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1 Institute of Physiology, Faculty of Medicine of Lisbon, Avenue Professor Egas Moniz, 1649-028 Lisbon, Portugal, Unit of Autonomic Nervous System, Instituto de Medicina Molecular, Lisbon, Portugal 2 Institute of Biophysics & Biomedical Engineering, Faculty of Sciences of Lisbon, Campo Grande, 1749-016 Lisbon, Portugal 3 CMAF, Lisbon, Portugal
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Abstract |
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(Received 28 March 2007;
accepted after revision 26 April 2007; first published online 27 April 2007)
Corresponding author I. Rocha: Instituto de Fisiologia, Faculdade de Medicina de Lisboa, Avenue Professor Egas Moniz, 1649-028 Lisbon, Portugal. Email: isabelrocha{at}fm.ul.pt
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Introduction |
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The analysis of heart rate and blood pressure variability by applying fast Fourier transform (FFT) and autoregressive spectral analysis to these signals has made a very important contribution to autonomic evaluation. In particular, FFT decomposes the signals into a series of sine and cosine functions of different frequencies and amplitudes, allowing the definition of a power spectrum in which three major ranges of frequencies for human subjects can be recognized: very low frequencies (VLF, 0–0.04 Hz), low frequencies (LF, 0.04–0.15 Hz) and high frequencies (HF, 0.15–0.4 Hz; Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology, 1996). The LF band has been related mainly to sympathetic outflow, while HF is related to parasympathetic outflow and respiratory rhythm. The LF/HF ratio is widely used as an indicator of the balance between sympathetic and parasympathetic outflows (Malliani et al. 1991a, 1994; Zaza & Lombardi, 2001). However, the application of FFT has an important limitation (Duhamel & Vetterli, 1990; Parati et al. 1999), which is that it requires a stationary signal and a long period of data collection (at least 5 min), making it an unsuitable tool for the analysis of short and transient changes of blood pressure and heart rate that occur during autonomic tests such as those described above. Wavelet analysis has been proposed (Mallat, 1998; Wiklund et al. 2002; Mainardi et al. 2002; Postolache et al. 2004; van den Berg et al. 2005, Urbancic-Rovan et al. 2006; Belova et al. 2007) as a method to overcome and complement information taken exclusively in the frequency domain. With discrete wavelet transform (DWT), a time–frequency analysis can be done to allow the visualization in time of the contribution of LF and HF to the observed changes of a particular signal.
In the present study, we describe the application of wavelet analysis to the acute changes of blood pressure and heart rate signals recorded during standard manoeuvres used to evaluate autonomic function (head-up tilt, HUT; cold pressor test, CPT; deep breathing, DB; and Valsalva manoeuvre, VM) and we discuss its usefulness for the investigation of the autonomic function.
A preliminary report of part of this study was communicated to the European Federation of Autonomic Societies (Silva-Carvalho et al. 2006; Ducla-Soares et al. 2006).
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Methods |
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Experimental protocol
After a rest period of 15 min in the supine position, the subject was head-up tilted to a level of 60 deg on an electrical table at a constant speed for 7 min and then returned to the horizontal position. The duration of the tilting manoeuvre to and from the supine position was of 15 s for each change of position. Following recovery to a supine position, a second rest period of 15 min in the supine position was allowed to guarantee a stable condition, after which the subject's right hand was immersed in ice-cold water (4°C) for 1 min. The subject was instructed to breath normally and to avoid sustained inspiration that would mimic a Valsalva manoeuvre. After a third resting period of 15 min in a sitting position, the subject was instructed to breath, for a period of 15 s, against a pressure of 40 mmHg after a deep inspiration (Valsalva manoeuvre). After this manoeuvre, a final rest period of 15 min was allowed to elapse before the same subject was instructed to breath deeply at a rate of 6 breaths min–1, guided by a metronome, for a period of 1 min (deep metronomic breathing).
