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Time–frequency analysis of variabilities of heart rate, systolic blood pressure and pulse transit time before and after exercise using the recursive autoregressive model
Biomedical Signal Processing and Control 6 (2011) 364–369
Contents lists available at ScienceDirect
Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc
Time–frequency analysis of variabilities of heart rate, systolic blood pressure and pulse transit time before and after exercise using the recursive autoregressive model夽 Q. Liu a , C.C.Y. Poon a , Y.T. Zhang a,b,c,∗ a
Joint Research Centre for Biomedical Engineering, Dept. of Electronic Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong Institute of Biomedical and Health Engineering, SIAT, Chinese Academy of Sciences, Shenzhen, China c Key Laboratory for Health Informatics, Chinese Academy of Sciences, Shenzhen, China b
a r t i c l e
i n f o
Article history: Received 2 June 2010 Received in revised form 12 January 2011 Accepted 29 March 2011 Available online 30 June 2011 Keywords: Time–variant spectrum Exercise Cardiovascular oscillations Pulse transit time Cuffless blood pressure
a b s t r a c t Time–frequency (T–F) analysis is often used to study the non-stationary cardiovascular oscillations such as heart rate and blood pressure variabilities in dynamic situations. This study intends to use the T–F recursive autoregressive technique to investigate variability in pulse transit time (PTT), which is a cardiovascular parameter of emerging interest due to its potential to estimate blood pressure non-invasively, continuously and without a cuff. Recent studies suggest that PTT is not only related to systolic blood pressure (SBP) but also to heart rate. Therefore, in this study, variability of PTT is analyzed together with the variabilities of R–R interval (RRI) from electrocardiogram and beat-to-beat SBP on 9 normotensive subjects before and shortly after three successive bouts of treadmill exercise. The results showed that both low frequency (LF) and high frequency (HF) components were found in the spectra of RRI, SBP and PTT in the 5-min recordings collected before and after exercise. Compared to the baseline, a decrease in the power of the HF component of RRI followed by an increase in its LF component indicated firstly a vagal withdrawal and then sympathetic activity enhancement after successive bouts of exercise. On the other hand, although changes in the LF and HF components of PTT were more similar to those of SBP than of RRI, the LF/HF ratio of SBP was almost 4 times higher than that of PTT. Based on the results, it is therefore suggested that the relationship between SBP and PTT is frequency-dependent. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction The beat-to-beat oscillations of cardiovascular parameters are thought to reflect the complex interaction between the autonomic nervous system (ANS) and cardiovascular system [1]. Variability of cardiovascular parameters are believed to be capable of indicating sympathetic and vagal activities of the ANS and thus found to be predictors of mortality and morbidity of various kinds of diseases. For example, changes of heart rate (HR) during and after exercise are predictors of sudden deaths and overall mortality [2–5]. Subjects with larger blood pressure variability (BPV) are also found to have higher risk of cardiovascular morbidity or target-organ damage [6–9].
夽 Expanded Paper from the work presented at the 2nd International Symposium on Applied Sciences in Biomedical and Communication Technologies held 24 September 2009. ∗ Corresponding author at: Room 427, Ho Sin Hang Engineering Building, Dept. of Electronic Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. E-mail address: [email protected] (Y.T. Zhang). 1746-8094/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.bspc.2011.03.009
The prognostic value of cardiovascular variabilities has encouraged the development of quantifiable interpretations of these variabilities by time domain analysis, frequency domain analysis and other nonlinear methods such as D2 correlation dimension, Kolmogorov entropy [10] and detrended fluctuations analysis [11]. Amongst these methods, frequency domain analysis is a relatively standardized and easy-to-interpret technique that allows direct linkage of the different components of the spectrum to the corresponding ANS activities. It has been generally accepted that spectral power concentrated in the very low frequency (VLF) is probably due to slow mechanisms of regulation such as humoral and thermoregulatory factors [12], while the low frequency (LF) and high frequency (HF) components of the spectrum are mainly the result of sympathetic modulation and parasympathetic (vagal) activity of the ANS respectively. Consequently, the ratio of LF to HF power is usually considered as an indicator of sympatho-vagal balance [1]. Classical methods for the spectral analysis can be generally classified into parametric and non-parametric approaches. Although non-parametric methods such as the Fourier transform are easier to compute, parametric approaches based on models of the signal
Q. Liu et al. / Biomedical Signal Processing and Control 6 (2011) 364–369 Table 1 Experiment procedure.
365
RRI
Condition
Trial no.
