Experimental Physiology
89.4 pp 397-405
DOI: 10.1113/expphysiol.2003.027094
© The Physiological Society 2004
The baroreflex is counteracted by autoregulation, thereby preventing circulatory instability
Roberto Burattini1,
Piet Borgdorff2 and
Nico Westerhof2
1 Department of Electromagnetism and Bioengineering, Polytechnic University of Marche, Via Brecce Bianche, 60131 Ancona, Italy2 Laboratory for Physiology, Institute for Cardiovascular Research (ICaR-VU), VU University Medical Center, van der Boechorststraat 7, 1081 BT Amsterdam, The Netherlands
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Abstract
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The aims of this study were (a) to apply in the animal with intact baroreflex a two-point method for estimation of overall, effective open-loop gain, G0e, which results from the combined action of baroregulation and total systemic autoregulation on peripheral resistance; (b) to predict specific baroreflex gain by correcting the effective gain for the autoregulation gain; and (c) to discuss why the effective gain is usually as low as 1–2 units. G0e was estimated from two measurements of both cardiac output, Q, and mean systemic arterial pressure, P: one in the reference state (set-point) and the other in a steady-state reached 1–3 min after a small cardiac output perturbation. In anaesthetized cats and dogs a cardiac output perturbation was accomplished by partial occlusion of the inferior vena cava and by cardiac pacing, respectively. Average (±S.E.M.) estimates of G0e were 1.4 ± 0.2 (n= 8) in the cat and 1.5 ± 0.4 (n= 5) in the dog. The specific baroreflex open-loop gain, G0b, found after correction for total systemic autoregulation, was 3.3 ± 0.4 in the cat and 2.8 ± 0.8 in the dog. A model-based analysis showed that, with G0e as low as 1.4, the closed-loop response of P to a stepwise perturbation in Q results in damped oscillations that disappear in about 1 min. The amplitude and duration of these oscillations, which have a frequency of about 0.1 Hz, increase with increasing G0e and cause instability when G0e is about 3. We conclude that autoregulation reduces the effectiveness of baroreflex gain by about 55%, thereby preventing instability of blood pressure response.
(Received 24 December 2003;
accepted after revision 20 April 2004; first published online 6 May 2004)
Corresponding author R. Burattini: Department of Electromagnetism and Bioengineering, Polytechnic University of Marche, Via Brecce Bianche, 60131 Ancona, Italy. Email: r.burattini{at}univpm.it
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Introduction
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Classically, the baroreflex regulation of blood pressure has been quantitatively characterized by open-loop gain (Sagawa, 1979; Scher et al. 1991). In so-called open-loop experiments, reflex changes in systemic pressure are provoked by putting various static fluid pressures into the blind sac of an isolated carotid (or aortic) receptor region (Moissejeff, 1926; Allison et al. 1969; Angell-James & de Burgh Daly, 1970; Donald & Edis, 1971; Sagawa, 1979; Chen & Bishop, 1983; Burattini et al. 1991; Scher et al. 1991). The ratio of the systemic pressure change to the isolated carotid (or aortic) pressure change, usually about 2 units, gives a measure of open-loop gain of the local, carotid (or aortic) baroreflex. Clinically more interesting is the overall open-loop gain of the entire baroreflex system. Although this gain can be determined from appropriate experiments (Angell-James & de Burgh Daly, 1970), the surgical trauma required does not allow application of this method in the intact organism.
