Decreasing motion artifacts in calcium-dependent fluorescence transients from the perfused mouse heart using frequency filtering

A strategy has been developed for the removal of motion artifact and noise in calcium-dependent fluorescence transients from the perfused mouse heart using frequency filtering. An analytical model indicates that the spectral removal of motion artifacts is independent of the phase shift of the motion waveform in the frequency domain, and thus to the time shift (or delay) of motion in the time domain. This is based on the "shift theorem" of Fourier analysis, which avoids erroneous correction of motion artifact when using the motion signal obtained using reflectance from the heart. Several major steps are adopted to implement this model for elimination of motion as well as detection noise from the fluorescence transient signals from the calcium-sensitive probe Rhod-2. These include (1) extracting the fluorescence calcium transient signal from the raw data by using power spectrum density (PSD) in the frequency domain by subtracting the motion recorded using the reflectance of excitation light, (2) digitally filtering out the random noise using multiple bandpass filters centralized at harmonic frequencies of the transients, and (3) extracting high frequency noise with a Gaussian Kernel filter method. The processed signal of transients acquired with excessive motion artifact is comparable to transients acquired with minimal motion obtained by immobilizing the heart against the detection window, demonstrating the usefulness of this technique.     

Comparison of first and second heart sounds after mechanical heart valve replacement

In this article, the spectral features of first heart sounds (S1) and second heart sounds (S2), which comprise the mechanical heart valve sounds obtained after aortic valve replacement (AVR) and mitral valve replacement (MVR), are compared to find out the effect of mechanical heart valve replacement and recording area on S1 and S2. For this aim, the Welch method and the autoregressive (AR) method are applied on the S1 and S2 taken from 66 recordings of 8 patients with AVR and 98 recordings from 11 patients with MVR, thereby yielding power spectrum of the heart sounds. Three features relating to frequency of heart sounds and three features relating to energy of heart sounds are obtained. Results show that in comparison to natural heart valves, mechanical heart valves contain higher frequency components and energy, and energy and frequency components do not show common behaviour for either AVR or MVR depending on the recording areas. Aside from the frequency content and energy of the sound generated by mechanical heart valves being affected by the structure of the lungs–thorax and the recording areas, the pressure across the valve incurred during AVR or MVR is a significant factor in determining the frequency and energy levels of the valve sound produced. Though studies on native heart sounds as a non-invasive diagnostic method has been done for many years, it is observed that studies on mechanical heart valves sounds are limited. The results of this paper will contribute to other studies on using a non-invasive method for assessing the mechanical heart valve sounds.     

New approach to the statistical analysis of cardiovascular data.

Fourier-based approaches to analysis of variability of R-R intervals or blood pressure typically compute power in a given frequency band (e.g., 0.01-0.07 Hz) by aggregating the power at each constituent frequency within that band. This paper describes a new approach to the analysis of these data. We propose to partition the blood pressure variability spectrum into more narrow components by computing power in 0.01-Hz-wide bands. Therefore, instead of a single measure of variability in a specific frequency interval, we obtain several measurements. The approach generates a more complex data structure that requires a careful account of the nested repeated measures. We briefly describe a statistical methodology based on generalized estimating equations that suitably handles this more complex data structure. To illustrate the methods, we consider systolic blood pressure data collected during psychological and orthostatic challenge. We compare the results with those obtained using the conventional methods to compute blood pressure variability, and we show that our approach yields more efficient results and more powerful statistical tests. We conclude that this approach may allow a more thorough analysis of cardiovascular parameters that are measured under different experimental conditions, such as blood pressure or heart rate variability.     