Time period
Before exercise Before exercise Treadmill exercise at 9 km/h After exercise Treadmill exercise at 9 km/h After exercise Treadmill exercise at 7 km/h After exercise
1 2 – 3 – 4 – 5
5 min 5 min 3 min 5 min 3 min 5 min 3 min 5 min
ECG signal PTT
First derivative of PPG signal SBP
generating mechanisms have the advantage of providing smoother spectral components and more accurate estimation of the power spectral density (PSD) when only a short segment of stationary signal is available [10]. However, a limitation of the classical spectral analytical methods is that they require the signal to be stationary in the analysis window, which is a condition that seldom holds for cardiovascular signals [13,14]. Therefore, time–frequency (T–F) analysis such as the Cohen class of distributions, wavelet transform, short time Fourier transform and recursive autoregressive (AR) model have been suggested for estimating the time–variant spectrum of a signal in dynamic conditions [13]. In particular, the time–variant spectral estimation based on recursive AR model has been used to study cardiovascular variabilities under non-stationary conditions, wherein a new set of AR parameters can be obtained each time a new sample is available [12]. The technique has been widely adopted in studies that investigate the beat-to-beat spectra of R–R interval (RRI) of electrocardiogram (ECG) and blood pressure (BP) at rest and during tilt test [12,13,15–19]. In this study, we intend to apply the recursive AR model on series of RRI and systolic blood pressure (SBP) obtained under another dynamic condition, i.e. before and shortly after exercise. In addition, we will extend the study using this model to pulse transit time (PTT) series obtained simultaneously with RRI and SBP. PTT, the time delay of a pressure pulse transmitting from the heart to a peripheral site, is another cardiovascular oscillation that has been recently studied extensively because of its high correlation with BP [20]. It has also been reported that PTT variability (PTTV) shows high correlation and moderate coherence with BPV when subjects are at rest and after exercise [21,22]. On the other hand, a strong relationship between changes in PTT and RRI has also been reported [23]. Therefore, in this study, the time–variant power spectrum of PTT will be examined together with those of RRI and SBP. 2. Materials and methods 2.1. Experiment protocol Nine normotensive subjects (aged 28 ± 4 years, including 6 males) participated in the experiment. Upon arrival, the subjects are required to sit quietly for 5 min. ECG, photoplethysmogram (PPG) and brachial BP were collected simultaneously during this period. Then the procedure was repeated once and another 5-min data were collected while the subjects remain at rest. The subjects were then directed to run on a treadmill for three times, each time for 3 min and at different speeds: 9, 9 and 7 km/h respectively. ECG, PPG and BP were captured simultaneously and continuously from the subjects after each bout of exercise. Thus, three 5-min data were further collected after exercise. ECG and PPG were collected from the subject’s fingers using an in-house system. Brachial BP was measured using Finapres® (Finapres Medical System, The Netherlands) and was calibrated before the experiment and after each exercise. The signals were all sampled at 1 kHz. The details of the experimental procedure are summarized in Table 1.
BP signal Fig. 1. Definition of RRI, SBP and PTT from ECG, BP and PPG signal.
2.2. Signal processing and spectral estimation Beat-to-beat analysis was performed for all data trials. As illustrated in Fig. 1, RRI was measured as the time lapse between the successive R peaks of ECG; SBP was defined as the maximum point of BP; and PTT was the time interval between the peaks of ECG R wave and the first derivative of PPG (dPPG) in each heart cycle. The recursive AR model [12,13] was used to estimate the beatto-beat spectra of RRI, SBP and PTT. Basically, series of RRI, SBP or PTT, {x(1) . . . x(n)}, can be viewed as a signal realization of a discrete-time stochastic process that is described by an AR model of order p: x(n) =
p
ak x(n − k) + ε(n)
(1)
k=1
where ak are the p parameters of the model and ε(n) is a white noise with zero mean and variance 2 . The AR coefficients were updated each time when a new sample was available, on the basis of previous coefficients and a forgetting factor ω. The recursive least square method was adopted to accomplish the time–variant AR coefficients estimation by minimizing the figure of merit: JN =
N
ωN−n |εN (n)|2
(2)
n=1
where εN (n) = x(n) −
p
ak x(n − k)
(3)
k=1
is the forward prediction error evaluated from a set of N data points. ω is a positive real scalar satisfying 0 < ω ≤ 1, and N is the index of the last sample considered. The figure of merit is exponentially weighted, and slowly varying signal parameters can be now tracked. The order p of the model was selected to be 12 and forgetting factor ω was selected to be 0.98 as suggested in [12]. We adopted the definitions of LF and HF bands as described in study [10], which defined LF to be between 0.04 and 0.15 Hz and HF to be between 0.15 and 0.4 Hz. The power of each beat of the three parameters was then calculated in the LF and HF bands. 3. Results Fig. 2 reveals typical T–F spectra of RRI, SBP and PTT. As shown in the figure, the spectrum of PTT was found to have two distinctive
366
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Fig. 2. Typical time–frequency spectra of RRI, SBP and PTT.
