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1 Department of Behavioral Science, 2 The Neuroscience Program, 3 Department of Surgery, Artificial Organs, Pennsylvania State University College of Medicine, Hershey, Pennsylvania 17033
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES
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To determine the
relationship between blood pressure (BP) variability and the open-loop
frequency domain transfer function (TF) of the baroreflexes, we
measured the pre- and postsinoaortic denervation (SAD) spectra and the
effects of periodic and step inputs to the aortic depressor nerve and
isolated carotid sinus of central nervous system-intact,
neuromuscular-blocked (NMB) rats. Similar to previous results in freely
moving rats, SAD greatly increased very low frequency (VLF)
(0.01-0.2 Hz) systolic blood pressure (SBP) noise power. Step
response-frequency measurements for SBP; interbeat interval (IBI);
venous pressure; mesenteric, femoral, and skin blood flow; and direct
modulation analyses of SBP showed that only VLF variability could be
substantially attenuated by an intact baroreflex. The 
3-dB frequency
for SBP is 0.035-0.056 Hz; femoral vascular conductance is similar
to SBP, but mesenteric vascular conductance has a reliably lower and
IBI has a reliably higher 3-dB point. The overall open-loop
transportation lag, of which 
0.1 s is neural, is 
1.07 s.
Constrained algebraic solution, over a range of frequencies, of the
pre- and postSAD endogenous noise spectra and the independently
determined relative frequency and absolute lag measurements was used to
calculate the absolute gain for the open-loop TF. The average gain at
0.02 Hz, the frequency of maximum sensitivity, was 1.47 (95%
confidence interval = ±0.48), which agrees well with estimates for the
dog reversible sinus. We found that, in the NMB rat, the effects of SAD
on the BP noise spectrum were accounted for by the open-loop properties
of the baroreflex.
baroreceptors; carotid sinus; aortic depressor nerve; systems analysis; transfer function; noise
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES
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MORE THAN 25 YEARS AGO, Cowley et al. (14) reported that compared with normal dogs, the blood pressure (BP) distributions of sinoaortic denervated (SAD) dogs "exhibited curves with twice the 24-h standard deviation." There have since been similar observations in various species, including humans. One interpretation of these observations is that the baroreflexes normally restrain minute-to-minute BP variability; this contrasts with a view of the baroreflexes as provoked to only occasional action by specific perturbations such as thermal stress, postural shifts, or hemorrhage. The physiology of the postSAD-BP variability is not known. Although the variability is reversed by ganglionic block and, thus probably neurally mediated, in unrestrained rats, brain lesions as extensive as precollicular decerebration do not eliminate it (39). Furthermore, ventilated, intensively maintained, neuromuscular-blocked (NMB) rats show similar ganglionic block-dependent and increased postSAD variability (16), indicating that it does not depend on fluctuating respiration or the skeletal activity of general behavior.
As expected for random data, the SAD variability is independent of the sampling interval (2, 7). However, we found that averaging observations over 30 s (16) also did not attenuate the variance and that suggested that the beat-to-beat variability was not uniformly random. A mean is effectively a time-domain filter, and taking differences between successive 30-s systolic BP (SBP) means (16) amounts to applying a 0.005- to 0.025-Hz band-pass filter to the data (see APPENDIX A). That postSAD variability was unattenuated by this averaging strongly suggested that, although random, its spectral power was concentrated in the very low frequencies (VLF).1
Because a negative feedback element constrains variability, noise increases when it is removed. Furthermore, it is fundamental that an element can oppose and neutralize noise only where its transfer function (TF) and the noise spectrum coincide; it is a corollary that the spectral change that occurs, when an element is removed, delineates the closed-loop system's TF. Dog- and rabbit-baroreflex response curves have corner frequencies at ~0.05 Hz (23, 25, 32), and the spectral effects of SAD in the rat predict a similar TF.
In the companion paper (16), we described the statistical variability of the BP in the NMB preparation, showed that it resembled the patterns of ambulatory rats, and then, by directly activating the carotid sinus (SINUS) and aortic depressor nerve (ADN) with hydraulic and electrical stimuli, measured the steady-state baroreflex responses of arterial (ABP) and venous BP (VBP), interbeat interval (IBI), and the skin (skBF), mesenteric (msBF), and femoral (fmBF) blood flow. In the studies described here, with the same preparations, stimulus modes, and response measures, we applied both step and periodic stimuli and, with the use of several straightforward methods, determined the open-loop frequency and phase response of the carotid and aortic reflexes, estimated the upper limit of the "central" lag for vagus and peroneal nerve activity, and calculated the absolute gain of the TF.