To avoid surgical opening of the regulation loop and to achieve a more natural condition, closed-loop methods have been proposed for indirect estimation of overall baroreflex open-loop gain (Valentinuzzi et al. 1972; Sagawa & Eisner, 1975; Hosomi & Yokoyama, 1981; Burattini & Borgdorff, 1984; Burattini et al. 1987a; O'Leary et al. 1989; Kawada et al. 1997). In most of these studies the results do not pertain to baroreflex regulation alone because of the simultaneous and opposing effects of total systemic autoregulation, which is the intrinsic ability to maintain a relatively constant blood flow during changes in perfusion pressure. Total systemic autoregulation has been demonstrated after elimination of nervous and hormonal control, and may be of considerable magnitude (Liedtke et al. 1973; Korner et al. 1976; Johnson, 1986; Metting et al. 1988; Borgdorff et al. 1990; Burattini et al. 1991, 1994). Therefore, the change in mean systemic arterial pressure after a change in cardiac output is determined by three factors: the magnitude of the change in cardiac output, a baroreflex-induced change in peripheral resistance and a simultaneous autoregulatory change in peripheral resistance.
The open-loop gain of the baroreflex alone, called the specific baroreflex open-loop gain, can be calculated only when the strength of autoregulation is known.
We have previously shown that in animals in which baroregulation was abolished by barodenervation, or ganglionic blockade, or by setting pressure in the isolated carotid sinuses constant after vagotomy, the degree of autoregulation, quantified by autoregulation resistance gain, Gra, is linearly related to the initial (control) value of total peripheral resistance. Thus, autoregulation resistance gain can be predicted in closed-loop conditions, i.e. without surgical or pharmacological autonomic denervation, on the basis of initial total systemic peripheral resistance and body weight (Burattini et al. 1991, 1994).
The aims of the present study were (a) to apply in the animal with intact baroreflex a two-point method for estimation of overall, effective open-loop gain, which results from the combined action of baroregulation and total systemic autoregulation on peripheral resistance; (b) to predict specific baroreflex gain by correcting the effective gain for the autoregulation gain; and (c) to discuss why the effective gain is usually as low as 1–2 units.
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Methods
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Experimental preparations
This investigation conforms with the Guide for the Care and Use of Laboratory Animals published by the National Institute of Health (NIH publication no. 85-23, revised 1985), and under the regulations of the Institutional Animal Care and Use Committee (DEC). The data in the present study were obtained from experimental preparations used in previous publications, but entirely newly analysed. Details on the preparation, protocols and interventions of both the cat and the dog studies have been described earlier (Randall et al. 1981; Burattini & Borgdorff, 1984; Burattini et al. 1987a).
Cats.
Eight cats under sodium pentobarbital anaesthesia were studied in open thorax condition. Aortic and venous pressures and ascending aortic flow were continuously measured. Vital functions (blood pH and PCO2, body temperature, fluid balance, etc.) were closely monitored and maintained. After completion of surgery a long-acting local anaesthetic (5% xylocaine salve) was applied to skin incisions and cut intercostal muscles. In some of the animals baroreflex regulation was affected by deepening anaesthesia using halothane (up to 1.5%). Cardiac output was varied by partial occlusion of the inferior vena cava using a thread around it. The loop of the thread was lifted with a micromanipulator to ensure a graded and stable reduction in venous return.
Dogs.
Five dogs were fitted with pacing electrodes and an ascending aortic electromagnetic flow sensor, at least 1 week before the actual experiment. The dogs were studied with closed thorax under sodium pentobarbital anaesthesia. Aortic flow was varied by cardiac pacing after induction of atrioventricular block produced by injecting 0.2–0.4 ml formalin into the His bundle via a stiff cannula introduced through the right jugular vein (Randall et al. 1981). A catheter tip manometer (Millar Micro TIP PL350 of 8F) was introduced in the ascending aorta via a femoral artery.
Two-point experimental data
In the linear range of the static relation between mean systemic pressure and cardiac output, two data points are obtained: one in the control state and the other 1–3 min after a small reduction in cardiac output. About 10 beats of the pulsatile pressure and flow during the steady state were recorded and digitized at a 200 Hz sampling rate. The ensemble signals were averaged across beats to compute mean systemic arterial pressure and cardiac output (denoted as P and Q, respectively, in the equations and figures) in individual cases.
