(Hypertension. 2001;37:1153.)
© 2001 American Heart Association, Inc.
Scientific Contributions |
Dynamic Analysis of Renal Nerve Activity Responses to Baroreceptor Denervation in Hypertensive Rats
From the Departments of Internal Medicine and Physiology and Biophysics, University of Iowa College of Medicine, and Veterans Administration Medical Center, Iowa City, Iowa.
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Abstract—Sinoaortic and cardiac baroreflexes exert important control over renal sympathetic nerve activity. Alterations in these reflex mechanisms contribute to renal sympathoexcitation in hypertension. Nonlinear dynamic analysis was used to examine the chaotic behavior of renal sympathetic nerve activity in normotensive Sprague-Dawley and Wistar-Kyoto rats and spontaneously hypertensive rats before and after complete baroreceptor denervation (sinoaortic and cardiac baroreceptor denervation). The peak interval sequence of synchronized renal sympathetic nerve discharge was extracted and used for analysis. In all rat strains, this yielded systems whose correlation dimensions converged to similar low values over the embedding dimension range of 10 to 15 and whose greatest Lyapunov exponents were positive. In Sprague-Dawley and Wistar-Kyoto rats, compete baroreceptor denervation was associated with decreases in the correlation dimensions (Sprague-Dawley: 2.42±0.04 to 2.16±0.04; Wistar-Kyoto: 2.44±0.04 to 2.34±0.04) and in the greatest Lyapunov exponents (Sprague-Dawley: 0.199±0.004 to 0.130±0.015; Wistar-Kyoto: 0.196±0.002 to 0.136±0.010). Spontaneously hypertensive rats had a similar correlation dimension, which was unaffected by complete baroreceptor denervation (2.42±0.02 versus 2.42±0.03), and a lower value for the greatest Lyapunov exponent, which decreased to a lesser extent after complete baroreceptor denervation (0.183±0.006 versus 0.158±0.006). These results indicate that removal of sinoaortic and cardiac baroreceptor regulation of renal sympathetic nerve activity is associated with a greater decrease in the chaotic behavior of renal sympathetic nerve activity in normotensive compared with hypertensive rats. This suggests that the central neural mechanisms that regulate renal sympathetic nerve activity in response to alterations in cardiovascular reflex inputs are different in spontaneously hypertensive rats from those in Sprague-Dawley and Wistar-Kyoto rats.
Key Words: nonlinear dynamics • denervation • baroreceptors • renal nerves
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Introduction |
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The sinoaortic and cardiac baroreceptor reflexes exert important control over sympathetic nerve activity. The details of these control mechanisms have been studied by observing steady state changes in mean arterial pressure (MAP), heart rate (HR), and sympathetic nerve activity at various times after complete disruption of these reflexes.
After sinoaortic baroreceptor denervation, MAP, HR, and
renal sympathetic nerve activity (RSNA) were increased on day 1 but
returned to control levels on day
14.1 On day 1, variability of
MAP was increased, while that of HR and RSNA was decreased. On day 14,
variability of MAP remained increased, while that of HR and RSNA
returned to control levels. MAP and RSNA were strongly (
90%)
negatively correlated before sinoaortic baroreceptor denervation but
only 30% negatively correlated on days 1 and 14 and 25% positively
correlated on days 1 and 14. These results indicate that low MAP
variability results from sinoaortic baroreflex–mediated fluctuations
in HR and RSNA that are inversely related and that high MAP variability
after sinoaortic baroreceptor denervation is infrequently positively
correlated with RSNA. Because MAP variability can be reduced by
interventions that block the sympathetic nervous
system,2 3 it
appears that MAP variability associated with sinoaortic baroreceptor
denervation is mediated largely by a permissive role of
peripheral sympathetic nervous system activity. This is
especially prominent in the conscious state, in which MAP, HR, and RSNA
responses to environmental alerting stimuli are
exaggerated.
Time series of normal heartbeat (ie, R-R intervals), arterial pressure, and peak intervals of synchronized RSNA display complex nonlinear dynamics, including deterministic chaos. In normal animals subjected to sinoaortic and cardiac baroreceptor denervation, the regulation of arterial pressure4 5 6 (dogs) and RSNA7 (rats) became more simple, with significant reduction in 2 indices of chaotic behavior, the correlation dimension and greatest Lyapunov exponent. Similarly, the heartbeat8 of patients and the RSNA7 of rats with congestive heart failure showed marked reduction in chaotic behavior compared with the normal state. This is of interest because human subjects and animals with congestive heart failure have impaired sinoaortic and cardiac baroreflex regulation of HR, arterial pressure, and RSNA.9 Since removal of sinoaortic and cardiac baroreceptor regulation of RSNA, occurring either physiologically or pathophysiologically, is associated with a reduction in both the transmission of afferent inhibitory information to the central nervous system and the chaotic behavior of RSNA, this suggests that the continued presence of tonic afferent inhibitory neurotransmission to the central nervous system contributes to sustaining the normal chaotic behavior of RSNA.
