Multiscale time irreversibility of heart rate and blood pressure variability during orthostasis

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Physiol. Meas. 33 (2012) 1747–1756 doi:10.1088/0967-3334/33/10/1747

Multiscale time irreversibility of heart rate and bloodpressure variability during orthostasis

L Chladekova1,3, B Czippelova1, Z Turianikova1, I Tonhajzerova1,A Calkovska1, M Baumert2 and M Javorka1

1 Department of Physiology, Comenius University, Jessenius Faculty of Medicine, Martin,Slovak Republic2 School of Electronic & Electrical Engineering, The University of Adelaide, Australia

E-mail: chladekova@jfmed.uniba.sk

Received 23 March 2012, accepted for publication 10 September 2012Published 26 September 2012Online at stacks.iop.org/PM/33/1747

AbstractTime irreversibility is a characteristic feature of non-equilibrium, complexsystems such as the cardiovascular control mediated by the autonomic nervoussystem (ANS). Time irreversibility analysis of heart rate variability (HRV)and blood pressure variability (BPV) represents a new approach to assesscardiovascular regulatory mechanisms. The aim of this paper was to assessthe changes in HRV and BPV irreversibility during the active orthostatictest (a balance of ANS shifted towards sympathetic predominance) in28 healthy young subjects. We used three different time irreversibility indices—Porta’s, Guzik’s and Ehler’s indices (P%, G% and E, respectively) derived fromdata segments containing 1000 beat-to-beat intervals on four timescales. Weobserved an increase in the HRV and a decrease in the BPV irreversibilityduring standing compared to the supine position. The postural change inirreversibility was confirmed by surrogate data analysis. The differences weremore evident in G% and E than P% and for higher scale factors. Statisticalanalysis showed a close relationship between G% and E. Contrary to this, theassociation between P% and G% and P% and E was not proven. We concludethat time irreversibility of beat-to-beat HRV and BPV is significantly alteredduring orthostasis, implicating involvement of the autonomous nervous systemin its generation.

Keywords: heart rate variability, blood pressure variability, time irreversibility,surrogate data, orthostatic challenge, sympathovagal balance

3 Author to whom any correspondence should be addressed.

0967-3334/12/101747+10$33.00 © 2012 Institute of Physics and Engineering in Medicine Printed in the UK & the USA 1747

1748 L Chladekova et al

1. Introduction

Analysis of spontaneous heart rate and blood pressure oscillations (heart rate variability—HRV and blood pressure variability—BPV) provides important information on the autonomiccontrol of circulation in healthy and diseased subjects (Javorka et al 2009, Porta et al 20082009, Turianikova et al 2011).

HRV and BPV are traditionally quantified in the time and frequency domains by linearmethods (Task Force of ESC/NASPE 1996). However, the healthy cardiovascular regulatorysystem comprises complex interactions of many control loops and manifests in nonlinearbehaviour (Casali et al 2008, Javorka et al 2009). Therefore, nonlinear methods measuringcomplexity and other system dynamic features appear more suitable for the detailed descriptionof cardiovascular control system characteristics. In addition, linear parameters correlate witheach other and therefore do not provide mutually independent information (Javorka et al 2009,Porta et al 2009).

From several nonlinear aspects of cardiovascular signals, time irreversibility has recentlygained increasing attention. A signal is said to be time irreversible if its statistical propertieschange after its time reversal, i.e. it is characterized by a temporal asymmetry (Javorkaet al 2009, Porta et al 2008, Hou et al 2010). This phenomenon is specific for nonequilibriumsystems (Hou et al 2010) and its presence in cardiovascular signals results from the complexityof the cardiovascular control system typical for a healthy human (Costa et al 2005).