components in the LF and HF respectively, corresponding to the LF and HF components in the spectra of RRI and SBP. The power of both components of all three spectra changed with time. Fig. 3 shows a typical T–F spectrum of RRI, the corresponding time series and LF/HF ratio of a 5-min data trial recorded after exercise. As shown in this figure, T1 is a time point where there is a sudden change in spectral power. The HF component of RRI dominated before T1, while three strong LF oscillations appeared shortly after T1 and drastically increased the power of the LF component thereafter. Fig. 4 gives an example of the time–variant power of RRI, SBP and PTT in LF and HF before and after exercise. Although beat-tobeat variation was found in the rest condition before exercise, the power in both LF and HF were relatively stationary in contrast to that after exercise. After exercise, abrupt and obvious changes in the LF and HF power were observed in all three parameters. Fig. 5 compares the averaged power in LF, HF and LF/HF ratio in the three parameters of the 9 subjects before (Trials 1 and 2) and
Fig. 3. A typical time–variant spectrum of RRI with the corresponding time series and LF/HF ratio of a 5-min data trial recorded after exercise.
after 3 bouts of exercise (Trials 3, 4 and 5). As shown in the figure, HF power of RRI (HF RRI) decreased moderately after the first bout of exercise (Trial 3; P < 0.05) and significantly after the second and third bouts of exercise (Trials 4 and 5; P < 0.001). The LF power of RRI (LF RRI) did not show significant increase until after the second and third bouts of exercise (P < 0.05). LF/HF ratio of RRI (LF/HF RRI) showed gradual increments after each exercise. On the other hand, the changes of LF and HF power of both PTT and SBP were mostly insignificant before and after exercise (P > 0.05). 4. Discussion and conclusions ECG, BP and PPG are all generated from the cardiovascular system which is mediated by ANS. All these three signals oscillate at defined LF and HF frequency bands corresponding to sympathetic and vagal activities. Previous study has shown the high coherence of HR variability (HRV) and pulse rate variability extracted from PPG during head-up tile using T–F analysis [24]. The three parameters analyzed in this study, PTT, RRI and SBP, also composed of LF and HF components. Nevertheless, since the regulating mechanisms are different for the three cardiovascular signals, i.e. ECG, BP and PPG, the LF and HF power changes in RRI, SBP and PTT are different. It is observed from this study that the LF and HF power of all three parameters vary even when a subject is at rest before exercise, as shown in the left panel of Fig. 4. This suggests that the intensities of the vagal and sympathetic activities change with time, confirming the suitability of using T–F analysis over traditional frequency domain analysis to study the cardiovascular oscillations. In particular, the two nervous activities can reach a new balance from one state to another within a very short period of time, as shown in Fig. 3. HRV during and after exercise has been extensively studied and a summary can be found in [25]. In short, increase in HR during exercise is firstly due to vagal withdrawal and then sympathetic activity enhancement. Therefore, sympathetic nervous system may be not greatly activated by low-intensity exercise. However, HR recovery after exercise is firstly due to sympathetic withdrawal and then vagal reactivation [26]. Furthermore, the reactivation of vagal activity as indicated by the HF power cannot return to baseline within 5 min after exercise [27]. These previous findings of HRV is further confirmed by the observations of this study, where a significant reduction in HF RRI is observed after all 3 bouts of exercise; while LF RRI only increased significantly after the second and third bouts of exercise. Changes in activation of sympathetic activity are always less significant than withdrawal of vagal activities compared to baseline after each bout of exercise. The results indicate a firstly withdrawal of vagal control and subsequently enhancement of sympathetic activities induced by accumulated bouts of exercise. Furthermore, since the last three data trials were recoded for 5 min immediately after cessation of
Q. Liu et al. / Biomedical Signal Processing and Control 6 (2011) 364–369
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Fig. 4. Time–variant power of RRI, PTT and SBP in LF and HF before and after exercise.
