Linear modelling analysis of baroreflex control of arterial pressure variability in rats
- Département de Physiologie et Pharmacologie Clinique, Faculté de Pharmacie, Université Claude Bernard Lyon 1, Lyon 69373, France
- Corresponding author C. Julien: Faculté de Pharmacie, 8, avenue Rockefeller, 69373 Lyon Cedex 08, France. Email: julien{at}univ-lyon1.fr
Abstract
The objective of the present study was to examine whether a simple linear feedback model of arterial pressure (AP) control by the sympathetic nervous system would be able to reproduce the characteristic features of normal AP variability by using AP and renal sympathetic nerve activity (RSNA) data collected in conscious sinoaortic baroreceptor denervated (SAD) rats. As compared with baroreceptor-intact rats (n = 8), SAD rats (n = 10) had increased spectral power (+ 680%) of AP in the low frequency range (LF, 0.0003–0.14 Hz) and reduced power (−19%) in the mid-frequency range (MF, 0.14–0.8 Hz) containing Mayer waves. In individual SAD rats, RSNA data were translated into ‘sympathetic’ AP time series by using the RSNA–AP transfer function that had been previously characterized in anaesthetized rats. AP ‘perturbation’ time series were then calculated by subtracting ‘sympathetic’ from actual AP time series. Actual RSNA and AP ‘perturbation’ time series were introduced in a reflex loop that was closed by using the previously identified baroreflex transfer function (from baroreceptor afferent activity to RSNA). By progressively increasing the open-loop static gain, it was possible to compute virtual AP power spectra that increasingly deviated from their progenitor spectra, with spectral power decreasing in the LF range (as a result of baroreflex buffering of haemodynamic perturbations), and increasing in the MF band (as a result of increasing transients at the resonance frequency of the loop). The most accurate reproduction of actual AP and RSNA spectra observed in baroreceptor-intact rats was obtained at 20–30% of the baroreflex critical gain (open-loop static gain resulting in self-sustained oscillations at the resonance frequency). In conclusion, while the gain of the sympathetic component of the arterial baroreceptor reflex largely determines its ability to provide an efficient correction of slow haemodynamic perturbations, this is achieved at the cost of increasing transients at higher frequencies (Mayer waves). However, the system remains fundamentally stable.
In freely moving rats, sympathetic nerve activity (SNA) and arterial pressure (AP) show parallel increases during the performance of common behaviours (Miki et al. 2003). In chronically sympathectomized rats, the same behaviours are accompanied by falls rather than increases in AP (Julien et al. 1990; Ferrari et al. 1996), which indicates that behaviourally coupled changes in SNA are effectively responsible for AP changes in the intact animal. From these simple observations, a tight coupling between AP and SNA variabilities would be expected. However, this is not the case. Using frequency-domain approaches, it was found that AP and SNA are correlated in a narrow frequency band (0.4 ± 0.2 Hz in rats). This band, usually referred to as the mid-frequency band, contains the so-called AP Mayer waves (Brown et al. 1994). The correlation (or coherence) between AP and SNA at lower frequencies, where the bulk of AP variability is concentrated, is either weak or inconsistent (Burgess et al. 1999, 2003; Bertram et al. 2000; Julien et al. 2003). Accordingly, the models predicting AP fluctuations from SNA fluctuations are valid over short time scales (from a few seconds to a few minutes) and the correlations between observed and predicted data are mainly due to Mayer waves and related SNA oscillations (Burgess et al. 1997a,b; Ringwood & Malpas, 2001).
