Does synchronization reflect a true interaction in the cardiorespiratory system?

Medical Engineering & Physics 24 (2002) 45–52 www.elsevier.com/locate/medengphy

Does synchronization reflect a true interaction in the cardiorespiratory system? E. Toledo a, S. Akselrod a,∗, I. Pinhas a, D. Aravot b a

The Abramson Center of Medical Physics, Sackler Faculty of Exact Sciences, Tel Aviv University, P.O. Box 39040, Tel Aviv 69978, Israel b Heart-Lung Transplant Unit, Rabin Medical Center, Beilinson Campus, Petach Tikva 41900, Israel Received 1 April 2001; accepted 12 November 2001

Abstract Cardiorespiratory synchronization, studied within the framework of phase synchronization, has recently raised interest as one of the interactions in the cardiorespiratory system. In this work, we present a quantitative approach to the analysis of this nonlinear phenomenon. Our primary aim is to determine whether synchronization between HR and respiration rate is a real phenomenon or a random one. First, we developed an algorithm, which detects epochs of synchronization automatically and objectively. The algorithm was applied to recordings of respiration and HR obtained from 13 normal subjects and 13 heart transplant patients. Surrogate data sets were constructed from the original recordings, specifically lacking the coupling between HR and respiration. The statistical properties of synchronization in the two data sets and in their surrogates were compared. Synchronization was observed in all groups: in normal subjects, in the heart transplant patients and in the surrogates. Interestingly, synchronization was less abundant in normal subjects than in the transplant patients, indicating that the unique physiological condition of the latter promote cardiorespiratory synchronization. The duration of synchronization epochs was significantly shorter in the surrogate data of both data sets, suggesting that at least some of the synchronization epochs are real. In view of those results, cardiorespiratory synchronization, although not a major feature of cardiorespiratory interaction, seems to be a real phenomenon rather than an artifact.  2002 IPEM. Published by Elsevier Science Ltd. All rights reserved. Keywords: Phase synchronization; Cardiorespiratory synchronization; Heart transplantation; Cardiorespiratory coordination; HR variability

1. Introduction Physiological systems serve as a fascinating playground for the study of analysis techniques, which stem from the discipline of nonlinear dynamics. The essential nonlinearities and the complexity of physiological interactions set the limit to the ability of linear analysis to provide a full description. This makes nonlinear dynamics an invaluable tool for the analysis of physiological systems. The coupling between the respiratory system and the heart is known to be both neurological [1] and mechanical [2]. The coupling between those systems is also known to be nonlinear [1]. It results in the wellknown modulation of HR by respiration, known as respiratory sinus arrhythmia; this modulation is expressed

* Corresponding author. Tel.: +972-3-6408669; fax: +972-36406237. E-mail address: [email protected] (S. Akselrod).

as the high frequency peak when referring to the power spectral pattern of HR fluctuations. Recently, however, an additional aspect of the interaction between respiration and the heart has been reported: synchronization between HR and respiration rate [3], termed cardiorespiratory synchronization. The methods applied to detect complex patterns of synchronization between respiration and HR, stemmed from the study of phase synchronization in chaotic oscillators. Cardiorespiratory synchronization has been reported in young healthy athletes [3,4], healthy adults [5–7], heart transplant patients [5], infants [8] and anesthetized rats [9]. The finding of synchronization in the human cardiorespiratory system may expand our knowledge about the interactions between the two subsystems. However, for cardiorespiratory synchronization to enter the cadre of cardiorespiratory interaction, it still has to be translated from phenomenology to physiology. In other words, cardiorespiratory synchronization remains a phenomenological observation, unless proven to result from a coup-

1350-4533/02/$22.00  2002 IPEM. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 0 - 4 5 3 3 ( 0 1 ) 0 0 1 1 4 - X

