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Joint symbolic analyses of heart rate, blood pressure, and respiratory dynamics
Available online at www.sciencedirect.com
ScienceDirect Journal of Electrocardiology 46 (2013) 569 – 573 www.jecgonline.com
Joint symbolic analyses of heart rate, blood pressure, and respiratory dynamics Mathias Baumert, PhD, a,⁎ Michal Javorka, PhD, b Muammar M. Kabir, PhD a, c a
School of Electrical and Electronic Engineering and Centre for Heart Rhythm Disorders, The University of Adelaide, Adelaide, Australia b Department of Physiology, Jessenius Faculty of Medicine, Comenius University, Martin, Slovak Republic c Department of Mechanical Engineering, Texas A&M University at Qatar, Doha, Qatar
Abstract
Introduction: The dynamics of cardiovascular variables are modulated by respiration. The aim of this study was to assess baroreflex function in normal subjects based on the joint symbolic dynamics of heart rate, blood pressure and respiration. Methods: ECG, continuous blood pressure and respiration were recorded in ten healthy subjects during rest in the supine position and upon standing. Beat-to-beat time series of heart rate, systolic blood pressure and respiratory phase were extracted and transformed into binary symbol sequences. Words of length two that were reflective of baroreflex activity were statistically analysed with respect to the respiratory phase. Results: Symbolic analysis showed a significant influence of the respiratory phase on the occurrence of baroreflex patterns. Upon standing, the frequency of baroreflex words increased and the effect of respiration appeared to be reduced. Conclusions: Symbolic dynamics provide a simple representation of cardiovascular dynamics and may be useful for assessing baroreflex function. © 2013 Elsevier Inc. All rights reserved.
Keywords:
Baroreflex; Heart rate variability; Blood pressure variability; Symbolic dynamics
Introduction Heart rate and blood pressure fluctuate spontaneously from beat to beat. Assessment of those spontaneous fluctuations is thought to provide insight into cardiac baroreflex control. Traditionally, assessment of spontaneous baroreflex activity has been carried out in the time and frequency domains, employing the sequence technique and the alpha index. 1 Both techniques provide indices of baroreflex sensitivity, i.e. the magnitude of the RR interval prolongation as a response to systolic blood pressure drop and vice versa. Other indices of baroreflex function include baroreflex effectiveness 2 and information transfer based measures. 3,4 We have previously developed an approach based on symbolic dynamics to quantify patterns in heart rate and blood pressure changes and demonstrated its usefulness for baroreflex assessment. 5,6 We later adopted this approach to quantify cardio-respiratory coupling and developed a measure of respiratory sinus arrhythmia. 7,8
⁎ Corresponding author. School of Electrical & Electronic Engineering, The University of Adelaide, SA 5005, Australia. E-mail address: [email protected] 0022-0736/$ – see front matter © 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jelectrocard.2013.07.009
As the interplay between blood pressure and heart rate is overarched by respiration, 9 its incorporation into the analysis has been proposed to obtain more reliable indices of baroreflex control. Using autoregressive models, distinct transfer functions for the relationships between respiration, heart rate and blood pressure have been delineated. 10 In this paper we propose a model-free approach for the joint assessment of heart rate, blood pressure as well as respiration based on symbolic dynamics. We applied this technique to study the effect of orthostasis on baroreflex control in healthy subjects and hypothesized that it provides detailed information on the coupling between blood pressure and heart rate with regard to the respiratory phase.
Methods Subjects Ten healthy athletes (5 males and 5 females) participated in this study. None of the subjects were taking medication before or during the study. Anthropometric data and peak oxygen uptake are shown in Table 1. The study conformed to the principles outlined in the Declaration of Helsinki. All
570
M. Baumert et al. / Journal of Electrocardiology 46 (2013) 569–573
Table 1 Anthropometric data and peak oxygen uptake of the athletes presented as medians and interquartile ranges (IQR). Gender
Men Median
Age (y) 26.6 Body Mass (kg) 72.0 Height (cm) 181 VO2 peak (ml/[kg*min]) 65.9
between heart rate, blood pressure and respiration were quantified by measuring the joint occurrences of word types across the three domains.