In previous studies, time irreversibility indices have been applied to HRV analysis todetect changes of the cardiovascular control in chronic heart failure patients (Porta et al 2009),patients after acute myocardial infarction (De La Cruz Torres and Naranjo Orellana 2010)and also in healthy subjects during physical activity (Costa et al 2005, De La Cruz Torres andNaranjo Orellana 2010), during passive head-up tilt (Casali et al 2008, Porta et al 2008) andactive orthostatic challenge (Casali et al 2008). However, it might be useful to test variousirreversibility indices on various timescales in different physiological and clinical settings inorder to extract more information about this phenomenon. Moreover, little is known aboutasymmetric features of BPV, though the existence of this phenomenon in the BPV signal hasbeen already described (Guzik et al 2010a).

The postural change from the supine to the standing position is a well-known manoeuvrecharacterized by a shifted balance of the autonomic nervous system (ANS) towards sympatheticpredominance. The aim of our study was to determine the effect of the orthostatic test on thetime irreversibility of the RR interval time series and the systolic blood pressure (SBP) timeseries in healthy young subjects comparing three commonly used time irreversibility indices:Porta’s (P%), Guzik’s (G%) and Ehlers’ (E) index. Considering the fact that cardiovascularcontrol acts over multiple timescales, introducing a significant amount of complexity into theheart rate and blood pressure time series, we also explored the behaviour of these indices onvarious timescales (Turianikova et al 2011).

2. Methods

2.1. Subjects

We investigated the recordings from 28 healthy young volunteers (21 female, 7 male) aged20.4 ± 0.2 years (SEM) (range: 17.9–23.8 years). The subjects were instructed to avoidsubstances influencing cardiovascular system activity (caffeine, alcohol) and smoking for 12 hbefore the examination. They were normotensive, non-obese (BMI: 21.7 ± 0.5 kg m−2) andwere taking no medication for the duration of the study. The study was approved by the Ethics

Time irreversibility of heart rate and blood pressure 1749

Committee of Jessenius Faculty of Medicine, Comenius University and all participants gavetheir informed consent prior to the examination.

2.2. Protocol

After the stabilization period (15 min resting in a supine position), the ECG signal andsimultaneously measured SBP signal were recorded for 20 min in a supine position.Subsequently, the subjects were asked to stand up slowly (in about 5 s) before continuingrecording in the standing position for another 15 min. A complete study protocol can be foundin Javorka et al (2009).

2.3. Data recording and pre-processing

The ECG signal (bipolar thoracic ECG lead) was obtained from Cardiofax ECG-9620(NihonKohden, Japan). The SBP recordings were measured using a beat–to-beat bloodpressure monitor (Finapres, Ohmeda, USA). All analogue signals were transmitted to a PCusing analogue-digital converter (Advantech PCL 711, Taiwan) at a sampling rate of 500 Hz.

After the QRS complex detection, the RR interval was defined as the time interval betweentwo consecutive R peaks. Systolic and diastolic blood pressure values were detected as thelocal maxima and minima (respectively) in a continuous blood pressure signal. The resultswere visually checked and ectopic beats, which occurred rarely, were interpolated linearly.

2.4. Time irreversibility analysis

Irreversibility analysis was performed on the segments consisting of 1000 beats for eachposition (lying in the supine position—L, standing position—S) using a custom-made softwarepackage. The following indices were used to measure time irreversibility of the time series:

(1) Porta’s index P% (Porta et al 2008, Hou et al 2010) is based on evaluating the percentageof negative �x (i.e. �x−) with respect to the total number of �x �= 0. �x representsthe difference of two consecutive RR intervals (HRV) and two consecutive SBP (BPV),respectively:

P% = N(�x−)

N(�x �= 0)100. (1)

Consequently, P% ranges from 0 to 100 and time irreversibility is characterized by valuesof P% significantly larger or smaller than 50. A P% > 50 implies that the number of�x− is larger than that of �x+.