46

E. Toledo et al. / Medical Engineering & Physics 24 (2002) 45–52

ling between the two interacting subsystems. The question rising is whether cardiorespiratory synchronization is real or whether it results from the random matching between respiratory rate and HR. In other words, is there a mechanism, passive or active, which induces cardiorespiratory synchronization or is it an artifact? There are two ways to address this question. The first is to associate a quantitative estimate of cardiorespiratory synchronization with distinct physiological conditions as reflected by a range of experimental and clinical data. This will elucidate the physiology, which underlies this phenomenon, hereby proving that the synchronization is a true phenomenon and not an artifact. The second way to address this question, is to prove that the cardiorespiratory synchronization in a specific data set is real and not accidental using statistical measures. In this study, we address this question in both ways. In any case, the need for an algorithm for objective quantification of cardiorespiratory synchronization is common to both approaches. An algorithm for the automatic and objective detection of epochs of synchronization is presented. The quantification algorithm is then applied to two kinds of data sets, each of which reflects a very different physiological condition. Our aim, as part of the first way to deal with the nature of cardiorespiratory synchronization, is to find and characterize synchronization for each of these different data sets. The first data set was obtained from normal healthy subjects and the second one, from heart transplant patients. These two groups of subjects represent markedly different cardiovascular conditions. During the standard surgical procedure, the left and right atria of the recipient’s heart are sutured to the atria of the transplanted heart. The recipient’s SA node is fully denervated but the electrical signal originating from it cannot cross the suture line. The HR is determined by the transplanted SA node, which is fully denervated and subjected only to slow humoral control [2,10,11]. Partial sympathetic reinnervation was detected several months after surgery [2,10,11], whereas parasympathetic reinnervation is scarce, even several years after surgery [12]. From the point of view of the coupling between the respiratory and the cardiac systems, normal subjects exhibit bidirectional coupling, i.e. both HR and respiratory rate are determined by reflexes mediated by the brain, and can affect each other. In contrast, in heart transplant patients, control over respiration is unchanged, yet control over HR is very slow. The mechanical coupling between the respiration and the heart is probably unchanged, yet it is known to be weak [2]. Another relevant consequence of the surgical denervation in the heart transplant subjects is that mean HR is higher and HR fluctuations are markedly reduced compared to normal subjects. In a previous study, we have shown that the heart

transplant patients can be classified naturally into three groups according to their HR response to a change in posture [13]. The three groups exhibit a different type of coupling between the respiratory system and the heart: mechanical coupling (group 1), mechanical coupling accompanied by increased cardiac sensitivity to noradrenaline (group 2) and finally partial sympathetic reinnervation in conjunction with a fast control mechanism (group 3). The second way of verifying the existence of real epochs of cardiorespiratory synchronization is a comparison of the statistical properties of those epochs in the original data and in surrogate data constructed from the original data. Surrogate data analysis is a widely used approach in the field of nonlinear dynamics, especially when trying to assess a functional relation between a property of a system (e.g. the correlation dimension) to one of the system’s features [14]. The essence of surrogate analysis is the construction of a large (surrogate) data set derived from the original data. This is typically achieved by randomizing a data feature, the influence of which is under investigation, while all other features of the data are preserved. The observation of a difference in the measured property between the real and the surrogate data, then indicates that it is related to that specific feature which is absent in the surrogates. In our case, a full model of the cardiorespiratory system is not available. Therefore, a simple randomization of the signals (such as maintaining the power spectrum but randomizing the phase of the Fourier transform) would destroy some basic features of the signals, which might be relevant for the generation of cardiorespiratory synchronization. Moreover, such randomization might produce signals which are physiologically unrealistic. We therefore present another type of surrogate data, which we believe suits the analysis of the interaction between two systems, the features of which cannot be fully characterized. This kind of surrogate data extends the typical interpretation of surrogate date [15,16], as the surrogate date we use does not share any linear properties with the original data. By combining the two approaches, namely the analysis of the cardiorespiratory system under two distinct physiological conditions and the comparison with surrogate data, we were able to establish that synchronization is indeed a true phenomenon, and therefore should be considered one of the cardiorespiratory interactions.

