Suresh Chandra Saxena

Sampling frequency of the RR interval time series for spectral analysis of heart rate variability

Spectral analysis of heart rate variability (HRV) is an accepted method for assessment of cardiac autonomic function and its relationship to numerous disorders and diseases. Various non-parametric methods for HRV estimation have been developed and extensive literature on their respective properties is available. The RR interval time series can be seen as a series of non-uniformly spaced samples. To analyse the power spectra of this series using the discrete Fourier transform (DFT), we need to interpolate the series for obtaining uniformly spaced intervals. The selection of sampling period plays a critical role in obtaining the power spectra in terms of computational efficiency and accuracy. In this paper, we shall analyse the RR interval time series from selected subjects for different sampling frequencies to compare the error introduced in selected frequency-domain measures of HRV at a constant frequency resolution for a specific duration of electrocardiogram (ECG) data. It should be pointed out that, although many other error causes are possible in the frequency-domain measures, our attention will be confined only to the performance comparison due to the different sampling frequencies. While the choice of RR interval sampling frequency (fs) is arbitrary, the sampling rate of RR interval series must be selected with due consideration to mean and minimum RR interval; fs = 4 Hz was proposed for a majority of cases. This is an appropriate sampling rate for the study of autonomic regulation, since it enables us to compute reliable spectral estimates between dc and 1 Hz, which represents the frequency band within which the autonomic nervous system has significant response. Furthermore, resampled RR intervals are evenly spaced in time and are synchronized with the samples of the other physiologic signals, enabling cross-spectral estimates with these signals.

Technical communication: Improved modified AZTEC technique for ECG data compression: Effect of length of parabolic filter on reconstructed signal

The existing techniques for electrocardiogram (ECG) data compression have been classified into three major categories, namely, direct data compression (DDC), transformation compression (TC) and parameter extraction compression (PEC). This paper deals with an efficient DDC algorithm, which has been developed over existing modified Amplitude Zone Time Epoch Coding (AZTEC) technique, named as improved modified AZTEC and tested on Common Standard for quantitative Electrocardiography (CSE) database. The performance has been evaluated on the basis of compression ratio (CR), percent-root-mean-square difference (PRD) and fidelity of the reconstructed signal. A comparison of the wavelet-derived features of compressed and original signals has been used for performance evaluation of the compressed signal. In this paper, the effect of length of least-square polynomial smoothing filters, i.e., parabolic filters, on the reconstructed signal has been analyzed. The use of 7-point parabolic filter has been found to improve the percent-root-mean-square difference (PRD), i.e. lower PRD, compared to reconstruction process of ECG signal without filter. It is also observed that the use of parabolic filters rejects high frequency noise, which is reflected in the form of reduced electromyographic noise.

Effects of RR segment duration on HRV spectrum estimation

Although patterns of heart rate variability (HRV) hold considerable promise for clarifying issues in clinical applications, the inappropriate quantification and interpretation of these patterns may obscure critical issues or relationships and may impede rather than foster the development of clinical applications. The duration of the RR interval series is not a matter of convenience but a fine balance between two important issues: acceptable variance and stationarity of the time series on one hand, and acceptable resolution of the spectral estimate and reduced spectral leakage on the other. Further, in the standard short-term HRV analysis, it has been observed that the previous studies in HRV spectral analysis use a wide range of RR interval segment duration for spectral estimation by Welchs algorithm. The standardization of RR interval segment duration is also important for comparisons among studies and is essential for within-study experimental contrasts. In the present study, a comparative analysis for RR interval segment durations has been made to propose an optimal RR interval segment duration. Firstly a simulated signal was analyzed with Hann window and zero padding for the segment lengths of 1024, 512, 256 and 128 samples resampled at 4 Hz with 50% overlapping. Again, the above procedure was applied to RR interval series and it was concluded that segment length of 256 samples with 50% overlapping provides a smoothed spectral estimate with clearly outlined peaks in low- and high-frequency bands. This easily understandable and interpretable spectral estimate leads to a better visual and automated analysis, which is not only desirable in basic physiology studies, but also a prerequisite for a widespread utilization of frequency domain techniques in clinical studies, where simplicity and effectiveness of information are of primary importance.