Women IQR
Median
IQR
Surrogate analysis
26.5–28.8 69.0–86.8 181–182 61.4–74.6
24.8 54.8 163 51.1
24.7–26.4 50.4–61.8 162–168 48.9–52.2
R-R interval and SBP time series were randomly shuffled to test whether symbolic encoding and word formation are able to capture non-random features. Respiratory phases were measured at the time instants of the cumulated surrogate R-R interval time series. Ten sets of surrogate data were generated for each of the ten subjects' recordings during rest. Thus, symbolic analysis was performed for 100 surrogate data. Relative word frequencies were subsequently averaged for each of the ten surrogates, originating from the same recording.
participants provided written informed consent. More details on the study group have been published elsewhere. 11,12 Data and pre-processing High resolution (1600 Hz) ECG, respiration (piezo sensor belt, placed around the chest) and non-invasive continuous blood pressure (Portapres M2, TNO Biomedical Instrumentation, The Netherlands) were recorded simultaneously for 30 minutes under standardized resting conditions in the supine position and subsequently for 20 minutes upon standing. Custom-written computer software was used for the detection of ECG R-peaks, systolic blood pressure and inspiratory/expiratory onsets of respiratory signal. The R-R time series, obtained from the time intervals between consecutive R-peaks, were visually scanned for artefacts and, if necessary, manually edited. Systolic blood pressure (SBP) was determined as the peak amplitude of the continuous blood pressure signal between two consecutive R-peaks. The respiratory signal was low-pass filtered at 0.5 Hz using a zero-phase forward and reverse digital filter. The respiratory phase (RP) was measured at the time instants of R-peaks, using the Hilbert transform. The R-R time series were aligned to the SBP time series such that the nth R-peak with corresponding R-R interval (time distance from Rn to Rn + 1) is the one that follows the nth SBP (i.e. the cardiac cycle following the systolic blood pressure pulse). The n th respiratory phase was measured at Rn − 1.
Baroreflex pattern analysis Combinations of word types where the symbol pattern in S is the inverse of H, i.e. S00H11, S01H10, S10H01, and S11H00 were regarded as baroreflex activity and considered for analysis. Statistics Relative frequencies of all 64 word type combinations of S, H and R were considered for statistical analysis. The distributions of word types were quantified using Shannon entropy. The student's t-test was used to compare entropy values obtained in supine position, during standing and from surrogate data. Distributions of relative frequencies of baroreflex word types with respect to the respiratory phase were compared between the supine measurement and surrogate data and between supine data and recording obtained during standing, respectively; using a two-way ANOVA repeated measurement design. Data are presented as mean ± standard deviation. Values of p 0.05 were considered to be statistically significant.
Joint symbolic dynamics
Results
From the time series of R-R interval, SBP and RP we established three symbolic sequences, s H (H denoting the heart rate − reciprocal of R-R interval) s S and s R, based on the differences between successive R-R intervals, SBP values and R-instant respiratory phases, respectively, as described previously 7: 0 if RRiþ1 −RRi N4 H si ¼ ð1Þ 1 if RRiþ1 −RRi ≤4
Surrogate analysis
sSi
¼
sRi
¼
0 if SBPiþ1 −SBPi ≤0 1 if SBPiþ1 −SBPi N0
ð2Þ
0 if jRPiþ1 j−jRPi jN0 1 if jRPiþ1 j−jRPi j≤0
ð3Þ
Using these symbolic time series, words of length two were formed for each series and denoted as H, S and R, resulting in four different word types each. The interactions
The relative frequencies of word types that occurred in the supine position during rest as well as those of randomized surrogates are shown in Fig. 1 (top panel). The Shannon entropy of surrogate data was significantly higher than those of original data, indicative of non-random dynamics captured by symbol analysis (5.79 ± 0.04 vs.4.90 ± 0.31, p 0.0001). The word distribution of surrogate data appears to be different from uniform distribution and follows a specific pattern. The percentage of baroreflex patterns in the supine position was 27 ± 16% and not significantly different from surrogate data (28 ± 1%). Distributions of baroreflex words with respect to the respiratory phase are displayed in Fig. 1 (bottom panel). During respiratory phase pattern R11 (inspiration) word type S00H11 occurred significantly more frequently in the supine measurement compared to surrogate data (ANOVA: group
M. Baumert et al. / Journal of Electrocardiology 46 (2013) 569–573
571
Fig. 1. Upper panel: Relative frequency of joint heart rate, blood pressure and respiratory phase word types (see methods for details) of measurements carried out in the supine position versus randomly shuffled surrogates. Box plots and whiskers of original data indicate median, inter-quartiles ranges and total ranges. Boxes of surrogate data indicate min-max values. Lower panel: Relative frequencies of baroreflex word types of systolic blood pressure (S) and heart rate (H) with respect to respiratory phases (R). **p b 0.01; ***p b 0.001.
