This paper shows that variations in breathing patterns broaden heart rate variability (HRV) spectral bands and increase the power amplitude of low-frequency bands. Because of these influences, spectral markers for HRV signals, such as the quotient between spectral power at different frequency bands, should be compared only under controlled breathing conditions or after considering the effect of variations in breathing patternsPeer Reviewe

García González, Miguel Ángel

Pallàs Areny, Ramon

Vázquez Seisdedos, Carlos

Physiological Measurement

English

M A  García-González

C Vázquez-Seisdedos

R Pallàs-Areny

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Variations in breathing patterns increase low frequency contents in HRV spectra

Pallàs-Areny, Ramon

UPCommons. Portal del coneixement obert de la UPC

Physiol. Meas. 21 (2000) 417–423. Printed in the UK PII: S0967-3334(00)13410-0Variations in breathing patterns increase low frequencycontents in HRV spectraM A Garcı´a-Gonza´lez†, C Va´zquez-Seisdedos†‡ and R Palla`s-Areny†† Instrumentation and Bioengineering Division (DIB), Department of Electronic Engineering(DEE), Universitat Polite`cnica de Catalunya (UPC), C/Jordi Girona 1–3, Campus Nord EdificiC-4, 08034 Barcelona, Spain‡ Department of Telecommunication, Universidad de Oriente, 90900 Santiago de Cuba, CubaE-mail: magarcia@eel.upc.esReceived 20 April 2000Abstract. This paper shows that variations in breathing patterns broaden heart rate variability(HRV) spectral bands and increase the power amplitude of low-frequency bands. Because ofthese influences, spectral markers for HRV signals, such as the quotient between spectral power atdifferent frequency bands, should be compared only under controlled breathing conditions or afterconsidering the effect of variations in breathing patterns.Keywords: heart rate variability, spectral analysis, respiratory sinus arrhythmia, controlledrespiration1. IntroductionHeart rate variability (HRV) analysis has become a useful tool to study the relationship betweenthe autonomic nervous system (ANS) and the cardiovascular system (CS). HRV is usuallystudied from the RR time series, either by time-domain methods (Kleiger et al 1993), nonlineardynamics (Wada et al 1993), or spectral analysis (Pagani et al 1986). HRV analysis hasbeen applied, for example, to study the risk of cardiac electrical instability after myocardialinfarction (Bigger et al 1991), to diagnose diabetic neuropathy (Pagani et al 1988), to assessre-innervation after cardiac transplantation (Sands et al 1989) and to evaluate exercise training(Arai et al 1989).Spectral analysis describes the frequency distribution of signal power. Analysis ofrhythmic events in the RR time series permits us to infer the state of biological oscillatorsthat modulate the CS, the sympathetic and vagal efferent activity, humoral factors and thesinus node (Task Force 1996). Usually, the power spectrum of the RR time series is dividedinto three bands: the very-low-frequency (VLF) band, the low-frequency (LF) band, and thehigh-frequency (HF) band. Vagal activity is the major contributor to the HF component mostlybecause of the respiratory sinus arrhythmia (Pomeranz et al 1985). The LF band is assumedto reflect sympathetic modulations or both sympathetic and vagal activity. In HRV spectralanalysis, the biological oscillators that modulate the CS are commonly considered to remaininvariable. Nevertheless, the amplitude and frequency of that modulation is seldom stationaryin practice.0967-3334/00/030417+07$30.00 © 2000 IOP Publishing Ltd 417418 M A Garcı´a-Gonza´lez et alThis work investigates the effects of breathing-frequency variations in the spectralquantification of HRV signals. Respiratory activity causes a modulation in RR time seriesat the breathing frequency, which is termed respiratory sinus arrhythmia. The amplitude ofthis modulation depends on vagal tone (Kollai and Mizsei 1990) and on the breathing frequencyitself (Womack 1971) (high breathing frequencies yield smaller amplitude oscillations in theRR spectrum than low breathing frequencies). Hence, changes in breathing frequency shouldbe reflected in the RR time series as a modulation in both amplitude and frequency, and resultin a modified spectrum of