The diagrams in Fig. 1 represent the
cardiovascular system with and without the baroreceptor feedback path
[H(s)]. In both, the source of variability or
noise input [N1(s)] is the same and located in the central nervous system (CNS); and feedback is from the
BP through the baroreceptors. There is a neural summing point (
CNS) in the CNS, which combines
N1(s) with the baroafferents' output, and a hydraulic point at the baroreceptors that reflects the
net action of the cardiovascular effectors relative to the sensory
reference or adaptation level. The implied hypothesis is that,
normally, the baroreflex counteracts endogenous variability propagated
from N1(s) and that the difference
between the Pre and Post spectra is due to the
action of the baroreflex.
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An alternative hypothesis is that noise is a de novo experimental artifact introduced by random firing of damaged baroreceptors, which, although severed from their receptive endings, remain connected to nucleus of the solitary tract (NTS) target neurons. Primary afferents in other sensory systems, e.g., dorsal root ganglion cells, show spontaneous activity after distal axotomy (9, 29); however, on the basis of several kinds of neurophysiological and statistical evidence, random activity of axiotomized baroreceptors is not a likely source of the postSAD variability (see analysis in APPENDIX B).
Relationship Between the Pre and PostSAD Models
The baroreflex is characterized by the open-loop TF, G(s)H(s). With the use of electrical modulation of the ADN and volumetric modulation of a carotid sinus2 as experimental inputs, the phase and relative gain, as a function of frequency, can be directly measured. Combining these data with the pre- and postSAD spectra, which contain independent information of the system's response to endogenous noise, the absolute gain of the intact system can be estimated as follows. Figure 1: preSAD the system is intact and the reflex is completely normal; thus
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(1) |
, to represent the error between the
two kinds of measurement, we obtain
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(2) |
, as a function of k, and minimized in the
least-squares sense over all frequencies yields the value of
k that gives the best fit between the spectral and TF ratios
(calculated from the open-loop measurements). Multiplying the relative
open-loop gains for each frequency by k will give the
absolute gain function of the reflex, as it was, before any surgery
took place.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES
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The subjects, surgery, and general methods are identical to and described in the companion paper (16). All actual surgery or possibly irritating manipulation was done under controlled and carefully monitored, deep isoflurane anesthesia. The protocol is supervised and certified to be in compliance with National Institutes of Health Guidelines by the Pennsylvania State University College of Medicine Institutional Animal Use and Care Committee. The specific protocols and data analysis are as follows.
Noise Spectra
SBP. For each rat, 50 randomly chosen 90-s postSAD-SBP samples were automatically extracted to binary files from 4-h 6-kHz digital audio tape (DAT) records of undisturbed baseline. Systole was algorithmically detected and backward-step interpolated into a 1-kHz array, and the spectra were obtained by a fast Fourier transform (FFT) (Hanning; 8.3-mHz resolution) of the detrended data. For rat EH, both pre- and postSAD 6-kHz samples (within 24 h at 0.15% isoflurane) were analyzed, and the VLF (0.01-0.2) and low-frequency (LF) (0.2-0.6) power were measured by integration. For all rats, 2.5-s/sample data pre- and postSAD (within 24 h at 0.15% isoflurane) were analyzed for VLF power. Differences due to SAD were evaluated by ANOVA and post hoc t-tests.
Sympathetic (peroneal) nerve. Fifty parallel 90-s postSAD sympathetic trials for each rat were extracted from 6-kHz records, and the spectra were calculated.
Open-Loop Transfer Function
Modulation frequency analysis. ADN. Current levels were selected to activate A or A + C fibers (17, 18; see Ref. 16 for criteria). A fibers were stimulated with the use of a 100-µs pulse width (PW) at 50-60 µA; A + C fibers with 300 µs at 80-100 µA. The test parameters were 110% of the minimum and 90% of the maximum linear range (see Ref. 16): 20-50 impulses/s for A; 3-20 ips for A + C. The periodic stimuli were symmetrical on-off cycles of 0.02-0.4 Hz for 120 s. ADN modulation analysis was done in three rats. SINUS. Stimulation was done by inflating a microballoon in a vascularly isolated sinus (16); the range was determined as above 1.7-3.2 µl (peak-to-peak) at frequencies of 0.02-0.4 Hz. Complete analyses were done in two rats.