exercise, the vagal activity may not completely reactivated to the baseline at the end of data recording, however, it is supposed to be sufficient for sympathetic recovery. In contrast to RRI, no such clear tendency is observed in the LF power, HF power and LF/HF ratio of SBP and PTT. A significant decrease (P < 0.01) in LF SBP is only observed after the first bout of exercise. LF SBP basically returns to the level measured before exercise after the second and third bouts of exercise. HF SBP slightly decrease after exercise but the reduction is only significantly after the third bouts of exercise (P < 0.05). Similarly, LF PTT and HF PTT show no significant changes after all three bouts of exercise. The differences in power changes of RRI and SBP may due to the different mediation mechanisms on them. Previous studies have demonstrated the two main components in RRI and SBP spectra. For RRI, a peak at respiratory frequency (i.e. HF) that corresponds to respiratory sinus arrhythmia is due to vagal activity, whereas a peak centered at about 0.1 Hz (i.e. LF), related to arterial pressure control, is mediated by both cardiac vagal and sympathetic nerves but mainly sympathetic activity [25]. For SBP, the HF component probably reflects the mechanical effect of breathing on SBP, whereas the LF component, which is also defined as Mayer wave [28], only reflects the sympathetic activity to the ␣-adrenergic receptors of vascular. The vascular tone is however maintained not only by ANS, but also endothelial function. Hence, there is a tonic balance between the release of vasoconstriction factors from sympathetic nerve terminals and vasodilatation factors from the endothelium [29]. This indicates that the effects of ANS reflecting on SBP are
buffered and balanced by other factors such as endothelial functions. As a result, SBP did not show a consistent and significant increase or decrease after each bout of exercise. Similar to the changes in BP, PTT shows no significant changes in spectral power after exercise. Although BP is often expressed as a logarithmic equation of PTT [20], the results of this study showed that their relationship can be frequency-dependent. In particular, the LF/HF ratio of SBP is almost 4 times higher than that of PTT. This may be due to the frequency dependency of artery properties that determine the relationship between PTT and BP [30–32]. Thus, it is postulated that in order to estimate SBP from PTT, different gains should be considered for the different frequency components. To better model cardiovascular signals using the recursive AR model, some other issues need to be studied. Order and forgetting factor selections are two key points for the parametric AR model estimation. The order of the model depends on the property of signal and system itself, and can be only determined empirically [33]. The forgetting factor should be adjusted appropriately according to sampling rate as well as physiological behaviors [18]. In addition, spectrum decomposition methods should be considered to obtain more accurate power value in respective frequency bands [10]. In summary, the main purpose of this study is to investigate the power alteration of PTT, together with RRI and SBP before and after exercise, by obtaining the time–variant spectra using recursive AR model, for a better understanding of the ANS modulating on these cardiovascular oscillations in a dynamic situation. The results showed that the non-stationarity of the oscillations can be reflected
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Fig. 5. Comparison of LF, HF power and LF/HF ratio of RRI, SBP and PTT before and after exercise. Trial 1: resting 1 before exercise; Trial 2: resting 2 before exercise; Trial 3: after exercise 1; Trial 4: after exercise 2; Trial 5: after exercise 3. Paired Student’s t-test was employed to examine the significance of difference between trials 2–5 and trial 1 (*P < 0.05; **P < 0.01; ***P < 0.001).
using the T–F analysis. Beat-to-beat variations of spectra existed before and after exercise in all the three parameters; a significant increase in LF power and decrease in HF power thus an increase in LF/HF ratio was observed in RRI spectrum. The sequentially decrease in HF RRI and increase in LF RRI indicates a firstly vagal withdrawal and then sympathetic activity enhancement induced by exercise. However, power changes of PTT were more similar to that of SBP since both of them did not reveal such a clear tendency and maintained basically baseline level within 5 min after exercise. In addition, the LF/HF ratio of SBP is almost 4 times higher than that of PTT, suggests that a frequency-dependent model is required in order to better estimate SBP from PTT. However, ANS is complex and has not been fully understood. The mediation mechanisms of ANS on cardiovascular system and inherent correlations between the cardiovascular oscillations should be further investigated by multi-modal T–F analysis methods [34,35], so that the beat-to-beat transfer function can also be obtained. Acknowledgements This work was supported in part by the Hong Kong Innovation and Technology Fund (ITF), the 973 Project Fund (2010CB732606), and the Guangdong LCHT Innovation Research Team Fund in China. The authors are grateful to Standard Telecommunication Ltd., Jetfly Technology Ltd., Golden Meditech Company Ltd., Bird International Ltd. Bright Steps Corporation and PCCW for their supports to the ITF projects. The authors would also like to acknowledge Dr. Mico Wong for helping with the data collection. References [1] L.T. Mainardi, On the quantification of heart rate variability spectral parameters using time–frequency and time-varying methods, Phil. Trans. R. Soc. A. 367 (2009) 255–275.
