The human heart’s ability to adapt to changing circumstances can be observed in the variability of the heart rate (HR). Heart Rate Variability (HRV) analysis has become a powerful measure to quantify and evaluate the control of the HR. HRV measures reflect the direct regulative influence of the Autonomous Nervous System (ANS) on the cardiac system and can deliver insights to the state of cardiac health. A healthy person normally shows a balanced sympathetic-parasympathetic autonomous control of the HR, while an unbalanced influence represents an increased risk of cardiac death.
The respiration also influences HR and HRV. The effect is called Respiratory Sinus Arrhythmia (RSA) and describes the lengthening of R-peak to R-peak (RR) intervals of the heart during expiration and shortening during inspiration. This respiratory influence might therefore make an HRV interpretation more complex. In spectral HRV measures the power in the frequency range between 0.15 and 0.4 Hz is considered to be a measure for para-sympathetic control of the heart rate, while the spectral component of RSA also has its major influence in this interval . Nevertheless, the respiration rate is generally not restricted to the frequency interval from 0.15 to 0.4 Hz. The breathing rate can be as low as 0.1 Hz, when the person is very relaxed. In this case the ANS influence would be estimated inaccurately. In literature, it is often proposed to record the HR signals for HRV analysis while the subject is breathing at a constant respiration rate between 0.15 and 0.4 Hz, to fix its spectral bandwidth.
This paper proposes to separate the respiratory influence on HRV by filtering the constant respiratory component in the RR time series in the time domain using an adaptive notch filter. The removal allows to analyze the HRV parameters and their ANS influence without respiration. The RSA element in RR spectra is identified and a matching notch filter is designed, which removes the respiratory component while leaving the power at other frequencies unchanged. Lastly, the new respiration free HRV parameters are compared to the original ones to visualize new possible HRV interpretation approaches.
2.1 Experimental setup and data
To evaluate the developed methods data from the publicly available data set ”Exaggerated Heart Rate Oscillations During Two Meditation Techniques” from Physionet  were used. The recorded data comprises RR time series and its respective time sampling points of 9 healthy women and 5 healthy men. The age of the subjects ranges between 20 and 35. The signals were recorded for 10 min, while the subjects were breathing at a constant respiration rate of 0.25 Hz in a supine position.
Prior to the actual respiration removal algorithm the RR time series had to be analyzed for artifacts. The RR time series might comprise falsely detected R-peaks or a physiological correct R-peak might have not been classified correctly during R-peak detection in the ECG signal. For this reason a common approach proposed by  was chosen to detect and remove erroneous RR intervals from the RR time series. Every RR interval was compared to its successor and its predecessor by computing the ratio:(1)(2)
The ratio of successive RR intervals was compared to a threshold D (0 <D < 1). This detection method was based on the fact, that successive RR intervals do not differ by approximately more then 20% . For this reason D was set to 0.2. The RR intervals, which do not fulfill both inequalities (1), (2) are removed from the time series. Subsequently, the RR time series had to be interpolated for spectral analysis and decoupling, since they are not equidistantly sampled. The interpolation was performed using the hermite interpolation method at a sampling rate of Fs = 4 Hz .
2.3 Decoupling HR from respiration
2.3.1 Detection of the respiratory component in the RR spectrum
The power spectral density (PSD) of the RR time series had to be estimated, for spectral HRV parameters as well as for detecting the frequency of the constant respiratory influence.
The PSD estimation was performed using Welch’s method . Three parameters, the Welch segment length, the segment overlap and the zeropadding length have to be selected, to enable good spectral analysis. These parameters were chosen based on the HRV guidelines in .
At first the center frequency of the respiratory influence on the RR-PSD was detected, since the subjects might not be able to breath at the exact predetermined rate. It was assumed that the respiration rate is always higher than 0.05 Hz and below 0.5 Hz. Higher respiration rates are normally not detectable in the RR time series. This is due to the fact, that the instantaneous HR is the sampling rate of the RR time series, thus aliasing can appear. In this PSD interval [0.05 Hz,0.5 Hz] the global maximum Presp and its corresponding spectral sampling point fresp were obtained. The maximum search is applicable due to the fact, that the respiratory effect has the largest power component in the RR-PSD apart from possible very low power below 0.04 Hz.
The Full Width Half Maximum (FWHM) was selected as design parameter for the spectral width fw of the removal filter. The closest sampling points to fresp with P (f) Presp/2 were calculated to the left fL and to the right fR of the respiratory peak with fw = |fR − fL| as the resulting filter width. In case one of the neighboring minima fminL or fminR was closer to fresp than fL or fR the filter width was reset to fw = |fminR − fminL|.