Low coherence between variables usually points to a non-linear relationship. An alternative explanation for the lack of coupling between slow SNA and AP fluctuations is that SNA changes serve, on the one hand, to directly generate AP changes (e.g. during natural behaviours) and, on the other hand, to buffer the impact of haemodynamic disturbances on AP. Therefore, over sufficiently long time scales, similar SNA fluctuations may well be associated with quite different AP changes (in terms of direction, shape and size), which will inevitably result in low coherence. This interpretation is supported by studies in chronically sinoaortic baroreceptor denervated (SAD) rats. In these animals, AP becomes extremely unstable, mainly due to sharp movement-related falls in AP and to longer lasting hypertensive episodes usually observed when the animal is engaged in more intense behaviours (Trindade & Krieger, 1984; Zhang et al. 1995). In addition, the pressor response to aversive stimuli is markedly exaggerated in SAD rats (Zhang et al. 1996; Barrès et al. 2004). It can therefore be proposed that the baroreceptor reflex alters SNA to oppose movement-related falls in AP, and limits the centrally induced increases in SNA that accompany natural behaviours and response to environmental stressors. Considering the overall variability of SNA, both effects would tend to cancel each other out, which is indeed suggested by the observation that the overall short-term variability of renal SNA (RSNA) is quantitatively unaltered in the conscious SAD rat (Barrès et al. 1992; Julien et al. 2003). Another effect of arterial baroreceptor denervation is to abolish Mayer waves and accompanying oscillations of RSNA (Kunitake & Kannan, 2000; Julien et al. 2003; Barrès et al. 2004), which suggests that these oscillations are a by-product of the normal operation of the baroreceptor reflex (Burgess et al. 1997b; Bertram et al. 1998).
The objective of the present study was to examine whether a simple linear feedback model (Fig. 1) would be able to reproduce the characteristic features of normal AP and RSNA variabilities observed over long periods of time in conscious baroreceptor-intact rats (closed-loop conditions) by using data collected in conscious SAD rats (open-loop conditions). For this purpose, we first characterized the transfer function from RSNA to AP in anaesthetized rats. Then, we used this transfer function to translate RSNA time series from conscious SAD rats into ‘sympathetic’ AP time series and deduce AP ‘perturbation’ time series. Finally, we closed the loop, using the previously published transfer function of central baroreflex pathways (Petiot et al. 2001), and compared resulting AP and RSNA spectra obtained at various open-loop static gains with actual spectra observed in baroreceptor-intact rats.
Methods
All procedures involving animals were conducted in accordance with the guidelines of the French Ministry of Agriculture for animal experimentation.
Data collection
To examine the ability of our model to predict AP and RSNA variabilities over long periods of time, we used two sets of previously collected data.
One set of data was used to characterize the transfer function from RSNA to AP under strictly controlled conditions. Briefly, in this first series of experiments (Petiot et al. 2001), RSNA and AP were recorded in urethane-anaesthetized, artificially ventilated rats with cardiac autonomic blockade (n = 14) during sinusoidal stimulation of the aortic depressor nerve at 11 discrete frequencies (from 0.03 to 1 Hz). RSNA was amplified (× 50 000) and band-pass filtered (300–3000 Hz). The AP and RSNA signals were sampled at 500 and 1000 Hz, respectively, using an analog-to-digital data acquisition card (National Instruments, Austin, TX, USA) and a program written in the LabVIEW graphical programming language (National Instruments). For offline data processing, the RSNA signal was rectified digitally. AP and RSNA signals were then resampled at 50 Hz by an averaging procedure. At each modulation frequency of the aortic depressor nerve, cross-spectral techniques using a fast Fourier transform algorithm were employed to calculate coherence, gain and phase between RSNA (input signal) and AP (output signal). In each rat, the RSNA–AP transfer function was parameterized by fitting equations of first- and second-order linear systems to experimental gain and phase values using an iterative least-squares procedure (SigmaPlot 2000; SPSS, Chicago, IL, USA).