2. Methods 2.1. Data sets The algorithm for the quantification of cardiorespiratory synchronization was applied to two data sets: normal subjects and heart transplant patients. Recordings

E. Toledo et al. / Medical Engineering & Physics 24 (2002) 45–52

from 14 normal male subjects (age 28–59, mean=41±6 years) were analyzed in this work. The heart transplant group included 13 male heart transplant patients (age: 28–68, mean=52±12 years). All patients underwent the standard orthotopic procedure, and received the standard immunosuppressive therapy with Cyclosporin, Prednisone and Azathioprine. In this group, 25 recordings were performed. The time elapsed since transplant surgery ranged between 0.5–62.5 months. All patients were in stable conditions with respect to their clinical signs and symptoms. None had any sign of graft rejection prior to a recording session. The study was approved by the Institutional Review Committee. All subjects gave their written informed consent. In each recording session, all subjects were monitored continuously in three subsequent positions, including the active transitions between postures: 45 min in supine position, 5 min during upright standing and 10 min while sitting. The transitions between postures lasted 10 s. All recordings began following 10 min of supine rest. Heart transplant patients were classified according to their HR response to the change in posture (CP) [13]: 앫 Group 1: no change of HR in response to CP. 앫 Group 2: slow HR increase (rise time⬎60 s). 앫 Group 3: fast HR increase (less than 20 s). Recordings, which included severe cardiac arrhythmias or a noisy respiration signal, were not subjected to the analysis of cardiorespiratory synchronization. Therefore, the group of normal subjects ended up to include 13 recordings, whereas for the heart transplant patients, group 1 included three recordings, groups 2 and 3 included six recordings each. 2.2. Data acquisition and preprocessing Lead I ECG (using Biopac MP100), continuous BP (Finapres–Ohmeda) and respiration (Respitrace, Ambulatory Monitoring) were non-invasively monitored. R– waves were extracted automatically from the ECG and visually examined to exclude artifacts and arrhythmias. Before detecting the peaks of the respiratory signal, this signal had to be low-pass filtered, in order to reduce the noise. The asymmetrical breathing pattern compelled us to consider the first four harmonics of the respiration. Moreover, the asymmetrical shape of the respiration signal is highly sensitive to dispersion of the filter, since a frequency dependent group-delay would alter the signal. Such alteration of the signal results in timing error when detecting the peaks of the signal, thus introducing effective noise to the series of the times of maxima. The respiration signal was therefore low-pass filtered digitally using a Chebyshev filter with cutoff frequency fc=1 Hz and passband ripple of 0.01 dB. The respiration signal was filtered twice: first in the usual way and then in the

47

reversed direction. While this filtering technique is not causal, it cancels the group delay of the filter. 2.3. The Synchrogram The Synchrogram is a visualization tool, designed to enable the detection of synchronization epochs in bivariate data. It is most valuable in cases where one of the signals resembles a point process, i.e. almost periodic and wideband, such as the human ECG. The Synchrogram is a stroboscopic view of the phase of the respiration signal at the times of the R-waves [3,4]. The first step in the Synchrogram construction is the computation of the phase of the respiratory signal. There are several ways to define the phase of a signal (see Pikovsky et al. [17] for a tutorial). A possible method for the assessment of this phase is the analytical signal approach [3,4]. This applies to narrow band signals. However, in our case, the respiratory signal was obtained from abdominal and/or chest movements and was therefore rather asymmetric. Consequently, the analytic signal approach could not be used. Therefore, we used the detection of local maxima, which represent the onset of expiration and the fact that the signal has completed one full cycle. For each local maximum, we assigned a phase increase of 2p to the phase of the signal. The discretetime phase signal is interpolated to provide the continuous unwrapped phase of the signal: fr(t). For narrowband signals, the phase fr(t) can be assessed from the Hilbert transform of the signal [4]. The phase of the respiration signal is then assessed at the times of R–waves tk. Synchronization with ratio of n:m means that respiration completes m cycles (and its phase increases by 2pm) while the ECG completes n cycles (and its phase increases by 2pn). The mathematical implication of the last observation is that in the case of n:m synchronization: fr(tk+n)=fr(tk)+2pm. We therefore define: yr(tk)⬅fr(tk) mod 2pm. Plotting yr(tk) versus tk results in n horizontal lines in case of m:n synchronization (see Fig. 1A). Epochs of synchronization can be easily detected visually, provided that m has been chosen adequately. It is important to note that the Synchrogram enables the detection of synchronization in the presence of modulation of the HR by respiration. This property is essential when searching for synchronization in the cardiorespiratory system, where modulation exists in most physiological conditions. In the absence of modulation, the phases of the horizontal lines are equally spaced (vertical distance between lines is equal). However, modulation of the HR by respiration results in unevenly spaced lines. 2.4. Quantification of the Synchrogram The objective quantification process is based on the automation of the search for horizontal parallel straight

