Keywords

1 Introduction

Reduction of motor activity leads to a significant decrease in functional reserves of the human organism, which is clearly manifested during tests with postural (ortho- and anti-orthostatic) loads. Such postural loads cause a complex of conjugate reactions from the cardiovascular system of human organism. Severity of these reactions depends on the intensity of the effects (angles of elevation/inclination, speed of movement, sequence and duration of loads) and the initial state of organism [1, 2].

The hemodynamic response to the change of passive ortho- and anti-orthostatic positions is based on the alternating deposition of blood in vessels of the lower and upper body, accompanied by vasoconstrictor and vasodilator vascular reactions. At the same time, changes are occurred in the inotropic response of heart, cardiac output, arterial and venous pressures, heart rate, changes in the circulating blood volume [3, 4, 7, 8].

These changes are associated with the action of the cardiovascular system regulatory mechanisms, including the arterial baroreceptor reflex (ABR), acting according to the principle of negative feedback. For example, the result of decreasing arterial blood pressure (BP), and, consequently, the frequency of impulses from ABR coming to the vasomotor center, is a reflex reaction aimed at increasing ABP, i.e., decreasing the activity of parasympathetic nerve endings in heart and activating vasomotor sympathetic nerves. As a result, the heart rate and its contractility increase simultaneously with the narrowing of arterioles and veins in most body organs, except for the brain and heart [3, 4].

In conclusion, we can say that, for research and diagnostic purposes, it is rather important to consider degree of different components of ABR involvement in cardiovascular system regulation and, in particular, the role of vasoconstrictor and vasodilator reactions. It can be studied by the means of synchronous analysis of beat-to-beat values of ABP and stroke volume (SV) dynamics. Such analysis provides information about value of total peripheral vascular resistance (TPR) and its changes. At the same time, this paper does not consider the effect of ABR itself.

Thus, the aim of this study was to develop an algorithm for the joint analysis of beat-to-beat arterial blood pressure and stroke volume signals for studying systemic vasoconstrictor and vasodilator responses under various impacts, including postural loads. The development of such algorithm will make it possible to solve a number of tasks together with other techniques:

  1. 1.

    To determine the functional reserves of the whole organism, whose value is connected with the ability to regulate the TPR and hence the total volume of circulating blood;

  2. 2.

    To study the adaptive abilities of organism related to the rate of reactions to various influences;

  3. 3.

    To differentiate the diagnosis in pathologies of the cardiovascular system [5,6,7].

2 Materials and Methods

Proposed algorithm is based on the electrodynamic model of cardiovascular system, known as three-element Frank Windkessel (WK) model. Figure 10.1 shows schemes implementing this model: in hemodynamic (Fig. 10.1, a) and electrodynamic (Fig. 10.1, b) representations (according to [10]). There are also known variants of this simple model consisting of two, four and more elements. The history of this question is considered in details by N.Westerhof et al. [10]. In this scheme RP corresponds to the total peripheral resistance, C to the total arterial compliance, RZ to the characteristic aortic resistance.

Figure. 10.1.
figure 1

Three-element WK model: a) in hemodynamic, b) and c) in electrodynamic representation, REC is single half-period rectifier

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As it was shown in earlier researches, the results of three-element WK model analysis have a significant contradiction with cardiovascular system functioning [11]. Current passing through RZ resistance (similar to the flow entering the artery from heart) can have two directions: forward during the pulse simulating systole, and reverse during the pause simulating diastole (Fig. 10.1, b). This result contradicts cardiac function – there should be no return flow to the left ventricle.

This contradiction is eliminated by using an additional nonlinear element (Fig. 10.1, c), simulating the work of the heart left ventricle and corresponding to a single half-period rectifier (REC). At the same time, responses from the original circuit (Fig. 10.1, b) and the circuit with REC (Fig. 10.1, c), with equal values of RZ, RP and C in both circuits differ significantly. The main difference is expressed in the rise time and pressure drop. REC scheme provides a relatively constant P level and unidirectional flow. Estimated values of model parameters RZ, RP, C, and signal from V1, obtained by using the scheme with half-period rectifier are more adequate [11], therefore used in further simulations.