Power spectral analysis (SBP).
The test stimulus modes were SINUS (2 rats), ADN-A (3 rats), and
ADN-A + C (1 rat). The test frequencies for SINUS were
0.02, 0.03, 0.0375, 0.045, 0.055, 0.0625, 0.0875, 0.1, 0.1125, 0.1375, 0.15, 0.1625, 0.175, 0.2, 0.25, and 0.4 Hz; for ADN-A: 0.02, 0.025, 0.0375, 0.05, 0.0625, 0.075, 0.0875, 0.1, 0.1375, 0.175, 0.25, 0.3, and 0.4 Hz; and for ADN-A + C: 0.025, 0.03, 0.0375, 0.05, 0.0625, 0.075, 0.0875, 0.1, 0.125, 0.1375, 0.175, 0.2, and 0.4 Hz. For
each rat, stimulus mode, and test frequency, 5 to 27 spectra were
averaged (see Table 1). Each spectrum was obtained by an FFT (8.3-mHz
resolution) on the 120-s interpolated, Hanning-windowed responses. The
amplitude TF were calculated from the normalized square-root power and
interpolated to estimate the 3- and 20-dB frequencies and 0.4-Hz
amplitude.
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Sinusoidal fit. The ensemble-averaged signals were iteratively fit to a sine function. The variables of the fit were the amplitude, phase lag, and frequency. The amplitude TF were directly estimated by calculating the output-to-input amplitude ratio and extrapolated as above.
Step-frequency analysis.
ADN.
The parameters were the maximums used for periodic stimulation. For A
fibers, it was 20-50 ips; and, for A + C fibers, it was
9-20 impulses/s. Analyses were completed for five rats.
SINUS. Balloon volume was 80% of the linear range
maximum (2.25-3.2 µl); analyses were completed for three rats.
Transient response.
The output variables were systolic BP (SBP), IBI, mesenteric vascular
conductance (msVC), and femoral vascular conductance (fmVC). For each
rat, for ADN-A, A + C, and SINUS, 20 stimuli at each of 2-4
strengths were ensemble averaged. With the use of the difference
between the stimulation period and mean of the 12-s prestimulus
baseline, the initial 50 s of the averaged response was
iteratively fit to y(t) = A(1 e
t/T), where
A is the asymptotic response amplitude, T is the
time constant, and the TF of the step is defined as
sY(s).
Transportation lag estimates. SBP. For each of five rats, SINUS, ADN-A, and A + C, open-loop transportation lags were measured. Each data set was composed of 50 prestimulus and 80 stimulus-on cardiac cycles. A least-squares line was fit to the prestimulus data, and an exponential was fit to the stimulus data (see Fig. 6); simultaneous solution relative to t0 gave the transportation lag (see Fig. 6). CNS. Fifteen 3.0-µl SINUS step responses were extracted from 6-kHz DAT; the IBI was measured, back interpolated, and represented as instantaneous frequencies (fi). The balloon volume, heart frequency, and absolute value of the vagus and sympathetic neurograms were ensemble averaged and smoothed by a 10-point second-order Savitzky-Golay algorithm. The stimulus onset was defined with respect to the peak volume rate of change and threshold volume. The response onsets were defined at 3 SD above the baseline.
Gain-Scaling Factor [k]
Rat EH.
For each of the n 20-modulation test frequencies,
fi, the normalized RMS amplitudes,
GHi were obtained from FFT modulation TF
estimates. Spectral ratio was determined by division of the preSAD by
the postSAD amplitude spectra, and the lumped open-loop system lag,
lag, and estimated first-order phase lag,
arctan(2
fT), were used to calculate the phase. The error, , between the TF and spectral measurements (Eq. 3)
was differentiated with respect to k, and the value of
k, corresponding to the minimum, was determined for each
kind of stimulation.
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(3) |
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES
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PostSAD spectra.
BLOOD PRESSURE. Figure
2D shows that the normalized
high-resolution postSAD-SBP spectra of five undisturbed NMB rats
(including rat EH) are very similar. The corresponding
postSAD and preSAD spectra for rat EH are shown in the
main panel of Fig. 2. The key feature is the large
increase in VLF power (
PSD = 1.2 × 105
mmHg2/Hz, df = 49, t = 3.65, P < 0.001); there is also a smaller decrease in LF
power1 [change in power
spectral density (PSD) = 1.5 × 103, df = 49, t = 2.02, P < 0.05].