Estimation of effective and specific baroreflex open-loop gains
We have shown earlier that (a) in the absence of resistance regulation (i.e. no baroregulation and no autoregulation) P is proportionally related to Q (Fig. 1, thin continuous line); (b) when autoregulation is present, without baroregulation, a curve convex to the flow axis results (Fig. 1, dotted line); (c) when the baroreflex combines with autoregulation, the P–Q relation becomes convex to the pressure axis (Fig. 1, thick continuous line); and (d) in the presence of baroregulation alone, convexity is stronger (Fig. 1, dashed line). A possible zero-flow pressure intercept may be neglected (Burattini & Borgdorff 1984; Burattini et al. 1987a, 1991, 1994).
Resistance regulation by combined action of baroregulation and autoregulation can be characterized by the effective open-loop gain, G0e, whereas baroreflex regulation alone can be characterized by the specific open-loop gain, G0b. Both G0e and G0b can be estimated on the basis of two measurements of mean systemic arterial pressure and cardiac output, i.e. in control (P0 and Q0) and in the steady-state (P, Q) after a relatively small flow reduction (
Q) (see Fig. 1). Briefly, to determine G0e we first determine how, for a given Q reduction, P would change in the absence of any resistance regulation. This initial pressure change, Pi, can be inferred from the control resistance, R0, and flow reduction (Pi=R0Q), as shown in Fig. 1. The effective baroreflex open-loop gain is calculated (Burattini et al. 1987a) by comparing Pi with the pressure change in the steady-state, P: G0e=Pi/P– 1 (Fig. 2A).
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Figure 2. Models of systemic arterial pressure regulation
A, block scheme of linearized model of short-term regulation of mean systemic arterial pressure, which applies in steady-state conditions. Q and P represent cardiac output and mean pressure changes from control to a new steady state, respectively. Pi is the mean pressure change that would be observed in the absence of resistance regulation. R0 is the reference value of total peripheral resistance. The relationship between Pi and P in the presence of resistance regulation (by the combined action of baroregulation and autoregulation) is 1/(1 +G0e), where G0e is the effective open-loop gain. B, improved model, which allows separation of baroreflex from autoregulation effects. Pia is the mean pressure change that would be observed in the absence of baroreflex regulation of peripheral resistance but in the presence of autoregulation. Gra is autoregulation resistance gain. The relationship between Pia and P taking into account actual baroreflex regulation is 1/(1 +G0b), where G0b is the specific baroreflex open-loop gain. C, block scheme of linearized dynamic model of short-term regulation of arterial pressure. The variable s is the Laplace operator, Q(s) and P(s) are cardiac output perturbation and the consequent mean pressure change, respectively. Pi(s) is the mean pressure change that would be observed in the absence of resistance regulation. T(s) is the generalized transfer function of the windkessel arterial load (eqn A1). The transfer function between Pi(s) and P(s) in the presence of resistance regulation is 1/[1 +H(s)], where H(s) is the pressure-to-pressure open-loop transfer function.
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For measurement of the specific baroreflex open-loop gain (G0b) the autoregulation resistance gain (Gra) is required. We have previously shown (Burattini et al. 1994) that Gra depends on the control value of peripheral resistance (R0, initial resistance) normalized for body weight. After normalization of cardiac output and peripheral resistance for body weight, the relation between Gra and R0 can be mathematically described as Gra=K1R0+K2, with K1= 17.9 x 10–3 min kg ml–1 andK2=–14.5 x 10–3 mmHg min2 kg2 ml–2. This relation implies that for values of R0 lower than 0.8 mmHg min kg ml–1 the magnitude of autoregulation resistance gain, Gra, is negligible. At this low level of initial resistance, high values of cardiac output are found and the higher the cardiac output per kg (and the higher the oxygen availability-to-demand ratio) the lower the autoregulatory gain (Shepherd et al. 1973; Burattini et al. 1994). From Gra and the pressure and flow in the reference state, the pressure response due to autoregulation alone can be derived as Pia= (R0+GraQ0)Q (Burattini et al. 1991). The specific baroreflex open-loop gain can now be calculated as G0b=Pia/P– 1 (Fig. 2B).