Data analysis
Data were analysed using discrete wavelet transform (Db12; see signal acquisition and processing section below) applied to systolic blood pressure (SBP) and R–R intervals (RRI) derived from arterial blood pressure and ECG, respectively. For each autonomic test, data analysis was done as follows.
Head-up tilt. The analysis of SBP and RRI was done on four periods: (1) the last 2 min of the resting period, as a control (CTR); (2) during the 15 s that involved the change from supine to standing position (TT); (3) at 60 deg, during the first minute of tilt adaptation (TA1); and (4) at 60 deg, during the first minute after TA1 (TA2). In each of these 1 min periods, data analysis was performed in periods of 10 s, the period of 10 s that had the largest change from maximum to minimum was the one chosen to compare with CTR.
Cold pressor test. The analysis of the cardiovascular variables was done during two periods: (1) the last 2 min of the resting period just prior to the test (CTR); and (2) during 1 min, divided into six epochs of 10 s, the period of 10 s with the larger change from maximum to minimum was the one chosen to compare with CTR.
Valsalva manoeuvre. The analysis of SBP and RRI was done on three periods: (1) the last minute of the resting period just prior to the test (CTR); (2) during 15 s of the Valsalva manoeuvre (VM); and (3) during the next 35 s after VM (postVM).
Deep breathing test. Data analysis was done on two periods: (1) the last minute of the resting period just prior to the test (CTR); (2) during 1 min of DB, divided into six epochs of 10 s, the period of 10 s that had the largest change from maximum to minimum was the one chosen to compare with CTR.
Signal acquisition and processing
All data were acquired at 1 kHz and were analysed on the time–frequency domain using discrete wavelet transform (DWT) using wavelet Daubechies 12 (Db12). This was selected because the shape of this particular wavelet resembles the type of feature present in the time series (Postolache et al. 2003, 2004).
Data were processed in an Origin environment (OriginLab, Origin Lab Scientific Graphing and Analysis Software, Origin Lab Corporation, Northampton, MA, USA). A peak-to-peak routine was implemented in order to detect blood pressure and ECG peaks and to reconstruct the time evolution curve of systolic blood pressure and heart rate, which was then computed in an Matlab environment (MathWorks, Natick, MA, USA). The RRI and SBP were interpolated by cubic spline and resampled (resampling period = 0.193 s) to ensure that the centre of the frequency range of interest matched the central frequency associated to one of the scales of the DWT analysis. The Matlab Wavelet Toolbox (Matlab, MathWorks) was used to implement the DWT Db12 analysis of the resampled data.
Briefly, the resampled RRI and SBP time series were decomposed (fRR(t) and fSBP(t)) into a sum of details and approximation at different scales of resolution. The central frequency associated with each scale, fc, was calculated by fc
=
where Fc is the central frequency of the used wavelet, a is equal to 2–j where the scale is j and 
is the resampling period. The signal was decomposed in 12 scales. The wavelet transform of the analysed signals at scale j and position µ is computed using the relation
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| (1) |
is a wavelet function, Wf(µ, j) are the wavelet coefficients at scales and f(t) either fRR(t) or fSBP(t). The selected wavelet coefficients for each detail relate to signal frequencies between 0.038–0.15 Hz (LF) and 0.15–0.6 Hz (HF; Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology, 1996). The square of the details amplitude (SqA) was then calculated and, for a certain interval of time, the representative value of LF and HF was considered as the average of SqA across the details associated with the frequency ranges of interest. Wavelet analysis was implemented on data collected at the different time periods, as described above.
Statistical analysis
For CPT and DB, statistical analysis of the differences of LF, HF and LF/HF between the mean of control values and the mean values of each individual period of analysis was made using Student's unpaired t test and differences were considered significant where P < 0.05 (GraphPAD Instruments). Statistical analysis for HUT and VM data was performed using repeated ANOVA (Bonferroni test). All data were expressed as means ± S.E.M.
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Results |
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In all subjects, head-up tilt evoked the characteristic fall in systolic blood pressure followed by a recovery accompanied by a further increase followed by a decrease of heart rate (Low, 1997; Imholz et al. 1990), as shown in Fig. 1.