Another set of data was used first, to compute the amount of AP fluctuations that could be predicted from spontaneous RSNA fluctuations under open-loop conditions, i.e. in conscious SAD rats (Fig. 1A), and secondly, to examine whether artificially closing the loop would reproduce the features of normal AP and RSNA variabilities observed in baroreceptor-intact rats (Fig. 1B). In this experiment, AP and RSNA were simultaneously and continuously recorded in conscious freely behaving rats for at least 3 h (Julien et al. 2003). Animals underwent surgical denervation of sinoaortic baroreceptors (n = 10) or a sham operation (n = 8) 2 weeks before the recording. The day before study, a recording electrode was implanted around the left renal sympathetic nerve. AP was measured from a catheter inserted into the lower abdominal aorta through a femoral artery. RSNA was amplified (× 50 000), filtered between 300 and 3000 Hz, full-wave rectified, and integrated using a low-pass filter with a cut-off frequency of 5 Hz. The AP and rectified RSNA signals were sampled at 500 Hz. The background noise of RSNA was determined as the minimal activity recorded after intravenous administration of the ganglionic blocker trimethaphan (10 mg kg−1). On completion of the experiments, rats were killed by an intravenous overdose of sodium pentobarbitone. For all offline analyses, data were filtered at 3 Hz using a finite impulse response filter and resampled at 10 Hz. These 10 Hz time series were segmented into seven data segments of 32 768 points (54.6 min) overlapping by half. For each data set, power spectral density was calculated using a fast Fourier transform algorithm after linear trend removal and application of a Hanning window.
Numerical simulations
Both open- and closed-loop models of the baroreceptor reflex (Fig. 1) were implemented using the Matlab/Simulink software package (MathWorks, Natick, MA, USA). The various elements that constitute and act on the models were provided as time series (actual RSNA and AP ‘perturbation’), linear coefficients (delays) and linear functions (central and peripheral transfer functions).
Statistical analysis
Values were expressed as means ± s.e.m. and compared by the non-parametric Mann-Whitney U test.
Results
Identification of the transfer function from RSNA to AP in anaesthetized rats
Rhythmic stimulation of the aortic depressor nerve induced regular oscillations of RSNA and AP (see Fig. 2 in Petiot et al. 2001) that were tightly and linearly coupled up to 0.4 Hz, as indicated by coherence values close to unity (Fig. 2A). As expected (Bertram et al. 2000), the shape of experimental gain and phase functions (Fig. 2B,C) suggested that a simple linear model could characterize the transfer function (Hp) from RSNA to AP. It was found that the equation of a second-order low-pass filter combined with a fixed time delay could
be fitted satisfactorily (r2 = 0.987 ± 0.003; n = 14) to experimental gain and phase values:
where j and f are the imaginary operator and frequency (Hz), respectively; K is the static gain (1.16 ± 0.21 mmHg %−1 of RSNA change); fn is the natural frequency (0.089 ± 0.007 Hz) and λ the damping coefficient (1.23 ± 0.14) of the low-pass filter; T is the fixed time delay (0.476 ± 0.020 s).
Characteristics of AP and RSNA variabilities in conscious baroreceptor-intact and SAD rats
Considering the 18 rats of the study, the mean duration of recordings was 3 h 35 min. AP and RSNA time series were checked for the elimination of artefacts, the total duration of which never exceeded 3 min. Mean values of AP were 115.7 ± 2.3 and 111.2 ± 0.9 mmHg in SAD and sham-operated rats, respectively. Mean values of RSNA after background noise subtraction were 2.27 ± 0.20 and 1.53 ± 0.18 μV in SAD and control rats, respectively. The results of spectral analysis of AP and RSNA variabilities are summarized in Table 1. The upper frequency limit defining the low-frequency (LF) band (0.14 Hz) was determined as the frequency below which AP spectral power in SAD rats was consistently above that in control rats (P < 0.05 over 3 consecutive frequency components). This frequency range was thus considered as the range over which the baroreceptor reflex effectively reduces AP variability. The upper frequency limit defining the mid-frequency (MF) band was set at 0.8 Hz. The main effects of baroreceptor denervation on AP variability were a large increase in the LF power and a decrease in the MF power, the latter effect resulting from the almost complete disappearance of the peak centred at ∼0.4 Hz (Fig. 3A). In baroreceptor-intact rats, MF power accounted for 17.6 ± 2.8% of the total power whereas in SAD rats, this contribution fell to 3.0 ± 0.7% (P < 0.001). Regarding RSNA variability, baroreceptor denervation tended to decrease LF power and markedly attenuated oscillations in the MF band (Fig. 3B). The contribution of MF power to total power was significantly (P < 0.001) lower in SAD (27.0 ± 1.1%) than in control (35.6 ± 0.7%) rats. In both groups of rats, coherence between RSNA and AP was usually weak in the LF band (Fig. 3C), but rose above the significance threshold of 0.486 (Barrès et al. 2004) in the MF band where it reached a maximum near 0.4 Hz.