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Contents lists available at ScienceDirect
Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc
Time–frequency analysis of variabilities of heart rate, systolic blood pressure and pulse transit time before and after exercise using the recursive autoregressive model夽 Q. Liu a , C.C.Y. Poon a , Y.T. Zhang a,b,c,∗ a
Joint Research Centre for Biomedical Engineering, Dept. of Electronic Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong Institute of Biomedical and Health Engineering, SIAT, Chinese Academy of Sciences, Shenzhen, China c Key Laboratory for Health Informatics, Chinese Academy of Sciences, Shenzhen, China b
a r t i c l e
i n f o
Article history: Received 2 June 2010 Received in revised form 12 January 2011 Accepted 29 March 2011 Available online 30 June 2011 Keywords: Time–variant spectrum Exercise Cardiovascular oscillations Pulse transit time Cuffless blood pressure
a b s t r a c t Time–frequency (T–F) analysis is often used to study the non-stationary cardiovascular oscillations such as heart rate and blood pressure variabilities in dynamic situations. This study intends to use the T–F recursive autoregressive technique to investigate variability in pulse transit time (PTT), which is a cardiovascular parameter of emerging interest due to its potential to estimate blood pressure non-invasively, continuously and without a cuff. Recent studies suggest that PTT is not only related to systolic blood pressure (SBP) but also to heart rate. Therefore, in this study, variability of PTT is analyzed together with the variabilities of R–R interval (RRI) from electrocardiogram and beat-to-beat SBP on 9 normotensive subjects before and shortly after three successive bouts of treadmill exercise. The results showed that both low frequency (LF) and high frequency (HF) components were found in the spectra of RRI, SBP and PTT in the 5-min recordings collected before and after exercise. Compared to the baseline, a decrease in the power of the HF component of RRI followed by an increase in its LF component indicated firstly a vagal withdrawal and then sympathetic activity enhancement after successive bouts of exercise. On the other hand, although changes in the LF and HF components of PTT were more similar to those of SBP than of RRI, the LF/HF ratio of SBP was almost 4 times higher than that of PTT. Based on the results, it is therefore suggested that the relationship between SBP and PTT is frequency-dependent. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction The beat-to-beat oscillations of cardiovascular parameters are thought to reflect the complex interaction between the autonomic nervous system (ANS) and cardiovascular system [1]. Variability of cardiovascular parameters are believed to be capable of indicating sympathetic and vagal activities of the ANS and thus found to be predictors of mortality and morbidity of various kinds of diseases. For example, changes of heart rate (HR) during and after exercise are predictors of sudden deaths and overall mortality [2–5]. Subjects with larger blood pressure variability (BPV) are also found to have higher risk of cardiovascular morbidity or target-organ damage [6–9].
夽 Expanded Paper from the work presented at the 2nd International Symposium on Applied Sciences in Biomedical and Communication Technologies held 24 September 2009. ∗ Corresponding author at: Room 427, Ho Sin Hang Engineering Building, Dept. of Electronic Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. E-mail address: [email protected] (Y.T. Zhang). 1746-8094/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.bspc.2011.03.009
The prognostic value of cardiovascular variabilities has encouraged the development of quantifiable interpretations of these variabilities by time domain analysis, frequency domain analysis and other nonlinear methods such as D2 correlation dimension, Kolmogorov entropy [10] and detrended fluctuations analysis [11]. Amongst these methods, frequency domain analysis is a relatively standardized and easy-to-interpret technique that allows direct linkage of the different components of the spectrum to the corresponding ANS activities. It has been generally accepted that spectral power concentrated in the very low frequency (VLF) is probably due to slow mechanisms of regulation such as humoral and thermoregulatory factors [12], while the low frequency (LF) and high frequency (HF) components of the spectrum are mainly the result of sympathetic modulation and parasympathetic (vagal) activity of the ANS respectively. Consequently, the ratio of LF to HF power is usually considered as an indicator of sympatho-vagal balance [1]. Classical methods for the spectral analysis can be generally classified into parametric and non-parametric approaches. Although non-parametric methods such as the Fourier transform are easier to compute, parametric approaches based on models of the signal
