Relation between HF HRV and Respiratory Frequency

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1 Proc. of Int. Conf. on Emerging Trends in Engineering and Technology Relation between HF HRV and Respiratory Frequency A. Anurupa, B. Dr. Mandeep Singh Ambedkar Polytechnic/I& C Department, Delhi, India anuscorpiok4@gmail.com ThaparUniversity/ EIE Department, Patiala, India mandy_tiet@yahoo.com Abstract Heart Rate Variability reflects directly the balance between Sympathic nervous system and Parasympathic nervous system. This paper discusses detailed study and characteristics of HRV and it has been found that by detecting respiratory peak, a narrowbandedmeasure of the high-frequency (HF band of the HRV can be definedas the respiratory frequency ±0.04 Hz. We have used respiratory frequency ±0.04, a narrower band to compare the error of the correlation estimate between the frequency ofthe respiratory peak and the power of the HRV with the power inthe usual Hz frequency band. The results show that using this band for the power estimationgives stronger correlation than earlier band and relation between the two is also analyzed for HRV in LF band. Index Terms Heart rate variability, Respiratory frequency, correlation. I. INTRODUCTION Heart rate variability (HRV is an extremely interesting and important scientific field, which enables the understanding of many physiological features related to autonomic activity and cardiovascular system. It also enables the development of novel, sophisticated methods for the analysis of fluctuations under steady and dynamic unsteady conditions. It has opened a wide range of new research topics and clinical applications. HRV refers to the beat-to-beat fluctuations in Heart Rate derived from the instantaneous inter-beat time intervals, RR intervals, around their mean values (HR or RR interval and is analyzed in two ways, i.e. in Time Domain and Frequency Domain []. It is usually calculated by analyzing a time series of beat-to-beat intervals derived from ECG as shown in Figure. Figure : An ECG Wave DOI: 03.AETS Association of Computer Electronics and Electrical Engineers, 03

2 Alternately beat-to-beat intervals can be derived from atrial pressure or from pulse wave signal measured by means of a photo-plethysmograph (PPG. In recent years, the study of changes in HR was being done with the purpose of finding new parameters and new criteria for better diagnosis of diseases associated with abnormal ANS activity. The effects of drugs and of external stimuli can be also better understood with analysis of HRV [-4]. A. Frequency domain characteristics of HRV The spectral components of HRV and blood pressure data can be used clinically to assess the ANS, providing separate measures of the sympathetic and parasympathetic systems. The high-frequency component in HRV appears to be mediated almost entirely by parasympathetic tone and low-frequency component is an indicator of sympathetic tone, but it is modulated by parasympathetic activity also [5-6]. The heart rate is recorded in terms of beats per minute Frequency plot of RR intervals is given in Figure. HRV signals contain well defined rhythms which include physiological information. Low frequency (LF range between 0.04 to 0.5 Hz and are usually considered as markers of sympathetic modulation. High frequency (HF range is between 0.5 to 0.4 Hz [0]and can contain the rhythms regulated by parasympathetic activity shown in Figure. Figure : Plot of RR interval in frequency domain with specific bands Parasympathetic activity is the major contributor to the HF component of HRV. Although many researchers consider LF area to involve sympathetic activity and some suggest that the LF area corresponds to both sympathetic and parasympathetic activity. II. STEPS INVOLVED IN DETERMINING PSD A. Power spectral density Measures of heart rate variability are increasingly being done in applications ranging from basic investigations of central regulation of autonomic system, to studies of fundamental links between psychological processes and functions. The classical time domain heart signal having RR intervals: I n = t n -t n - Where t n is the time instant at which the nth QRS peak occurs. From Figure 3, it becomes immediately clear that the RR intervals are non-equispaced in time [7]. Figure 3: Cardiac Event Series 479