effect: p N 0.05; baroreflex pattern effect p b 0.001, interaction effect p b 0.0001). During respiratory phase pattern R10 (transition from inspiration to expiration) word type S11H00 occurred significantly more frequently in the supine measurement than in surrogate data and word types S01H10 and S10H01 occurred significantly less often (ANOVA: group effect: p N 0.05; baroreflex pattern effect p b 0.0001, interaction effect p b 0.0001). For respiratory pattern R00
(expiration) baroreflex pattern S11H00 occurred significantly more frequently during the measurement in the supine than in surrogate data. Conversely, words of type S01H10 were less frequently observed in the supine position than in surrogate data (ANOVA: group effect: p b 0.001; baroreflex pattern effect p b 0.0001, interaction effect p b 0.01). During respiratory phase pattern R01 (transition from expiration to inspiration) word type S00H11 occurred
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M. Baumert et al. / Journal of Electrocardiology 46 (2013) 569–573
significantly more frequently in the supine recordings compared to surrogate data. Word type S01H10, on the other hand, occurred significantly less in the supine recordings than in surrogate data (ANOVA: group effect: p N 0.05; baroreflex pattern effect p b 0.0001, interaction effect pb 0.0001). Symbolic dynamics measured in the supine position versus standing The mean R-R interval shortened significantly after postural change from the supine position to standing (1095 ± 178 ms vs. 776 ± 105 ms; p b 0.001); the mean respiratory interval was not affected (4.6 ± 1.0 s vs. 4.8 ± 0.8 s, p N 0.05). The Shannon entropy of word distribution was significantly higher during standing than during the supine measurement (5.23 ± 0.30 vs. 4.90 ± 0.31, p b 0.05). The percentage of baroreflex patterns was significantly increased during standing compared to the supine position (47 ± 9% vs. 27 ± 16%, p ; 0.01). Distributions of baroreflex words with regard to respiratory phases are summarized in Fig. 2. During inspiration (R11) baroreflex word types upon standing were similarly frequent as in the supine position (ANOVA: group effect: p N 0.05; baroreflex pattern effect p b 0.0001, interaction effect p N 0.05). The frequency of baroreflex word types during respiratory phase transition from inspiration to expiration (R10) was significantly increased upon standing (ANOVA: group effect: p b 0.003; baroreflex pattern effect p b 0.0001, interaction effect p b 0.02). Baroreflex word type S11H00 was significantly more frequent during standing. During expiration (R00), the frequency of
word types S00H11 and S11H00 was significantly increased upon standing compared to the supine position (ANOVA: group effect: p b 0.001; baroreflex pattern effect p b 0.0001, interaction effect p b 0.01). The transition from expiration to inspiration (R01) was associated with a significant increase in word types S00H11 and S11H00 upon standing (ANOVA: group effect: p b 0.004; baroreflex pattern effect p b 0.0001, interaction effect p b 0.0001). Discussion In this paper we describe a novel approach to study the inter-relationship between respiration and baroreflex activity, quantifying the joint symbolic dynamics of heart rate, blood pressure and respiratory phase. Our results show that the respiratory phase has a strong influence on heart rate and blood pressure patterns that are associated with baroreflex activity. Upon standing, the respiratory influence on baroreflex patterns appears to be reduced. Eckberg reported that the gain of baroreflex activation depends on the phase of respiration. 9 The cardio-inhibitory response of the baroreflex is usually smaller during inspiration than during expiration. The decrease during inspiration might be caused by a reduction in vagal-cardiac motor-neuron responsiveness as a consequence of inhibition originating from inspiratory motor-neurons and lung stretch receptors. Symbolic analysis of supine data shows that inspiration was associated with a blood pressure drop paralleled by increase in heart rate (S00H11). Negative intra-thoracic pressure during inspiration causes excessive flow of blood in
Fig. 2. Relative frequencies of baroreflex word types of systolic blood pressure (S) and heart rate (H) with respect to respiratory phases (R) measured in the supine position and upon standing. Box plots and whiskers indicate median, inter-quartile ranges and total ranges. *p b 0.05; ***p b 0.001; ****p b 0.0001.