48

E. Toledo et al. / Medical Engineering & Physics 24 (2002) 45–52

Fig. 1. Synchrograms of characteristic recordings. Synchronization, marked by the black dots, is characterized by the arrangement of the wrapped phase in horizontal lines. A—a normal subject, note the 5:1 synchronization epochs around 1200 sec and 1500 sec. The second synchronization epoch is too short and therefore discarded. B—a heart transplant patient, note the 200 sec synchronization epoch at 2600– 2800 sec. C—a surrogate recording composed from the respiration of a normal subject and the HR of a heart transplant patient. One 70 sec synchronization epoch and two short ones are found.

lines in the Synchrogram. The search is performed for every couple of m and n (the ratio of the instantaneous frequencies). The first step is choosing the m and n and constructing the Synchrogram. Next, the phases yr(tk) are divided into n subgroups alternatively (see the different markers in Fig. 2). Note that when the Synchrogram exhibits an n lines structure, every subgroup will coincide with one of the lines. We then use the transformation: yr(tk)→eiyr(t)k in order to avoid phase discontinuities. The geometrical average of every subgroup is then computed. The resulting vector has a magnitude of 1 and its phase is the average of all the subgroup members’ phases. The averaged phase is then subtracted from all group members, thus eliminating the vertical distance between the lines (Fig. 2B). The width of the resulting line, which is effectively the collection of all points after subtraction of the differences between the lines, is a measure of the synchronization between the two signals. This measure, denoted by d was computed in a sliding window in order to assess the dynamical behavior of synchronization (see Fig. 2C). It is important to note, that modulation of the HR by respiration, which results in uneven phase differences between the lines, does not affect the width of the line

Fig. 2. The steps in the algorithm of the quantification of synchronization. The points are divided into n subgroups, marked by the different markers in graph A. The average phase of each subgroup is then subtracted from each subgroup. Epochs of synchronization are characterized by a thick horizontal line, as seen in the middle of graph B. The vertical width of this line, d is computed over a moving window, shown in graph C. Low values of d indicate synchronization. A threshold of 0.03 was set (marked by the dotted line in graph C). The HR and respiration are considered synchronized when d is below this threshold.

d. Therefore, the quantification algorithm preserves this important feature of the Synchrogram. The length of the window was set to 31 sec, hence discarding too short epochs and transients. A threshold for d was set to 0.03. The cardiorespiratory system is considered to be synchronized when d is below this threshold. A misdetected R-wave or an arrhythmia, increase locally the value of d. Therefore, gaps shorter than 11 sec between synchronization epochs were discarded. The search for synchronization was limited to n:2 and n:1 ratios. The values of the parameters were set to detect epochs, which were identified visually as synchronization epochs. 2.5. Construction of the surrogate data The delicate part of surrogate data analysis is always the construction of the surrogates. The easy task of generating surrogates when analyzing simulated data becomes a difficult one when analyzing real data. In principle, the surrogates should be the respiration and the HR of a subject, but without the coupling between them. This approach to the surrogates construction is impossible, when considering data acquired from a natural system, since the exact nature of the subsystems is

