Synchronization of heart rhythm by weak external forcing

The ability to control heart rhythm is of vital importance for treatment and prevention of heart diseases. However, most methods for heart rhythm control are either invasive (e.g. involving surgery), or require the use of drugs, or some activity from the subject like breathing periodically with the prescribed frequency. We propose to exploit forced synchronization phenomenon for the manipulation of the frequency of heart beats. In most general terms, forced synchronization is adjustment of frequency of the system oscillations to the frequency of external forcing. A remarkable property of synchronization phenomenon is that it can occur when the strength of forcing is very small. An introduction to the theory of synchronization can be found here.

It is intuitively clear that a rhythmic sound can influence heart rate. E.g. listening to music with fast rhythm can speed the heart up. With this in mind, we propose to subject a human to a rhythmic sound and light stimulus with the hope to adjust his/her heart rate accordingly. In order to exclude the responses caused by personal preferences in music, we strip our stimulus of any emotional content as described below.

Description of experiments
Measurements A signal reflecting the electrical activity of a heart is an electrocardiogram (ECG) [see Figure 1 bottom below]. An ECG of a human relaxing in an armchair was registered during 10 minutes with the sampling frequency 900 Hz, and then resampled down to 180Hz.

Description of experiments

Measurements

A signal reflecting the electrical activity of a heart is an electrocardiogram (ECG) [see Figure 1 bottom below]. An ECG of a human relaxing in an armchair was registered during 10 minutes with the sampling frequency 900 Hz, and then resampled down to 180Hz.

Figure 1

Left: Scheme of an experiment. Endings of yellow lines on the human body show the positions of electrodes.

Bottom: The view of a typical ECG of a healthy human.

Estimation of instantaneous heart period

Instantaneous heart period can be estimated as the time interval Ti between the two successive R-peaks of ECG as illustrated in Figure 2(a) below. This is called RR interval.

Generation of external forcing

External forcing was realized as follows. With the help of a computer a sequence of sound and light pulses was generated, each pulse lasting tau=0.1 sec [Figure 2(b)]. The time intervals between the pulses were fixed in case of periodic forcing, and varied in agreement with variation of RR intervals of another human in case of aperiodic forcing. Sound was generated by the speaker of a computer, and the light pulse looked as a red square appearing on the screen [Figure 3]. The sound volume was quite small in order not to cause noticeable changes in the activity of cardiovascular system, like marked speeding up of heart rate, the increase of stroke volume or the rise of blood pressure. Thus, the applied forcing can be considered as weak.

Figure 2

a) A typical human ECG b) the forcing signal

Periodic and aperiodic forcing
The forcing was either periodic or aperiodic. Periodic forcing: the time interval between the pulses was constant and close to the average RR interval Ti of the same subject at rest. The maximal difference between the forcing period and average Ti was 25 per cent. Aperiodic forcing: the instantaneous period of pulses coincided with the RR intervals of another human subject. Namely, the pulse was produced at the time moment when in an ECG of another human the R-peak occurred like in Figure 2(b) above.

Periodic and aperiodic forcing

The forcing was either periodic or aperiodic.

Periodic forcing: the time interval between the pulses was constant and close to the average RR interval Ti of the same subject at rest. The maximal difference between the forcing period and average Ti was 25 per cent.

Aperiodic forcing: the instantaneous period of pulses coincided with the RR intervals of another human subject. Namely, the pulse was produced at the time moment when in an ECG of another human the R-peak occurred like in Figure 2(b) above.

Figure 3

In the course of experiments the subjects looked at the screen of the computer sitting in an armchair, and we extracted the sequence of RR intervals using ECGs measured from the I, II and III standard leads (see the figure in the description of the experiment). As a result, for every subject two signals were measured: the RR sequences at rest state and under forcing. The third signal of interest was the forcing signal itself. Our task was to establish the degree of synchronism between the forcing signal and the signal of response of CVS.