(2) Guzik’s index G% (Porta et al 2008, Hou et al 2010, Guzik et al 2006) is defined as thepercentage of the sum of the square distances between �x+ and the main diagonal inPoincare plot (scatterplot of nth versus (n+1) th value of a given signal) with respect tothe sum of the squared distances between all �x and the main diagonal:

G% =

N(�x+)∑i=1

�x+2(i)

N(�x)∑i=1

�x2(i)

100. (2)

Contrary to the P% index, G% also considers the magnitude of the difference betweentwo RR intervals or SBP values, respectively.

1750 L Chladekova et al

G% also ranges from 0 to 100 and irreversible series are characterized by valuessignificantly larger (or smaller) than 50. If G% > 50, the averaged magnitude of |�x+| islarger than that of |�x−| and the distribution of �x is skewed towards positive values.

(3) Ehlers’ index E (Porta et al 2008) is based on evaluating the skewness of the distributionof �x:

E =

N(�x)∑i=1

�x(i)3

(N(�x)∑

i=1�x(i)2

)3/2. (3)

E does not have a pre-defined range, but a significant distance from 0 indicates timeirreversibility. If E > 0, the distribution of �x is skewed toward positive values.

In order to increase the information gained from irreversibility analysis, we investigatedtime irreversibility on various timescales. The multiscale time approach employed in our studyinvolves a coarse-graining procedure (Costa et al 2008). Given the original time series (RRand SBP time series), defined as x = {x(i), i = 1, 2, . . . ,N}, where N is the number of datapoints, coarse-graining was performed as follows. The data inside non-overlapping windowsof τ points are averaged (τ is a scale factor). Each element of the coarse-grained time series{xτ} is then defined as

xτ ( j) = 1

τ

jτ∑i=( j−1)τ+1

xi, 1 � j � N

τ. (4)

The irreversibility indices were calculated for each coarse-grained time series. Becausethe length of each analysed time series was 1000 samples (i.e. 1000 heartbeats), the maximalvalue of τ was set to 4.

2.5. Surrogate data analysis

Surrogate data analysis was used to confirm the presence of time irreversibility in HRV andSBP time series. In general, surrogate time series are designed to preserve certain statisticalproperties of the original data in accordance with the null hypothesis. In order to detect timeirreversibility, we tested the hypothesis that the time series arise from a linear Gaussian process,possibly distorted by nonlinear static invertible process, which does not alter time reversibility.Iteratively amplitude adjusted Fourier transform (IAAFT) surrogates were generated accordingto the procedure described by Schreiber and Schmitz (2000) to test this null hypothesis.IAAFT surrogates maintain the second-order statistical properties (i.e. power spectrum) andthe distribution of the original time series.

One hundred realizations of surrogate data were constructed from each original time seriesto test if P% and G% are significantly different from 50 and E is significantly different from 0.Irreversibility indices were calculated for all original surrogate data. An irreversibility valueof an original time series falling within the 2.5th and 97.5th percentile of the index’ surrogatedata distribution was considered to be consistent with the null hypothesis. Otherwise, the nullhypothesis of the presence of a reversible linear process (possibly distorted by nonlinear staticinvertible function) was rejected and the original series was considered to be time irreversible.

Time irreversibility of heart rate and blood pressure 1751

Figure 1. Box –and whisker plots representing irreversibility indices (P%, G% and E) derived fromthe RR interval time series for multiple timescales (τ = 1, 2, 3, 4), in the lying (L) and standing(S) position. #: significant postural difference of the corresponding index value.

Figure 2. Box and whisker plots representing irreversibility indices (P%, G% and E) derived fromthe SBP time series for multiple timescales (τ = 1, 2, 3, 4), in the lying (L) and standing (S)position. #: significant postural difference of the corresponding index value.

2.6. Statistics

The differences in time irreversibility indices between standing (S) and supine (lying—L)positions were analysed nonparametrically with the Wilcoxon signed-rank test. A p value<0.05 (two-tailed) was considered to be statistically significant.