Q. Liu et al. / Biomedical Signal Processing and Control 6 (2011) 364–369 Table 1 Experiment procedure.
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RRI
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Time period
Before exercise Before exercise Treadmill exercise at 9 km/h After exercise Treadmill exercise at 9 km/h After exercise Treadmill exercise at 7 km/h After exercise
1 2 – 3 – 4 – 5
5 min 5 min 3 min 5 min 3 min 5 min 3 min 5 min
ECG signal PTT
First derivative of PPG signal SBP
generating mechanisms have the advantage of providing smoother spectral components and more accurate estimation of the power spectral density (PSD) when only a short segment of stationary signal is available [10]. However, a limitation of the classical spectral analytical methods is that they require the signal to be stationary in the analysis window, which is a condition that seldom holds for cardiovascular signals [13,14]. Therefore, time–frequency (T–F) analysis such as the Cohen class of distributions, wavelet transform, short time Fourier transform and recursive autoregressive (AR) model have been suggested for estimating the time–variant spectrum of a signal in dynamic conditions [13]. In particular, the time–variant spectral estimation based on recursive AR model has been used to study cardiovascular variabilities under non-stationary conditions, wherein a new set of AR parameters can be obtained each time a new sample is available [12]. The technique has been widely adopted in studies that investigate the beat-to-beat spectra of R–R interval (RRI) of electrocardiogram (ECG) and blood pressure (BP) at rest and during tilt test [12,13,15–19]. In this study, we intend to apply the recursive AR model on series of RRI and systolic blood pressure (SBP) obtained under another dynamic condition, i.e. before and shortly after exercise. In addition, we will extend the study using this model to pulse transit time (PTT) series obtained simultaneously with RRI and SBP. PTT, the time delay of a pressure pulse transmitting from the heart to a peripheral site, is another cardiovascular oscillation that has been recently studied extensively because of its high correlation with BP [20]. It has also been reported that PTT variability (PTTV) shows high correlation and moderate coherence with BPV when subjects are at rest and after exercise [21,22]. On the other hand, a strong relationship between changes in PTT and RRI has also been reported [23]. Therefore, in this study, the time–variant power spectrum of PTT will be examined together with those of RRI and SBP. 2. Materials and methods 2.1. Experiment protocol Nine normotensive subjects (aged 28 ± 4 years, including 6 males) participated in the experiment. Upon arrival, the subjects are required to sit quietly for 5 min. ECG, photoplethysmogram (PPG) and brachial BP were collected simultaneously during this period. Then the procedure was repeated once and another 5-min data were collected while the subjects remain at rest. The subjects were then directed to run on a treadmill for three times, each time for 3 min and at different speeds: 9, 9 and 7 km/h respectively. ECG, PPG and BP were captured simultaneously and continuously from the subjects after each bout of exercise. Thus, three 5-min data were further collected after exercise. ECG and PPG were collected from the subject’s fingers using an in-house system. Brachial BP was measured using Finapres® (Finapres Medical System, The Netherlands) and was calibrated before the experiment and after each exercise. The signals were all sampled at 1 kHz. The details of the experimental procedure are summarized in Table 1.
BP signal Fig. 1. Definition of RRI, SBP and PTT from ECG, BP and PPG signal.
2.2. Signal processing and spectral estimation Beat-to-beat analysis was performed for all data trials. As illustrated in Fig. 1, RRI was measured as the time lapse between the successive R peaks of ECG; SBP was defined as the maximum point of BP; and PTT was the time interval between the peaks of ECG R wave and the first derivative of PPG (dPPG) in each heart cycle. The recursive AR model [12,13] was used to estimate the beatto-beat spectra of RRI, SBP and PTT. Basically, series of RRI, SBP or PTT, {x(1) . . . x(n)}, can be viewed as a signal realization of a discrete-time stochastic process that is described by an AR model of order p: x(n) =
p
ak x(n − k) + ε(n)
(1)
k=1
where ak are the p parameters of the model and ε(n) is a white noise with zero mean and variance 2 . The AR coefficients were updated each time when a new sample was available, on the basis of previous coefficients and a forgetting factor ω. The recursive least square method was adopted to accomplish the time–variant AR coefficients estimation by minimizing the figure of merit: JN =
N
ωN−n |εN (n)|2
(2)
n=1
where εN (n) = x(n) −
p
ak x(n − k)
(3)
k=1
is the forward prediction error evaluated from a set of N data points. ω is a positive real scalar satisfying 0 < ω ≤ 1, and N is the index of the last sample considered. The figure of merit is exponentially weighted, and slowly varying signal parameters can be now tracked. The order p of the model was selected to be 12 and forgetting factor ω was selected to be 0.98 as suggested in [12]. We adopted the definitions of LF and HF bands as described in study [10], which defined LF to be between 0.04 and 0.15 Hz and HF to be between 0.15 and 0.4 Hz. The power of each beat of the three parameters was then calculated in the LF and HF bands. 3. Results Fig. 2 reveals typical T–F spectra of RRI, SBP and PTT. As shown in the figure, the spectrum of PTT was found to have two distinctive
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Fig. 2. Typical time–frequency spectra of RRI, SBP and PTT.