M. Baumert et al. / Journal of Electrocardiology 46 (2013) 569–573
the pulmonary vessels and hence a delay of flow to the left ventricle, causing the SBP to fall and likely to generate a baroreflex response. At the same time, inspiration results in an increase in venous return, which leads to a delayed increase in aortic pressure. This delay appears to be reflected in the increase in S11H00 baroreflex patterns in the transition from inspiration to expiration (R10) and throughout expiration (R00). Expiration reduces venous return and decreases the capacity of pulmonary circulation, resulting in a moderate aortic blood pressure increase. This may be reflected in the delayed increase in the S00H11 baroreflex pattern during the transition from expiration to inspiration (R01) and throughout inspiration (R11). Interestingly, respiratory phase transition and expiration word types were also associated with occurrences of baroreflex words with frequencies less than chance. A physiological interpretation of those word types may be difficult due to their low frequency. Of importance, the symbol transformation rules give preferences to certain word types as indicated by the non-uniform distribution of surrogate data. Analysis of symbolic dynamics upon standing suggests a decoupling of baroreflex patterns from the respiratory phase. With exception of R11, all respiratory phases were associated with significantly increased frequencies of word S11H00 upon standing, where expiration and phase transition from expiration to inspiration were also linked with increases in word S00H11. Standing elicits the baroreflex by increasing heart rate and vasomotor tone through vagal withdrawal and sympathetic activation. In line with our finding, previous studies of heart rate and blood pressure during tilt reported an increase in the coherence of low frequency oscillations. 13 There are limitations associated with our approach. Firstly, our method does not provide information on the change in magnitude. We used a threshold of 4 ms for the encoding of RR interval changes to make our technique insensitive to noise. Secondly, the size of the symbol alphabet and the length of words are limited by the need for robust statistical representation and thus by the amount of available data. Longer recordings may allow for longer words that capture cardiovascular and respiratory dynamics more faithfully. Previous studies used slightly longer words to encode basic cardiovascular short-term dynamics. 14,15 Entropy analysis of the word distribution obtained with our current method demonstrates the ability to capture nonrandom dynamics. On the other hand, the relative frequency of baroreflex word types, independent of respiratory phase and the particular pattern of blood pressure and heart rate sequences, was comparable between surrogate data and real data measured in the supine position. This may indicate that basic symbolic encoding of the baroreflex by opposing blood pressure and heart rate changes is not specific enough, or alternatively, baroreflex patterns in the supine position occur at a rate that is not different from chance. In conclusion, joint symbolic analysis of heart rate, blood pressure and respiratory dynamics demonstrates the associ-
573
ation between baroreflex activity and respiratory phase. Assessment of joint symbolic dynamics may be useful to quantify cardio-respiratory and cardio-vascular interactions.
Acknowledgments MB was supported by a project grant and fellowship from the Australian Research Council (DP 110102049). MJ was supported by projects of Centre of Excellence for perinatological research (no. 26220120016) and grant VEGA no. 1/0059/13.
References 1. Persson PB, DiRienzo M, Castiglioni P, et al. Time versus frequency domain techniques for assessing baroreflex sensitivity. J Hypertens 2001;19:1699. 2. Di Rienzo M, Parati G, Castiglioni P, Tordi R, Mancia G, Pedotti A. Baroreflex effectiveness index: an additional measure of baroreflex control of heart rate in daily life. Am J Physiol Regul Integr Comp Physiol 2001;280:R744. 3. Porta A, Castiglioni P, Di Rienzo M, Bari V, Bassani T, Marchi A, et al. Information domain analysis of the spontaneous baroreflex during pharmacological challenges. Autonomic neuroscience: basic & clinical. 2013. 4. Porta A, Catai AM, Takahashi AC, et al. Information transfer through the spontaneous baroreflex in healthy humans. Methods Inf Med 2010;49:506. 5. Baumert M, Walther T, Hopfe J, Stepan H, Faber R, Voss A. Joint symbolic dynamic analysis of beat-to-beat interactions of heart rate and systolic blood pressure in normal pregnancy. Med Biol Eng Comput 2002;40:241. 6. Baumert M, Baier V, Truebner S, Schirdewan A, Voss A. Short- and long-term joint symbolic dynamics of heart rate and blood pressure in dilated cardiomyopathy. IEEE Trans Biomed Eng 2005;52:2112. 7. Kabir MM, Saint DA, Nalivaiko E, Abbott D, Voss A, Baumert M. Quantification of cardiorespiratory interactions based on joint symbolic dynamics. Ann Biomed Eng 2011;39:2604. 8. Baumert M, Brown R, Duma S, Broe GA, Kabir MM, Macefield VG. Joint symbolic dynamics as a model-free approach to study interdependence in cardio-respiratory time series. Conf Proc IEEE Eng Med Biol Soc 2012;2012:3680. 9. Eckberg DL. The human respiratory gate. J Physiol 2003;548:339. 10. Porta A, Bassani T, Bari V, Pinna GD, Maestri R, Guzzetti S. Accounting for respiration is necessary to reliably infer Granger causality from cardiovascular variability series. IEEE Trans Biomed Eng 2012; 59:832. 11. Baumert M, Brechtel L, Lock J, et al. Heart rate variability, blood pressure variability, and baroreflex sensitivity in overtrained athletes. Clin J Sport Med 2006;16:412. 12. Baumert M, Brechtel LM, Lock J, Voss A, Abbott D. Scaling graphs of heart rate time series in athletes demonstrating the VLF, LF and HF regions. Physiol Meas 2006;27:N35. 13. Furlan R, Porta A, Costa F, et al. Oscillatory patterns in sympathetic neural discharge and cardiovascular variables during orthostatic stimulus. Circulation 2000;101:886. 14. Voss A, Kurths J, Kleiner HJ, et al. The application of methods of nonlinear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death. Cardiovasc Res 1996;31:419. 15. Porta A, Tobaldini E, Guzzetti S, Furlan R, Montano N, GnecchiRuscone T. Assessment of cardiac autonomic modulation during graded head-up tilt by symbolic analysis of heart rate variability. Am J Physiol Heart Circ Physiol 2007;293:H702.