Classification of electrocardiogram signals with support vector machines and genetic algorithms using power spectral features

This paper proposes a new power spectral-based hybrid genetic algorithm-support vector machines (SVMGA) technique to classify five types of electrocardiogram (ECG) beats, namely normal beats and four manifestations of heart arrhythmia. This method employs three modules: a feature extraction module, a classification module and an optimization module. Feature extraction module extracts electrocardiogram's spectral and three timing interval features. Non-parametric power spectral density (PSD) estimation methods are used to extract spectral features. Support vector machine (SVM) is employed as a classifier to recognize the ECG beats. We investigate and compare two such classification approaches. First they are specified experimentally by the trial and error method. In the second technique the approach optimizes the relevant parameters through an intelligent algorithm. These parameters are: Gaussian radial basis function (GRBF) kernel parameter σ and C penalty parameter of SVM classifier. Then their performances in classification of ECG signals are evaluated for eight files obtained from the MIT–BIH arrhythmia database. Classification accuracy of the SVMGA approach proves superior to that of the SVM which has constant and manually extracted parameter.     

Comparison of various techniques used to estimate spontaneous baroreflex sensitivity (the EuroBaVar study)

This study compared spontaneous baroreflex sensitivity (BRS) estimates obtained from an identical set of data by 11 European centers using different methods and procedures. Noninvasive blood pressure (BP) and ECG recordings were obtained in 21 subjects, including 2 subjects with established baroreflex failure. Twenty-one estimates of BRS were obtained by methods including the two main techniques of BRS estimates, i.e., the spectral analysis (11 procedures) and the sequence method (7 procedures) but also one trigonometric regressive spectral analysis method (TRS), one exogenous model with autoregressive input method (X-AR), and one Z method. With subjects in a supine position, BRS estimates obtained with calculations of alpha-coefficient or gain of the transfer function in both the low-frequency band or high-frequency band, TRS, and sequence methods gave strongly related results. Conversely, weighted gain, X-AR, and Z exhibited lower agreement with all the other techniques. In addition, the use of mean BP instead of systolic BP in the sequence method decreased the relationships with the other estimates. Some procedures were unable to provide results when BRS estimates were expected to be very low in data sets (in patients with established baroreflex failure). The failure to provide BRS values was due to setting of algorithmic parameters too strictly. The discrepancies between procedures show that the choice of parameters and data handling should be considered before BRS estimation. These data are available on the web site (http://www.cbi.polimi.it/glossary/eurobavar.html) to allow the comparison of new techniques with this set of results.     

Long-term spectral analysis of heart rate variability — An algorithm based on segmental frequency distributions of beat-to-beat intervals

Reduced heart rate variability has been reported as a predictor of long-term mortality in recent myocardial infarction patients. However, it has not been systematically investigated whether the reduction in heart rate variability in those post myocardial infarction patients who later suffer death or severe arrhythmias is caused by a reduction of short-term variability of heart rate (such as respiratory arrhythmia) or whether the differences in long term variability (such as diurnal rhythm) are involved. In order to perform such an evaluation, a new algorithm has been developed which permits different wavelength components (including the long-term components due to diurnal rhythm) of heart rate variability to be approximated. In general, the method uses segmental frequency distributions of durations of intervals between successive normal cardiac beats. To assess the spectral components of heart rate variability, a scale of wavelength limits is used and for each limit of this scale, the algorithm excludes the rate changes of wavelength longer than the given bound. The method was applied to the analysis of electrocardiograms recorded in 14 post myocardial infarction patients who later suffered death or ventricular tachycardia, and in 14 other randomly selected patients with an uncomplicated course following acute myocardial infarction. The rate variability spectra obtained for both groups of patients were compared statistically and the results showed that the groups of positive and negative cases were most significantly distinguished when including both short- and long-term components of heart rate variability. Separate evaluation of different wavelength components showed that the very long-term components of heart rate variability were more powerful in distinguishing between positive and negative cases than the short term components.     