Compared with the genetically normotensive control Wistar-Kyoto rat (WKY), the genetically spontaneously hypertensive rat (SHR) has altered sinoaortic10 and cardiac11 baroreflex regulation of RSNA. Consequences of these alterations are that for a given level of arterial or left-sided cardiac filling pressure, afferent inhibitory input to the nucleus tractus solitarius is less and RSNA is greater in SHR than in WKY. Basal values for MAP, HR, and RSNA are greater in SHR and WKY. In comparison to Wistar rats, the RSNA of stroke-prone SHR (SHRSP) appeared to represent a simpler system with a significantly lower correlation dimension but a similar greatest Lyapunov exponent.12 These several studies suggested that removal of sinoaortic and cardiac baroreceptor regulation of RSNA might have different effects on the chaotic behavior of RSNA in SHR compared with WKY.
This purpose of the present study was to examine the dynamic and chaotic behavior of RSNA in SHR and WKY before and after complete baroreceptor (sinoaortic and cardiac baroreceptor) denervation.
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Methods |
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SHR, WKY, and Sprague-Dawley rats, aged 14 to 16 weeks, allowed free access to normal sodium rat pellet diet (Teklad) and tap water, were used for all experiments. All animal procedures were performed in compliance with the University of Iowa Policies and Guidelines Concerning the Use of Animals in Research and Teaching and the US Public Health Service Guide for the Care and Use of Laboratory Animals.
Anesthesia
Rats were anesthetized with pentobarbital 50
mg/kg IP with supplemental doses of 5 to 10 mg/kg IV at regular
intervals.
Sinoaortic and Cardiac Baroreceptor
Denervation
Sinoaortic and cardiac baroreceptor denervation was
performed by methods previously used and validated in this
laboratory.9 13
Sinoaortic baroreceptor denervation was verified by noting the absence
of decreases in RSNA after the administration of 3 µg/kg IV
phenylephrine. Cardiac (vagotomy) baroreceptor denervation
was verified by noting the absence of decreases in RSNA after the
administration of 50 µg/kg IV
2-methyl-serotonin.14
Procedures
Catheterization
Catheters were placed in the right carotid artery and
jugular vein for the measurement of pulsatile arterial
pressure (PAP), MAP, and HR and infusion of solutions (0.9% NaCl at
0.05 mL/min) or drugs, respectively.
RSNA Electrode
The left kidney was exposed through a left flank
incision via a retroperitoneal approach. With the use of a dissecting
microscope, a renal nerve branch from the aorticorenal ganglion was
isolated and carefully dissected free. The renal nerve branch was then
placed on a recording electrode. RSNA was amplified (x20 000
to 50 000) and filtered (low, 30 Hz; high, 3000 Hz) via a Grass HIP511
high-impedance probe, which led to a Grass P511 bandpass amplifier. The
amplified and filtered neurogram signal was channeled to a Tektronix
5113 oscilloscope and Grass model 7D polygraph for visual evaluation
and to an audio amplifier/loudspeaker (Grass model AM 8) for aural
evaluation. The quality of the RSNA signal was assessed by its pulse
synchronous rhythmicity; signal-to-noise ratio ranged between 3:1 and
5:1. An additional assessment was made during an injection of
phenylephrine 3 µg/kg IV; as MAP increased, RSNA
decreased. When an optimal RSNA signal was observed, the
recording electrode was fixed to the nerve preparation with a
silicone cement (Wacker Sil-Gel). The electrode cable was sutured to
the back muscles and tunneled to the back of the neck, where it was
exteriorized. The left flank incision was closed in
layers.
Experimental Protocols
Conscious Rats
Marked suppressive effects of pentobarbital
anesthesia on basal values of MAP, HR, and RSNA and, more
importantly, on PAP, HR, and RSNA spectral power have been demonstrated
in Sprague-Dawley rats.15 To
examine whether a similar effect occurs in WKY and SHR, additional WKY
and SHR were anesthetized, and surgical insertion of the
arterial and venous catheters and implantation of the RSNA
recording electrode were performed by the aforementioned
methods. Then the rats were allowed to recover from the effects of
anesthesia and surgery in their home cages overnight (15
hours) before experimental use. At that time, the arterial
and venous catheters and the RSNA recording electrode were
connected to the appropriate measuring device, and after an additional
30-minute equilibration period, a 30-minute recording period
was made in the conscious state. Thereafter, sinoaortic and cardiac
baroreceptor function was tested. Then the rat was killed, and
postmortem RSNA was recorded for 30 minutes; this value was
subtracted from all experimental values of RSNA.
Sinoaortic and Cardiac Baroreceptor Denervation
in Anesthetized Rats
SHR, WKY, and Sprague-Dawley rats were
anesthetized, and surgical insertion of the
arterial and venous catheters and implantation of the RSNA
recording electrode were performed by methods described above.