Similar analysis of 2.5 s/sample data (Nyquist 0.2 Hz) for all five
rats showed a large increase in VLF power (PSD = 0.75 × 105 mmHg2/Hz, df = 4, t = 3.69, P < 0.01), which
probably accounts for most increased postSAD variability (see
Fig. 2 in Ref. 16). PERONEAL (SYMPATHETIC) NERVE.
The postSAD spectra plotted in Fig. 3
estimate the postSAD N1(s) (Fig. 1)
and shows that the nerve activity spectrum is nearly flat; thus the LF
skew of the SBP spectrum is most likely due to
G(s) (See Fig. 5).
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Modulation time-domain responses.
The series of traces in Fig. 4 are
examples of the step response (0 Hz) and modulation of the component
responses by ADN-A + C stimulation. [The abdominal conductance
(msVC) includes the aorta below the superior mesenteric artery.]
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Periodic input
POWER SPECTRAL ANALYSIS.
Figure 5 is the SBP-amplitude
spectra (EH, ADN-A, ADN-A + C, SINUS) for eight test frequencies.
The procedure was the same as for the power spectra shown in Fig. 2,
except the absolute value of the amplitude per square root Hertz is
plotted; the corresponding normalized FFT amplitudes for all rats are
in Table 1. The solid lines are the
average spectra during the specified test stimulus (e.g., ADN-A, 0.1 Hz), and the gray areas are average spectra during the baseline periods
that immediately preceded the onset of that kind of test stimulus. The
averages are across all trials for the specified mode (e.g., ADN-A + C). The figure illustrates the relationship between the noise and the
modulation amplitudes at various frequencies, which are both products
of G(s). SINUSOIDAL FITS. An
iterative least-squares fit of a sine function to the modulated output
is a straightforward measure of the peak-to-peak response amplitude.
Table 2 gives the normalized amplitudes
for SBP for each rat and stimulus mode; the 3- and 20-dB
frequencies were calculated directly from the power ratios.
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Step input.
For SBP, the mean 3-dB frequency was 0.035 Hz for ADN-A, 0.046 Hz for
A + C, and 0.056 Hz for SINUS; the magnitude at 0.4 Hz was
6-18% of the maximum response. fmVC was similar to SBP, but msVC
had a reliably lower and IBI had a reliably higher 3-dB frequency.
Table 3 summarizes the results and
statistical tests for five rats.
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Transportation lags.
BARORECEPTOR TO SBP.
The mean ADN lag was 1.07 s (Table
4 and Fig.
6). After subtracting the
transportation lag, cross-correlation analyses of the modulated SBP at
each test frequency did not reveal an additional phase shift. However,
for >0.15 Hz, the modulation was weak, and at <0.05 Hz, there was
considerable VLF noise (see Fig. 2); thus given the close exponential
approximation of the response, nonlinear phase effects were assumed to
be present. BARORECEPTOR TO VAGUS. Vagus recordings of 15 SINUS stimulations (rat EH) are shown in Fig.
7. The ensemble average of these, of the
corresponding heart rate (HR) traces, and of the balloon volume are
shown in Fig. 8. The 3-SD (above
baseline) increase in vagus activity occurred in <30 ms, and the time
to first peak of vagus activity was ~95 ms; thus the estimated
maximum delay from balloon inflation to vagus firing was 30-95 ms.
BARORECEPTOR TO SYMPATHETIC. The peroneal nerve data in
Fig. 8 parallel the vagus data. With the use of the same stimulus onset
definition, the 3-SD change was at <20 ms, and the time to the first
peak was 84 ms.
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Estimation of the gain-scaling factor [k].