Open-loop modelling of AP variability of neural and non-neural origin
Mean parameters of the RSNA–AP transfer function determined in anaesthetized rats (fn, λ and T) were used to translate RSNA fluctuations into AP fluctuations. In each SAD rat, the static gain of the transfer function was estimated as the maximum AP change divided by the maximum RSNA change induced by the administration of the ganglionic blocker trimethaphan. Finally, the AP level observed in the absence of sympathetic influences (i.e. after trimethaphan administration) was added to all AP values (Fig. 4). These ‘sympathetic’ AP time series were subtracted from actual AP time series to provide the so-called AP ‘perturbation’ time series (Fig. 5). Spectral analysis revealed a striking similarity between patterns of variability for actual AP, ‘sympathetic’ AP and AP ‘perturbation’ (Fig. 6), especially in the LF band. This indicates that slow fluctuations of RSNA were able to induce large slow fluctuations of AP. It is important to note, however, that AP fluctuations of neural and non-neural origin were not necessarily in the same direction (Fig. 5). For this simple reason, neural influences on AP were sometimes reinforced and sometimes obscured by haemodynamic disturbances unrelated to RSNA. As a consequence, spectral power of actual AP did not appear as the simple addition of powers of ‘sympathetic’ AP and AP ‘perturbation’ time series.
Closed-loop modelling of AP and RSNA variabilities
Using actual RSNA data and simulated AP ‘perturbation’ time series, a model was developed to simulate AP and RSNA variabilities
in the physiological closed-loop configuration (Fig. 1B). The model used the previously identified transfer function of central baroreflex pathways (Hc, Petiot et al. 2001) combining a derivative gain (defined by its corner frequency, fc), a second-order low-pass filter (defined by its natural frequency, fn, and its damping coefficient, λ) and a fixed time delay (T):
Numerical values for parameters of this transfer function can be found in Petiot et al. (2001). It was assumed that, in the frequency range relevant to the study (< 1 Hz), arterial baroreceptors did not introduce any
significant time delay, behaved as an all-pass filter, and only contributed to the static gain K (see Discussion). To perform the simulations, it was necessary to vary the value of the pressure-to-pressure open-loop static
gain, i.e. the product of all static gains in the loop. We chose to express this value as a fraction of a critical gain, defined
as the gain leading to instability in the baroreflex loop.
Determination of the baroreflex critical gain.
A negative feedback control loop is unstable, i.e. generates self-sustained oscillations of the controlled variable, when gain is unity at the resonance frequency of the loop. The resonance frequency is the frequency at which the fixed time delays and dynamic components of the loop generate a 180 deg phase shift between the input and output signals. As the minus sign in the loop already introduces a 180 deg phase shift, the control loop shows positive feedback properties (the input and output are in phase) at the resonance frequency (Bertram et al. 1998), and thus can be unstable. In each anaesthetized rat of the study, individual parameters of the central (Petiot et al. 2001) and peripheral (see section headed Identification of the transfer function from RSNA to AP in anaesthetized rats) transfer functions were used to calculate the resonance frequency. With this method, our estimate of the resonance frequency of the rat baroreflex loop was 0.29 ± 0.01 Hz. In each animal, we calculated the critical value of the pressure-to-pressure open-loop static gain (7.41 ± 0.78) yielding a gain equal to 1 at the resonance frequency. This average value was then used in all simulations.
Effect of varying the baroreflex gain on closed-loop AP and RSNA variabilities.
In the simulation trials, the baroreflex gain was varied from 0 to 100% of the critical gain (7.41). Increasing the gain resulted in a progressive attenuation of LF power and a progressive increase of MF power in the AP spectra (Fig. 7). Regarding SNA variability, increasing the baroreflex gain tended to increase LF power while strongly enhancing MF power. For both AP and RSNA, the increase in MF power was mainly secondary to an amplification of the peak centred at the resonance frequency (Fig. 7). The most accurate reproduction of actual AP and RSNA spectral powers measured in the group of baroreceptor-intact rats was obtained at 20–30% of the baroreflex critical gain (Fig. 8), which corresponds to an absolute value in the 1.5–2.2 range.