Time course of pressure response to perturbation
According to our earlier reports (Burattini et al. 1987b,d), the dynamics of a pressure response to a stepwise change in cardiac output can be described by the model shown in Fig. 2C. We show in the Appendix that the time course of the pressure response to a change in cardiac output is the combined effect of the so-called transfer function of the feedback loop and the three-element windkessel, which represents the arterial load of the heart (Burattini et al. 1987b,c,d; Burattini, 2001).
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Results
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Table 1 shows the cardiovascular data in the control steady state and in response to a change in cardiac output. It also shows the autoregulation resistance gain, Gra, normalized for body weight, together with estimates of effective, G0e, and specific, G0b, baroreflex open-loop gains.
In cats, estimates of G0e averaged 1.4 ± 0.2 (±S.E.M., n= 8). After correction for the effects of autoregulation (average Gra was 20.3 ± 3.1 x 10–3 mmHg min2 kg2 ml–2) the values of G0b averaged 3.3 ± 0.4 and the ratio G0e/G0b was 0.43 ± 0.01. This implies that, on average, total systemic autoregulation masks 57% of the specific baroreflex open-loop gain. After deepening anaesthesia by adding halothane to the ventilation gas, in cats 6, 7 and 8, average G0e decreased from 1.9 ± 0.3 to 1.2 ± 0.2, whereas G0b decreased from 4.1 ± 0.7 to 2.7 ± 0.4. Autoregulation resistance gain, Gra, decreased from 22.9 ± 6.9 to 17.2 ± 4.7 x 10–3 mmHg min2 kg2 ml–2, which was in accordance with a reduction of R0 from 2.1 ± 0.4 to 1.8 ± 0.3 mmHg kg min ml–1. G0e/G0b did not change: 0.44 ± 0.01.
In dogs, average G0e was 1.5 ± 0.4 (n= 5), whereas G0b averaged 2.8 ± 0.8. In dogs 1–4, Gra was 9.5 ± 0.8 x10–3 mmHg min2 kg2 ml–2 and G0e/G0b was 0.46 ± 0.03. In dog 5, the control level of total peripheral resistance (Table 1) fell below the value of 0.81 mmHg kg min ml–1. Because at this condition autoregulation is negligible (see Methods) effective and specific baroreflex gains are equal.
Estimates from cats and dogs indicate that total systemic autoregulation masks 
55% of the baroreflex open-loop gain.
Effect of open-loop gain on the dynamics of pressure response
A stepwise reduction in cardiac output can result in an oscillatory response in mean arterial pressure depending on the magnitude of the gain. This can be derived from the dynamic model shown in Fig. 2C. To simulate the responses in the cat, mean arterial pressure was set at 140 mmHg and the cardiac output perturbation was chosen such that it caused a Pi of 24 mmHg. Natural pulsation and damping were given the values of 
n= 0.4 rad s–1 and 
= 0.4, respectively (Scher & Young, 1963; Levison et al. 1966; Suga & Oshima, 1971; Kenner et al. 1974; Sagawa, 1979; Burattini et al. 1987b,d; Scher et al. 1991; Liu et al. 2002). Windkessel parameters (eqn A3) were 
1= 1.1 s, 2= 0.063 s, and R0= 0.54 mmHg min ml–1 (Burattini et al. 1987b,d). Figure 3A–C show the simulated pressure responses for G0e values of 1.4, 2.0 and 3.0, respectively. With G0e= 1.4 (Fig. 3A) the pressure response shows damped oscillations that disappear in about 1 min, whereas the pressure returns to 130 mmHg (P=–10 mmHg). When G0e= 2 the pressure response (Fig. 3B) shows a mild improvement in mean pressure compensation (P=–8 mmHg), but with augmented amplitude of oscillations and much longer settling time. When G0e= 3.0 the system begins to exhibit maintained oscillations of increasing amplitude (system instability, Fig. 3C).
