Keywords

1 Introduction

Arterial baroreceptor reflex (ABR) is the most important mechanism for the short-term regulation of blood pressure. The reflex arc includes sensitive receptors (arterial baroreceptors), afferent pathways, integrate centers in the central nervous system, efferent pathways (cardiovascular sympathetic and cardiac parasympathetic nerves) and effector organs (heart and peripheral blood vessels). ABR is a continuously functioning regulatory system. ABR automatically adjusts to prevent abnormalities in the activity of heart and blood vessels that could lead to significant changes in mean arterial blood pressure (BP). The ABR mechanism regulates blood pressure through negative feedback. For example, a decrease in the frequency of pulses from ABR entering the vasomotor center results in a reflex reaction aimed at increasing blood pressure, i.e. decreasing of parasympathetic nerve activity endings of the heart and the activation of vasomotor sympathetic nerves. As a result, heart rate and contractility of the heart increase simultaneously with the narrowing of arterioles and veins in most organs of whole body (with the exception of brain and heart) [1].

Numerous effects occur with the participation of ABR activity through the sympathetic and parasympathetic fibers innervating heart and blood vessels. These effects are manifested by heart rate variability (HRV), changes in the values of beat-to-beat systolic (SBP) and diastolic (DBP) arterial blood pressure (for example, the Traube–Hering–Mayer wave in a range of 0.1 Hz [2, 3]), as well as vascular resistance. These manifestations can be evaluated by synchronous analysis of HRV oscillations [4,5,6] and beat-to-beat values of SBP and DBP spectral density dynamics [3, 7]. Such analysis provides information about distribution of power depending on the frequency of fluctuations and allows quantifying various frequency components of the fluctuations in heart rate and blood pressure. In addition, it helps graphically present the ratio of different components of their rhythm, reflecting the activity of certain parts of regulatory mechanism [8, 9]. The most important indicators of regulation effectiveness are the power and power balance of the frequency components that form them.

The action of ABR determines the short-term regulation of blood pressure [1], related to the high frequency (HF) range of heart rate fluctuations and beat-to-beat values of SBP and DBP.

Since the origin of the low frequency (LF) components of heart rhythm is associated with central oscillation mechanisms, their properties can’t be determined by any single factor, including baroreflex [10]. In particular, G. Nollo et al. in their work showed that non-baroreflex factors make a major contribution in the interaction of slow fluctuations of heart rhythm and systemic blood pressure [11]. A number of studies have shown the inverse effect of heart rate variability (HRV) on blood pressure variability [10]. In addition, fluctuations with a frequency of 0.1 Hz in humans are also detected in the variability of blood vessels in the microvasculature of the skin and skeletal muscles, which may also indicate that these oscillations are predominantly non-baroreflex in nature [10, 12].

In conclusion, we can say that for research and diagnostic purposes it’s important to distinguish between the effects of ABR and other mechanisms of blood pressure regulation. The effectiveness of arterial baroreflex action can be studied through the assessment of phase and antiphase of signals, as well as the assessment of correlation between HRV and beat-to-beat values of blood pressure.

Thus, the main aim of the study was to develop an algorithm for extracting signal sections with predominantly in-phase, antiphase and uncertain relationships in the standard HRV frequency ranges: High Frequency (HF) 0.15–0.4 Hz; Low Frequency (LF) 0.04–0.15 Hz and Very Low Frequency (VLF) 0.003–0.04 Hz [4,5,6].

2 Materials and Methods

The algorithm is based on the Fourier transform and window calculation of correlation coefficients, the window width is determined from the standard frequency ranges of the cardiac rhythm. Spectral analysis is used for a generalized qualitative assessment of the relationship between signals of beat-to-beat BP and heart rate. To test the algorithm, we used synchronous records of beat-to-beat BP and heart rate for 300 s, obtained from healthy subjects in conditions of calm wakefulness [13, 14].

As an example, we consider synchronously recorded signals of SBP (red curve) and heart rate (blue curve) (Fig. 62.1). In these signals, we can see regions with predominantly in-phase, antiphase, and uncertain relationships.

Fig. 62.1
figure 1

Synchronous recordings of SBP (red curve) and HRV (blue curve), values are reduced to a single scale. We can see an example of oscillations in SBP and HRV with a predominantly antiphase ratio (I) of 5.6 s duration and an example with in-phase ratio (II) of 34.6 s

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In Fig. 62.1, examples of oscillations with predominantly antiphase (I) and in-phase (II) relations between SBP and heart rate in the low-frequency range are highlighted. The oscillation type (I) is characterized by a coincidence in time of the maximum with the minimum (and vice versa); its duration for the given records is 5.6 s. This section is quite long: it starts from 24 s and lasts up to 84 s. This attitude characterizes the effect of baroreflex.