As an example, let us consider the signals obtained from model on the 10 s simulation section (Fig. 10.2): ABP is voltage at the RP resistor (red, green and blue curves) and stroke volume (SV) is current through resistor RZ (three gray curves, they are visible only in the area of peaks, the scale of SV is chosen in conventional units). All these signals were obtained at different values of TPR –resistance of RP resistor. If we take RP0 (green curve) as the reference value of RP resistance, then RP1 = 0.75 RP0 (blue curve), RP2 = 1.25 RP0 (red curve). Values of arterial pressure, as well as systolic (SBP) and diastolic (DBP) blood pressures depend on the values of TPR, and the absolute values of SV also change.

Figure. 10.2.
figure 2

Plot of signals: ABP is voltage across resistor RP: RP = RP0 (green curve), RP1 = 0.75 RP0 (blue curve), RP2 = 1.25 RP0 (red curve); SV is current through resistor RZ (three gray curves, made in conventional units and given for qualitative comparison with ABP curves)

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3 Results

The first stage of proposed algorithm is the extraction of maximal beat-to-beat values from all the signals. For blood pressure, this is SBP, for stroke volume – peak values in the ejection phase. The next step is to compare these maximal values and plot them on the phase plane. At this stage, the assumption is made that these maximal values are synchronous. Figure 10.3, a shows an example of such construction for three different RP (TPR) values: RP = RP0 (green markers), RP1 = 0.75 RP0 (blue markers), RP2 = 1.25 RP0 (red markers).

Figure. 10.3.
figure 3

Phase plane of SBP, SV: (a) in enlarged and (b) normal scales (1 for vasoconstriction boundary, 2 for vasodilation boundary)

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The third step is devoted to determining the limits of vasoconstriction and vasodilation (Fig. 10.3, b). For each of the RP values, not a specific value but some set of values is obtained. These sets intersect at the selected change of RP. The boundaries of the sets are found as straight lines passing through the extreme points of these sets and the origin of the coordinates. Accordingly, the limits of vasoconstriction and vasodilation are the extreme upper and extreme lower limits. The average value of TPR over the measurement period is determined by the standard formula.

4 Discussion

It should be noted that the obtained scattergrams for three RP values are not concentrated at certain points, but have a significant scatter. Moreover, as can be seen from Fig. 10.3, a, the same pairs of SBP-SV at different RP values are possible (see distribution boundaries). This means that in the case of definition TPR values as the ratio of SBP to TRP, we would obtain different values despite the constancy of RP (Fig. 10.4). This effect is related to the presence of C (total arterial elasticity) and RZ (aortic characteristic resistance). Consequently, it is reasonable to determine non-specific (absolute) value of total peripheral resistance, but some set of values when assessing TPR. For this purpose the duration of ABP and SV records at calm position of test subject should exceed 2 min as it is related to durations of regulatory processes [12,13,14].

Figure. 10.4.
figure 4

The qualitative distribution of TPR values, calculated as the ratio of ABP to SV values

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In order to induce meaningful changes in TPR, sufficient physiological loads are required. As it was mentioned in the introduction section, the most adequate and universal for this purpose are postural loads performed on a special tilt-table.

In addition, during calculation of TPR we must take into account values of C and RZ. The development of appropriate methods for this challenge are the main directions for future work.

Thus, the use of the developed algorithm makes it possible to study the limits of systemic vasoconstrictor and vasodilator responses under various loads. When the algorithm described above and the one presented earlier (devoted to evaluation of the arterial baroreceptor reflex effectiveness [16]) are used together, it makes it possible to determine the types of response as well as the variants of functional reserves reduction, i.e., the ways for their recovery. The developed algorithm is intended for use in research and diagnostic systems.