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Figure 3. Time course of mean systemic arterial pressure
Shown is the pressure response to a stepwise reduction of cardiac output in the cat as predicted by the model of Fig. 2C when the effective open-loop gain, G0e, is 1.4 (A), 2.0 (B) and 3.0 (C).
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Simulations of the mean arterial pressure response to a cardiac output perturbation in the dog, using the data of Table 1 together with values of natural frequency, damping factor and time constants of the windkessel load as found in the literature (Scher & Young, 1963; Levison et al., 1966; Suga & Oshima, 1971; Kenner et al. 1974; Sagawa, 1979; Scher et al. 1991; Burattini, 2001; Liu et al. 2002), showed similar behaviour as the response in the cat.
Thus, with an open-loop gain of 3, an unstable pressure response is predicted. However, the total systemic autoregulation keeps G0e as low as 1.5, so that the behaviour of the pressure control system to a step change in cardiac output is stable.
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Discussion
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We have applied a two-point method to estimate the effective, G0e, and the specific, G0b, baroreflex open-loop gains in closed-loop conditions. During an experimental perturbation of cardiac output, its change just after intervention might be greater than steady state, Q. Because cardiac output is under baroreflex control it will be partly restored after the perturbation and will contribute to the rise in blood pressure. Our two-point method uses steady-state values of pressure and cardiac output and avoids involvement of transients in calculations. The measurement of the new steady-state level of cardiac output includes its increase by baroregulation so that the computed value of G0e quantifies the rise of pressure induced by a net increase of peripheral resistance alone. Thus, the gain G0e characterizes the effectiveness of the negative-feedback regulation of systemic pressure via peripheral resistance in the short term. This is a result of the interaction of cardiopulmonary and baroreceptor reflex regulation and the opposing contribution of total systemic autoregulation. Estimates of this effective gain (which averaged 1.4 in the cat and 1.5 in the dog) were about 45% of the specific baroreflex open-loop gain, G0b, showing that the counteracting effect of total systemic autoregulation is considerable.
Because this gain represents the vasomotor response to an arterial pressure perturbation, it is expected to decrease with deeper halothane anaesthesia (Price, 1960). This indeed was seen in our cats 6, 7 and 8 (see Results). Reduction of G0e by adding halothane to the ventilation gas was associated with a reduction in both the specific baroreflex gain, G0b, and the autoregulation gain, Gra. A reduction in autoregulation may be an effect of the lowered initial resistance, resulting from anaesthesia.
Our closed-loop method requires only two measurements of cardiac output and mean aortic pressure (two-point, closed-loop method). One measurement is taken in the reference state (set point) and the other in a steady state reached 1–3 min after a cardiac output perturbation obtained by cardiac pacing (dogs) or partial vena cava occlusion (cats). Estimates of G0e were practically the same as those obtained previously (Burattini & Borgdorff, 1984; Burattini et al. 1987a) by fitting the non-linear relation between mean pressure and cardiac output over a wide range. Of course, the use of repeated measurements of mean arterial pressure and cardiac output would give a far more accurate estimation of gains, but a two-point method is more practical with little loss of accuracy. In principle, the arteriovenous pressure difference should be computed and used to estimate open-loop gains, but using arterial pressure alone causes only small errors (Burattini & Borgdorff, 1984; Burattini et al. 1987a, 1991; Borgdorff et al. 1990). A further point of criticism may be related to the effects on gain estimates caused by the possible presence of a significant zero-flow intercept, Pzf, of mean systemic arterial pressure. We have investigated these effects previously and found that the estimates of baroregulation and autoregulation gains obtained from linearization of P–Q curves about the set-point, with Pzf intercept taken into account, did not deviate significantly from those obtained when this intercept was neglected (Burattini & Borgdorff, 1984; Burattini et al. 1987a, HREF="#B7"> 1991, 1994). Neglecting Pzf has the advantage that peripheral resistance can simply be defined as the ratio of mean aortic pressure to cardiac output. This may pave the way to future testing of our two-point method in humans so that it might become a practical tool for estimating baroreflex effectiveness.
