Experimental Evidence for Phase Synchronization Transitions in the Human Cardiorespiratory System

Transitions in the dynamics of complex systems can be characterized by changes in the synchronization behavior of their components. Taking the human cardiorespiratory system as an example and using an automated procedure for screening the synchrograms of 112 healthy subjects we study the frequency and the distribution of synchronization episodes under different physiological conditions that occur during sleep. We find that phase synchronization between heartbeat and breathing is significantly enhanced during non-rapid-eye-movement (non-REM) sleep (deep sleep and light sleep) and reduced during REM sleep. Our results suggest that the synchronization is mainly due to a weak influence of the breathing oscillator upon the heartbeat oscillator, which is disturbed in the presence of long-term correlated noise, superimposed by the activity of higher brain regions during REM sleep.

Figure 1

Illustration of our automated phase synchronization detector: (a) section of a typical synchrogram in raw form, (b) the same section as in (a) after applying a moving average filter with windows of $\tau =30\mathrm{s}$ around each breathing cycle; the window averages are shown together with their standard deviations (error bars), (c) contiguous phase points of (b) where the standard deviation is below a threshold (see text) are detected as synchronization episodes if their durations exceed $T$ seconds (here $T=30\mathrm{s}$).

Figure 2

Medians, upper and lower quartiles (bars) and means (filled symbols) for the detected synchronization rates (a) versus $T$ for all original data (dotted bars and circles) and surrogate data (striped bars and triangles), (left of dotted line $\delta =6$, right of dotted line $\delta =5$); (b),(c) versus age, BMI, and gender, for wakefulness (dotted bars and circles), REM sleep (blank bars and triangles), and non-REM sleep (striped bars and diamonds) for $T=30\mathrm{s}$. Note the similar synchronization behavior in all groups.

Figure 3

Normalized histograms of all detected synchronization ratios as well as distributions of the frequency ratios between heartbeat and breathing during (a) wakefulness, (b) REM sleep, (c) light sleep, and (d) deep sleep. Note that $4:1$ synchronization is remarkably increased in light sleep and deep sleep, whereas in REM sleep $3:1$ synchronization dominates. In (e) the quotient of the synchronization ratio histogram with the distribution of the frequency ratios is shown for the original data (crosses) as well as for the surrogate data (circles).