components in the LF and HF respectively, corresponding to the LF and HF components in the spectra of RRI and SBP. The power of both components of all three spectra changed with time. Fig. 3 shows a typical T–F spectrum of RRI, the corresponding time series and LF/HF ratio of a 5-min data trial recorded after exercise. As shown in this figure, T1 is a time point where there is a sudden change in spectral power. The HF component of RRI dominated before T1, while three strong LF oscillations appeared shortly after T1 and drastically increased the power of the LF component thereafter. Fig. 4 gives an example of the time–variant power of RRI, SBP and PTT in LF and HF before and after exercise. Although beat-tobeat variation was found in the rest condition before exercise, the power in both LF and HF were relatively stationary in contrast to that after exercise. After exercise, abrupt and obvious changes in the LF and HF power were observed in all three parameters. Fig. 5 compares the averaged power in LF, HF and LF/HF ratio in the three parameters of the 9 subjects before (Trials 1 and 2) and
Fig. 3. A typical time–variant spectrum of RRI with the corresponding time series and LF/HF ratio of a 5-min data trial recorded after exercise.
after 3 bouts of exercise (Trials 3, 4 and 5). As shown in the figure, HF power of RRI (HF RRI) decreased moderately after the first bout of exercise (Trial 3; P < 0.05) and significantly after the second and third bouts of exercise (Trials 4 and 5; P < 0.001). The LF power of RRI (LF RRI) did not show significant increase until after the second and third bouts of exercise (P < 0.05). LF/HF ratio of RRI (LF/HF RRI) showed gradual increments after each exercise. On the other hand, the changes of LF and HF power of both PTT and SBP were mostly insignificant before and after exercise (P > 0.05). 4. Discussion and conclusions ECG, BP and PPG are all generated from the cardiovascular system which is mediated by ANS. All these three signals oscillate at defined LF and HF frequency bands corresponding to sympathetic and vagal activities. Previous study has shown the high coherence of HR variability (HRV) and pulse rate variability extracted from PPG during head-up tile using T–F analysis [24]. The three parameters analyzed in this study, PTT, RRI and SBP, also composed of LF and HF components. Nevertheless, since the regulating mechanisms are different for the three cardiovascular signals, i.e. ECG, BP and PPG, the LF and HF power changes in RRI, SBP and PTT are different. It is observed from this study that the LF and HF power of all three parameters vary even when a subject is at rest before exercise, as shown in the left panel of Fig. 4. This suggests that the intensities of the vagal and sympathetic activities change with time, confirming the suitability of using T–F analysis over traditional frequency domain analysis to study the cardiovascular oscillations. In particular, the two nervous activities can reach a new balance from one state to another within a very short period of time, as shown in Fig. 3. HRV during and after exercise has been extensively studied and a summary can be found in [25]. In short, increase in HR during exercise is firstly due to vagal withdrawal and then sympathetic activity enhancement. Therefore, sympathetic nervous system may be not greatly activated by low-intensity exercise. However, HR recovery after exercise is firstly due to sympathetic withdrawal and then vagal reactivation [26]. Furthermore, the reactivation of vagal activity as indicated by the HF power cannot return to baseline within 5 min after exercise [27]. These previous findings of HRV is further confirmed by the observations of this study, where a significant reduction in HF RRI is observed after all 3 bouts of exercise; while LF RRI only increased significantly after the second and third bouts of exercise. Changes in activation of sympathetic activity are always less significant than withdrawal of vagal activities compared to baseline after each bout of exercise. The results indicate a firstly withdrawal of vagal control and subsequently enhancement of sympathetic activities induced by accumulated bouts of exercise. Furthermore, since the last three data trials were recoded for 5 min immediately after cessation of
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Fig. 4. Time–variant power of RRI, PTT and SBP in LF and HF before and after exercise.