The values of k that gave the minimum summed squared error
between the spectrum-determined pre-to-postSAD ratio and the
experimentally determined open-to-closed-loop TF ratio (see
equations 1 and 3) are the maximum entries in
Table 5. Figure
9 shows the "k
corrected" rhs (TF ratio; right-hand side) and
the lhs (spectral ratio; left-hand side) of
equation 1 plotted against frequency (left
panels) and one another (right panels). The
plots and correlation analyses show a close correspondence between the
theoretically equivalent functions derived from entirely different
kinds of data in the same rat (ADN-A: n = 20, r = 0.95, P < 0.0001; ADN-A + C:
n = 19, r = 0.89, P < 0.0001; and SINUS: n = 21, r = 0.92, P < 0.0001). It should be
particularly noted that, in scaling, the same value of k was
used at each frequency; the procedure was thus a linear transformation
and did not change the correlation coefficient or its statistical
reliability. The conventional correlation coefficients, r,
in Fig. 9 are for the best-fitting regression lines. The theoretical absolute identity lines are drawn to show the relationship to the
actual data, and the correlations were also calculated with the fit
constrained to these (m = 1; b = 0) lines with a result (ADN-A: n = 20, rI = 0.94, P < 0.0001; ADN-A + C: n = 19, rI = 0.87, P < 0.0001; and SINUS: n = 21, rI = 0.90, P < 0.0001)
that is very similar to the unconstrained "best-fit" line. Applying the derived k values to the normalized open-loop TF gives
estimates of absolute gain at each frequency (Table 5). At >0.3 Hz,
the left-hand (lhs) and right-hand side (rhs)
ratios of equation 1 conform to one another better for the
SINUS than for the ADN (Fig. 9). This is consistent with the
established adaptation characteristics of barosensitive stretch endings
(24) and is supported by Table 5 and Fig.
10, which show that, for SINUS, the
open-loop gain and the feedback gain
(|GH| · |N1| · |Post|1 = |GH| · |G|1 = |H|)
are comparatively larger at higher frequencies. In the closed-loop, i.e., preSAD, the net phase shift becomes 180° at 0.28 Hz, thus for the SINUS, which has increasing sensitivity in
this range, the positive feedback is enhanced and endogenous noise is
correspondingly amplified. In that the preSAD spectral estimates (which
are the same for all stimulus modes) include stretch endings, the SINUS
open-loop measurements, which (unlike the ADN measurements) also
include stretch endings, should more authentically emulate the detailed
properties of the natural intact system; hence, the better fit at the
higher frequencies. RATS DY, EC, AND EF. With the use of
the 2.5-s/sample preSAD data for rat EH, the absolute gain was
1.39 ± 0.35 (compared with 1.71 ± 0.52 for the
high-resolution estimate); taken overall, on the basis of the 2.5-s
data, the mean absolute gain for rats DY, EC, EF, and EH was 1.47 (3 df, 95% CI = ±0.48).
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES
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To gauge the absolute gain of the intact baroreflex, the open-loop TF was used as a template by constraining the explicitly measured open-loop lag and relative magnitude at each frequency to the ratio of the pre- to postSAD endogenous noise spectra. In contrast to the periodic and step inputs of the open-loop analysis, the properties of the endogenous noise input are not explicitly defined. However, because most postSAD variability is blocked by chlorisondamine, the sympathetic nerve firing rate spectrum (Fig. 3) probably approximates N1(s), and if the noise is wide band, because the noise terms cancel, the actual spectrum is not critical (see APPENDIX B). The gain estimates obtained for four NMB rats, including the detailed data from rat EH, were similar to one another (1.47 ± 0.48) and to published values for other preparations, including those from the unanesthetized and reversibly isolated-sinus dog (35, 36), the open-loop baroreflex preparation that is most nearly physiological (Ref. 5 gives 1.19 ± 0.24, and Ref. 19 gives 1.36 ± 0.25).
Differences between hydraulic and electrical stimulation. The gain calculation assumed that numerators and denominators on both sides of equation 1 were identical. In principle, this is correct for the SINUS, but not for the ADN, where nerve stimulation bypasses natural stretch endings. If these have a frequency-dependent TF, the lhs and rhs quotients will not multiplicatively scale to superimposable curves; this defect is evident in Fig. 9 for higher frequencies of the ADN-A and A + C.
Anatomically, H is the feedback path from the baroreceptor stretch endings (BR) to CNS
(Fig. 1, preSAD). Functionally, H transforms BP into neural
activity; but, the TF cannot be accounted within a purely physical
framework. The best that can be done is to indirectly estimate the
relative attenuation. Normally, the postganglionic sympathetic outflow
[Fig. 1, preSAD: between CNS and
G(s)] is a function of both H and the
endogenous variability (N1); however, in the
open-loop, i.e., postSAD, H is eliminated. If the
sympathetic activity has a level spectrum (Fig. 3) and is the principal
input to G, |G| is the ratio of sympathetic
and SBP spectra, and |H| = |GH|/|G|. The result (Fig. 10) is
consistent with |H| being relatively flat in the VLF,
and for the SINUS, which includes the stretch endings, having
increasing gain at >0.3 Hz (see also Figs. 3 and 6 in Ref. 22).