Wavelet analysis (Db12) of SBP values showed a significant increase of the LF band during TA1 periods (Fig. 2, left panels, and Table 1). No significant changes were observed in HF bands (see Table 1).
The RRI values computed by wavelets (Db12) showed a significant increase of the LF band during the TA1 period but a significant decrease of the HF band in the TA1 and TA2 periods (Fig. 2, right panels, and Table 1). The LF/HF ratio for RRI increased significantly during the TA1 and TA2 periods (Table 1).
Cold pressor test
The cold pressor test provoked the typical progressive increase of blood pressure (Hilz & Dutsch, 2006) that persisted during the time of immersion (Fig. 3, left panels). Wavelet analysis (Db12) of the SBP signal showed an increase in LF and the LF/HFSBP ratio without significant changes in HF values (Fig. 3, right panels).
Valsalva manoeuvre
In all subjects, the Valsalva manoeuvre, a sustained expiratory effort or strain against a closed glottis, evoked the characteristic changes in blood pressure and heart rate (Felker et al. 2006). Four clearly defined phases were evident: phase I, an increase in blood pressure due to the onset of the strain and a decrease in heart rate; phase II, a sharp decrease in blood pressure below baseline levels during the maintenance of the strain that was followed by an increase in pressure accompanied by an increase in heart rate; phase III, a short decrease in arterial pressure related to the release of the strain and an increase in heart rate; and phase IV, an overshoot of blood pressure and bradycardia (Fig. 4).
Wavelet analysis (Db12) of SBP values showed a significant increase of the LF band during both VM and postVM periods (Fig. 5, left panels, and Table 2).
The RRI values computed by wavelets (Db12) showed a significant increase of the HF band during the postVM period (Fig. 5, right panels, and Table 2).
Deep breathing
The deep metronomic breathing test is one of the most used autonomic tests that attempts to standardize respiratory changes and their relation to heart rate, hence to vagal activity. An expiratory–inspiratory difference or ratio can be calculated from the maximum and minimum heart rate values during testing (Genovely & Pfeifer, 1988; Mathias & Bannister, 1999; Hilz & Dutsch, 2006). The deep breathing test elicited the typical modulation of blood pressure by respiration and particularly marked changes in R–R intervals (Fig. 6).
On wavelets analysis (Db12) of the RRI signal, the parasympathetic band is shifted to the frequency range of the LF band with a significant increase of its amplitude (Fig. 6, middle and bottom panels).
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Discussion |
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The variability of biological signals, mainly heart rate signals, was initially regarded as a disturbance of the physiological rhythm until 1965, when Hon and Lee reported a possible clinical significance for absence or reduction of variability in the fetal heart rhythm (Hon & Lee, 1965). Also, with the work of Ewing et al. (1985, 1991), a relation between a reduced heart rate variability and the degree of autonomic neuropathy in diabetic patients was inferred. Since then, the use of non-invasive methodologies to evaluate autonomic function has increased, and both time domain and frequency domain methods are used to analyse biological signal variability. The fast Fourier transform in the frequency domain has been used most commonly. The computed result of FFT is a power spectrum which indicates the frequency and the power of the different components of the signal. The FFT spectrum shows a set of three bands, two of which have autonomic significance: the HF reflecting parasympathetic activity and the LF, despite being more related to sympathetic activity, giving an indication of the relation between sympathetic and parasympathetic outflow (Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology, 1996). However, FFT can only be applied when the signal is stationary and with a duration of at least 5 min. To overcome this deficit, in the present study we have used a different method of time–frequency domain analysis. The discrete wavelet transform has been shown by us (Postolache et al. 2003, 2004; Silva-Carvalho et al. 2006; Ducla-Soares et al. 2006) and others (Mallat, 1998; Wiklund et al. 2002; Mainardi et al. 2002; van den Berg et al. 2005, Urbancic-Rovan et al. 2006; Moriguchi et al. 2006) to be applicable to cardiovascular signals.
