Phase synchronization of baroreflex oscillations of blood pressure and pulse interval in rats: the effects of cardiac autonomic blockade and gradual blood loss

The study was conducted on three to four month old male Wistar rats obtained from the animal unit of the Institute for Biomedical Problems, Russian Academy of Sciences. All experimental procedures were approved by the Biomedical Ethics Committee of the Institute (protocol No 426).

The rats were anesthetized with an intraperitoneal injection of Zoletil (12 µg × kg⁻¹, Virbac Sante Animale) and Xylazine (12 µg × kg⁻¹, Pharmamagis, Ltd, Hungary). Polyethylene catheters (PE10/PE50) were implanted into the left femoral artery and the right jugular vein. The catheters were tunneled subcutaneously and exteriorized at the dorsal neck region. After a recovery period of two days the rats were individually placed in cages (30  ×  30  ×  30 cm) in which they could move freely and had free access to water. The arterial catheter was connected to a BLPR2 pressure transducer (World Precision Instruments, USA). The arterial catheter was continuously flushed with heparinized (50 U × ml⁻¹) saline (0.2 ml × h⁻¹), to avoid clotting. The experimental room was kept quiet and dimly lit.

The recordings (30–60 min duration) were performed after 30–40 min acclimation period when cardiovascular parameters had stabilized. The blood pressure signal was amplified, digitized at 1000 Hz using an analog-to-digital converter (USB-6211, National Instruments, USA) and processed beat-to-beat to estimate mean arterial pressure (MAP) and PI values. Data acquisition and beat-to-beat processing were performed using an original software written in the LabVIEW programming language (National Instruments, USA).

To suppress sympathetic and parasympathetic cardiotropic influences, β₁-adrenoceptor antagonist atenolol and peripheral M-cholinoceptor antagonist methylatropine were used, respectively (1 mg × kg⁻¹ for both, Sigma-Aldrich, USA). The blockers were injected after baseline recording through the venous catheter which was extended by 35 cm long PE10 tubing, so that the rat could not see the manipulations of the experimenter. Data sampling started 5 min after drug injection and lasted for 30–40 min.

Baroreflex oscillations of MAP and PI during gradual decrease of blood volume were studied in rats instrumented with catheters in the left femoral artery and right carotid artery two days before the experiment. The femoral catheter was used for blood pressure recording similar to that described above, but the rats were restricted in water consumption. The carotid catheter was connected to a motorized syringe, to bleed the rats at a constant rate over 30 min. The withdrawn blood volume was 20 ml × kg⁻¹ body weight (approx. 30% of total blood volume).

Spectral analysis was performed using an original LabVIEW-based software. Beat-to-beat data were displayed on screen for visual inspection, and artifacts due to obstruction of the arterial catheter or rat movements were eliminated. In order to find periods of relative stationarity during the recording, a running short-term standard deviation (SD) (30 points) was plotted for each variable, and by moving a threshold cursor, periods of continuously low SD could be separated from periods of high SD. Usually, 30–40 min of the total could be selected for further analysis.

Stationary beat-to-beat MAP and PI data were interpolated by cubic spline and resampled at 20.48 Hz. The resulting time series were divided into half-overlapping sequential sets of 100 s. Each set was subjected to linear trend removal and cosine tapering. The auto- and cross-power spectra were calculated for each segment using the fast Fourier transform and then subjected to ensemble averaging. To investigate to what extent fluctuations of MAP influence fluctuations of PI, the transfer gain between MAP and PI was calculated as the ratio between the modulus of the cross spectrum and the AP power. In addition, the phase shift between MAP and PI and the squared coherence function were calculated using the cross-power spectra.

In experiments with autonomic blockade, spectral power values were calculated in the low frequency (0.25–0.6 Hz) band as the area under the curve, whereas transfer gain and coherence were calculated by averaging all values in this frequency band.