The question arises as to why the evolution of cardiovascular baroreceptor control has yielded such a low gain of the short-term pressure compensation system. An answer to this question is found in Fig. 3, which illustrates the effect of increasing baroreflex gain on the dynamic characteristics of pressure regulation. When the natural frequency (n) and the damping factor () of this regulatory system are assumed to be 0.4 rad s–1 and 0.4, respectively, an increase in gain from 1.4 to 2 and 3.0 will lead to oscillations of increasing amplitude and, eventually, to instability (Fig. 3). If the effectiveness of baroreflex gain is not reduced (55%) by total systemic autoregulation the behaviour of the cardiovascular system in response to a cardiac output perturbation could become unstable. A different way to interpret the interaction between autoregulation and baroregulation is that, to have an effect, the specific open-loop baroreflex gain needs to be sufficiently large to overcome the opposing autoregulatory change in peripheral resistance. However, it should be not so large as to induce instability.
With a simulation approach the effect of gain on stability of the regulatory system was also shown by Kawada et al. (2003) for linear and non-linear versions of their simulator with the system becoming unstable when G0 increased above 2, thus providing a similar critical value to that shown in Fig. 3.
The dynamic performance of the baroreceptor reflex in dogs, cats and rabbits has been investigated in several studies (Scher & Young, 1963; Levison et al. 1966; Suga & Oshima, 1971; Kenner et al. 1974; Sagawa, 1979; Scher et al. 1991; Liu et al. 2002; Kawada et al. 2003). Almost all investigations were performed on the carotid sinus reflex system. A transfer function with two dominant poles (second-order transfer function) multiplied by a pure delay term, e–jT, where T is the time delay, was found. In this representation, T plays a key role, together with open-loop gain, in explaining oscillations observed in the pressure response in closed-loop conditions. The effect of non-linearity (sigmoidal relation in the static pressure-to-pressure characteristics of the regulatory system) has also been analysed (Kawada et al. 2003). We neglect this aspect here because we assume that, in the physiological range, with rather small perturbations, the relation may be approximated to be linear (Fig. 1).
In this limited pressure range we demonstrated (Burattini et al. 1987b,d) that a suitable description of the dynamics of baroreflex regulation of mean arterial pressure via peripheral resistance, in closed-loop conditions, is obtained by a model (Fig. 2C) that incorporates a third-order transfer function, H(s), described by eqn (A3). In this equation the term 1/(1 +1s), represents a first-order delay and the parameter 1 is the time constant with which aortic pressure decreases in diastole (Burattini et al. 1987b,c,d; Burattini, 2001). Thus, the dynamics of blood pressure regulation also depends on the arterial system in terms of total arterial compliance and systemic vascular resistance as determinants of the aortic decay time in diastole, 1.
When the pressure response to a step perturbation is simulated, a theoretical requirement is that, after the input variable has been changed, the new level has to remain constant over the period of observation of the response. Our simulation by the dynamic model of Fig. 2C assumes a stepwise change in cardiac output and in Fig. 3 shows the transient pressure response caused by the properties of the resistance regulator and the windkessel-based representation of the arterial system. Because the new level of cardiac output has to remain constant, its regulation by the baroreflex is prevented and the oscillatory response is a result of resistance regulation. In an experimental setting cardiac output is expected to be partly restored by baroreflex. However, when venous return is limited by a partial occlusion of the inferior vena cava or by artificial pacing of the heart, cardiac output regulation is limited as well and regulation is largely controlled by resistance changes.