Discussion
Analysis of AP and RSNA variabilities in conscious SAD rats, i.e. under open-loop conditions, indicate that the circulatory system is continuously challenged by large slow (< 0.14 Hz) haemodynamic perturbations of both neural and non-neural origin. When open-loop time series of AP and RSNA are fed into a simple linear model of the arterial baroreceptor reflex, it is possible to reproduce the characteristic features of normal (closed-loop) AP and RSNA variabilities such as they are observed in conscious baroreceptor-intact rats. The arterial baroreceptor reflex effectively buffers slow haemodynamic perturbations and thus stabilizes AP in the LF range. This is achieved at the cost of transient AP and RSNA fluctuations at the resonance frequency of the loop. However, the baroreflex gain value resulting in the most accurate reproduction of normal AP and RSNA variabilities remains well below (20–30%) the value leading to instability.
Quantification of open- and closed-loop variabilities
The present study confirms and extends previous observations (Pires et al. 2001) that the arterial baroreceptor reflex limits AP variability over a large frequency range in rats, starting from at least 0.0003 Hz up to 0.14 Hz. For calculation of spectral powers, the upper limit of the LF band was defined on this basis, and is therefore lower than that used in previous studies from our laboratory (0.27 Hz – Julien et al. 1995, 2003; Barrès et al. 2004). The upper limit of the MF band was set at 0.8 Hz first because AP fluctuations that can be induced by the sympathetic nervous system above 0.8 Hz are of negligible amplitude (Bertram et al. 1998, 2000). Secondly, it was observed in the SAD rats of the present study that AP spectral power sometimes showed mild elevations at frequencies above 0.8 Hz. The presence of peaks at 0.8–1 Hz in the AP spectra is suggestive of interference of respiratory movements in this frequency range. Routine watching of the animals during recording sessions revealed that SAD rats tended to breathe more slowly than baroreceptor-intact rats, possibly as a consequence of chemoreceptor denervation (Martin-Body et al. 1985).
The input signals in the model
The sympathetic perturbations.
In the model, one input signal was the overall sympathetic drive to the cardiovascular system in the absence of baroreflex modulation. It was considered that overall SNA was continuously altered by the central command and by cardiovascular reflexes other than the arterial baroreceptor reflex. The RSNA measured in SAD rats was assumed to provide a reliable sample of this input signal. On the one hand, the ability of the model to simulate normal AP variability validates a posteriori this major assumption. On the other hand, it must be acknowledged that this is an approximation, for at least two reasons. First, the extent of arterial baroreceptor denervation never reaches 100%, especially in the chronic phase, as indicated by measurable heart rate and RSNA responses to the administration of vasoactive drugs (Barrès et al. 1992; Julien et al. 2003). Secondly, the classical procedure of sinoaortic baroreceptor denervation (Krieger, 1964) involves denervation of carotid sinus chemoreceptors.
The AP perturbations.
The second input in the model was what we have termed AP perturbations, by referring to all haemodynamic disturbances of non-neural origin (Julien et al. 1993). We have previously provided some evidence that the myogenic responses of resistance vessels are probably one major cause of AP variability in the absence of baroreflex control (Zhang et al. 1994; Létienne et al. 1998). The new finding of the study is that the amplitude of AP perturbations was comparable to that of actual AP fluctuations so that the power spectra of both time series exhibited strikingly similar ‘1/f’ patterns (Holstein-Rathlou et al. 1995).
The transfer functions of the model
The peripheral transfer function.
During the application of a strong baroreflex stimulus (electrical stimulation of one aortic depressor nerve) in anaesthetized rats, RSNA and AP were tightly coupled. This was especially true at low modulation frequencies of the aortic nerve where coherence frequently reached unity, which means that 100% of the AP variation could be explained by the RSNA variation. In other words, baroreflex-induced changes in SNA were essentially uniform across regional circulations, which indicates that baroreflex operation does not uncouple RSNA from other regional sympathetic drives (Morrison, 2001). Parameters of the RSNA–AP transfer function were similar to those previously reported for the transfer function relating stimulation of the lumbar sympathetic chain and hindlimb vascular conductance in the urethane-anaesthetized rat (Bertram et al. 2000).