ScienceDirect Journal of Electrocardiology 46 (2013) 569 – 573 www.jecgonline.com
Joint symbolic analyses of heart rate, blood pressure, and respiratory dynamics Mathias Baumert, PhD, a,⁎ Michal Javorka, PhD, b Muammar M. Kabir, PhD a, c a
School of Electrical and Electronic Engineering and Centre for Heart Rhythm Disorders, The University of Adelaide, Adelaide, Australia b Department of Physiology, Jessenius Faculty of Medicine, Comenius University, Martin, Slovak Republic c Department of Mechanical Engineering, Texas A&M University at Qatar, Doha, Qatar
Abstract
Introduction: The dynamics of cardiovascular variables are modulated by respiration. The aim of this study was to assess baroreflex function in normal subjects based on the joint symbolic dynamics of heart rate, blood pressure and respiration. Methods: ECG, continuous blood pressure and respiration were recorded in ten healthy subjects during rest in the supine position and upon standing. Beat-to-beat time series of heart rate, systolic blood pressure and respiratory phase were extracted and transformed into binary symbol sequences. Words of length two that were reflective of baroreflex activity were statistically analysed with respect to the respiratory phase. Results: Symbolic analysis showed a significant influence of the respiratory phase on the occurrence of baroreflex patterns. Upon standing, the frequency of baroreflex words increased and the effect of respiration appeared to be reduced. Conclusions: Symbolic dynamics provide a simple representation of cardiovascular dynamics and may be useful for assessing baroreflex function. © 2013 Elsevier Inc. All rights reserved.
Keywords:
Baroreflex; Heart rate variability; Blood pressure variability; Symbolic dynamics
Introduction Heart rate and blood pressure fluctuate spontaneously from beat to beat. Assessment of those spontaneous fluctuations is thought to provide insight into cardiac baroreflex control. Traditionally, assessment of spontaneous baroreflex activity has been carried out in the time and frequency domains, employing the sequence technique and the alpha index. 1 Both techniques provide indices of baroreflex sensitivity, i.e. the magnitude of the RR interval prolongation as a response to systolic blood pressure drop and vice versa. Other indices of baroreflex function include baroreflex effectiveness 2 and information transfer based measures. 3,4 We have previously developed an approach based on symbolic dynamics to quantify patterns in heart rate and blood pressure changes and demonstrated its usefulness for baroreflex assessment. 5,6 We later adopted this approach to quantify cardio-respiratory coupling and developed a measure of respiratory sinus arrhythmia. 7,8
⁎ Corresponding author. School of Electrical & Electronic Engineering, The University of Adelaide, SA 5005, Australia. E-mail address: [email protected] 0022-0736/$ – see front matter © 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jelectrocard.2013.07.009
As the interplay between blood pressure and heart rate is overarched by respiration, 9 its incorporation into the analysis has been proposed to obtain more reliable indices of baroreflex control. Using autoregressive models, distinct transfer functions for the relationships between respiration, heart rate and blood pressure have been delineated. 10 In this paper we propose a model-free approach for the joint assessment of heart rate, blood pressure as well as respiration based on symbolic dynamics. We applied this technique to study the effect of orthostasis on baroreflex control in healthy subjects and hypothesized that it provides detailed information on the coupling between blood pressure and heart rate with regard to the respiratory phase.
Methods Subjects Ten healthy athletes (5 males and 5 females) participated in this study. None of the subjects were taking medication before or during the study. Anthropometric data and peak oxygen uptake are shown in Table 1. The study conformed to the principles outlined in the Declaration of Helsinki. All
570
M. Baumert et al. / Journal of Electrocardiology 46 (2013) 569–573
Table 1 Anthropometric data and peak oxygen uptake of the athletes presented as medians and interquartile ranges (IQR). Gender
Men Median
Age (y) 26.6 Body Mass (kg) 72.0 Height (cm) 181 VO2 peak (ml/[kg*min]) 65.9
between heart rate, blood pressure and respiration were quantified by measuring the joint occurrences of word types across the three domains.
Women IQR
Median
IQR
Surrogate analysis
26.5–28.8 69.0–86.8 181–182 61.4–74.6
24.8 54.8 163 51.1
24.7–26.4 50.4–61.8 162–168 48.9–52.2
R-R interval and SBP time series were randomly shuffled to test whether symbolic encoding and word formation are able to capture non-random features. Respiratory phases were measured at the time instants of the cumulated surrogate R-R interval time series. Ten sets of surrogate data were generated for each of the ten subjects' recordings during rest. Thus, symbolic analysis was performed for 100 surrogate data. Relative word frequencies were subsequently averaged for each of the ten surrogates, originating from the same recording.