A transformation‐based approach to Gaussian mixture density estimation for bounded data

Finite mixture of Gaussian distributions provide a flexible semiparametric methodology for density estimation when the continuous variables under investigation have no boundaries. However, in practical applications, variables may be partially bounded (e.g., taking nonnegative values) or completely bounded (e.g., taking values in the unit interval). In this case, the standard Gaussian finite mixture model assigns nonzero densities to any possible values, even to those outside the ranges where the variables are defined, hence resulting in potentially severe bias. In this paper, we propose a transformation‐based approach for Gaussian mixture modeling in case of bounded variables. The basic idea is to carry out density estimation not on the original data but on appropriately transformed data. Then, the density for the original data can be obtained by a change of variables. Both the transformation parameters and the parameters of the Gaussian mixture are jointly estimated by the expectation‐maximization (EM) algorithm. The methodology for partially and completely bounded data is illustrated using both simulated data and real data applications.     

The variability of respiratory pattern and gas exchange

It is known, that spectral analysis of heart rate and respiratory variability allows to find out the very low frequency (VLF) rhythm. However it is not known, it is necessary to carry this rhythm to what type of wave processes. The purpose of the present researches was to study the respiratory variability and the variability of gas exchange parameters. 10 healthy subjects have been surveyed. The pneumogramms within 30 minutes spent record, and then a method "breath-by-breath" within 30 minutes registered gas exchange parameters (Ve--lung ventilation, V(O2) -O2 consumption and other parameters). Fast Fourier transform method has found out two groups of the basic peaks. The first--in a range 0.2-0.3 Hz (a time cycle--3-5 s), that corresponds respiratory frequency which size at subjects varied from 12 to 20 per minute. The second--in a range 0.002-0.0075 Hz, that corresponds VLF diapason (a time cycle--1-3.5 minutes). At the analysis pneumogramms rhythms in the same ranges have been established. The carried out researches allow to draw a conclusion on steady character of wave process in a VLF-range. It can be carried to quasi-periodic oscillations type. First oscillator or respiratory frequency it is formed by means of mechanisms of chemoreception. Considering, that V(O2) and V(CO2) are function energy exchange, it is possible to believe, what exactly energy demand define the second oscillator.     

Nonstationary Heart Rate Variability in Respiratory Tests

A new method was proposed for processing a nonstationary heart rate by using frequency-modulated signals rather than amplitude-modulated signals equally spaced over several points of time as in the conventional method. A frequency-modulated signal is a set of identical Gaussian peaks that coincide with the true time points of heart beats. A continuous wavelet transform was used to quantitatively describe the heart rhythm signal. A test with controlled breathing was performed as an example and included three consecutive stages: rest, rhythmic breathing at a specified frequency, and exhalation. Tachograms recorded during the breath test was found to be a nonstationary signal with the alternation of peaks of different spectral ranges. A system of quantitative parameters was developed to describe the dynamics of changes in the spectral properties of the tachogram in transitional areas. A static clustering by the effect of the respiratory test and a dynamic clustering in order to identify the time points when the autonomic nervous system is stressed were performed for all subjects. The article discusses the prospects of using the method as a means to analyze the transient effects in various functional tests and as biofeedback that would help to change the heart rhythm.     

Heart rate regulation processed through wavelet analysis and change detection: some case studies

Heart rate variability (HRV) is an indicator of the regulation of the heart, see Task Force (Circulation 93(5):1043-1065, 1996). This study compares the regulation of the heart in two cases of healthy subjects within real life situations: Marathon runners and shift workers. After an update on the state of the art on HRV processing, we specify our probabilistic model: We choose modeling heartbeat series by locally stationary Gaussian process (Dahlhaus in Ann Stat 25, 1997). HRV is then processed by the combination of two statistical methods: (1) Continuous wavelet transform for calculating the spectral density energy in the high frequency (HF) and low frequency (LF) bands and (2) Change point analysis to detect changes of heart regulation. Next, we plot the variations of the HF and LF energy in extreme conditions for both populations. This puts in light, that physical activities (rest, moderate sport, marathon race) can be ordered in a logical continuum. This allows to define a new index based on HF and LF energy that is log HF + log LF which appears relevant to measure HR regulation. The results obtained are pertinent but have to be completed by further studies.     