The central transfer function.
As mentioned in the Results section, the transfer function from aortic nerve stimulation to RSNA was used to close the baroreflex loop. This implies that the dynamic properties of arterial baroreceptors were ignored in the frequency range investigated in the study, i.e. below 1 Hz. Brown et al. (1978) have shown by using an in vitro rat aortic arch–aortic nerve preparation that these dynamic properties become apparent above 1 Hz. Accordingly, the transfer function from carotid sinus pressure to RSNA (a preparation involving arterial baroreceptors – Sato et al. 2003) is quite comparable to the transfer function from aortic nerve stimulation to RSNA up to 0.8 Hz (Petiot et al. 2001).
Limitations of the study
The complex system combining the peripheral and central transfer functions showed a resonance frequency ∼0.3 Hz, whereas the resonance frequency of the simple transfer function relating AP to aortic nerve stimulation is ∼0.4 Hz (Bertram et al. 1998, 2000), which is closer to the average frequency of Mayer waves in conscious rats. One possible explanation is that the low-pass filter characteristics of the vascular neuroeffector junction are not correctly estimated by the RSNA–AP transfer function in the MF band. Specifically, the phase of the RSNA–AP transfer function at 0.4 Hz is ∼205 deg whereas the phase between stimulation of the lumbar sympathetic chain and hindlimb vascular conductance is ∼180 deg (Bertram et al. 2000). Even a slight overestimation of the phase shift introduced by the peripheral transfer function would result in an underestimation of the resonance frequency of the whole system. It would therefore be interesting to carry out a study similar to the present one by using another peripheral SNA such as lumbar SNA to examine whether the prediction of the central frequency of Mayer waves can be improved.
The present study assumes that SNA is the sole controller of AP variability in rats. This is justified when one considers the lack of effect of acute atropine administration on overall indices of AP variability in conscious rats (Ferrari et al. 1996). On the other hand, it is possible that the accuracy of the model in predicting MF power of AP could be improved by including the parasympathetic control of heart rate (Perlini et al. 1995).
Conclusions
The pressure-to-pressure open-loop static gain yielding the most accurate simulation of normal AP and RSNA variabilities lied between 20 and 30% of the critical gain value leading to instability of the baroreflex loop. This corresponds to absolute gain values of 1.5–2.2, which is quite compatible with data previously reported in the literature for the open-loop static gain between carotid sinus pressure and systemic AP in the anaesthetized rat (Shoukas et al. 1991; Sato et al. 1999, 2003). The baroreflex system is therefore fundamentally stable. Mayer waves should thus be regarded as transient AP responses to haemodynamic disturbances rather than true feedback oscillations. According to this hypothesis, the amplitude of Mayer waves would then depend on the frequency of occurrence and amplitude of triggering perturbations as well as on the sympathetic baroreflex sensitivity (Cheng et al. 2004).
Perspectives
The ability of the model to predict closed-loop AP and RSNA variabilities should now be examined at frequencies below 0.0003 Hz because there is substantial AP variability in this frequency range (Holstein-Rathlou et al. 1995). It has been suggested that these very slow AP fluctuations might be modulated and/or generated by the interaction between the arterial baroreceptor reflex and hormonal and renal factors (Malpas,2004).