The calculations were performed using a specially developed program working under MATLAB (MathWorks Inc., USA). Using linear interpolation, beat-to-beat MAP and PI data were transformed into equidistant (Δt  =  50 ms) values. Obtained time series were filtered using band-pass Butterworth filters with central frequencies (F₀) in the range 0.01 to 2.5 Hz, the width of each filter was F₀/2. To prevent phase shift, the procedure was performed twice—in the forward and reverse directions. Narrow-band signals received as a result of digital filtering were then presented in the form of analytic signal:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{S}_{{\rm MAP},{\rm PI}}}=Y_{{\rm MAP}.{\rm PI}}^{{\rm exp}}+i\cdot Y_{{\rm MAP},{\rm PI}}^{{\rm hilbert}}={{A}_{{\rm MAP},{\rm PI}}}\cdot \exp (i\cdot {{\varphi}_{{\rm MAP},{\rm PI}}}),\nonumber \end{align} \tag{ 1 }$$

where $Y_{{\rm MAP},{\rm PI}}^{{\rm exp}}$ is the time series of filtered MAP and PI, respectively, and $Y_{{\rm MAP},{\rm PI}}^{{\rm hilbert}}$ is their Hilbert transformants. For every frequency, the phase shift between filtered PI and MAP was then calculated:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \Delta \varphi =({{\varphi}_{{\rm PI}}}-{{\varphi}_{{\rm MAP}}})/2\pi \bmod 1\nonumber \end{align} \tag{ 2 }$$

and the histogram of Δφ distribution was constructed. To estimate the extent of phase synchronization at a given frequency we used the PSI proposed in Tass et al (1998):

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm PSI}=({{S}_{\max}}-S)/{{S}_{\max}},\nonumber \end{align} \tag{ 3 }$$

where $S=-\sum\limits_{k=1}^{N}{{{p}_{k}}\cdot \ln {{p}_{k}}}$ is the Shannon entropy of Δφ distribution and ${{S}_{\max}}=\ln N$, where N is the number of histogram bins (N  =  40).

Using this algorithm, phase synchronization for every frequency in the range of interest were calculated; that is, PSI spectra were constructed.

To study time dynamics of low-frequency MAP and PI oscillations wavelet analysis was used. The calculations were performed using MATLAB-based program. Using linear interpolation, beat-to-beat MAP and PI data were transformed into equidistant (Δt  =  100 ms) time series. To study MAP and PI dynamics in both the frequency and time domain, discrete wavelet transformation was performed using a Symlet wavelet of order eight.

Intrinsic dynamics of MAP and PI were investigated in a band of baroreflex waves (f  ~ 0.4 Hz), and a smoothed signal was obtained as well. The amplitudes of oscillations were calculated using an analytic signal approach according to equation (1).

In dynamics studies, amplitude values for the low-frequency oscillations, smoothed signals of MAP and PI, as well as PSI values, were averaged over sequential 120 s intervals with a time shift of 30 s.

Statistical analysis was performed in GraphPad Prism 7.0. The normality of the data distribution was studied using the Shapiro–Wilk test. The data are given as mean and SD (if data distribution was normal) or as median and interquartile range (if data distribution was different from normal). The Wilcoxon matched-pair rank test was used to analyze the effects of cardiac autonomic blockade. Pearson correlation was used to estimate the statistical relationship between two studied parameters. Statistical significance was reached at P  <  0.05; n represents the number of animals.

The MAP and PI spectra, as well as cross-spectral transfer gain, coherence and phase angle between MAP and PI from 25 rats were averaged, as shown in figure 1. The power spectra of MAP (figure 1(a)) and PI (figure 1(c)) demonstrated sharp low-frequency peaks centered at 0.4 Hz, which corresponds to the frequency of Mayer waves in rats (Stauss 2007). Calculation of the coherence between MAP and PI showed a strong phase coupling of low-frequency MAP and PI oscillations (figure 1(d)) with an average phase of  −0.22  ±  0.09π (figure 1(e)). The PSI spectrum was very similar to the spectrum of coherence, and it also demonstrated a prominent peak in the low-frequency band (figure 1(b)). However, transfer gain was prominent in the high-frequency band and smaller in the low-frequency band (figure 1(f)).