3 This is well known that the Power spectral Density of RR interval series can be estimated with a number ofanalytical expressions. The different researchers have explained different methods to find out the heart rate variability in frequency domain. Till now, studies only mention the frequency band ranges i.e. VLF ( , LF ( , HF ( but no research explains the whole process of finding the powers in these frequency bands. The present aim is defining an appropriate procedure for finding the powers in the frequency bands and to discuss relation between HRV power and Respiratory frequency. B. Resampling&Choice of sampling frequencycorrelation Earlier the time series had been re-sampled using wide range of sampling frequencies i.e.,,.7, 3, 3. Hz etc. But many research papers have showed that the choice of re-sampling frequency should be arbitrary 4 hertz. The sampling frequency defines the number of samples per second taken from a signal to make a discrete signal. The common notation for sampling frequency is f s which stands for frequency (subscript sampled. Previously it was considered that RR interval is equi-spaced if the deviation of RR intervals from RR mean is small. In this case, the sampling frequency was taken as the reciprocal of the average of RR interval. Nyquist theorem states that the Nyquist rate is the minimum sampling rate which is required to avoid aliasing and is equal to twice the highest frequency. F max = Fs/ Where, F max is the maximum frequency and Fs = Sampling frequency directly taken by taking the reciprocal of average of RR interval, as the data is considered equispaced. In this case frequency chosen is 4Hz as it is best to avoid aliasing [7]. C. Interpolation &Normalization of RR interval Most of the DSP algorithms are designed for equispaced samples. These algorithms thus cannot be applied to RR beat signals as these signals are not equispaced. Many researchers assumed the samples to be equispaced if the deviation of intervals from RR mean is small i.e. in the interval spectrum method as sampling is function of beat number. Secondly many research papers has showed different techniques to find out the power spectral density without interpolation by using the parametric methods i.e. auto regressive approach and Lomb periodogram but the problem with the auto regressive approach is that it is very tedious because for this technique the order for the model should be exactly known and there is not any consistent approach for finding the order and Lomb periodogram results in ectopic beats and erroneous measurements. Two goals of the normalization process are: eliminating redundant data and ensuring data dependencies. RR interval Normalization can be done with the help of mathematical equation where Y is the signal after resampling and B is the normalized signal: Where, A is the mean of RR series. A = mean (Y (: B (: = (Y (: A/A D. Fast Fourier transform using Hann Window To convert a signal from the time domain to the frequency domain and vice versa is defined as jf t s( t e dt s( t jf t f e df Here, s(t is time signal, is frequency signal and f is frequency signal and j. 480

4 TABLE I. 58 MINUTE ANALYSIS OF SIGNAL MGH007 RESPIRATORY FREQUENCY, POWER IN HF BAND IN STANDARD, ±0.04 (RFBAND AND ±0.05(RFBAND signal mgh007( Every two minute Respi-ratory Frequeny New HF band definition(0.05 New HF band definition(0.04 HF(power using Standard Band( HF band using Respiratory Frequency ±0.05 HF band using Respiratory Frequency ± Correlation with respiratory frequency and HRV HF band Some more signals were analyzed for 30 minutes duration and correlation between respiratory frequency and HF HR and correlation is coming out more negative in ±0.04 RF Band. Some of the signals were analyzed with Welch Method,8 Window Length,Overlap 99(Hann and 50(Hann such as MIMIC 3, MGF/MGH

5 The expression is sometimes used. s( t e jt dt s ( t S e jt d ( s( t e jt dt j t s( t e d Fourier Transform is used for continuous time signals. And in order to do frequency analysis, the time signal infinitely observed. Under these conditions, the FT defined above yields frequency behavior of a time signal at every frequency, with zero frequency resolution. Stepwise calculation of the fast Fourier transform is; C = ^nextpow (N Where, N is the length of the RR interval series nextpow is the next highest power of. For example any integer n in the range from 53 to 04, nextpow (n is 0. Y = fft (hann, C/N Z = abs(y Where abs is the absolute value of values obtained after applying FFT. The results obtained after applying the FFT are the combination of real and imaginary values i.e. complex numbers. The plot shows the variation of amplitude with respect to frequency, the amplitude is taken on the Y-axis and frequency is on the X-axis. E. Power spectral density Power spectral density (PSD, describes how the power of a signal or time series is distributed with frequency. Power spectral density function (PSD shows the strength of the variations (energy as a function of frequency. The unit of PSD is energy per frequency (width and you can obtain energy within a specific frequency range by integrating PSD within that frequency range. PSD computation is done directly by the method called FFT: Power = Z (: ^ Y X Figure 4: Correlation between HF HRV and Respiratory frequency 48

