systems with time-varying interference. Hence, in this paper, we propose a novel approach based on frequency domain interference detection to suppress MTI experiencing a time-varying fading channel. Our approach operates in two steps. Firstly, we calculate the interference decision threshold by the probability of false alarm based on the Neyman-Pearson (NP) criterion. Secondly, we consider that the frequency bin is corrupted by interference, and the corresponding point is set to zero if the magnitude of the received signal exceeds the threshold. The simulation results demonstrate that our proposed method can mitigate time-varying MTI effectively, and can approach the interference-free performance limit over practical ranges of interference power levels and mobility levels.     

Estimation of quasiperiodic signal parameters by means of dynamicsignal models

The problem of estimating the parameters of a quasiperiodic signal consisting of a sum of a given number of sinusoidal signals with known frequencies but unknown time-varying amplitudes and phases superimposed by some additive noise sources is treated in this paper. Different estimation techniques that solve the problem are presented in this paper. The reason to do that is twofold: (1) to present the derivation of a new estimator for quasiperiodic signals, which is based on Kalman filtering theory and a random walk model, and to illustrate its structure and parametrization; and (2) to compare the new estimator with another Kalman filter-based estimator that uses an “oscillator model” and with the more classical running recursive discrete Fourier series method     

Respiratory compensation in projection imaging using a magnification and displacement model

Respiratory motion during the collection of computed tomography (CT) projections generates structured artifacts and a loss of resolution that can render the scans unusable. This motion is problematic in scans of those patients who cannot suspend respiration, such as the very young or intubated patients. Here, the authors present an algorithm that can be used to reduce motion artifacts in CT scans caused by respiration. An approximate model for the effect of respiration is that the object cross section under interrogation experiences time-varying magnification and displacement along two axes. Using this model an exact filtered backprojection algorithm is derived for the case of parallel projections. The result is extended to generate an approximate reconstruction formula for fan-beam projections. Computer simulations and scans of phantoms on a commercial CT scanner validate the new reconstruction algorithms for parallel and fan-beam projections. Significant reduction in respiratory artifacts is demonstrated clinically when the motion model is satisfied. The method can be applied to projection data used in CT, single photon emission computed tomography (SPECT), positron emission tomography (PET), and magnetic resonance imaging (MRI).     

Assessment of autonomic regulation of heart rate variability by the method of complex demodulation

Complex demodulation was used to examine the effect of both divisions of the autonomic nervous system (sympathetic and parasympathetic) on heart rate. Data were analyzed from dogs during classical conditioning procedures which caused different changes in the autonomic regulation of heart rate. Two significant peaks in the heart rate variability spectrum were examined by this technique. The amplitude of the peak at the respiration frequency showed parasympathetic changes, while the amplitude of the low frequency peak (0-0.124 Hz) showed both sympathetic and parasympathetic effects. Complex demodulation results at these frequencies clearly showed the activities of both branches of the autonomic nervous system in regulating heart rate. During the CS+ period, when trained dogs were presented with a tone predicting a subsequent shock, the observed tachycardia was due to decreased parasympathetic activity and a transient increase in sympathetic activity. During the CS- period where a different tone predicts no shock, parasympathetic and sympathetic activities were unchanged from the baseline condition. The use of complex demodulation enables us to examine autonomic contributions to heart rate regulation in conditioning and a variety of other physiological and environmental conditions where autonomic input can be expected to change rapidly.     

Power spectral density of unevenly sampled data by least-squareanalysis: performance and application to heart rate signals

This work studies the frequency behavior of a least-square method to estimate the power spectral density of unevenly sampled signals. When the uneven sampling can be modeled as uniform sampling plus a stationary random deviation, this spectrum results in a periodic repetition of the original continuous time spectrum at the mean Nyquist frequency, with a low-pass effect affecting upper frequency bands that depends on the sampling dispersion. If the dispersion is small compared with the mean sampling period, the estimation at the base band is unbiased with practically no dispersion. When uneven sampling is modeled by a deterministic sinusoidal variation respect to the uniform sampling the obtained results are in agreement with those obtained for small random deviation. This approximation is usually well satisfied in signals like heart rate (HR) series. The theoretically predicted performance has been tested and corroborated with simulated and real HR signals. The Lomb method has been compared with the classical power spectral density (PSD) estimators that include resampling to get uniform sampling. The authors have found that the Lomb method avoids the major problem of classical methods: the low-pass effect of the resampling. Also only frequencies up to the mean Nyquist frequency should be considered (lower than 0.5 Hz if the HR is lower than 60 bpm). It is concluded that for PSD estimation of unevenly sampled signals the Lomb method is more suitable than fast Fourier transform or autoregressive estimate with linear or cubic interpolation. In extreme situations (low-HR or high-frequency components) the Lomb estimate still introduces high-frequency contamination that suggest further studies of superior performance interpolators. In the case of HR signals the authors have also marked the convenience of selecting a stationary heart rate period to carry out a heart rate variability analysis     

Comparison Identities for Wave Propagation in a Time-Varying Plasma Medium

An unbounded space-invariant but time-varying medium conserves the wave number k of the wave but alters the frequency of the wave. Thus a switched medium acts like a frequency transformer, the frequencies of the newly created waves (output waves) are easily computed. The amplitudes of the output waves depend on the rise time Tr of the profiles of the parameters of the switched medium.     

The Analysis of Respiratory Sinus Arrhythmia Using Spectral Analysis and Digital Filtering

Respiratory sinus arrhythmia is the phenomenon by which respiration modulates heart rate in normal humans and in many animals. This investigation was divided into the following three categories: 1) the development of a mathematical model relating respiration to those variations that it causes in heart rate; 2) the use of digital filtering techniques to attenuate fluctuations in heart rate which are due to respiration; and 3) the development of methods that use only heart rate to get information about respiration.     

Time-varying threshold integral pulse frequency modulation

Several methods have been proposed so far for the analysis of the integral pulse frequency modulation (IPFM) model and detecting its corresponding physiological information. Most of these methods rely on the low-pass filtering method to extract the modulating signal of the model. In this paper, we present an entirely new approach based on vector space theory. The new method is developed for a more comprehensive form of the IPFM model, namely the time-varying threshold integral pulse frequency modulation (TVTIPFM) model. The new method decomposes the driving signals of the TVTIPFM model into a series of orthogonal basis functions and constructs a matrix identity through which the input signals can be obtained by a parametric solution. As a particular case, we apply this method to R-R intervals of the SA node to discriminate between its autonomic nervous modulation and the stretch induced effect.