participants provided written informed consent. More details on the study group have been published elsewhere. 11,12 Data and pre-processing High resolution (1600 Hz) ECG, respiration (piezo sensor belt, placed around the chest) and non-invasive continuous blood pressure (Portapres M2, TNO Biomedical Instrumentation, The Netherlands) were recorded simultaneously for 30 minutes under standardized resting conditions in the supine position and subsequently for 20 minutes upon standing. Custom-written computer software was used for the detection of ECG R-peaks, systolic blood pressure and inspiratory/expiratory onsets of respiratory signal. The R-R time series, obtained from the time intervals between consecutive R-peaks, were visually scanned for artefacts and, if necessary, manually edited. Systolic blood pressure (SBP) was determined as the peak amplitude of the continuous blood pressure signal between two consecutive R-peaks. The respiratory signal was low-pass filtered at 0.5 Hz using a zero-phase forward and reverse digital filter. The respiratory phase (RP) was measured at the time instants of R-peaks, using the Hilbert transform. The R-R time series were aligned to the SBP time series such that the nth R-peak with corresponding R-R interval (time distance from Rn to Rn + 1) is the one that follows the nth SBP (i.e. the cardiac cycle following the systolic blood pressure pulse). The n th respiratory phase was measured at Rn − 1.
Baroreflex pattern analysis Combinations of word types where the symbol pattern in S is the inverse of H, i.e. S00H11, S01H10, S10H01, and S11H00 were regarded as baroreflex activity and considered for analysis. Statistics Relative frequencies of all 64 word type combinations of S, H and R were considered for statistical analysis. The distributions of word types were quantified using Shannon entropy. The student's t-test was used to compare entropy values obtained in supine position, during standing and from surrogate data. Distributions of relative frequencies of baroreflex word types with respect to the respiratory phase were compared between the supine measurement and surrogate data and between supine data and recording obtained during standing, respectively; using a two-way ANOVA repeated measurement design. Data are presented as mean ± standard deviation. Values of p 0.05 were considered to be statistically significant.
Joint symbolic dynamics
Results
From the time series of R-R interval, SBP and RP we established three symbolic sequences, s H (H denoting the heart rate − reciprocal of R-R interval) s S and s R, based on the differences between successive R-R intervals, SBP values and R-instant respiratory phases, respectively, as described previously 7: 0 if RRiþ1 −RRi N4 H si ¼ ð1Þ 1 if RRiþ1 −RRi ≤4
Surrogate analysis
sSi
¼
sRi
¼
0 if SBPiþ1 −SBPi ≤0 1 if SBPiþ1 −SBPi N0
ð2Þ
0 if jRPiþ1 j−jRPi jN0 1 if jRPiþ1 j−jRPi j≤0
ð3Þ
Using these symbolic time series, words of length two were formed for each series and denoted as H, S and R, resulting in four different word types each. The interactions
The relative frequencies of word types that occurred in the supine position during rest as well as those of randomized surrogates are shown in Fig. 1 (top panel). The Shannon entropy of surrogate data was significantly higher than those of original data, indicative of non-random dynamics captured by symbol analysis (5.79 ± 0.04 vs.4.90 ± 0.31, p 0.0001). The word distribution of surrogate data appears to be different from uniform distribution and follows a specific pattern. The percentage of baroreflex patterns in the supine position was 27 ± 16% and not significantly different from surrogate data (28 ± 1%). Distributions of baroreflex words with respect to the respiratory phase are displayed in Fig. 1 (bottom panel). During respiratory phase pattern R11 (inspiration) word type S00H11 occurred significantly more frequently in the supine measurement compared to surrogate data (ANOVA: group
M. Baumert et al. / Journal of Electrocardiology 46 (2013) 569–573
571
Fig. 1. Upper panel: Relative frequency of joint heart rate, blood pressure and respiratory phase word types (see methods for details) of measurements carried out in the supine position versus randomly shuffled surrogates. Box plots and whiskers of original data indicate median, inter-quartiles ranges and total ranges. Boxes of surrogate data indicate min-max values. Lower panel: Relative frequencies of baroreflex word types of systolic blood pressure (S) and heart rate (H) with respect to respiratory phases (R). **p b 0.01; ***p b 0.001.