The vibrational relationship of type (II) is characterized by a coincidence in time of maximum with maximum and minimum with minimum. The highlighted area, about 34.6 s, marks an example of in-phase relationships.

It is obvious that for the signal under consideration, in-phase relations are associated with a frequency of 1/5.6 s = 0.18 Hz - this is the respiratory HF range, and antiphase 1/34.6 s = 0.03 Hz is the VLF range. Thus, the relations under consideration can be assigned to one or another frequency range of HRV. In example on Fig. 62.1, the manifestation of the frequency components of these ranges (HF and VLF) occurs on the same period for 24–84 s.

Search and selection of synchronized recordings of blood pressure and heart rate of such areas with the determination of their frequency composition is the main task of the algorithm. We need to remember that the areas under consideration are often located on the same time intervals.

The algorithm is based on spectral and correlation analysis. But since it’s necessary to analyze continuous spectral changes in time, the algorithm uses a combination of three band-pass filters with bands corresponding to the standard frequency ranges of HRV (HF, LF, or VLF) [15].

3 Results

The first stage of the algorithm is the acquisition of synchronously recorded signals spectrum, for example, SBP and heart rate. Then we compare their frequency compositions. This is done qualitatively or by calculating power over the frequency subbands and comparing their values. The conclusion about the similarity of the frequency composition is made by the criterion of power values proximity in the same frequency subbands and the presence of spectral maximum at close frequencies. In case of conclusion about the similarity of frequency components, such records are used to further analysis.

Subsequently, the signals are decomposed into frequency components in three standard HRV ranges: HF, LF, and VLF. For this purpose we use three corresponding band-pass filters [8]. A variant of the practical implementation of filters is not of fundamental importance. This method allows to obtain values of continuous changes in signal power from corresponding frequency ranges. The choice of HF, LF and VLF ranges is determined by the fact that they are associated with physiological processes in the cardiovascular system [3, 4]. To obtain the power level of the spectrum, we use absolute values of signals, and then they go through smoothing with a low-pass filter (LPF). Each of the smoothing LPF has its own cutoff frequency, associated with the corresponding range of HF, LF or VLF.

The received signals are shifted to compensate the group delay from all filters, just to provide adequate comparison of signals at their outputs.

In pairs, SBP and HR signals are compared in HF, LF and VLF ranges (DBP and heart rate can also be compared) using local maximum and minimum. If they correspond to each other and coincide or close in time, then a conclusion is made about the phase matching of signals frequency components in the considered range for the corresponding signal section. If the maximum of one signal coincide with the minimum of the other and vice versa, then a conclusion is made about the antiphase of the considered signals frequency components for the corresponding section. If such sections are absent, it leads to the conclusion about absence of in-phase or antiphase relations in the considered frequency range. An example of such comparison for the HF and LF ranges is presented in Fig. 62.2.

Fig. 62.2
figure 2

Synchronous recordings of SBP (red curve) and HRV (blue curve). HF range (a) and LF range (b)

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At the last stage of the algorithm, a window correlation analysis is made between the SBP and heart rate signals in HF, LF and VLF ranges. The window width is selected in accordance with the HRV range of the analyzed signals. The conclusion about the signal ratio is made when the correlation coefficient exceeds a certain threshold.

4 Discussion

As we can see from the graphs for the subject in calm wakefulness for SBP and heart rate signals in HF range, there are clearly antiphase relations over almost the entire length of the signal, which indicates the effective action of the baroreflex (Fig. 62.2a). In the LF range, in addition to the initial segment, in-phase relations are clearly present (Fig. 62.2b). An assessment was also made in the VLF range: antiphase relations were clearly present in it during the first half of the signal.

Thus, using the developed algorithm, we can study the effectiveness of the arterial baroreceptor reflex. We can make it by evaluating the in-phase and antiphase signals of beat-to-beat blood pressure and heart rate, and determining the corresponding sections of the signal, as well as by determining their correlation in the standard frequency ranges of HRV: HF, LF and VLF. Subsequently, the identified areas on synchronously recorded blood pressure and heart rate signals can be compared under the impact of the test or natural load.

The developed algorithm is intended for use in research and diagnostic systems in order to distinguish between the effects of ABR and other mechanisms of blood pressure regulation.