The main task of the removal was the spectral filter design. Two adequate Notch filter approaches were chosen: a standard Infinite Impulse Response (IIR)-Notch Filter and a Raised Cosine filter approach. The RR time series was filtered in time domain calculating the convolution with the impulse response of the filter. The two approaches are explained in the following.
2.3.2 Decoupling using an IIR-Notch filter
A second order IIR-Notch filter can be designed to have two poles at z = r·e±j2πf0ts and two zeros at z = e±j2πf0ts . The center frequency of the notch is set to f0 = fresp, while the parameter r (0<r<1) defines the radius of the poles in the z-plane. The distance (1-r) between poles and zeros thus defines the width of the notch. The trade off has to be made between width of the notch and steepness of the filter. To further increase the steepness of the filter, while allowing wider notches, a higher order Notch filter can be designed, cascading second order notches:(3)(4)
Equation 4 represents the z-transform of the IIR-Notch filter. K = 5 second order notches are cascaded for the applied decoupling method. The parameters ri have to be computed in order to match with the previously calculated peak width fw of the respiratory peak in the RR-PSD. This is done using an optimization method pre-implemented in MATLAB®.
The RR time series is finally filtered in time domain using a forward-backward filtering approach to prevent phase shift induced by the filter. Therefore, a filter with the order 10 is convoluted twice with the RR time series resulting in a total order of 20.
2.3.3 Decoupling using a Raised Cosine filter
The Raised-Cosine filter is commonly used in telecommunications engineering for impulse shaping. The filter allows signal transmission with no intersymbol interference . This is achieved by designing a filter with an impulse response, which has zeros at all multiples of the symbol duration time Tw of the communication channel. The impulse response of the filter is given by:(5)
with . The inverse of Tw is the symbol or Baud rate and is equal to the FWHM width of the filter in the spectral domain. For the purpose of removing the effect of respiration from the RR time series, the Baud rate had to be set to the width of the respiratory peak fw in the RR-PSD. The second parameter (0 1) in equation 5 defines the steepness of the filter in the spectral domain or the rate the side lobes decrease in the impulse response. For = 0 the z-transformation describes a rectangular curve filter and a sin (t)/t function describes the impulse response. This is the steepest possible filter. To avoid a phase shift, the parameter was set to a small value = 0.1. Still the Raised Cosine filter does not remove the spectral respiratory component in its original form. To remove the respiratory component by filtering in time domain the fillter filt(n) had to be set up the following way:(6)
The Raised Cosine impulse response has to be modulated with the center frequency of the spectral respiratory component in the RR time series fresp and subtracted from a dirac function to invert the filter and become a notch filter. The factor a hereby adjusts the filter to have a gain of 0 at fresp. The filtering is finally performed using the convolution.
2.4 Heart rate variability analysis
The respiration removal method returns a decoupled RR time series without the respiratory component in the PSD. This time series is still sampled with the interpolation sampling rate of Fs = 4 Hz, which is appropriate, if we want to compute the spectral HRV parameters. Nevertheless, for the time domain HRV analysis, it is adequate to have sample values at the original RR time series sampling points, in order to compare the HRV measures before and after decoupling. The decoupled RR time series is therefore re-sampled to the original sampling points, again using the hermite interpolation method.
The HRV parameters SDNN, rMSSD, pNN50, HF, LF and  were chosen to analyze the ANS control of the RR time series and compare HRV measures before and after decoupling HR from the RSA influence.
The filters remove the effect of the respiration from the RR time series, which is visually verified in Fig. 2. Both Notch and Raised Cosine filter perform well with no significant difference. Exemplary for subject 5, the notch filter reduces the SDNN HRV measure, which represents the total power in the RR time series, by 77.5%, while the Raised Cosine filter reduces it by 78.25%. Therefore the HRV has decreased and has been seperated from the respiration.
Comparing the new uncoupled parameters to the original HRV measures, it could be postulated, that the major deviation in the HRV parameters among different subjects is induced by respiration, since the boxplots of the uncoupled HRV paramters in Fig. 3 show smaller interquantile distances than the original HRV boxplots.
5 Limitations and outlook
The implemented method is able to decouple an RR time series from its respiratory influence in cases of constant harmonic breathing. To include cases, when the subject is breathing naturally at spontaneous respiration rates, the algorithm must be extended.
Accuracy could be improved by including respiration signals or estimating them from the ECG. Furthermore more data is needed to definitely evaluate the performance of the methods.
Finally it could be analyzed if the decoupling techniques are also suitable for other HRV applications such as risk stratification after myocardial infarction.
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About the article
Published Online: 2015-09-12
Published in Print: 2015-09-01
Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent has been obtained from all individuals included in this study. Ethical approval: The research related to human use has been complied with all the relevant national regulations, institutional policies and in accordance the tenets of the Helsinki Declaration, and has been approved by the authors’ institutional review board or equivalent committee.