effect: p N 0.05; baroreflex pattern effect p b 0.001, interaction effect p b 0.0001). During respiratory phase pattern R10 (transition from inspiration to expiration) word type S11H00 occurred significantly more frequently in the supine measurement than in surrogate data and word types S01H10 and S10H01 occurred significantly less often (ANOVA: group effect: p N 0.05; baroreflex pattern effect p b 0.0001, interaction effect p b 0.0001). For respiratory pattern R00
(expiration) baroreflex pattern S11H00 occurred significantly more frequently during the measurement in the supine than in surrogate data. Conversely, words of type S01H10 were less frequently observed in the supine position than in surrogate data (ANOVA: group effect: p b 0.001; baroreflex pattern effect p b 0.0001, interaction effect p b 0.01). During respiratory phase pattern R01 (transition from expiration to inspiration) word type S00H11 occurred
572
M. Baumert et al. / Journal of Electrocardiology 46 (2013) 569–573
significantly more frequently in the supine recordings compared to surrogate data. Word type S01H10, on the other hand, occurred significantly less in the supine recordings than in surrogate data (ANOVA: group effect: p N 0.05; baroreflex pattern effect p b 0.0001, interaction effect pb 0.0001). Symbolic dynamics measured in the supine position versus standing The mean R-R interval shortened significantly after postural change from the supine position to standing (1095 ± 178 ms vs. 776 ± 105 ms; p b 0.001); the mean respiratory interval was not affected (4.6 ± 1.0 s vs. 4.8 ± 0.8 s, p N 0.05). The Shannon entropy of word distribution was significantly higher during standing than during the supine measurement (5.23 ± 0.30 vs. 4.90 ± 0.31, p b 0.05). The percentage of baroreflex patterns was significantly increased during standing compared to the supine position (47 ± 9% vs. 27 ± 16%, p ; 0.01). Distributions of baroreflex words with regard to respiratory phases are summarized in Fig. 2. During inspiration (R11) baroreflex word types upon standing were similarly frequent as in the supine position (ANOVA: group effect: p N 0.05; baroreflex pattern effect p b 0.0001, interaction effect p N 0.05). The frequency of baroreflex word types during respiratory phase transition from inspiration to expiration (R10) was significantly increased upon standing (ANOVA: group effect: p b 0.003; baroreflex pattern effect p b 0.0001, interaction effect p b 0.02). Baroreflex word type S11H00 was significantly more frequent during standing. During expiration (R00), the frequency of
word types S00H11 and S11H00 was significantly increased upon standing compared to the supine position (ANOVA: group effect: p b 0.001; baroreflex pattern effect p b 0.0001, interaction effect p b 0.01). The transition from expiration to inspiration (R01) was associated with a significant increase in word types S00H11 and S11H00 upon standing (ANOVA: group effect: p b 0.004; baroreflex pattern effect p b 0.0001, interaction effect p b 0.0001). Discussion In this paper we describe a novel approach to study the inter-relationship between respiration and baroreflex activity, quantifying the joint symbolic dynamics of heart rate, blood pressure and respiratory phase. Our results show that the respiratory phase has a strong influence on heart rate and blood pressure patterns that are associated with baroreflex activity. Upon standing, the respiratory influence on baroreflex patterns appears to be reduced. Eckberg reported that the gain of baroreflex activation depends on the phase of respiration. 9 The cardio-inhibitory response of the baroreflex is usually smaller during inspiration than during expiration. The decrease during inspiration might be caused by a reduction in vagal-cardiac motor-neuron responsiveness as a consequence of inhibition originating from inspiratory motor-neurons and lung stretch receptors. Symbolic analysis of supine data shows that inspiration was associated with a blood pressure drop paralleled by increase in heart rate (S00H11). Negative intra-thoracic pressure during inspiration causes excessive flow of blood in
Fig. 2. Relative frequencies of baroreflex word types of systolic blood pressure (S) and heart rate (H) with respect to respiratory phases (R) measured in the supine position and upon standing. Box plots and whiskers indicate median, inter-quartile ranges and total ranges. *p b 0.05; ***p b 0.001; ****p b 0.0001.