Wavelets are oscillating mathematical functions of short duration that separate a signal into its different component frequencies and then analyse each frequency with a resolution matched to its scale. The signal is decomposed into approximation and detailed signals at several scales (Postolache et al. 2003, 2004; Marques-Neves et al. 2004). There are several types of wavelet functions but, in our opinion, those which appear most suitable for blood pressure and heart rate signal profiles belong to the Daubechie family (Postolache et al. 2004). The main advantage of using a wavelet-based approach to perform a time–frequency analysis of physiological signals is the ability to capture more efficiently transient fluctuations in a non-stationary signal in specific frequency bands. Wavelet methodologies have been fine-tuned over the years for time-dependent spectral analysis (Mallat, 1998; Resnikoff & Wells, 1998). Presently, it is possible to choose from a wide range of convolution kernels, according to the specific features of the signal to be analysed. Another important point is that wavelet analysis provides a resolution in time and frequency that is dependent on the frequency. In other words, the detection of resolution in time and frequency is dependent on the central frequency under analysis. In many cases, capturing the relative frequency changes of a physiological signal, as opposed to absolute changes, is most important. For instance, a 0.5 Hz change would be more meaningful if the central frequency was 2 Hz rather than 30 Hz. Therefore, in many cases it is more desirable to have a better frequency resolution at lower frequencies, and that is a reason to choose wavelet analysis. It should also be noted that the wavelet decomposition is, nowadays, a widely accepted approach for performing time–frequency analysis of heart rate signals (see Petretta et al. 1999; Verlinde et al. 2001; Toledo et al. 2003).
In relation to the physiological significance of LF and HF bands, from pharmacological studies (Akselrod et al. 1981, 1985) it became clear that the HF band is under the control of the parasympathetic system and is related to the respiratory rhythm. The full significance and origin of LF values are not yet completely understood but, according to Malliani (2000), the LF characterizes sympathetic excitation independently of its genesis. However, another index, the LF/HF ratio, is also important, since it allows the quantification of the relation between the two branches of the autonomic nervous system in certain physiological or pathophysiological conditions (Malliani et al. 1991b). In the present study, by choosing the limits of each detail, we studied the contribution of two sets of frequencies, LF (0.038–0.15 Hz) and HF (0.15–0.6 Hz; Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology, 1996), to rapid and acute changes in heart rate (using RRI) and systolic blood pressure evoked by each of the four autonomic tests described.
In head-up tilt (HUT), where an orthostatic challenge is performed, a decrease of blood pressure related to a redistribution of blood by gravity is observed which, consequently, affects the baroreceptor reflexogenic areas to evoke a baroreceptor unloading (Rowell, 1984). Classically, in HUT two phases of adaptation have been described: an earlier cardiovascular acute response that could be observed during the first 30 s and a second phase, the stabilization period, that itself is composed of two periods, an early adaptation period occurring 1–2 min after orthostasis and a second period related to prolonged orthostasis that lasts for more than 5 min (Hilz & Dutsch, 2006); FFT is usually applied to this last period. As an overall consequence of this manoeuvre, an activation of the sympathetic nervous system occurs, together with a decrease of parasympathetic activity acting to re-establish blood pressure levels. Our results show clearly the modifications of autonomic outflow, as seen in LF, HF and LF/HF values of RRI and LF of SBP, that underlie the changes of blood pressure and heart rate during all the four periods of observation (in a total period of analysis of 195 s) but which are particularly important in the TA1 period. During TA1, the change in the sympathetic/parasympathetic activity shown by the LF/HF index derived from RRI analysis reflects an increase of sympathetic outflow that is responsible for the increase in heart rate (and, in this case, indirectly for a decrease of RRI).