With n= 0.4 rad s–1 and = 0.4, the baroreflex response to a stepwise perturbation, under open-loop conditions, described by the transfer function H(s), would be oscillatory with a damped natural frequency [d=n
(1 –
2)] of 0.06 Hz, i.e. with a period of 17 s. This period is consistent with the period (15–30 s) of resistance oscillations in muscular vessels during maintained vasomotor stimulation as described by Koepchen et al. (1963), and with the period of oscillations observed by Penáz et al. (1968) in the vasomotor and autoregulatory response of resistance vessels of the splanchnic and femoral bed in rabbits and cats.
Figure 3 demonstrates that also under closed-loop conditions the response is oscillatory, but that the frequency of the oscillations increases to about 0.1 Hz. This frequency varied from 0.09 Hz, with an effective gain of 1.4 (Fig. 3A), to 0.11 Hz, with an effective gain of 3 (Fig. 3C). Our finding is consistent with the low-frequency rhythm of 0.10–0.12 Hz reported by Pagani et al. (1986) for blood pressure variability of conscious dogs, and with a similar rhythm observed by Cevese et al. (1995) in the chloralose-anaesthetized dog. Scher & Young (1963) did not find significant differences in the dynamics of the baroreflex regulation between dogs and cats. Cevese et al. (1995) concluded that, in the chloralose-anaesthetized dog, arterial pressure and heart rate oscillate with frequencies corresponding to those described in conscious humans, and low-frequency arterial pressure oscillations are due to changes in peripheral vascular resistance. The nature of these so-called Mayer vasomotor waves has long been a matter of debate (Koepchen, 1984; Wesseling & Settels, 1985; Malliani et al. 1991; Karemaker, 1997; Malpas, 2002; Seydnejad & Kitney, 2001; Ursino & Magosso, 2003).
Based on the approach suggested by Wesseling & Settels (1985), several complex models have been proposed to explain the origin of these low-frequency oscillations. The instability in blood pressure regulation has been related to time delays, non-linearities and an open-loop gain effect. It appears that the gain effect is greater than the other two factors (Wesseling & Settels, 1985; Abbiw-Jackson & Langford, 1998; Seydnejad & Kitney, 2001; Kawada et al. 2003; Ursino & Magosso, 2003). Autoregulation was disregarded in these models, but our model shows that autoregulation plays a significant role. It is the combination of the arterial decay time and the effective gain that determines the amplitude and frequency of the oscillations. We suggest that the following mechanism plays a role in the origin of Mayer waves. In a poor cardiovascular state, when peripheral resistance is low, the autoregulatory gain is small. Baroregulation is hardly counteracted by autoregulation and the gain of the effective regulation is high, leading to the oscillations.
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Appendix
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Time course of pressure response to perturbation
The dynamics of a pressure response to a stepwise change in cardiac output is described by the model shown schematically in Fig. 2C (Burattini et al. 1987b,d) where s is the Laplace's operator, T(s) is the transfer function between cardiac output perturbation, Q(s), and mean pressure change, Pi(s), which would be observed in the absence of resistance regulation (R0 is constant). Assuming a three-element windkessel (Burattini et al. 1987b,d) as left ventricular load, the transfer function T(s) assumes the following generalized expression (Burattini, 2001):
| (a1) |
In the presence of resistance regulation (resulting from the combined action of autoregulation and baroregulation), with an effective open-loop gain of G0e, the Laplace's transform of mean pressure change, P(s), is:
| (a2) |
where
| (a3) |
is the transfer function of the feedback loop. Characteristic parameters of H(s) are the time constant, 1, characterizing the decrease of aortic pressure in diastole, the natural frequency, n, and the damping factor, , of the resistance regulator (Burattini et al. 1987b, d).
The time course of non-regulated, pi(t), and regulated, p(t), pressure responses is obtained from the inverse transform of Pi(s) andP(s), respectively.
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Acknowledgement
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This work was supported in part by the Italian Ministero dell'Istruzione, dell'Università e della Ricerca (MIUR & COFIN 2001).
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