Open- and closed-loop models of AP control by the sympathetic nervous system The diagrams show the sympathetic component of the arterial baroreceptor reflex in the open-loop (A) and closed-loop (B) configurations. In A, which corresponds to the situation in the SAD rat, baroreceptor afferents have been interrupted so that the feedback from AP to SNA is not functioning. Hc and Hp are the transfer functions of the central and peripheral limbs of the baroreceptor reflex, respectively. Both transfer functions provide a steady-state gain. Note that Hc incorporates the arterial baroreceptors themselves. ‘Sympathetic’ AP(t) is the AP variability secondary to fluctuations of SNA. p(t) is the AP ‘perturbation’, i.e. all haemodynamic disturbances of non-neural origin. s(t) is the RSNA in the absence of baroreflex modulation, i.e. the actual RSNA recorded in SAD rats. RSNA is taken as a reflection of the overall sympathetic drive to the cardiovascular system. Note that in B, when the gain of Hc is set to zero, the system is open-loop and AP(t) and RSNA(t) are the respective time series measured in the SAD rat.
Transfer function from RSNA to AP in anaesthetized rats Graphs show mean coherence and transfer function from 14 anaesthetized rats. RSNA and AP were recorded during sinusoidal stimulation of the aortic depressor nerve at 11 discrete frequencies ranging from 0.03 to 1 Hz. At each modulation frequency, coherence (A), gain (B) and phase (C) were computed. The equation of a second-order low-pass filter with a fixed time delay was fitted to experimental gain and phase functions.
Spectral analysis of AP and RSNA variabilities in conscious baroreceptor-intact and SAD rats Group-average power spectra of AP (A), RSNA (B) and coherence (C) computed from 3.5 h recordings (segmented into 55 min periods) in conscious sham-operated (n = 8) and SAD (n = 10) rats. Individual RSNA data sets were normalized (normalized units, n.u.) by their respective mean before spectral analysis. Standard error lines have been omitted for legibility.
Generation of AP time series from RSNA time series in SAD rats In each SAD rat, actual RSNA data were converted into ‘sympathetic’ AP data by using mean parameters of the RSNA–AP transfer function determined in anaesthetized rats, and a static gain determined from AP and RSNA responses to acute ganglionic blockade (in this example, 21.17 mmHg μV−1). A DC component (AP level during ganglionic blockade, 60 mmHg in this example) was added to all simulated AP values in order to take into account the influence of non-neural factors in sustaining AP.
Calculation of AP ‘perturbation’ time series in SAD rats Graphs show a 1000 s recording (A) of AP together with AP predicted from the simultaneous RSNA recording (‘sympathetic’ AP,) in a conscious SAD rat. The lower trace is the difference between ‘sympathetic’ and actual AP values, which is referred to in the text as the AP ‘perturbation’ time series. B and C show the 100 s portions delimited by the arrows in A, emphasizing periods of relatively good (B) and poor (C) predictions of actual AP.
Spectral analysis of actual and simulated AP time series in the open-loop configuration Group-average power spectra of AP, ‘sympathetic’ AP, and AP ‘perturbation’ (the difference between actual and ‘sympathetic’ AP). Spectra were computed from 3.5 h recordings (segmented into 55 min periods) in 10 SAD rats.
Spectral analysis of simulated AP and RSNA time series in the closed-loop configuration Group-average power spectra of AP (A) and RSNA (B) were calculated from 3.5 h time series obtained after closing the loop in the baroreflex model depicted in Fig. 1B. The pressure-to-pressure open-loop static gain was increased from 0 to 20, 50 and 100% of a critical value resulting in instability, i.e. self-sustained oscillations, at the resonance frequency of the loop.
Spectral powers of simulated AP and RSNA at increasing values of the baroreflex open-loop static gain Spectral powers were calculated in the low-frequency (LF, 0.0003–0.14 Hz) and mid-frequency (MF, 0.14–0.8 Hz) bands for AP (A) and RSNA (B). Black bars show actual data from 8 baroreceptor-intact (sham-operated) rats. Open bars show data simulated from actual AP and RSNA time series collected in 10 SAD rats. In the simulations, the pressure-to-pressure open-loop static gain of the arterial baroreceptor reflex was increased from 0 (which corresponds to actual data in SAD rats) to 100% of a critical value (7.41) leading to instability in the baroreflex loop. *P < 0.1; †P < 0.05 versus Sham.
Spectral powers of AP and RSNA in conscious sham-operated and SAD rats
Footnotes
-
- Accepted July 2, 2004.
- Received March 30, 2004.
- Revision received June 29, 2004.
- The Physiological society 2004