Spectral analysis of heart rate variability in the beluga (<Emphasis Type="Italic">Delphinapterus leucas</Emphasis>) during exposure to acoustic noise

The spectral parameters of heart rate variability are a measure of activation of the sympathetic and parasympathetic branches of the mammalian autonomic nervous system. In this study, spectral analysis was used for the first time to evaluate the impact of acoustic noise (one of the major anthropogenic factors) on a cetacean. We analyzed cardiac intervals in a captive beluga (a member of the Odontoceti whales) in response to a 10-min band-pass acoustic noise at an intensity of 150–165 dB and frequency of 19–38 kHz. The beluga’s response to acoustic noise, when examined shortly after the animal’s capture, was characterized by a sharp tachycardia (the first phase) followed by a decrease in the heart rate (the second phase). Based on spectral analysis, the frequency range of heart rate oscillations in the beluga decreased during the period of tachycardia while shifting to a lower frequency range (below 0.01 Hz) as compared with the control conditions. Accordingly, the spectral power of low-frequency components was reduced. During the second phase, the range of heart rate variability oscillations expanded and fully recovered only after the noise had been turned off. After one year in captivity, no significant changes in the heart rate parameters (both in time and frequency domain) were recorded in response to a similar noise exposure. Therefore, the changes in the heart rate spectral components in the studied beluga exposed to acoustic noise were comparable to those recorded in terrestrial mammals and in humans in stressful and emotionally negative situations. The spectral characteristics of heart rate oscillations can be used as a quantitative measure of beluga whales’ response to acoustic noise as a stress factor.     

Characterization of structure and properties of bone by spectral measure method

Novel mathematical method called spectral measure method (SMM) is developed for characterization of bone structure and indirect estimation of bone properties. The spectral measure method is based on an inverse homogenization technique which allows to derive information about the structure of composite material from measured effective electric or viscoelastic properties. The mechanical properties and ability to withstand fracture depend on the structural organization of bone as a hierarchical composite. Information about the bone structural parameters is contained in the spectral measure in the Stieltjes integral representation of the effective properties. The method is based on constructing the spectral measure either by calculating it directly from micro-CT images or using measurements of electric or viscoelastic properties over a frequency range. In the present paper, we generalize the Stieltjes representation to the viscoelastic case and show how bone microstructure, in particular, bone volume or porosity, can be characterized by the spectral function calculated using measurements of complex permittivity or viscoelastic modulus. For validation purposes, we numerically simulated measured data using micro-CT images of cancellous bone. Recovered values of bone porosity are in excellent agreement with true porosity estimated from the micro-CT images. We also discuss another application of this method, which allows to estimate properties difficult to measure directly. The spectral measure method based on the derived Stieltjes representation for viscoelastic composites, has a potential for non-invasive characterization of bone structure using electric or mechanical measurements. The method is applicable to sea ice, porous rock, and other composite materials.     

Identification of Human Vital Functions Directly Relevant to the Respiratory System Based on the Cardiac and Acoustic Parameters and Random Forest

Regarding sleep research, polysomnography (PSG) also called a sleep study, is a gold standard. It incorporates brain waves, the oxygen level in the blood, heart rate and breathing, and leg movement recordings. PSG is a complicated and expensive laboratory-based procedure, usually done in hospitals or special sleep center. In this study, an alternative technique for Sleep-Related Breathing Disorders (SRBD) based on selected cardiac and acoustic parameters and the Random Forest (RF) has been studied. A system dedicated to the detection of simultaneously acquired ECG and acoustic signals, which are collected during sleep at home environment is proposed. Results obtained indicate that classification and regression tree models such as RF are appropriate for the evaluation of sleep disorders like SRBD. The best identification of sleep irregularities at level 89.00 percent for the raw database was obtained. Thus, statistical predictive models allow identification of breathing events with high levels of sensitivity and specificity, providing an inexpensive and accurate diagnosis.     