Spectral evaluation of aging effects on blood pressure and heart rate variations in healthy subjects

The background to heart rate variability (HRV) and blood pressure variability (BPV), and their determinants and physiological correlates, remain obscure. The impact of age must be taken into account if HRV and BPV are used for predictive purposes in clinical settings. Healthy subjects show wide inter-individual variation in their heart rate behaviour and the factors affecting heart rate dynamics are not well known. This paper has undertaken to evaluate heart rate variability (HRV) and baroreflex sensitivity (BRS) in a random sample of subjects without evidence of heart disease, and to estimate the relation of HRV and BPV behaviour to age. The aim of this study was to analyse the effects of ageing on HRV and BPV for simultaneous recordings of electrocardiograph (ECG) and blood pressure (BP) signals at rest in healthy subjects. We studied eight young (21 – 34 years old) and eight elderly (68 – 85 years old) rigorously screened subjects from the Fantasia Database to make the reproducibility and comparability of the results more extensive. Time- and frequency-domain analysis of HRV and BPV was performed on 5-minute ectopic-free recordings. BRS on the heart was estimated by frequency-domain analysis of spontaneous variability of systolic blood pressure (SBP) and RR interval. It has been observed that compared to young the elderly subjects have (i) diminished HRV; (ii) a shift in the power spectral density and median frequency to low frequency side for HRV and to higher frequency side for BPV; and (iii) increased low-frequency alpha index and decreased high-frequency alpha index of BRS with overall alpha index augmented. The results convey that normal ageing in the absence of disease is associated with lesser parasympathetic regulation of heart rate. Thus it is concluded that the age is an important factor to be considered for prognosis and diagnosis by HRV and BPV. For reliable clinical applications, more research needs to be done on a broad spectrum of subjects. In addition, these observations will prove to be useful for dynamic modelling of cardiovascular regulation for testing the authentication of new techniques for analysis purposes.

Homomorphic wavelet thresholding technique for denoising medical ultrasound images.

A novel homomorphic wavelet thresholding technique for reducing speckle noise in medical ultrasound images is presented. First, we show that the speckle wavelet coefficients in the logarithmically transformed ultrasound images are best described by the Nakagami family of distributions. By exploiting this speckle model and the Laplacian signal prior, a closed form, data-driven, and spatially adaptive threshold is derived in the Bayesian framework. The spatial adaptivity allows the additional information of the image (such as identification of homogeneous or heterogeneous regions) to be incorporated into the algorithm. Further, the threshold has been extended to the redundant wavelet representation, which yields better results than the decimated wavelet transform. Experimental results demonstrate the improved performance of the proposed method over other well-known speckle reduction filters. The application of the proposed method to a realistic US test image shows that the new technique, named HomoGenThresh, outperforms the best wavelet-based denoising method reported in [1] by more than 1.6 dB, Lee filter by 3.6 dB, Kaun filter by 3.1 dB and band-adaptive soft thresholding [2] by 2.1 dB at an input signal-to-noise ratio (SNR) of 13.6 dB.

An improved windowing technique for heart rate variability power spectrum estimation

Spectral analysis of heart rate variability (HRV) is an accepted method for assessment of cardiac autonomic function and its relationship to numerous disorders and diseases. Discrete Fourier transform (DFT) based methods are widely used for their easy applicability, computational speed and the possibility for direct interpretation of results. This study assesses the limitations of windowing of the RR interval series for power spectrum estimation using DFT for heart rate variability studies. The mean value of the RR interval series should be subtracted before windowing. This may leave a small residual DC component after windowing, but the RR interval series is properly tapered to zero at the beginning and end of the window. However, if the windowed RR interval series has a non-zero mean then subtracting this mean will create an abrupt transition between the first and last data points, and the padded zeros. This is equivalent to superimposing upon the RR interval series a rectangular pulse of the same length as the window, with a height equal to the subtracted mean value. In the present paper an approach to overcome the above effects of the window in reducing the signal energy and introducing low frequency components into the spectrum has been suggested and incorporated. Results have been compared for DC biasing of windowed data spectrum, bias of windowed data removed by subtraction of mean from data, and data preprocessed to remove windowed mean level and to maintain mean power. Thus the preprocessing of RR interval series with this method improves the accuracy of HRV analysis methods. The study was carried out by smoothing the complete RR interval series by single Hann window and by 50% overlapping the data segments of 256 data points followed by DFT. Overlapping the data segments provides equal weight to all values in the RR interval series and a smoothed spectral estimate with clearly dominant peaks in low- and high-frequency regions.

