Conflict of interest statement The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Madaniyazi, L. The researchers are also hoping to establish careful heart-breathing correlations for patients with heart problems, the better to develop diagnostic devices. Materials provided by American Institute Of Physics. Note: Content may be edited for style and length. Science News. ScienceDaily, 1 February American Institute Of Physics. The animation guiding breathing ran for complete breath cycles.
The total number of guided intervals for the 22 volunteers considered in this work is Instantaneous breathing rate blue and heart rate red are shown from data for volunteer Regions of guided breathing are shaded. Not all of the minute rest interval at the beginning is shown, as this data is not explicitly analysed in this article.
Simultaneous recordings of ECG and respiratory signals were performed. According to the data processing procedure described in Methods section, both the breathing and the heart rates were derived in Hertz; however, for illustrative purposes in this paper, the rates are presented in beats-per-minute BPM. The heart and breathing rates plotted together in Fig. The heart rate demonstrates a response to a step change in breathing rates; these step responses will be discussed below.
Owing to the design of the experiment, the breathing rate during guided intervals was intended to be constant. Additionally, swallowing or coughing were observed in a few cases.
However, the mean breathing rates matched the guided values set by the metronome. For this volunteer Fig. The mean and standard deviation of the breathing rate for all intervals and volunteers are shown in Table SI1 of Supporting Information SI. The standard deviation of the breathing rate defines the minimal possible step increments between guided breathing rates. The dashed black lines represent the standard deviation of the rate, while the solid black line is the mean breathing rate for that interval.
Assuming a volunteer follows the metronome well, the range between standard deviation lines will be small. The normalisation demonstrates the proportional rate of breathing relative to RHR.
Data from volunteer The Shapiro-Wilk normality test showed that for 33 out of 66 guided intervals, the breathing rate is normally distributed.
Thus, the stochastic component in guided breathing rate can be represented as a Gaussian random process, and the breathing signal itself corresponds to stochastic quasi-harmonic oscillations with a constant amplitude and a variable frequency see Fig.
SI1 in SI. The mean and standard deviation of the heart rate for all intervals and volunteers are shown in Table SI2 of SI. The variability of this data is significantly stronger than that of the breathing rate data.
This can be explained by the nonstationary dynamics of heart rate. Conversely to the guided breathing rate, the KPSS test demonstrated that for 63 out of 66 high-rate breathing intervals, instantaneous heart rate is non-stationary. Furthermore, the Shapiro-Wilk test showed that 49 out of 66 heart rate intervals are not normally distributed.
The noticed non-stationarity is linked to transient adaptation periods which were observed for most guided intervals, with the heart rates rising to levels disproportionate to the prescribed breathing rate, forming a ramp response.
Adaptation was particularly visible during the first interval of high-rate breathing Fig. Regardless, assuming a volunteer relaxed and continued following the breathing metronome, their heart rate adjusted accordingly.
This transient period is less pronounced in the subsequent second and third intervals. To analyse the transient response, a slow trend of the heart rate was calculated via a moving average technique described in the Methods section. A variety of trend patterns was observed Fig. SI2 in SI and for some intervals there was no trend.
In the example presented in Fig. SI2 in SI. The patterns for the second and third intervals were more complex, but the majority included a transient increase of the rate. For some intervals, the heart rate seemed to begin to tend to a steady state value after the initial adaptation.
However, there was no clear steady state observed and for the majority of cases, the heart rate continued to diffuse. In fact, such wandering dynamics are a feature of heart rate 22 and ought to be considered when analysing synchronization. Trends in heart rate during the intervals of guided breathing. Black curves correspond to the trends. Red lines specify the mean value solid line and standard deviation dashed lines of the breathing rate for each interval.
All data normalised by the mean breathing rate of interval 2. The intended heart rate response should mean the black curve falls within the red dashed lines for as much of the interval as possible. An example of a synchrogram 6 encompassing all guided respiration intervals and spontaneous rest periods is shown in Fig. During this episode, wandering of the heart rate is limited and the heart rate fluctuates around a particular value Fig. Before and after this episode the heart rate shows a diffusive behaviour.
Synchrogram for volunteer Shaded regions correspond to the regions of guided breathing. For 18 of the 22 volunteers, CRS occurred within the third interval, when the guided breathing rate was higher than RHR. For four volunteers number 2, 10, 20 and 21 , episodes of synchronization were observed for the second interval when the breathing rate was intended to be equal to the RHR.
An additional analysis of heart rate during the minute rest interval prior to guided breathing suggests that the RHR value calculated for these was potentially too high, thus for this second interval breathing rate was above the actual RHR.
In many cases, more than one episode of CRS was observed within the same time interval. The longest episode was singled out and the total duration of all episodes in the given interval was calculated. All results are summarised in Table 1 with times given to the nearest second. The CRS durations calculated by the two methods produced close values.
One volunteer number 3 had very short CRS episodes. The dynamics of the phase difference and rates for the third interval for this volunteer and volunteer 2 are shown in Fig. SI3 in SI. Interpretation of these plots allows for visualisation of the durations specified in Table 1. The top panel plot a and e in Fig. The duration of synchronization episodes for different volunteers are shown in Table 1. The second panel plot b and f shows time dependence of the synchronization index. A value of the index close to one represents synchronization between two oscillating signals.
Extended episodes above the experimentally-justified threshold of 0. The third panel plots c and g shows the synchrogram for the entire interval of high-rate breathing. During the phase synchronization points on synchrogram demonstrate a plateau. The final panel plots d and h are a representation of the heart and respiratory rates for a comparison of instantaneous rates during episodes of synchronization with dynamics of phases.
The dashed red lines represent the high variability of breathing rate even for controlled breathing- the larger this range, the more variable the breathing rate and thus the worse a volunteer maintained a constant rate. The solid red line is the average breathing rate, and the blue line demonstrates the dynamics of the instantaneous breathing rate throughout the interval. The black line in plots d and h corresponds to heart rate with removed high-frequency oscillations via applying moving average techniques.
During episodes of phase synchronization, the black line is expected to fall wholly between the dashed red lines, representing the fact that the variability of heart rate is contained within the variability of breathing rate.
Synchronization measures for volunteer 2 left and volunteer 3 right. Figures a , e show the phase difference, figures b , f show the synchronization index, figures c , g show the synchrogram, and figures d , h show smoothed heart black line and respiratory blue line rates.
In figures d , h red lines specify the mean value solid line and standard deviation dashed lines of the breathing rate for each interval. In Fig. As mentioned, CRS episodes were observed in the second interval rate intended to be equivalent to RHR for four volunteers.
Therefore, their third interval corresponded to a breathing rate significantly higher than the RHR.