Ultrasonic tissue characterization for prostate diagnostics: spectral parameters vs. texture parameters.

An ultrasonic multi-feature tissue characterizing system for the detection of prostate cancer is presented. The system is based on the processing of radio frequency (RF) ultrasonic echo data. Data from 100 patients was acquired in a clinical study. Parameters are extracted from the RF echo data and classified using two adaptive network-based fuzzy inference systems (FIS) working in parallel as a nonlinear classifier. Next to spectral parameters, conventional texture parameters are calculated using demodulated and log-compressed echo data. In the first approach, the classifier is trained on both, spectral and texture parameters. In the second approach, the classifier is only trained on texture parameters. Classification results of both approaches are compared and it is demonstrated, that only the use of spectral parameters yields satisfying classification results. Results of a minimum distance classifier (MDC) are presented for comparison with the fuzzy inference system. For the final fuzzy inference systems used in this approach, the area under the ROC curve is between 84% and 86% for the combined approach and between 70% and 74% for the approach based on texture parameters only.     

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

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

Scattering of an ultrashort electromagnetic pulse in a plasma

An analytic approach is developed to describing how ultrashort electromagnetic pulses with a duration of one period or less at the carrier frequency are scattered in a plasma. Formulas are derived to calculate and analyze the angular and spectral probabilities of radiation scattering via two possible mechanisms-Compton and transition radiation channels-throughout the entire pulse. Numerical simulations were carried out for a Gaussian pulse. The effect of the phase of the carrier frequency relative to the pulse envelope on the scattering parameters is investigated.     

Parameters describing the pulse wave

Pulse wave analysis permits non-invasive assessment of arterial elasticity indices. The contour varies in different parts of the circulation. It depends on physiological or pathophysiological conditions of the organism. The pathological events like arteriosclerosis or diabetes have a primary effect to the artery elasticity. Hypertension or some heart diseases also influence the pulse wave velocity and resulted in earlier wave reflections. There are several methods of pulse wave measurements based on different principles and depending on the type of measured pulse wave. The evaluation parameters can be assessed from the time domain, derivations, velocity or frequency domain. The main aim of this review article is to offer a recent overview of pulse wave measurement parameters and main results obtained. The principles of pulse wave measurement and current experience in clinical practice are shortly discussed too.     

Quantification of two-dimensional NOE spectra via a combined linear and nonlinear least-squares fit

Summary Determining the volumes of peaks in 2D NMR spectra can be prohibitively difficult in cases of overlapping, broad lines. Deconvolution and parameter estimation can be attempted on either the time-domain or the frequency-domain data. We present a method of estimating spectral parameters from frequency-domain data, using a combination of Lorentzian and Gaussian lineshapes for reference lines. This approach combines a previously published method of projecting the data on a linear space spanned by reference lines with a nonlinear least-squares fitting algorithm. Comparison of this method with other published methods of frequency-domain deconvolution shows that it is both more precise and more accurate when estimating 2D volumes.     

A Fourier method for the analysis of exponential decay curves.

A method based on the Fourier convolution theorem is developed for the analysis of data composed of random noise, plus an unknown constant "base line," plus a sum of (or an integral over a continuous spectrum of) exponential decay functions. The Fourier method's usual serious practical limitation of needing high accuracy data over a very wide range is eliminated by the introduction of convergence parameters and a Gaussian taper window. A computer program is described for the analysis of discrete spectra, where the data involves only a sum of exponentials. The program is completely automatic in that the only necessary inputs are the raw data (not necessarily in equal intervals of time); no potentially biased initial guesses concerning either the number or the values of the components are needed. The outputs include the number of components, the amplitudes and time constants together with their estimated errors, and a spectral plot of the solution. The limiting resolving power of the method is studied by analyzing a wide range of simulated two-, three-, and four-component data. The results seem to indicate that the method is applicable over a considerably wider range of conditions than nonlinear least squares or the method of moments.