E. Toledo et al. / Medical Engineering & Physics 24 (2002) 45–52

unknown. Moreover, models for the cardiorespiratory system have been suggested, yet, none of them has succeeded in simultaneously describing the linear and nonlinear features of the system. We have thus adopted a different approach to deal with this problem. The surrogate HR–respiration couples were constructed by associating the respiration signal of every subject with the HR of all others. The main advantage of using combinations of respiration and HR signals is that all the intrinsic features of the signals, linear as well as nonlinear, are preserved, while only the coupling is eliminated. Any manipulation of the signals themselves, although allowing to generate large numbers of surrogates, is likely to destroy some basic features of the system. This would possibly obscure the determinants of cardiorespiratory synchronization. However, two problems arise. The first is the limited number of surrogates. This is in contrast with the conventional method of randomizing some specific feature of the signal, thus creating large quantities of surrogate HR–respiration couples. The second problem rises from the doubt that a couple of respiration and HR, originating from different subjects, represents a likely physiological condition. The second limitation of the method encourages the use of numerous kinds of surrogates, each preserving a different feature of the system. It is important to note that the surrogate date constructed in this method differ considerably from the typical notion of surrogate date, which share some linear properties with the original data [15]. In contrast, the surrogate data constructed here does not share any linear or nonlinear properties with the original data—the only common feature is its being the same physiological signal [16]. We constructed three groups of surrogate data: 앫 Group S1: all combinations of HR and respiration from different normal subjects, resulting in 156 surrogate recordings. 앫 Group S2: combinations of respiration from normal subjects and HR from group 2 heart transplant subjects, resulting in 78 surrogate recordings. 앫 Group S3: all combinations of HR and respiration obtained from different heart transplant subjects, all from group 2, resulting in 30 surrogate recordings.

49

posed of the respiratory signal of subject j and the HR of subject i. The recording ji represents a real one when i=j and a surrogate one when i ⫽ j. Let nji be the number of synchronization epochs detected in recording ji. The nji synchronization epochs of recording ji are each of duration Tpji,1ⱕpⱕnji. The total duration of synchronization epochs of every recording is:

冦冘 nji

Tji ⫽

Tjip nji ⬎ 0 . p⫽1

0

nji ⫽ 0

Note that due to our initial threshold, the smallest value of Tji is 0, and the next larger value is 31 sec. All the parameters were normalized by the total length of the recording involved. In order to test for a difference between two unrelated groups A and B (e.g. normal subjects and group 2 heart transplant subjects), we compared {nii|i苸A其 to {njj|j苸B其 and {Tii|i苸A其 to {Tjj|j苸B其. A nonparametric approach was used since none of these statistical quantities is Gaussian distributed. Therefore, both duration and number of synchronization epochs between unrelated groups were compared using the one-sided Mann– Whitney U-test [18]. Comparing the statistical properties of synchronization epochs between the real recordings and the surrogate recordings created from it, enabled to study the role of low HR variability (typical in heart transplant patients) in the creation of synchronization. If cardiorespiratory synchronization were an artifact of low variability, then synchronization would be similar in surrogate recordings composed of the same HR trace and respiration obtained from other recordings. On the other hand, reduction of synchronization in the surrogate recordings would indicate that the synchronization is not an artifact. Therefore, we tested, per HR trace, whether the number and duration of synchronization epochs tend to be higher in the original recordings compared with the surrogate recordings. We formed the two sets: {nii⫺ nji|i苸A,i ⫽ j其 and {Tii⫺Tji|i苸A,i ⫽ j其, and used the onesided Wilkinson rank sum test to determine whether those sets tend to be positive [18].

2.6. Measured parameters 3. Results Several parameters of the synchronization epochs were compared between the original and the surrogate data. Although synchronization was expected to appear in the surrogates, synchronization epochs in the surrogates were expected to be shorter and/or less frequent than synchronization epochs in the original data. We thus compared the duration and number of synchronization epochs in both the original and surrogate data. We first define the recording ji as the recording com-

Interestingly, synchronization between respiration and HR has been detected in all data sets: normal subjects, heart transplant subjects and the surrogate data generated from the real data. Nevertheless, differences were found in the prevalence of cardiorespiratory synchronization between the groups. Those differences may shed some light on the physiology of synchronization. Examples of synchronization epochs found in recordings obtained

