Some studies associate the development of stable oscillatory regimes in the heart rate with the interaction of several loops of autonomic regulation. Moreover, a change in the dynamics of such loops, compared, for example, with the evolution of pathological processes, led to a simplification of the dynamics of the heart rate and a decrease or disappearance of variability [1-5]. In the low-frequency (LF) range (0.04-0.15 Hz), the loops of autonomic regulation of blood circulation provide normal control of heart rate, contractile force, vascular tone, and other processes of the cardiovascular system, which allow the system to flexibly adapt to the needs of organism. At the same time, the humoral regulation system also has an effect on the functioning of the circulatory system .
The interaction of loops of autonomic regulation of blood circulation in LF range is often described as the interaction of weakly coupled oscillators [7-12]. The peculiarity of such systems is that their interaction leads to a change in the signal phase, while the amplitude remains uncorrelated. The aim of this work was to study the dynamics of the interaction between the autonomic regulation loops over long periods using the methods of phase analysis. This work develops further the research described in Ref. .
Material and Methods
The experimental studies involved ten healthy volunteers aged 19 to 24 years. We carried out simultaneous registration of electrocardiogram (ECG) and photoplethysmogram (PPG) signals (signal of blood filling of the finger and ear, recorded by an optical sensor with active backlight in reflected light) of the vessels. The data were registered with a standard polyrecorder EEGA-21/26 “Encephalan-131-03” (Medikom MTD Ltd, Taganrog, Russia). The bandpass was 0.05–100 Hz and the sampling rate was 250 Hz, digitized at 14 bits. ECG was recorded in the standard lead I according to Einthoven (differential signal from the wrists of two hands) and PPG was recorded from the distal (last, upper) phalanx of the ring finger and earlobe . The PPG signal from a finger was recorded using a reflected light sensor in the IR range (950 nm) and the PPG from the ear was recorded using a reflected green light sensor (560 nm) [15, 16].
The experimental data were recorded at rest in horizontal position. The length of each recording was 240 minutes. Figure 1 shows typical examples of experimental signals.
Figure 1. Typical examples of experimental data for ECG (bottom line) and interpolated sequence of RR-intervals (top line) (a) and PPG from ear (bottom line) and finger (top line) (b).
The study of heart rate variability from the ECG signals began with the extraction of the sequence of RR-intervals, i.e. a non-equidistant sequence of the time intervals between the R-peaks. Further, by the recommendation , we interpolated the obtained sequence using a cubic b-spline (Figure 1a).
The first step of the analysis included the estimation of epochs of phase synchronization between the LF-oscillations in RR-intervals and PPG using a technique proposed in Ref. . To calculate the phase of LF-oscillations in the experimental signal, we construct the analytic signal ξ(t) for the signal s(t) obtained as a result of bandpass filtration (0.06-0.14 Hz) of the experimental signal. The signal ξ(t) is a complex function of time defined as follows:
Where A(t) and φ(t) are, respectively, the amplitude and phase of the analytic signal and the function s ̃(t) is the Hilbert transform of s(t),
where P.V. means that the integral is taken in the sense of the Cauchy principal value. Phase φ(t) is defined from Eq. (1) as
Then we calculate the phase difference
where φ1 is the phase of LF-oscillations in RR-intervals and φ2 is the phase of LF-oscillations of PPG.
The determination of the phase synchronization epochs was carried out using a linear approximation of the phase difference Dφ in a moving window. The intervals with the phase difference value around some constant value |Dφ|˂const were diagnosed as phase synchronization intervals (4).
To quantitatively estimate the synchronization of the studied processes, we used the previously proposed total percentage of phase synchronization (index S). This index is the ratio of the sum of the lengths dk of the synchronization epochs to the total length T of the recording:
where k is the number of synchronization epoch and N is the number of epochs. Index S represents the percentage of time when the studied processes of autonomic regulation of circulation exhibited phase synchronization.
In this work, we calculated the lengths D of the synchronization epochs for the following pairs of signals: RR-intervals and finger PPG (Figure 2а), and RR-intervals and ear PPG (Figure 2b). The points in Figure 2 show the lengths of epochs of synchronization for the entire ensemble of records.
Figure 2. Dependences of the length D of synchronization epochs on the time t for the pairs of signals: RR-intervals and finger PPG (а), and RR-intervals and ear PPG (b). t indicates the time of the beginning of synchronization epoch.
