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. 2012 Jun 26;109(26):10181-6.
doi: 10.1073/pnas.1204568109. Epub 2012 Jun 12.

Phase transitions in physiologic coupling

Ronny P Bartsch  1 , Aicko Y Schumann, Jan W Kantelhardt, Thomas Penzel, Plamen Ch Ivanov
Affiliations

Phase transitions in physiologic coupling

Ronny P Bartsch et al. Proc Natl Acad Sci U S A. .

Abstract

Integrated physiological systems, such as the cardiac and the respiratory system, exhibit complex dynamics that are further influenced by intrinsic feedback mechanisms controlling their interaction. To probe how the cardiac and the respiratory system adjust their rhythms, despite continuous fluctuations in their dynamics, we study the phase synchronization of heartbeat intervals and respiratory cycles. The nature of this interaction, its physiological and clinical relevance, and its relation to mechanisms of neural control is not well understood. We investigate whether and how cardiorespiratory phase synchronization (CRPS) responds to changes in physiological states and conditions. We find that the degree of CRPS in healthy subjects dramatically changes with sleep-stage transitions and exhibits a pronounced stratification pattern with a 400% increase from rapid eye movement sleep and wake, to light and deep sleep, indicating that sympatho-vagal balance strongly influences CRPS. For elderly subjects, we find that the overall degree of CRPS is reduced by approximately 40%, which has important clinical implications. However, the sleep-stage stratification pattern we uncover in CRPS does not break down with advanced age, and surprisingly, remains stable across subjects. Our results show that the difference in CRPS between sleep stages exceeds the difference between young and elderly, suggesting that sleep regulation has a significantly stronger effect on cardiorespiratory coupling than healthy aging. We demonstrate that CRPS and the traditionally studied respiratory sinus arrhythmia represent different aspects of the cardiorespiratory interaction, and that key physiologic variables, related to regulatory mechanisms of the cardiac and respiratory systems, which influence respiratory sinus arrhythmia, do not affect CRPS.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Cardiorespiratory phase synchronization (CRPS) and synchrogram method. (A) Three consecutive breathing cycles (in black, blue, and red), and (B) a simultaneously recorded ECG signal. Horizontal arrows indicate an interbreath interval (IBI) and a RR beat-to-beat interval. (C) Demonstration of phase synchronization between the heartbeats and respiratory cycles shown in A and B. The respiratory signal is plotted versus its Hilbert Transform (HT) (3), and each breathing cycle appears as a close-to-circular trajectory in the same color as in A. The instantaneous phase ϕr(t) is defined as the angle of the respiratory signal and its HT relative to the beginning of each breathing cycle. For each breathing cycle, the first heartbeat occurs at the same respiratory phase formula image, and the second and third heartbeats within each cycle occur at formula image and formula image, respectively (symbols collapse), indicating robust CRPS. (D) Cardiorespiratory synchrogram method: Each heartbeat in the ECG signal (B) is shown with its phase ϕr(t) relative to the beginning of the breathing cycle in which it occurs. Different symbols represent heartbeats in different breathing cycles as in A and C; vertical dashed lines show the beginning of each breathing cycle. Three horizontal parallel lines formed respectively by the first, second, and third heartbeats in the three consecutive breathing cycles indicate 3∶1 phase synchronization. In our analysis, we consider a broad range of CRPS with different n∶m ratios, where n is the number of heartbeats synchronized with m breathing cycles.
Fig. 2.
Fig. 2.
Complex fluctuations in interbreath and heartbeat intervals, and corresponding cardiorespiratory synchrograms of a healthy young (Left) and a healthy elderly (Right) subject. Simultaneously recorded interbreath (IBI) and heartbeat (RR) intervals over a period of 400 s show higher variability for the young subject (A and B) and reduced variability for the elderly (D and E) subject (20, 21). Cardiorespiratory synchrogram for the young subject (C) obtained from the data in A and B, and for the elderly subject (F) corresponding to the data in D and E. Vertical dashed lines in C and F indicate segments of continuous phase synchronization (parallel, almost horizontal lines of red filled circles) between heartbeats and breathing cycles in the time intervals marked by vertical dashed lines in A and B, and D and E, respectively. An episode of 3∶1 synchronization is shown for the young subject (n = 6 heartbeats within m = 2 breathing cycles are consistently placed at the same respiratory phases ϕr over many consecutive breathing cycles), and a segment of 7∶2 synchronization (n = 7 heartbeats are synchronized with each m = 2 breathing cycles) for the elderly subject. Note that the young subject exhibits a longer period of CRPS despite significantly higher interbreath and heartbeat variability compared to the elderly subject.
Fig. 3.
Fig. 3.