50

E. Toledo et al. / Medical Engineering & Physics 24 (2002) 45–52

from the various groups are shown in Fig. 1, and the method applied for quantification of synchronization is presented in Fig. 2 (detailed in Section 2.4). 3.1. Comparisons between groups The most important and perhaps surprising finding of this analysis is the tendency of heart transplant subjects of group 2 to exhibit cardiorespiratory synchronization (see Fig. 3). HR and respiration in those subjects were synchronized in 20–76% of the recordings duration. One heart transplant subject of group 2 did not exhibit any synchronization, while the other five subjects exhibited abundant synchronization epochs. In contrast, HR and respiration of the normal subjects were synchronized in 1–21% of the recordings duration in 11 subjects. Two normal subjects did not exhibit any synchronization. Both the number and the duration of the synchronization epochs were significantly lower in the group of normal subjects compared to group 2 heart transplant subjects (number of synchronization epochs: p⬍0.05, duration: p⬍0.02, see Fig. 3). Both number and duration of the synchronization epochs appeared to be higher in groups 1 and 3 than in the normal group, yet lower than in group 2. These differences were not statistically significant, probably due to the relatively low number of subjects in these groups. 3.2. Comparisons within groups The number and duration of synchronization epochs were lower in the surrogates of the normal subjects (group S1) than in the original recordings. The distribution of differences in duration is shown in Fig. 4. The average reduction in the normalized number of synchronization epochs per recording was 0.47 (a reduction of 22%, p⬍0.02). The average reduction in the normalized total duration of synchronization epochs was 2.5 sec (a reduction of 2.7%, p⬍0.007).

Fig. 3. Histograms of {Tii|i苸Normal Subjects其 and {Tjj|j苸Group 2其, the duration of synchronization epochs of both normal subjects and heart transplant subjects of group 2. The two distributions differ significantly (p⬍0.02).

Fig. 4. Histogram of {Tii⫺Tji|i, j苸Normal Subjects, i ⫽ j其, the difference of the total duration of synchronization between the groups of normal subjects and their surrogates (group S1). The difference tends to be positive, indicating that the synchronization lasted longer in the original recordings. The decrease in duration of synchronization in the surrogates was significant, although small. Average reduction was of 2.5 sec, which are 2.7% of the average duration (p⬍0.01).

Reduction, in the surrogate data, of the measures of synchronization was also found in the results of heart transplant subjects of group 2 (see Fig. 5). The number and duration of synchronization epochs were both lower in the surrogate data of group 2 (group S3) than in the original data of this group. The difference was not significant due to the low number of recordings in each group. However, when we increased the number of surrogates by considering the HR of every heart transplant subject of group 2, with the respiration of all normal subjects (group S2), the trend became clearly statistically significant. The average reduction in the number of synchronization epochs (normalized by length of recording) was 0.65 (12%, p=0.06), and the average reduction in the total duration of synchronization epochs (again, normalized) was 57.7 sec (13%, p⬍0.05), when comparing group 2 and group S2.

Fig. 5. Histogram of {Tii⫺Tji|i苸Group 2, j苸Normal Subjects其, the difference of the total duration of synchronization between the heart transplant subjects of group 2 and its surrogates (group S2), constructed by considering the original HR trace and the respiration from normal subjects. The distribution clearly tends towards positive values, indicating that the synchronization lasted longer in the original recordings. The average reduction in the surrogates was of 57 sec, which are 13% of the average duration (p⬍0.05).