Figure 3. The autocorrelation function of D(t), averaged over the entire experimental records of all subjects (n=10) for RR-intervals and finger PPG (а), and RR-intervals and ear PPG (b).
It should also be noted that sufficiently long periods of phase synchronization are observed in healthy subjects. For example, Figure 2b has a synchronization epoch between RR-intervals and ear PPG, which length is 123 seconds. However, we found no significant correlation between the length of the synchronization epoch and the time of its beginning.
We also calculated the autocorrelation function for all epochs of synchronization. These functions quickly fall to 0, that is typical for a chaotic process (Figure 3).
Based on the results of Ref. , where two-hour signals were studied, we also estimated the total percentage of phase synchronization (index S).
Than we estimated the deviations DS from the mean S value for each pair of signals: RR-intervals and finger PPG, and RR-intervals and ear PPG. DS are calculated in moving non-overlapping windows w with a length of 1000 seconds. Figure 4 presents the dependences DS(w) averaged over the ensemble of records and the standard deviations.
Figure 4. Averaged values of deviations from the mean S value calculated in moving windows w. (a) RR-intervals and finger PPG; (b) RR-intervals and ear PPG. w value corresponds to the middle of the interval used for the calculation of index S. The whiskers designate the standard deviation.
In Ref. , it was found out that the length of records for assessing the index S should be at least 600 seconds. The deviation from the mean S in moving windows (1000 s) was estimated from two-hour data. A small but significant decrease in the index S from the mean value was observed in the middle of the second hour. After that, at the end of the record, S returned to its value at the beginning of the experiment. To explain this process, we proposed a hypothesis about the effect of immobilization stress on the regulatory mechanisms of blood circulation due to prolonged immobility of the subject. It is also possible that the observed features are caused by impact of the humoral regulation system on the studied processes. In the present study, we use longer recordings to examine the correctness of these hypotheses.
Figure 4b shows the greater change in the deviation of index S from the mean value than Figure 4a. The difference between the Figure 4a and Figure 4b may be associated with the peculiarities of local microcirculation, which we analyze by PPG from the ear. At the same time, PPG from the finger gives us mainly information about the mechanisms of the central nervous regulation of vascular tone [14-16]. It is worth paying attention to the sharp increase in the value of DS at the end of the record in both Figure 4a and Figure 4b. Earlier, we observed similar effect studying two-hour recordings  and assumed that it can be explained by the immobilization stress caused by a long stay in the immobile state and/or by slow humoral regulation. In this study, we increased the duration of the experiment to four hours, but the sharp increase in the value of DS was again observed at the end of the experiment. Probably, it may be associated with psychosomatic influences that could be triggered by reports of the remaining time of the experiment. We informed the subjects about the remaining time of recording every half hour of the experiment.
We studied the features of autonomic regulation of blood circulation using long-term four-hour simultaneous recordings of ECG and PPG signals. We estimated the lengths of epochs of phase synchronization between the LF oscillations in RR-intervals associated with the autonomic regulation of heart rate and both LF oscillations in finger PPG reflecting the tone of large vessels and LF oscillations in ear PPG reflecting the tone of small vessels and capillaries. For both pairs of signals, no significant correlation was found between the length of synchronization epoch and the time of its beginning.
We also tested the hypothesis about the increase in the average deviation of the total percentage of phase synchronization from the average value by the end of the two-hour experiment due to the influence of humoral regulation and/or the progress of immobilization stress . In the present study, we observed an increase in the deviation of index S from the mean value by the end of the four-hour experiment, which probably, may be associated with psychosomatic effects.
This study was funded by the Russian Science Foundation, Grant No. 19-12-00201.
All procedures performed in the studies involving human participants were in accordance with the ethical standards of the institutional and national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. Design of this study was approved by the Ethics Committee of the Saratov State Medical University (Saratov, Russia) in 2019 and written informed consent was obtained from all subjects who participated in this study.
Conflict of interest
The authors declare that they have no conflict of interest.
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Received 25 June 2020, Revised 14 September 2020, Accepted 2 November 2020
© 2020, Skazkina V.V., Karavaev A.S., Borovkova E.I., Simonyan M.A., Prokhorov M.D., Ponomarenko V.I., Dubinkina E.S., Bezruchko B.P., Gridnev V.I., Kiselev A.R.
© 2020, Russian Open Medical Journal
Correspondence to Anton R. Kiselev. Address: Research Institute of Cardiology, Saratov State Medical University, 112, Bolshaya Kazachya str., Saratov, 410012, Russia. Email: firstname.lastname@example.org.