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The power spectra of PI and, especially, MAP did not contain distinct peaks at frequencies higher than 0.8 Hz, where oscillations of these parameters are synchronous with respiration (Rubini et al 1993). Along with that, transfer gain, coherence and PSI prominently increased in the high-frequency band, pointing to the coupling of MAP and PI oscillations associated with respiration. Respiration-related peaks in coherence and PSI spectra were rather broad, due to significant variability of respiration frequency in the rat (Kabir et al 2010, Nalivaiko et al 2011). Importantly, high-frequency peaks in coherence and PSI spectra did not overlap with the low-frequency peaks. This allowed us to assume that the phase synchronization of MAP and PI at the frequency of Mayer waves was not affected by respiration.

To compare two different methods of evaluating the coupling of MAP and PI low-frequency oscillations, we calculated mean values of transfer gain/coherence or PSI in the low-frequency band (0.25–0.6 Hz) and then plotted their relationships, as shown in figure 2. A rather weak correlation was observed between PSI and transfer gain (figure 2(a)). Along with that, a strong correlation was observed between PSI and squared coherence (figure 2(b)). In other words, the two indexes of MAP and PI synchronization correlated well with each other.

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The effects of cardiac autonomic blockade of MAP and PI synchronization were studied in two experimental groups of ten rats. In the first group, sympathetic control of the heart was eliminated by atenolol. The second group received methylatropine, to suppress parasympathetic influences on the heart. Of note, no differences in baseline hemodynamic parameters and indexes of their variability were observed between the two experimental groups (table 1).

The obtained results are shown in figure 3 and table 1. Neither blocker affected MAP or MAP spectral power in the low-frequency band. PI was lengthened after sympathetic blockade but shortened after vagal blockade. Both blockers reduced PI spectral power and MAP-PI transfer gain in the low-frequency band, the effects of methylatropine were more pronounced compared to the effects of atenolol. Coherence and PSI were markedly diminished under the influence of methylatropine. Along with that, both indicators were moderately decreased by atenolol (p   <  0.1). Of note, the centrum frequency of high-frequency peaks in PSI and coherence spectra was not affected by any of the blockers. This observation suggests no change in respiratory rate after autonomic blockade.

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The next task in our study was to explore the dynamics of PSI of MAP and PI at the frequency of Mayer waves during long-term blood pressure recording in conscious rats. For this purpose, we calculated PSI spectra for short (120- second long) episodes and plotted them as a function of time (figure 4). During the 30 min period of baseline, the low-frequency peak was detected in all episodes, but its amplitude was not constant. This observation shows that the strength of phase coupling between MAP and PI may vary in time, probably because of changes in the behavioral activity of the rat.

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To correlate PSI dynamics with certain alterations in cardiovascular control, the rats were subjected to gradual blood loss (figures 4 and 5). During the approx. 10 min of blood loss, AP did not change (figure 5(a)) but PI was noticeably shortened (figure 5(c)). Wavelet analysis showed that the nonhypotensive phase of hemorrhage was marked by increased amplitudes of low-frequency MAP and PI oscillations (figures 5(b) and (d)), a prominent augmentation of PSI was observed as well (figures 4 and 5(e)). Further blood loss induced gradual hypotension and bradycardia (figures 5(a) and (c)); under such conditions amplitudes of low-frequency MAP and PI oscillations decreased (figures 5(b) and (d)). Phase synchrony of MAP and PI oscillations ceased, as was evident from the decrease in PSI (figures 4 and 5(e)). It should be noted that although the amplitude of the respiratory peak varied during the recording, its frequency did not change and was still higher than the frequency of Mayer waves (figure 4).

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