The Phi test was used to assess the correspondence and consistency of three irreversibilityindices in the detection of irreversibility as identified by surrogate data testing. A p value<0.05 was considered to be statistically significant.

3. Results

We calculated the values of P%(τ ), G%(τ ) and E(τ ) according to the equations (1)–(3). Theresults of the HRV and BPV analysis of irreversibility are summarized in figures 1 and 2,respectively. All indices were derived for both experimental conditions—lying [(PL%(τ ),GL%(τ ), EL(τ )] and standing [(PS%(τ ), GS%(τ ), ES(τ )] and for all investigated timescales(τ = 1, 2, 3, 4).

The HRV analysis revealed significantly higher values of P%(τ ) during the standingcompared to the supine position for all timescales. We found no postural differences of G%(τ )and E(τ ) for τ = 1. Significantly higher values of GS%(τ ) compared to GL%(τ ) were observedfor the scale factors τ = 2, 3, 4. The analysis of E(τ ) showed significantly higher values ofES(τ ) compared to EL(τ ) for scale factors τ = 2, 3.

1752 L Chladekova et al

Figure 3. Bar graphs representing the percentage of the irreversible dynamics detected in the RRinterval time series (HRV) by various indices (P%, G% and E) and on multiple timescales (τ = 1,2, 3, 4), in the lying (L) and standing (S) position.

Figure 4. Bar graphs representing the percentage of the irreversible dynamics detected in the SBPtime series (BPV) by various indices (P%, G% and E) and on multiple timescales (τ = 1, 2, 3, 4),in the lying (L) and standing (S) position.

The BPV analysis revealed a significant decrease in both G%(τ ) and E(τ ) during thestanding compared to the supine position for the scale factors τ = 2, 3, 4. The index PS%(τ )was significantly lower than PL%(τ ) only for timescale τ = 3.

Values significantly different from 50 for P% and G% and from 0 for E, indicate thepresence of time irreversible dynamics in HRV or BPV. The presence of significant timeirreversibility as identified with the IAAFT surrogate method was demonstrated only in afraction of recordings. The HRV series were irreversible in about 46%, 75% and 75% ofsubjects (evaluated by P%, G% and E respectively) in the supine position for scale τ = 1(i.e. the original time series without coarse-graining). These values increased in the standingposition up to 79%, 82% and 82% (for P%, G% and E, respectively). For all other timescales,the proportion of surrogate validated irreversible series significantly increased in the standingposition compared to the supine position. The analysis also showed a lower percentage ofdetected irreversibility when measuring P% as opposed to G% or E. This was true for alltimescales in both supine and standing positions. The results of HRV surrogate data analysisis illustrated on figure 3.

Unlike HRV, BPV showed a trend towards irreversibility decrease in the standing positioncompared to the supine position (figure 4). These postural differences were more evident forthe higher scales (τ = 2, 3, 4) and also more pronounced in G% and E as compared to P%.Furthermore, a higher percentage of irreversibility was detected by the former two indices.

Time irreversibility of heart rate and blood pressure 1753

Mutual relationships among all three indices were assessed by the Phi test and showed aclose relationship between G% and E for both HRV and BPV. Mutual relationships betweenP% and G% and P% and E were not proven. The Phi test results obtained from differenttimescales were analogous.

4. Discussion

The major finding of this study is that the three commonly used time irreversibility indices(Porta’s, Guzik’s and Ehlers’ indices— (P%, G% and E, respectively) are sensitive to theincrease in the sympathetic activity and decrease of parasympathetic activity during orthostasis.Postural changes in irreversibility were observed in both HRV and BPV at various timescales.