Implications of the TF for the SBP variability spectrum.
The physiological function of the baroreflex is to attenuate BP
variability, and its direct manifestation is a trough in the spectrum
that corresponds to the passband of the intact reflex. In the VLF
(<0.1 Hz) region, the attenuation due to feedback is approximately
uniform; this is because the phase is effectively constant, and the
feedback TF, H, is flat. Our open-loop estimates of the
3-dB frequency of the NMB rat baroreflex of 0.03-0.07 Hz
agree with determinations for the anesthetized dog and rabbit of
0.04-0.05 Hz (23, 25, 32); and, our spectral
measurements agree with previous studies in freely moving rats
(13, 20). Figure 9 compares the actual attenuation of BP
variability, by the baroreflex, with what was calculated from the
open-loop determinations of GH. Given that the estimated
absolute gain also agrees with applicable published values, the overall
correspondence is quite good.
lag, is 
= 2lagf; the system resonates when
= . Thus, e.g., lag = 1.05 s 
fres = 0.48 Hz. In addition to
lag, for first-order linear systems (see Fig. 6), the
phase lag, (f) = arctan(2fT), where T, the time
constant, is equivalent to a delay of
arctan(2fT) 
2f.
Burgess et al. (10, 11) modeled the rat baroreflex with
the use of a combination of transport and first-order delays, and they
concluded that the LF peak is a resonance. The data of their most
thoroughly analyzed rat (B: fres = 0.35 ± 0.05, lag = 0.8 ± 0.1, T = 3 ± 1) largely overlaps that of ours
[EH: fres0.33 (Fig. 2),
lag = 1.05 ± 0.03 (Table 4),
T = 2.8 ± 0.1], and both are in accord with
their analysis, given that the frequency reported for the LF peak, in
fact, encompasses a broad range (1, 10, 13, 20, 21, 31).
Finally, although the open-loop LF gain is very low and the LF
resonance is not a major component of BP variability (in terms of noise
power, the VLF-SAD increase is 100 times the LF decrease), if the LF
frequency depends on the delay between neural efferent and circulatory
events, it is potentially a useful and noninvasive index of sympathetic
vascular kinetics and status (12).
Calculating the gain from the spectra.
For rats, the relative gain, lag, and time constant estimates from
Tables 1, 3, and 4 can be combined in equation 3 with empirically determined pre- and postSAD amplitudes and minimized with the use of a least-squares algorithm. In each subject, preSAD measurements can be made with several different treatments; then, after
SAD, the baseline spectrum under each treatment determined and the
ratios calculated. [Conservatively, to assume that
N(s) is stationary, the postSAD treatment effects
must be small.] This method can substitute for pharmacological
determinations (37), and if recent evidence that HR does
not uniformly sample general baroreflex function is correct (6,
16), it might prove to be more valid.
Perspectives
In this and the companion paper (16), we examined the properties of the BP variability spectra and the baroreflex TF in the same chronic unanesthetized NMB rats. Our measurements were in accord with those from other species and preparations. Furthermore, we showed that when algebraically combined and mutually constrained, the spectra and TF could together gauge the absolute gain of the baroreflex. A form of this method may be useful in evaluating the effects of genetics, drugs, or other manipulations on baroreflex function.All in all, statistical analysis, computational models, and the experimental findings support the assertion that postSAD-increased variability is caused by removing the restraint of the baroreflex on endogenous sources of noise. This underscores that, rather than being only occasionally exercised, the baroreflex is constantly active, probably making adjustments equivalent to 10-20 mmHg, at least, every few minutes. The purpose, if any, of such ceaseless interplay between endogenous noise and the reflex remains to be elucidated (15, p. 79-84).
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APPENDIX A |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES
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Equation 1
We can accurately measure both GH and the spectra; by comparison, the estimate of G is rough, thus the algebraic aim is a pair of expressions relating the spectral ratio to the experimental TF ratio.Regardless of phase, the magnitude of the product (quotient) equals the
product (quotient) of the magnitudes, thus
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CNS; in
resolving it, the phase needs to be considered [by substituting
j
for s and representing
G(j) and
H(j) in magnitude-phase form]
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Averaging TF
(a) A "sliding block" average of N points is equivalent to convolution of the original data with
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APPENDIX B |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES
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Evaluation of the Random Noise Hypothesis
Neuroanatomic. On the basis of lesion studies, the baroreceptors themselves are probably not the noise source: lesions of the NTS that destroy both the presynaptic terminals and the second-order neurons appear to produce at least as much variability as peripheral axotomy (7, 8, 33, 38).