The cold pressor test is used to activate pain and temperature fibres by the immersion of one hand and arm in ice-cold water (0–4°C) for 40–180 s (Hilz & Dutsch, 2006). The sympathetic nervous system is activated through the spinothalamic tract, inducing an increase in blood pressure and heart rate, but systolic blood pressure is the more reliable measurement (Fasano et al. 1996; Cevese et al. 2001). During this test, we measured the acute and rapid changes in systolic blood pressure that have been compared between the resting period and the maximum response during the immersion of the subject's hand in iced water. The direct relation between sympathetic outflow and the increase of this cardiovascular variable is also well described in the present work through the computation of the SBP signal by wavelets. Wavelet analysis demonstrates an increase of LF induced by cold, with no significant changes in HF. This confirms, using a different technique of analysis, the results observed by other authors showing that in terms of autonomic influences on cardiovascular variables such as blood pressure and heart rate, the sympathetic nervous system has a more direct influence on blood pressure, whereas the parasympathetic nervous system predominantly affects heart rate. Also, the focus on blood pressure analysis during CPT is in accordance with the Ewing protocol that classically only evaluates blood pressure when the cold stimulus is applied, as justified by the reasons given above.
In the Valsalva manoeuvre, intrathoracic pressure increases abruptly owing to forced expiration against a closed glottis, and this causes an increase in heart rate mediated by the carotid baroreceptor reflex (Levin, 1966; Ekholm & Erkkola, 1996). In fact, inputs from the arterial baroreceptors play the main role in the reflex compensatory response to the increase in intrathoracic pressure (Sharpey-Schafer, 1955; Eckberg, 1980; Daly, 1997; Looga, 2005). The cardiovascular responses elicited during the Valsalva manoeuvre can be divided into four main phases (see Results). During phase I of VM, a small increase in pressure and a decrease in HR were observed and in phase II, the decrease of blood pressure unloads the baroreceptors, thus evoking an increase of sympathetic outflow. This is shown in our analysis as an increase in LF in SAP and RRI power. After the release of the respiratory strain in phase III, there is a decrease in blood pressure and an increase in heart rate. Phase IV of VM is characterized by an increase in blood pressure that evokes a baroreflex-mediated bradycardia, which is also well shown in the HF changes taken from the RRI signal analysis.
The most common means of eliciting parasympathetic activation is by deep breathing at 6 breaths min–1. At this respiratory rate, the processing of the RRI signal shows a shift of parasympathetic-mediated changes in the HF to the LF range, with a significant increase in the amplitude of the observed band (Malik, 1998). Accordingly, the parasympathetic outflow should be analysed on the LF range of frequencies, since this shifting is due to the fact that the respiratory rate is coincidental with the LF range of frequencies. This analysis is only valid in conditions in which the frequency and breathing volume are carefully controlled (Hartikainen et al. 1998).
With the present results, we also intended to relate the clinical evaluation of autonomic function by the standard autonomic tests performed routinely in an autonomic laboratory to the autonomic responses elicited by each manoeuvre analysed in a more detailed way by wavelets. In fact, in clinical practice it is accepted that heart rate changes during the Valsalva manoeuvre or deep breathing test reflect parasympathetic function, whilst the increase in arterial blood pressure during the cold pressor test reflects sympathetic outflow (Ewing & Clarke, 1982; Ewing et al. 1985; Low, 1997). Also, part of the routine testing of autonomic function is the evaluation of blood pressure responses to head-up tilt (Ewing & Clarke, 1982; Ewing et al. 1985; Low, 1997). That is the reason why in this study we focused mainly on blood pressure and heart rate responses to head-up tilt, blood pressure responses to the cold pressor test and heart rate responses to the Valsalva manoeuvre and deep breathing test. The present results clearly demonstrate the relative change in autonomic activity that is responsible for the cardiovascular changes in all four tests.
In conclusion, wavelet analysis provides new opportunities for analysing acute and transient changes in cardiovascular (and autonomic function) variables within periods of less than 5 min which are not accessible to FFT. Also, by overcoming the FFT requirement of a long and stationary signal recording, the analysis of variability of biological signals in the time–frequency domain using wavelets is a useful tool to evaluate autonomic function in routine medical practice.
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