exercise, the vagal activity may not completely reactivated to the baseline at the end of data recording, however, it is supposed to be sufficient for sympathetic recovery. In contrast to RRI, no such clear tendency is observed in the LF power, HF power and LF/HF ratio of SBP and PTT. A significant decrease (P < 0.01) in LF SBP is only observed after the first bout of exercise. LF SBP basically returns to the level measured before exercise after the second and third bouts of exercise. HF SBP slightly decrease after exercise but the reduction is only significantly after the third bouts of exercise (P < 0.05). Similarly, LF PTT and HF PTT show no significant changes after all three bouts of exercise. The differences in power changes of RRI and SBP may due to the different mediation mechanisms on them. Previous studies have demonstrated the two main components in RRI and SBP spectra. For RRI, a peak at respiratory frequency (i.e. HF) that corresponds to respiratory sinus arrhythmia is due to vagal activity, whereas a peak centered at about 0.1 Hz (i.e. LF), related to arterial pressure control, is mediated by both cardiac vagal and sympathetic nerves but mainly sympathetic activity [25]. For SBP, the HF component probably reflects the mechanical effect of breathing on SBP, whereas the LF component, which is also defined as Mayer wave [28], only reflects the sympathetic activity to the ␣-adrenergic receptors of vascular. The vascular tone is however maintained not only by ANS, but also endothelial function. Hence, there is a tonic balance between the release of vasoconstriction factors from sympathetic nerve terminals and vasodilatation factors from the endothelium [29]. This indicates that the effects of ANS reflecting on SBP are
buffered and balanced by other factors such as endothelial functions. As a result, SBP did not show a consistent and significant increase or decrease after each bout of exercise. Similar to the changes in BP, PTT shows no significant changes in spectral power after exercise. Although BP is often expressed as a logarithmic equation of PTT [20], the results of this study showed that their relationship can be frequency-dependent. In particular, the LF/HF ratio of SBP is almost 4 times higher than that of PTT. This may be due to the frequency dependency of artery properties that determine the relationship between PTT and BP [30–32]. Thus, it is postulated that in order to estimate SBP from PTT, different gains should be considered for the different frequency components. To better model cardiovascular signals using the recursive AR model, some other issues need to be studied. Order and forgetting factor selections are two key points for the parametric AR model estimation. The order of the model depends on the property of signal and system itself, and can be only determined empirically [33]. The forgetting factor should be adjusted appropriately according to sampling rate as well as physiological behaviors [18]. In addition, spectrum decomposition methods should be considered to obtain more accurate power value in respective frequency bands [10]. In summary, the main purpose of this study is to investigate the power alteration of PTT, together with RRI and SBP before and after exercise, by obtaining the time–variant spectra using recursive AR model, for a better understanding of the ANS modulating on these cardiovascular oscillations in a dynamic situation. The results showed that the non-stationarity of the oscillations can be reflected
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Fig. 5. Comparison of LF, HF power and LF/HF ratio of RRI, SBP and PTT before and after exercise. Trial 1: resting 1 before exercise; Trial 2: resting 2 before exercise; Trial 3: after exercise 1; Trial 4: after exercise 2; Trial 5: after exercise 3. Paired Student’s t-test was employed to examine the significance of difference between trials 2–5 and trial 1 (*P < 0.05; **P < 0.01; ***P < 0.001).
using the T–F analysis. Beat-to-beat variations of spectra existed before and after exercise in all the three parameters; a significant increase in LF power and decrease in HF power thus an increase in LF/HF ratio was observed in RRI spectrum. The sequentially decrease in HF RRI and increase in LF RRI indicates a firstly vagal withdrawal and then sympathetic activity enhancement induced by exercise. However, power changes of PTT were more similar to that of SBP since both of them did not reveal such a clear tendency and maintained basically baseline level within 5 min after exercise. In addition, the LF/HF ratio of SBP is almost 4 times higher than that of PTT, suggests that a frequency-dependent model is required in order to better estimate SBP from PTT. However, ANS is complex and has not been fully understood. The mediation mechanisms of ANS on cardiovascular system and inherent correlations between the cardiovascular oscillations should be further investigated by multi-modal T–F analysis methods [34,35], so that the beat-to-beat transfer function can also be obtained. Acknowledgements This work was supported in part by the Hong Kong Innovation and Technology Fund (ITF), the 973 Project Fund (2010CB732606), and the Guangdong LCHT Innovation Research Team Fund in China. The authors are grateful to Standard Telecommunication Ltd., Jetfly Technology Ltd., Golden Meditech Company Ltd., Bird International Ltd. Bright Steps Corporation and PCCW for their supports to the ITF projects. The authors would also like to acknowledge Dr. Mico Wong for helping with the data collection. References [1] L.T. Mainardi, On the quantification of heart rate variability spectral parameters using time–frequency and time-varying methods, Phil. Trans. R. Soc. A. 367 (2009) 255–275.
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