General statistical properties.
Assume that ABP is inversely proportional to the output of the
second-order neuron pool, which is proportional to the sum of the
firing rates of n baroreceptors. Each carotid sinus nerve and ADN has 625 fibers (3, 26); thus a
conservative (the postSAD variability is quantitatively consistent
across the literature, and fewer cells favor the random hypothesis),
but tenable, assumption is that of 2,000 baroreceptors, at least 100 are spontaneously active, and that their combined output is the system
input, N2(s) (Fig.
11, diagram).
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5-mmHg
SBP change (17), which is 0.5
of the postSAD ABP. Thus the spontaneous output of each baroreceptor is modeled as a
Poisson variate with 
1; and, for n = 100, such baroreceptors firing together, n= 100, which is well
approximated by the normal variate (µ= 100; 2 = 100). Thus the probability that the firing rate of the ensemble increases for 1 s by 1 (10 impulses/s) is 0.16. However,
nearly all of the spectral power of the postSAD variability
is at <0.05 Hz, and convolution of the firing rate time
series with a low-pass filter having this characteristic is
equivalent to requiring that this rate be sustained for 20 s,
which is an event with a probability 108
(see Fig. 2 and Ref. 30).
Finally, in view of the above information, random activity
predicts that with partial, in contrast to total, SAD, a smaller number
of damaged cells and smaller would lead to greater variability; however, rats without any baroreflex have significantly more
variability than those with partial function (34).
In sum, it is highly unlikely that postSAD BP variability could be the
product of summated independent random activity of damaged neurons.
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ACKNOWLEDGEMENTS |
|---|
The authors thank B. H. Natelson and S. S. Reisman. They also thank M. C. Andresen, who suggested a possible parallel between axiotomized dorsal root ganglion and nodose ganglion cells.
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FOOTNOTES |
|---|
The studies were supported by Grant HL-40837 (to B. R. Dworkin) from the National Heart, Lung, and Blood Institute, Division of Heart and Vascular Diseases.
Address for reprint requests and other correspondence: B. R. Dworkin, Pennsylvania State Univ. College of Medicine, Hershey, PA 17033 (E-mail: brd1{at}psu.edu).
1 Although the postSAD increases in VLF power are the prominent result of most spectral studies, the highlighted feature is often the much smaller (see Fig. 2, bar graph ordinates) decrease in the LF (0.3-0.5 Hz). Jacob et al. (20) found >10-fold increase in VLF, but their abstract, which does not mention VLF, says "a (0.3-0.5 Hz) spectral peak was found in Sham but not SAD animals, suggesting that it is associated with the baroreflex." Similarly, Cerutti et al. (13) found a greater than sixfold increase in VLF, but their abstract also ignored these effects, and said, "In SAD rats, the power spectral density of MAP, estimated by a fast Fourier transform, was reduced in the low-frequency (LF, 0.27- to 0.74-Hz) band." In their opening sentence, Abu-Amarah et al. (1) citing these studies said, "In rats, arterial baroreflexes operate largely on peripheral resistance within the frequency band of 0.25 to 0.7 Hz."
2 We have discussed the limitations of hydraulic pressure stimulation of the rat carotid sinus (16); in contrast, a volumetric balloon imposes accurate and consistent stretch on the receptors, and the receptors have an unaffected independent circulation (27, 28).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 31 January 2000; accepted in final form 7 June 2000.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
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is the application point for the test stimuli.
2 = 1.4, P > 0.999). D: highly similar normalized postSAD spectra of 5 different rats (including EH) without isoflurane.
;
lhs;
|Post(s)|/|Pre(s)|]
and right-hand side [
; rhs; TF] of
equation 1 plotted as a function of frequency and of one
another (
) for rat EH. The graphs compare the directly
measured attenuation of BP variability by an intact baroreflex
(lhs) with a predicted ratio that is calculated from the
open-loop modulation and phase measurements (rhs). The TF
magnitude data were from the normalized FFT with the use of procedures
identical to those for the noise spectra. The minimization was over
19-21 frequencies (see Table 