Phase synchronization as a measure of cardiorespiratory coupling across sleep stages. A significant increase in CRPS is observed during deep sleep (DS) and light sleep (LS) compared to REM sleep and quiet wake, indicating a significant modulation in cardiorespiratory coupling due to sleep regulation. Left bars represent the group mean n∶m phase synchronization obtained by averaging the percent of synchronization for each subject in the group. Error bars indicate the standard error. The analysis is based on data from 189 healthy subjects during 8 h of sleep by exploring all n∶m ratios, for n > 1 and m ≤ 3 (where n is the number of heartbeats occurring in m adjacent respiratory cycles). Statistical significance of the results for each sleep stage is demonstrated by a comparison to a surrogate test (right bars) performed on the same group of subjects, where the Fourier phases of the respiratory data from each subject were randomized (36) prior to phase-synchronization analysis. A Mann–Whitney rank sum test comparing the synchronization obtained from the real data to the synchronization of the surrogate data yields p < 10-3 for each sleep stage. See Materials and Methods for details on the surrogate data and test. Dashed line (not a fitting line) highlights the sleep-stage stratification pattern in CRPS.
Fig. 4.
Fig. 4.
Significant reduction of approximately 40% in CRPS with age indicates decreased cardiorespiratory coupling in elderly subjects. The n∶m synchronization is obtained from each subject during 8 h of sleep without differentiating between sleep stages and is averaged over all subjects in each age group (error bars represent standard error). The same data as in Fig. 3 are analyzed (see Materials and Methods). Right bars show a surrogate test for the subjects in each age group based on synchronization between heartbeats and Fourier phase-randomized respiratory data, indicating statistical significance of the results for all age groups (Mann–Whitney rank sum test for all age groups, p < 10-3). Dashed line (not a fit) highlights the decrease in synchronization with age.
Fig. 5.
Fig. 5.
Sleep-stage stratification pattern in CRPS for different age groups. All age groups exhibit the same stratification pattern with lowest percent synchronization during REM, higher during wake and LS, and highest during DS. This sleep-stage difference significantly decreases from a factor of 7 (comparing REM to DS) for the youngest subjects to a factor of 2 for the oldest age group. Error bars in all panels show the standard error. For different n∶m ratios see SI Text and Fig. S3.
Fig. 6.
Fig. 6.
CRPS and RSA represent different aspects of cardiorespiratory coupling. (A) Whereas RSA leads to periodic modulation of the heart rate within each breathing cycle (highlighted by a least-squares-fit sinusoid line to the data points) and is quantified by the amplitude of the heart rate modulation, CRPS leads to clustering of heartbeats at certain phases ϕr of the breathing cycle (highlighted by red ovals). Shown are consecutive heartbeats over a period of 200 s. The x axis indicates the phases ϕr of the breathing cycle where heartbeats occur, and the y axis indicates the deviation of each heartbeat interval RRi from the mean formula image calculated by averaging all RRi within a given breathing cycle (different cycles are characterized by different values of formula image). Heartbeats are plotted over pairs of consecutive breathing cycles, ϕr∈[0,4π], to better visualize rhythmicity. Data are selected from a subject during DS. (B) For the same subject as in A, heartbeats from another period of 200 s also during DS are plotted over pairs of consecutive breathing cycles. Data show well-pronounced RSA with a similar amplitude as in A, however, heartbeats are homogeneously distributed across all phases of the respiratory cycles, indicating absence of CRPS.
Fig. 7.
Fig. 7.
RSA and phase synchronization involve different mechanisms of cardiorespiratory coupling. (A) RSA gradually increases (> 250%) with decreasing breathing frequency and drops abruptly for very low breathing frequencies (Spearman’s rank order correlation, ρ = -0.42, p < 10-3). (B) In contrast to RSA, the length of phase-synchronization episodes is independent of the breathing frequency (Spearman ρ ≈ 0, p < 10-3). (C) RSA strongly increases with increasing values of RMSSD of heartbeat RR intervals (i.e., σΔRR, a measure of parasympathetic tone; ref. 25) (Spearman ρ = 0.69, p < 10-3). (D) In contrast to RSA, the length of phase-synchronization episodes does not significantly change with RMSSD (Spearman ρ ≈ 0, p < 10-3). Error bars represent the standard error. See Materials and Methods for the procedure used to obtain these dependencies. Data are averaged over all sleep stages and age groups.
Fig. 8.
Fig. 8.
Change in CRPS, RSA, and average breathing frequency (Bfreq) across sleep stages. Average values for each sleep stage are normalized on the corresponding values during REM sleep. Data are averaged over all age groups. The sensitivity of phase synchronization to sleep-stage transitions is by a factor of 10 higher than RSA, indicating that sleep regulation affects these two aspects of cardiorespiratory coupling differently. Error bars represent the standard error.
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