the RR time series as compared to that obtained during periodicbreathing. Consequently, we can expect that variations in breathing patterns change spectralmarkers in both the HF and LF bands of RR time series spectra. These changes exclusivelydue to the breathing pattern (i.e. the cause) should not be mistaken for abnormal changes inHRV (i.e. changes in the cause-to-effect relationship).This paper shows that variations of the breathing frequency increase the LF/HF index.First, the theoretical spectrum of FM and low-pass filtered signals is presented in order tosubstantiate the working hypothesis. Next, spectral estimation methods of actual time series arebriefly discussed in order to justify the spectral analysis method used here. Finally, simulationand experimental results are presented and discussed in order to draw some conclusions.2. Theoretical spectrum of FM and low-pass filtered signalsThe spectrum of a sine wave whose frequency is fc and variance σ 2c ,xc(t) = σc√2cos(2πfct) (1)is a spectral peak located at fc. If fc varies with time, the signal spectrum changes. Considerfor example the frequency modulated (FM) signalxFM(t) = σc√2cos(2πfct + 2πf∫xm(λ) dλ)(2)where f is the frequency deviation and xm(t) is the modulating signal with variance σ 2m andprobability distribution function (PDF)pxm (x). The quasi-static approximation (Peebles 1976)shows that the two-sided power spectrum of xFM(t) when the frequency of variation is slowcompared to fc isSxFMxFM(f ) =σ 2c σ2m2f[pxm(f − fcf)+ pxm(f + fcf)]. (3)Therefore, frequency variation implies a broadening of the spectral peak, which depends onthe PDF of the modulating signal.Since there is a low-pass filtering action between breathing frequency and heart ratefluctuation (Womack 1971), we are interested in the spectrum of the output y(t) of that filter,which isSy(f ) = σ2c σ2m2f[pxm(f − fcf)+ pxm(f + fcf)]|HLP(f )|2. (4)That is, the power spectrum of y(t) is that of xFM weighted by the filter transfer function. Hence,the low-frequency components of xFM(t) will be enhanced as compared to the high-frequencycomponents.Breathing patterns influence HRV spectral bands 4193. Spectral estimation of RR time seriesThe spectral estimation of time series must consider the finite number of samples available andthe sampling process itself. In an RR time series (tachogram), the information is provided byeach QRS arrival, which results in non-uniform sampling, leading to spectral artifacts (Mateoand Laguna 2000). Resampling the tachogram with splines yields a uniformly sampled andinterpolated RR time series, which avoids artifacts.Spectral estimation methods can be either non-parametric, such as the periodogram andits modifications (Barlett, Welch and Blackman–Tukey periodograms), or parametric (AR,MA and ARMA modelling). The need for high-frequency resolution, the finite length ofthe time series, the smoothness of the spectra and its capability of identifying periodicalcomponents immersed in noise favoured the extended use of parametric estimation methods.Nevertheless, non-parametric methods are more accurate than parametric methods to quantifypower distribution in frequency bands (Mateo and Laguna 2000), which is the basis for markersin HRV spectral analysis. Hence, we estimate the spectra from the periodogram (squaredmodulus of the FFT) of the tachogram resampled and interpolated by cubic splines.Finally, frequency bands in HRV variability analysis must be delimited according to theintended application. Since the narrower the LF band, the smaller the LF/HF index, wenormalize the LF/HF index to the signal bandwidth according toLF/HFn = SLFSHFBWHFBWLF. (5)We are interested in variations in the LF/HFn index because of variations in breathingfrequency. Therefore, we will analyse RR time series during different breathing patternsthat involve respiratory frequencies from 0.1 Hz to 0.2 Hz. Consequently, we define the threefollowing frequency bands (see figure 1):f  0.03 Hz VLF band0.03 Hz < f  0.09 Hz LF band0.09 Hz < f < 0.4 Hz HF band.