M. Baumert et al. / Journal of Electrocardiology 46 (2013) 569–573
the pulmonary vessels and hence a delay of flow to the left ventricle, causing the SBP to fall and likely to generate a baroreflex response. At the same time, inspiration results in an increase in venous return, which leads to a delayed increase in aortic pressure. This delay appears to be reflected in the increase in S11H00 baroreflex patterns in the transition from inspiration to expiration (R10) and throughout expiration (R00). Expiration reduces venous return and decreases the capacity of pulmonary circulation, resulting in a moderate aortic blood pressure increase. This may be reflected in the delayed increase in the S00H11 baroreflex pattern during the transition from expiration to inspiration (R01) and throughout inspiration (R11). Interestingly, respiratory phase transition and expiration word types were also associated with occurrences of baroreflex words with frequencies less than chance. A physiological interpretation of those word types may be difficult due to their low frequency. Of importance, the symbol transformation rules give preferences to certain word types as indicated by the non-uniform distribution of surrogate data. Analysis of symbolic dynamics upon standing suggests a decoupling of baroreflex patterns from the respiratory phase. With exception of R11, all respiratory phases were associated with significantly increased frequencies of word S11H00 upon standing, where expiration and phase transition from expiration to inspiration were also linked with increases in word S00H11. Standing elicits the baroreflex by increasing heart rate and vasomotor tone through vagal withdrawal and sympathetic activation. In line with our finding, previous studies of heart rate and blood pressure during tilt reported an increase in the coherence of low frequency oscillations. 13 There are limitations associated with our approach. Firstly, our method does not provide information on the change in magnitude. We used a threshold of 4 ms for the encoding of RR interval changes to make our technique insensitive to noise. Secondly, the size of the symbol alphabet and the length of words are limited by the need for robust statistical representation and thus by the amount of available data. Longer recordings may allow for longer words that capture cardiovascular and respiratory dynamics more faithfully. Previous studies used slightly longer words to encode basic cardiovascular short-term dynamics. 14,15 Entropy analysis of the word distribution obtained with our current method demonstrates the ability to capture nonrandom dynamics. On the other hand, the relative frequency of baroreflex word types, independent of respiratory phase and the particular pattern of blood pressure and heart rate sequences, was comparable between surrogate data and real data measured in the supine position. This may indicate that basic symbolic encoding of the baroreflex by opposing blood pressure and heart rate changes is not specific enough, or alternatively, baroreflex patterns in the supine position occur at a rate that is not different from chance. In conclusion, joint symbolic analysis of heart rate, blood pressure and respiratory dynamics demonstrates the associ-
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ation between baroreflex activity and respiratory phase. Assessment of joint symbolic dynamics may be useful to quantify cardio-respiratory and cardio-vascular interactions.
Acknowledgments MB was supported by a project grant and fellowship from the Australian Research Council (DP 110102049). MJ was supported by projects of Centre of Excellence for perinatological research (no. 26220120016) and grant VEGA no. 1/0059/13.
References 1. Persson PB, DiRienzo M, Castiglioni P, et al. Time versus frequency domain techniques for assessing baroreflex sensitivity. J Hypertens 2001;19:1699. 2. Di Rienzo M, Parati G, Castiglioni P, Tordi R, Mancia G, Pedotti A. Baroreflex effectiveness index: an additional measure of baroreflex control of heart rate in daily life. Am J Physiol Regul Integr Comp Physiol 2001;280:R744. 3. Porta A, Castiglioni P, Di Rienzo M, Bari V, Bassani T, Marchi A, et al. Information domain analysis of the spontaneous baroreflex during pharmacological challenges. Autonomic neuroscience: basic & clinical. 2013. 4. Porta A, Catai AM, Takahashi AC, et al. Information transfer through the spontaneous baroreflex in healthy humans. Methods Inf Med 2010;49:506. 5. Baumert M, Walther T, Hopfe J, Stepan H, Faber R, Voss A. Joint symbolic dynamic analysis of beat-to-beat interactions of heart rate and systolic blood pressure in normal pregnancy. Med Biol Eng Comput 2002;40:241. 6. Baumert M, Baier V, Truebner S, Schirdewan A, Voss A. Short- and long-term joint symbolic dynamics of heart rate and blood pressure in dilated cardiomyopathy. IEEE Trans Biomed Eng 2005;52:2112. 7. Kabir MM, Saint DA, Nalivaiko E, Abbott D, Voss A, Baumert M. Quantification of cardiorespiratory interactions based on joint symbolic dynamics. Ann Biomed Eng 2011;39:2604. 8. Baumert M, Brown R, Duma S, Broe GA, Kabir MM, Macefield VG. Joint symbolic dynamics as a model-free approach to study interdependence in cardio-respiratory time series. Conf Proc IEEE Eng Med Biol Soc 2012;2012:3680. 9. Eckberg DL. The human respiratory gate. J Physiol 2003;548:339. 10. Porta A, Bassani T, Bari V, Pinna GD, Maestri R, Guzzetti S. Accounting for respiration is necessary to reliably infer Granger causality from cardiovascular variability series. IEEE Trans Biomed Eng 2012; 59:832. 11. Baumert M, Brechtel L, Lock J, et al. Heart rate variability, blood pressure variability, and baroreflex sensitivity in overtrained athletes. Clin J Sport Med 2006;16:412. 12. Baumert M, Brechtel LM, Lock J, Voss A, Abbott D. Scaling graphs of heart rate time series in athletes demonstrating the VLF, LF and HF regions. Physiol Meas 2006;27:N35. 13. Furlan R, Porta A, Costa F, et al. Oscillatory patterns in sympathetic neural discharge and cardiovascular variables during orthostatic stimulus. Circulation 2000;101:886. 14. Voss A, Kurths J, Kleiner HJ, et al. The application of methods of nonlinear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death. Cardiovasc Res 1996;31:419. 15. Porta A, Tobaldini E, Guzzetti S, Furlan R, Montano N, GnecchiRuscone T. Assessment of cardiac autonomic modulation during graded head-up tilt by symbolic analysis of heart rate variability. Am J Physiol Heart Circ Physiol 2007;293:H702.