E. Toledo et al. / Medical Engineering & Physics 24 (2002) 45–52

4. Discussion

An interesting observation in this study is the finding of synchronization in all groups of subjects: normal, heart transplant and surrogates. The presence of synchronization in the surrogate data of both the normal subjects and the heart transplant subjects is intriguing. The immediate conclusion from this result is that, at least some of the synchronization epochs in the real data occur randomly. However, the conclusion that all synchronization epochs are the result of random matching of HR and respiration rate is not supported by the results of this work. The more reasonable conclusion from the existence of synchronization epochs in the surrogate data is that most of the synchronization epochs in the real data occur at random, while others are the result of true synchronization. The difference in the statistical properties of the synchronization epochs between the real and surrogate data leads to the last conclusion. The reduced incidence of synchronization in the surrogates of the normal subjects in comparison with the original recordings (as expressed by the reduction in number and duration of the synchronization epochs) provides a strong indication that some of the cardiorespiratory synchronization found in normal subjects is true. The statistical analysis also unveils the role of the HR trace in producing spurious synchronization epochs. Cardiorespiratory synchronization has been associated with diminished HR fluctuations, in particular with reduced levels of respiratory sinus arrhythmia [3], indicating reduced parasympathetic stimulation to the heart [4,5]. It is possible that a low HR variability is related to synchronization by the fact that the system is less noisy, rather than by the physiological condition it reflects. This may explain the abundant cardiorespiratory synchronization in the recordings obtained from heart transplant subjects, in whom HR variability is indeed very low. If this hypothesis were true, then parts of their HR trace which seem to be synchronized with respiration should also be synchronized with respiration from other subjects. However, the reduction of synchronization in the surrogates of the normal subjects (group S1) suggests that this hypothesis is not true. Moreover, the surrogate data of group 2 heart transplant subjects also exhibited reduced synchronization relative to the original data. If low HR variability was a sufficient condition of cardiorespiratory synchronization, then surrogate recordings composed of various respiration traces with every HR trace from heart transplant subject of group 2 (group S2) would exhibit the same amount of synchronization as the original data. However, a reduction of 13% in the total length of synchronization epochs was found when comparing the real and surrogate data. The conclusion from this analysis is that cardiorespiratory synchronization is

51

real, both in the normal and the heart transplant subjects, and is not an artifact of the low HR variability. Another fascinating result is the abundant cardiorespiratory synchronization in heart transplant subjects relative to normal subjects. This finding suggests that in these subjects, the unique kind of coupling between the respiratory system and the transplanted heart, promotes synchronization. A previous study has shown that the subjects of group 2 lack both sympathetic and parasympathetic control over the heart. They do, however, exhibit a slow control mechanism over the HR, which probably involves the adrenal gland [13]. It is also probable that those subjects exhibit increased cardiac sensitivity to noradrenaline [13]. However, both the sluggish control over the HR and the enhanced sympathetic sensitivity do not provide a pertinent explanation for the prevalence of cardiorespiratory synchronization. Two other possibilities arise: the first is that the mechanical coupling between the heart and the respiratory system, not blunted by fast neural control mechanisms (as in normal subjects), causes the synchronization, and the second possibility is that respiration adapts its rhythm to HR. It is impossible to pinpoint the exact reason for synchronization due to the low number of cases in the three different heart transplant subgroups. Further study may reveal whether the abundant synchronization exhibited by group 2 subjects is common also to the other two groups, or whether it is the result of special features of cardiorespiratory interaction which are unique to this group. In most of the recordings, synchronization appears for only short periods. In those cases, synchronization does not play a major role in cardiorespiratory interaction. In comparison, modulation of the HR by respiration is present, to some extent, most of the time. The hypothesis that synchronization may only play a secondary role in cardiorespiratory interaction is also supported by the fact that the difference between real and random synchronization epochs is statistical in nature. The mechanisms by which HR and respiration rate synchronize can only be hypothesized at this stage. Synchronization can be the consequence of the mere coupling between two nonlinear systems, as has been shown in other systems [17,19]. Such synchronization, being only a secondary mechanism as suggested by the present analysis, does not necessarily bear physiological advantages. Another possibility is that such synchronization bears an energetic benefit, since the reduction in intrathoracic pressure, which occurs during inspiration, increases cardiac filling and thus cardiac output. Therefore, synchronizing heart rate and respiration may increase cardiac output while conserving energy. This mechanism may have been brought forward by natural selection during evolution. Thus, cardiorespiratory synchronization may be important in extreme physio-

52

E. Toledo et al. / Medical Engineering & Physics 24 (2002) 45–52

logical conditions, where such energetic benefit is crucial. However, those hypotheses are neither supported nor negated by the analysis presented here. Analysis of cardiorespiratory synchronization in different physiological conditions may shed light on the mechanisms of synchronization and its clinical merits.