(6)According to this definition, BWLF = 0.06 Hz and BWHF = 0.31 Hz.4. Results from simulated tachogramsThe first step in assessing how variations in respiratory frequency affect the LF/HFn index isto analyse simulated tachograms that include different beat-to-beat interval modulations. A5 min fragment of a periodic RR signal (in milliseconds) with fc = 0.15 Hz isRRp(n) = 1000 + 100 cos(2π × 0.15n) n ∈ [1, . . . , 300] (7)where n is the heartbeat number. Hence, the shortest RR interval is 900 ms, the longest is1100 ms and the average is 1000 ms. A 5 min fragment of an FM modulated RR signal (inmilliseconds) with the same maximum, minimum and mean of RRp and with fc = 0.15 Hz,f = 0.05 Hz and fm = 0.01 Hz isRRFM(n) = 1000 + 100 cos[2π × 0.15n + 2π × 0.05n∑i=1cos(2π × 0.01i)]n ∈ [1, . . . , 300]. (8)Both tachograms are resampled at 4 Hz prior to the spectral estimation. Figure 1 shows thatthe respective frequency spectra are quite different in spite of the average breathing frequency420 M A Garcı´a-Gonza´lez et alFigure 1. Spectra of simulated RRFM and RRp.Table 1. Normalized power-spectra ratio index (LF/HFn) for the RR time series under periodic(RRp) and FM modulated (RRFM) breathing after low-pass filtering with different cut-offfrequencies.0.05 Hz 0.07 Hz 0.10 Hz 0.13 Hz 0.15 Hz 0.20 HzPeriodic 796× 10−6 6.9× 10−6 0.7× 10−6 5.80× 10−9 2.07× 10−9 3.62× 10−6FM 0.68 0.48 0.23 0.12 0.09 0.05being the same (0.15 Hz). The LF/HFn index is also very different: 0.03 for RRFM and7× 10−9 for RRp.An improved simulation includes the low-pass filtering effect reported by Womack (1971).We have computed the LF/HFn index for the outputs of several low-pass filters whose inputswere RRp and RRFM. The filters used were Butterworth fourth-order and bidirectional, withcutoff frequencies 0.05 Hz, 0.07 Hz, 0.10 Hz, 0.13 Hz, 0.15 Hz and 0.20 Hz. Table 1 showsthe results. For the RRFM signal, the lower the cut-off frequency, the higher the LF/HFn index.For the RRp signal, the cut-off frequency strongly affects the LF/HFn index because of thesmall power in the LF band. In any case, the LF/HFn index is always smaller for periodic RRsignals than for FM RR signals.Actual RR signals will be influenced by other heart rate variability factors in addition tothe respiration. Therefore, in order to consider the spectral power in the LF band resulting onlyfrom the breathing pattern, we will high-pass filter the tachogram before performing spectralanalysis. We have filtered the signals with a Butterworth fourth-order bidirectional high-passfilter with a cut-off frequency of 0.05 Hz. The results show that this filter has a negligibleeffect on the LF/HFn index for the simulated signals.5. Experimental resultsWe have recorded RR time series and breathing signals in 20 healthy subjects (30.9±5.1 years)in supine position. Measurements for each subject induced five stages with well definedconditions. Each stage lasted for 5 minutes and was followed by a 2 minute resting interval.Breathing patterns influence HRV spectral bands 421Figure 2. Measurement system.Before starting, subjects were in supine position for 5 minutes. In the first stage, subjectsbreathed at will. In the second stage, subjects were asked to breathe periodically at 0.15 Hzby following a signal on an oscilloscope screen. In the third stage, subjects were asked tobreathe according to an oscilloscope displaying a 0.15 Hz signal modulated in frequency by0.01 Hz with a 0.05 Hz frequency deviation. In the fourth stage, subjects returned to periodicalbreathing at 0.15 Hz, and during the fifth stage, subjects breathed at will again.Figure 2 shows the measurement setup. The isolated ECG amplifier (bandwidth 0.5 Hzto 500 Hz, gain 1000) recorded the standard II ECG lead. A nasal NTC thermistor yielded thebreathing rhythm and amplitude. Since we were interested in the effects of breathing frequency,not amplitude, records whose amplitude were too different were discarded. ECG and breathingsignals were sampled at 500 Hz in eight subjects and at 4 kHz in twelve subjects by a plug-in PC data-acquisition card (DT2821, Data Translation) and stored for further processing.RR time series were derived in two steps. The first step yielded an estimated location ofeach QRS complex by detecting when the ECG signal, low-pass filtered at 30 Hz and furtherdifferentiated, exceeded a threshold set at 75% of the maximal amplitude of the filtered signal.The second step corrected the estimated location by maximizing the