6 F.Correlation between respiratory frequency and HRV The correlation coefficient is measures of the degree of linear relationship between two variables, X and Y. The correlation coefficient may take on any value between + and - as shown in figure 4 and correlation between HF and Respiratory Frequency for a signal mgh007 is given in table. There is a relationship exists between HRV and respiratory frequency. Spectral analysis of HRV provides an estimate of autonomic control of heart and has become a common standard in physiological and medical research. The oscillations around 0.5 Hz in spectrum constitute HF band and are related to respiration that is RSA. During expiration, the heart rate decreases and during inspiration, it increases. Thus, central frequency of HF component closely follows the respiratory frequency. HF variability, or RSA, mainly reflects parasympathetic or vagal activity [8]. The cross-power spectrum is nonparametric approach to characterize the correlation between two stationary processes x(n and y(n. Where x(n may be a HRV signal and y(n can be respiratory signal. The crosspower spectrum is defined as the DTFT of the cross-correlation function r (k, j S j r k ( k e jk Where ( k E x n yn k r ( The cross-power spectrum S e can be interpreted as the correlation between x(n and y(n at a given frequency. The normalized cross-power spectrum is defined by: j x S S and is known as the coherence function; normalization is done with the square-root of the two power spectra [9]. Magnitude squared coherence is given by: j j x S j S S y j S j j y j 0 j III. CONCLUSIONS The choice of this HF range in this case is not necessarily the optimal and other frequency ranges can be evaluated for the purpose of finding stronger correlation of HRV and respiratory frequency. This new definition of the HF band that is respiratory frequency ±0.04 gives a higher coherence (negative correlation between the respiratory frequency and the power of the HRV than the correlation using the traditional frequency band. Also correlation analysis of other HRV bands (LF Band with respiratory frequency is done and it is found that also there is negative relationship exists between respiratory frequency and LF HRV band. REFERENCES [] Anurupa, Mandep Singh, Relation between Heart Rate Variability and Respiratory Frequency: A Review", International Conference on Biomedical Engineering and Assistive Technologies (Beats-00, December 7-9, 00, NIT Jalandhar, INDIA. [] Leslie Cromwell, Fred J Weibell, Erich A. Pfeiffer, Biomedical Instrumentation and Measurements, nd Edition, Pearson Education, 003. [3] B. MeA. Sayers Analysis of Heart Rate Variability, Imperial College, London, Ergonomics, vol. 6, No., pp 7-3, 973. [4] Luczak H, Lauring WJ., An analysis of heart rate variability, Ergonomics, 6, pp 85-97, 973. [5] M. V. Kamath, E. L. Fallen. Power spectral analysis of HRV: a non-invasive signature of cardiac autonomic functions, Critical Review Biomedical Engineering, pp 45-3, 993. [6] R.D Berger, S. Aksalrod, D. Gorden and R.J.Cohen, An efficient algorithm for spectral analysis of heart rate variability, IEEE Transactions on Biomedical Engineering, vol. 33, pp ,

7 [7] D. Singh,K.Vinod,SCSaxena, Sampling frequency of RR interval time series for spectral analysis of HRV, Journal of Medical Engineering & Technology, 8:6, 63-7, 004. [8] Aysin,B, Aysin,E, Effect of Respiration in Heart Rate Variability (HRV Analysis, EMBS: 8th Annual International Conference of the IEEE,pp ,Aug 006. [9] Leif Sornmo, Pablo Laguna, Bioelectrical Signal processing in cardiac and Neurological Applications, ELSEVIER Academic Press. [0] Maria Hansson-Sandsten, Member, IEEE, and Peter Jönsson, Multiple Window Correlation Analysis of HRV Power and Respiratory Frequency, IEEE transactions on biomedical engineering, vol. 54, No. 0, pp ,October

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