A comparative study on spectral parameters of HRV in yogic and non-yogic practitioners

The autonomic nervous system regulates the heart rate through its sympathetic and para-sympathetic nervous system to maintain body visceral homeostasis. The sympathetic tone enhances the heart rate whereas the para-sympathetic tone inhibits this rise. The continuous variation of heart rate in synchronism with visceral systems is termed as heart rate variability. This heart rate variability is higher in normal and healthy conditions, whereas it is reduced in case of cardiac abnormalities. The present study is regarding heart rate variability in non-yogic practitioners and yogic practitioners. The spectral parameters were evaluated in two groups, where one group is having forty two normal and healthy male subjects who are non-yogic practitioners, and the other group is also having forty two normal and healthy male subjects who are experienced yoga practitioners. The subjects in both groups are in the age group of 18-48 years. The power in low frequency (LF) has been observed to be higher in non-yogic practitioners as compared to those of yogic practitioners. Moreover, the heart rate variability in yogic practitioners has shown to be higher than the subjects who do not practise yoga.

Wavelet based compression of medical ultrasound images using vector quantization

In this paper, an efficient technique for compression of medical ultrasound (US) images is proposed. The technique is based on wavelet transform of the original image combined with vector quantization (VQ) of high-energy subbands using the LBG algorithm. First, we analyse the statistical behaviour of wavelet coefficients in US images across various subbands and scales. The analysis show that most of the image energy is concentrated in one of the detail subband, either in the vertical detail subband (most of the time) or in the horizontal subband. The other two subbands at each decomposition level contribute negligibly to the total image energy. Then, by exploiting this statistical analysis, a low-complexity image coder is designed, which applies VQ only to the highest energy subband while discarding the other detail subbands at each level of decomposition. The coder is tested on a series of abdominal and uterus greyscale US images. The experimental results indicate that the proposed method clearly outperforms the JPEG2000 (Joint Photographers Expert Group) encoder both qualitatively and quantitatively. For example, without using any entropy coder, the proposed method yields a peak signal to noise ratio gain of 0.2 dB to 1.2 dB over JPEG2000 on medical US images.

A fast learning algorithm for training feedforward neural networks

This paper deals with a fast and computationally simple Successive Over-relaxation Resilient Backpropagation (SORRPROP) learning algorithm which has been developed by modifying the Resilient Backpropagation (RPROP) algorithm. It uses latest computed values of weights between the hidden and output layers to update remaining weights. The modification does not add any extra computation in RPROP algorithm and maintains its computational simplicity. Classification and regression simulations examples have been used to compare the performance. From the test results for the examples undertaken it is concluded that SORRPROP has small convergence times and better performance in comparison to other first-order learning algorithms.

Joint thresholding and quantizer selection for compression of medical ultrasound images in the wavelet domain

This paper introduces a simple and efficient technique for compression of medical ultrasound (US) images in the wavelet domain. The statistics of subband wavelet coefficients are modelled using the generalized Gaussian distribution (GGD). By exploiting these statistics, a uniform scalar quantizer is designed which adapts very well to the changing statistics of the signal across various subbands and scales. To increase the quantization performance, a threshold is chosen adaptively to zero-out the insignificant wavelet coefficients in the detail subbands before quantization. A distinctive feature of the proposed technique is that it unifies the two approaches to image adaptive coding: rate-distortion (R-D) optimized quantizer selection and R-D optimal thresholding, in order to increase the compression performance of the coder. The operational R-D criterion used for joint optimization is derived in the minimum description length (MDL) framework. The experimental results show that the joint R-D optimization leads to significant improvement in the compression performance of the proposed coder, named JTQ-WV, over the best state-of-the-art image coder, SPIHT. For example, the coding of US images at 0.25 bpp by JTQ-WV yields a PSNR gain of 1.0 dB over the benchmark SPIHT.