Time irreversibility of the cardiovascular parameters is a newly observed and poorlyunderstood phenomenon. Especially asymmetric properties of BPV have been described onlyrecently (Guzik et al 2010a). The mathematical representation of these phenomena is basedon the irreversible dynamics of the heart rate increments and decrements from one beatto another—HRV asymmetry originates from the difference in runs of decelerations andaccelerations (Piskorski and Guzik 2011). Similarly, the asymmetric properties of BPV arebased on the unequal contributions of SBP increases and reductions to the BPV (Guzik et al2010a). In has been suggested that decelerations have a significantly larger contribution toshort-term HRV. Conversely, increases in systolic blood pressure contribute more to short termBPV than reductions (Guzik et al 2010a). However, contrary to short-term HRV, long-termand total HRV is more effectively determined by the accelerations (Piskorski and Guzik 2011).Moreover, it appears that HRV and BPV asymmetries are two independent phenomena, asthey are weakly correlated with no relation between their coexistence (Guzik et al 2010a).

Time irreversibility is clearly present in HRV and BPV of healthy resting subjects, butthe physiological mechanisms responsible for these phenomena remain unclear. Although,various physiological mechanisms might be responsible for HRV and BPV irreversibility, theyare all assumed to be partially influenced by the autonomic nervous system. For example, thebaroreflex may induce asymmetry as baroreflex sensitivity was shown to be different for BPincreases compared to BP reductions even for the same magnitude of BP absolute changes(Parlow et al 1995, Rudas et al 1999). Another potential mechanism might be respiratorysinus arrhythmia (RSA), as the primary physiological mechanism generating short-term HRV.RSA is characterized by the shortening of consecutive RR intervals during inspiration andtheir prolongation during expiration. Usually, the duration of inspiration and expiration is notequal; therefore, it could contribute to asymmetric patterns in cardiovascular signals (Piskorskiand Guzik 2011).

From figures 3 and 4, the different behaviour of the time irreversibility importance(occurrence rate) for higher scales (>1) in HRV and BPV signals can be found. The timeirreversibility can be frequently detected for all assessed timescales in HRV signal pointingtowards multidimensionality of this phenomenon in heart rate oscillations. The importance oftime irreversibility in HRV increases (mostly in higher scales) with the shift of sympathovagalbalance associated with standing. The increased importance of slower oscillations in heartrate associated with vagal withdrawal during standing can be also responsible for this generalenhancement of time irreversibility occurrence rate. On the other hand, the time irreversibilityon higher scales of BPV diminishes in the standing position. It could indicate that the lowfrequency blood pressure oscillations—Mayer waves— dominating in the standing position aremore symmetric than low frequency heart rate oscillations predominantly transferred from theBPV signal to the HRV signal via baroreflex. The nonlinear transfer properties of the baroreflex

1754 L Chladekova et al

and its delay could be responsible for the assymetricity of the resulting low-frequency HRVoscillations.

Given the similar irreversibility occurrence in the BPV signal to HRV signal in the supineposition when the baroreflex sensitivity is higher, we hypothesize that the time irreversibilityin the BPV signal is at least partially transferred from the heart rate to blood pressure signal viabaroreflex. These hypotheses could be confirmed in future by studies using pharmacologicalblockades to find the effects of ANS components on the time irreversibility phenomenon onvarious timescales.

Irreversibility in cardiovascular signals can be quantified by various time asymmetrymeasures. Recent studies suggest that even simple irreversibility indices (Porta’s, Guzik’s andEhlers’ index) are sensitive to shifts in sympathovagal balance. Porta’s index (P%) comparesthe number of the increments and decrements (i.e. RR decelerations and accelerations,BP increases and reductions). Contrary to the P%, Guzik’s index (G%) also considers themagnitude of the difference between two heart beats. The information about the skewnessof the increments/decrements distribution between two heart beats (i.e. �RR and �SBP) isrepresented by Ehlers’ index. These different methods may provide partially independentinformation and their simultaneous quantification might be useful in order to detect theirreversibility comprehensively. Although, our results indicate a close relationship betweenG% and E and our data suggest better performance in irreversibility detection, one should notdismiss P% as it was the only index detecting RR irreversibility increase upon postural changeon scale one.