Effect of periodic forcing: 1:1 synchronization
Figure 4. Pulses of forcing (green) and positions of R-peaks in a human ECG (black) (a) No forcing (green pulses are shown for reference only) (b) forcing is applied

In the Figure 4 pulses of external forcing (green) and pulses corresponding to R-peaks in experimental ECG (black) are shown. In (a) a segment of sequence of R peaks measured from a subject at rest (i.e. without forcing) is given. For comparison, a part of periodic forcing signal is shown in the same figure. Even when a frequency of periodic forcing is equal to averaged heart rate, due to variability R-peaks appear at different stages of forcing. But if forcing is applied, variability decreases and the behavior of R-peaks becomes closer to periodic with frequency equal to frequency of forcing and the R-peaks appearing almost at the same stages of forcing (b). That means that synchronization 1 : 1 takes place.

Synchronization vs detuning between frequency of forcing and averaged heart rate (AHR)

Terminology:

Frequency of periodic forcing f_for is an inverse of the forcing period. Can be estimated as the number of forcing pulses N_F divided by observation time T=250 sec.

Average heart rate (AHR) is an inverse of the average RR interval. Can be estimated as the number of heartbeats N_H divided by observation time T=250 sec. AHR_rest is the AHR at rest, i.e. when there was no forcing.

Initial detuning Delta:

Results: In Figure 5 the results of experiments with one of the examined subjects are shown illustrating frequency locking phenomenon. The NH to NF ratio versus detuning Delta is plotted. It is clearly seen that this ratio is close to 1 for the detuning in the interval 5% (red circles), i.e. within this range the number of heartbeats is almost equal to the number of forcing pulses. This is called the 1 : 1 effective synchronization.

Figure 5

Ratio of the number of heart beats N_H to the number of forcing pulses N_F during observation time depending on the initial detuning Delta between the heart and the forcing.

Effect of aperiodic forcing: synchronization 6:7
Figure 6. Pulses of forcing (green) and positions of R-peaks in a human ECG (black) (c) No forcing (green pulses are shown for reference only) (d) forcing is applied
When no forcing is applied, R peaks behave independently of the forcing signal [Figure 6(c)]. Under forcing the RR intervals are tuned in accordance with the forcing pulses [Figure 6(d)]. Unlike in case of periodic forcing illustrated above, here the relationship between the forcing and response signals is more complex. Namely, during 7 pulses of forcing 6 heartbeats occur. Moreover, the last R-peak from each group of 6 appears within approximately the same time interval after the last forcing pulse from the respective group of 7, as indicated by dashed lines. This is 6:7 phase synchronization.

Effect of aperiodic forcing: synchronization 6:7

Figure 6. Pulses of forcing (green) and positions of R-peaks in a human ECG (black) (c) No forcing (green pulses are shown for reference only) (d) forcing is applied

When no forcing is applied, R peaks behave independently of the forcing signal [Figure 6(c)]. Under forcing the RR intervals are tuned in accordance with the forcing pulses [Figure 6(d)]. Unlike in case of periodic forcing illustrated above, here the relationship between the forcing and response signals is more complex. Namely, during 7 pulses of forcing 6 heartbeats occur. Moreover, the last R-peak from each group of 6 appears within approximately the same time interval after the last forcing pulse from the respective group of 7, as indicated by dashed lines. This is 6:7 phase synchronization.

More details can be found in

V.S. Anishchenko, A.G. Balanov, N.B. Janson, N.B. Igosheva and G.V Bodyugov, ”Entrainment between heart rate and weak noninvasive forcing”, Int. J. of Bifurcation. & Chaos 10, No. 10, 2339-2348 (2000) (link to journal).

V.S. Anishchenko, A.G. Balanov, N.B. Janson, N.B. Igosheva and G.V. Bordyugov, “Synchronization of cardiorhythm by weak external forcing”, Discrete Dynamics in Nature and Society 4, 201--206 (2000) (link to journal).

Please do not hesitate to contact Dr. Natalia Janson (n.b.janson@lboro.ac.uk) and Dr. Alexander Balanov (a.balanov@lboro.ac.uk) for reprints and discussions.