correlation between thefirst QRS detected and the following ones. After properly detecting each QRS, the tachogramwas computed by differentiating the position of each QRS. From the tachogram, a resampledRR time series was obtained with a sampling frequency of 4 Hz by interpolating with cubicsplines. In order to remove low-frequency components present in the tachogram but unrelatedto breathing patterns, the tachogram was high-pass filtered with a Butterworth fourth-orderbidirectional filter with cut-off frequency at 0.05 Hz. Next, the periodogram was estimated foreach subject and each stage, and the LF/HFn was computed.Figure 3 summarizes the results for the 20 subjects. Both sampling frequencies yieldedthe same results. The LF/HFn index is largest when breathing freely and smallest whenTable 2. Significance of the differences between LF/HFn for the different breathing stages. Ifp < 0.05, the difference is considered to be significant.Periodic 1 FM Periodic 2 Free 2Free 1 0.0009 0.0254 0.0006 0.1926Periodic 1 0.0014 0.3390 <0.0001FM 0.0144 0.0003Periodic 2 <0.0001422 M A Garcı´a-Gonza´lez et alFigure 3. LF/HFn index for the 20 subjects measured and the five stages (starting and finishingwith breathing at will—‘free’). Mean, standard deviation, fifth and 95th percentiles, and maximumand minimum are represented for each stage.breathing periodically. FM breathing yields an intermediate index value. Differences betweenstages were tested by a paired Student t-test whose results are shown in table 2. There are nosignificant differences between the two stages of free breathing, nor between the two stagesof periodic breathing. There are significant differences between free and periodic breathingbetween free and FM breathing and between periodic and FM breathing.6. DiscussionThe experimental results for periodic breathing show an LF/HFn index smaller than that forFM breathing, the same as for the simulated data in figure 1 (signal RRp). Nevertheless, theLF/HFn index is larger for experimental than for simulated data. This is because the LF bandof experimental data includes other modulations, such as those of the baroreceptor that arenot completely rejected by the high-pass filter applied to the tachogram. It may also be dueto drifts of the mean heart rhythm, to the non-sinusoidal waveform of the respiratory sinusarrhythmia and to changes in the transfer function between the breathing rhythm and the heartrate.FM breathing yields a large LF/HFn index as predicted from the theoretical analysis andfrom simulated data (RRFM). Free breathing yields even larger values for the LF/HFn indexthan FM breathing, which is consistent with the large variability in breathing patterns whensubjects are allowed to breathe at will. Therefore, interpreting changes in the LF/HFn indexrequires us to consider the breathing patterns simultaneous with the recorded RR series.7. ConclusionsThe respiratory sinus arrhythmia reflects the relationship between the autonomic nervoussystem and the cardiovascular system, but it also reflects the breathing pattern. Any variation inthis pattern influences the RR time series and modifies its power spectrum. Periodic breathingyields low values for the LF/HFn index. Breathing at will yields the larger LF/HFn values.Therefore, comparisons between the LF/HFn index for different subjects in HRV studies mustconsider the actual breathing pattern.Breathing patterns influence HRV spectral bands 423ReferencesArai Y, Saul J P, Albrech P et al 1989 Modulation of cardiac autonomic activity during and immediately after exerciseAm. J. Physiol. 256 H132–H141Bigger J T, Fleiss J L, Rolnitzky L M, Steinman R C and Schneider W J 1991 Time course of recovery of heart periodvariability after myocardial infarction J. Am. Coll. Cardiol. 18 1643–9Kleiger R E, Bosner M S, Rottman J N and Stein P K 1993 Time-domain measurements of heart rate variabilityJ. Ambul. Monit. 6 1–18Kollai M and Mizsei G 1990 Respiratory sinus arrhythmia is a limited measure of cardiac parasympathetic control inman J. Physiol. 424 329–42Mateo J and Laguna P 2000 Improved heart rate variability signal analysis from the beat occurrence times accordingto the IPFM model IEEE Trans. Biomed. 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