Recent studies indicate that simple irreversibility indices (Porta’s, Guzik’s and Ehlers’index) counting small values of time lag are sensitive to the increase in the sympathovagalbalance in healthy subjects produced by active orthostasis (Chladekova et al 2011) and head-up tilt at highest inclination angles (i.e. 75◦ and higher) (Casali et al 2008, Porta et al 2008).However, Casali et al (2008) performed the two- and five-dimensional irreversibility testduring active orthostatic challenge using Ehlers’ index. But contrary to our results, Ehlers’index reflected the increase in irreversible dynamics only in the five-dimensional space (Casaliet al 2008).

The selection of timescale may play a major role. Hou et al (2010) suggest that multiscaletime irreversibility analysis (Pm%, Gm%) of a high-dimensional space can reveal moreinformation about the underlying complex dynamic systems (Hou et al 2010). The high-dimensional phase space approach, however, requires relatively long and stationary timeseries. Moreover, whether the natural time series is stationary or not, requires the definitionof a timescale of interest (Costa et al 2008). Porta et al (2008) suggested that temporalasymmetries in RR variability are more likely to occur over short timescales than over longerones. Our results suggest that asymmetry indices may be more sensitive to the autonomicnervous balance shift on the timescales different from the scale one.

Actually, recent results show that the HR asymmetries in healthy people are more frequentduring the head-up tilt at the highest degrees of tilt table inclination (75◦ and 90◦) or duringthe late period of pregnancy (25th–40th week) indicating the link to the amplified sympatheticmodulation (Porta et al 2008). HRV time irreversibility is also likely to be different in thepatients with chronic heart failure, in post-infarction patients with the increased risk ofmortality during a 2 year follow-up and in the patients with type-1 diabetes mellitus of atleast 25 yr (Porta et al 2009, Guzik et al 2010b, 2012). Moreover, the most recent studiesshow that the asymmetrical properties could be also found and assessed in the BPV series.Thus, they surprisingly provide information independent from that obtained from the RRanalysis, they are related to the actual sympathetic/parasympathetic activity as well as in HRV(Guzik et al 2010a).

Time irreversibility of heart rate and blood pressure 1755

4.1. Study limitations

The analysis in our study was limited to only 1000 heart beats corresponding to quasi-stationary state for both supine and standing positions. This limited the multiscale approachto scales below 4. For the analysis of irreversibility on higher scales, the longer recordingsand/or indices enabling irreversibility calculation from shorter recordings would be needed.

Traditionally, coarse-graining is performed by averaging of successive time series valueswithout overlapping as was originally proposed by Costa et al (2008). Recent research byValencia et al (2009) proposed an improved approach (‘refined mutiscale entropy’). In ourstudy, we applied classical averaging coarse graining. Refined multiscale entropy analysiswas performed on a subgroup and showed similar results. However, the effect of the variousfiltering approaches deserves further research.

The gender differences and the effect of ageing on the observed phenomena shouldbe studied in a larger group of subjects. Additionally, the study considers only two differentstates of sympathovagal balance. The changes of HRV and BPV irreversibility during gradualshift of ANS balance (at different angles during head-up tilt test) or during other manoeuvreschanging sympathovagal balance (e.g. mental stress and cold stress test) should be studied forbetter characterization of irreversibility indices behaviour.

5. Conclusion

Heart rate and blood pressure signals both showed time irreversibility and its presenceand magnitude appears to be sensitive to shifts in autonomic nervous system balance.The characteristics of time irreversibility were different between heart rate and bloodpressure signals, indicating independent phenomena and a different origin. Time irreversibilityanalysis of cardiovascular signals may be useful to detect autonomic dysregulation in variouspathological conditions.

Acknowledgments

This study was supported by project of Centre of Excellence for perinatological researchno 26220120016, grant VEGA no. 1/0033/11 and Australian Research Council (grant DP110102049).

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