[7]

[8]

[9]

Acknowledgements [10]

The study was supported in part by grant no. 4283 from the Chief Scientist’s Office of the Ministry of Health, Israel and in part by the Welcome Foundation. The authors would like to thank Dr Orna Oz for providing some of the data.

References [1] Guyton AC. Text book of medical physiology, 8th ed. Philadelphia (PA): Saunders, 1991. [2] Bernardi L, Salvucci F, Suardi R, Solda PL, Calciati A, Perlini S, Falcone C, Ricciardi L. Evidence for an intrinsic mechanism regulating heart rate variability in the transplanted and the intact heart during submaximal dynamic exercise? Cardiovasc Res 1990;24(12):969–81. [3] Scha¨ fer C, Rosenblum MG, Kurths J, Abel H-H. Heartbeat synchronized with ventilation. Nature 1998;392(6673):239–40. [4] Scha¨ fer C, Rosenblum MG, Abel HH, Kurths J. Synchronization in the human cardiorespiratory system. Phys Rev E 1999;60:857–70. [5] Toledo E, Rosenblum MG, Scha¨ fer C, Kurths J, Akselrod S. Quantification of cardiorespiratory synchronization in normal and heart transplant subjects. In: Proc of Int Symposium on Nonlinear Theory and its Applications, vol. 1. Lausanne: Presses polytechniques et universitaires romandes, 1998, pp. 171–174. [6] Toledo E, Rosenblum MG, Kurths J, Akselrod S, 1999. Cardiorespiratory synchronization: is it a real phenomenon? In: Computers

[11]

[12]

[13]

[14]

[15] [16] [17]

[18] [19]

in Cardiology, vol. 26, Los Alamitos (CA), IEEE Computer Society, pp. 237–240. Lotric MB, Stefanovska A. Synchronization and modulation in the human cardiorespiratory system. Physica A 2000;283(34):451–61. Mrowka R, Patzak A. Quantitative analysis of cardiorespiratory synchronization in infants. Int J of Bifurcation and Chaos 2000;10(11):2479–88. Stefanovska A, Haken H, McClintock PVE, Hozic M, Bajrovic F, Ribaric S. Reversible transitions between synchronization states of the cardiorespiratory system. Phys Rev Lett 2000;85(22):4831–4. Bengel FM, Ueberfuhr P, Ziegler SI, Nekolla S, Reichart B, Schwaiger M. Serial assessment of sympathetic reinnervation after orthotopic heart transplantation A longitudinal study using PET and C–11 hydroxyephedrine. Circulation 1999;99(14):1866–71. Uberfuhr P, Ziegler S, Schwaiblmair M, Reichart B, Schwaiger M. Incomplete sympathic reinnervation of the orthotopically transplanted human heart: observation up to 13 years after heart transplantation. Eur J Cardiothorac Surg 2000;17(2):161–8. Bernardi L, Valenti C, Wdowczyck-Szulc J, Frey AW, Rinaldi M, Spadacini G, Passino C, Martinelli L, Vigano M, Finardi G. Influence of type of surgery on the occurrence of parasympathetic reinnervation after cardiac transplantation. Circulation 1998;97(14):1368–74. Toledo, E, Pinhas, I, Almog, Y, Aravot, D, Akselrod, S. Cardiovascular control in heart transplant subjects: phenomenology and physiology. Submitted to Circ Res. Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer JD. Testing for nonlinearity in time series: the method of surrogate data. Physica D 1992;58(1-4):77–94. Schreiber T, Schmitz A. Improved surrogate data for nonlinearity tests. Phys Rev Lett 1996;77(4):635–8. Schreiber T, Schmitz A. Surrogate time series. Physica D 2000;142(3-4):346–82. Pikovsky A, Rosenblum M, Kurths J. Phase synchronization in regular and chaotic systems. Int J of Bifurcation and Chaos 2000;10(10):2291–305. Ott L. An introduction to statistical methods and data analysis, 4th ed. Belmont (CA): Duxbury Press, 1993. Rosenblum MG, Pikovsky AS, Kurths J. Phase synchronization of chaotic oscillators. Phys Rev Lett 1996;76(11):1804–7.