At this point, intact sinoaortic and cardiac baroreceptor function was
verified by the methods described above. Then isolation and
identification of the nerves (looped ligatures) required for sinoaortic
and cardiac baroreceptor denervation were done to allow subsequent
complete baroreceptor denervation in as little time as possible.
Sinoaortic and cardiac baroreceptor function was again tested to verify
that the isolation and identification procedure had not disrupted it.
Thereafter, 1 hour was allowed to elapse for stabilization. Then,
during continuous measurement of MAP, HR, and RSNA, a 30-minute control
period was made. Thereafter, sinoaortic and cardiac baroreceptor
denervation was performed as rapidly as possible (generally within 30
seconds). Continuous measurement of MAP, HR, and RSNA was continued
through this rapid denervation procedure and for an additional
30-minute experimental period. Then sinoaortic and cardiac baroreceptor
function was again tested. The rat was killed, and postmortem RSNA was
recorded for 30 minutes; this value was subtracted from all
experimental values of RSNA.
Analytical Protocols
The amplified and filtered renal neurogram was full
wave rectified and integrated (Grass 7P3 Resistance-Capacitance
Integrator, 20 ms time constant) and stored as RSNA on videotape
(Vetter 4000A PCM) along with the neurogram, PAP, and HR (Grass 7P4
Tachograph) signals for later offline analysis, as described
below.
Sympathetic Peak Detection Program
The steady state RSNA displayed positive deflections
that were proportional to the frequency discharge in the original
neurogram and generally occurred with each cardiac cycle. Individual
nerve bursts, still observable in the RSNA record, were smoothed by
subsequent filtering at 35 Hz. This smoothed RSNA was used for
analysis of synchronized renal sympathetic nerve discharge
characteristics. With the use of an analog-to-digital converter
(Laboratory-PC+) and standard data acquisition software (LabVIEW), the
steady state RSNA was sampled at 200 Hz over the identical 30-minute
periods as used above. The characteristics of RSNA were determined with
a statistically based computerized algorithm, the Sympathetic Peak
Detection
Program.16 17 18 19
The Sympathetic Peak Detection Program allows the
simultaneous determination of the amplitude (height),
duration, and periodicity (peak interval) of synchronized sympathetic
discharges or peaks. The minimum acceptable peak height was set at
>25% of the maximum peak height in the data series. Since peak height
depends on the number of active fibers, this choice indicates that a
sufficient number of fibers is active so as to generate a peak whose
height is >25% of the peak generated by the maximum number of fibers
active in the data series, ie, the maximum peak height. After the
synchronized peaks had been identified for each data series, data on
interpeak interval (ms), individual peak height (mV), MAP, and HR were
extracted.
Power Spectral Analysis and Transfer
Function
Tape-recorded signals of PAP and RSNA were
sampled continuously at 50 Hz with an analog-to-digital converter in a
Pentium IBM compatible computer (30-minute record=90 000 samples).
All signals were corrected by subtraction of the death signals. The
dynamic fluctuations in PAP and RSNA were investigated in the frequency
domain with spectral analysis
techniques.20 The time
series was divided into half-overlapping sequential blocks of 1024 data
points (20.5 seconds). Each block was subjected to linear trend removal
and cosine tapering of the first and last 60 data points before
calculation of spectral density power. For each parameter,
spectral density power was calculated as the average over the
sequential blocks for each period in each rat.
To analyze the influence of fluctuations in RSNA on
the fluctuations in PAP, the transfer function between RSNA (input
signal) and PAP (output signal) was calculated as the quotient of the
cross spectrum and the input spectrum. The value of the transfer
function represents the degree to which fluctuations in the
RSNA signal are transferred into the PAP signal, with lower values
(closer to 0) reflecting less and higher values (closer to 1)
reflecting more transfer; values >1 suggest that the RSNA fluctuations
are possibly either amplified or generated within the
cardiovascular system. The phase of the transfer
function reflects the temporal relationship between the input and
output signals in the frequency domain, ie, that
oscillations in the one signal may induce a similar
frequency oscillation in the other signal delayed in time.
The phase angle enables the determination of whether one rhythm is
preceding or following the other rhythm. A phase angle of 0° (0
radians) indicates synchrony between the 2 signals, and a phase signal
of 180° (
radians) indicates a reciprocal relationship between the
2 signals. The phase spectra were converted into time delay spectra by
dividing by the product of 2 and the respective frequency. The
coherence function yields a value that varies between 0 and 1 and is a
frequency domain estimate of a linear regression coefficient,
indicating the degree to which variance in one signal can be explained
by a linear operation on the variance in the other signal. For each
period in each rat, results from these analyses were averaged
over the sequential data blocks to reduce
variance.
Nonlinear Dynamic Analysis
Data
Each original data set consisted of approximately
11 000 to 13 000 interpeak intervals. The data sets were continuous
without artifacts. For assessment of stationarity, the original
data set was divided into 2 equal portions. The values of correlation
dimension and greatest Lyapunov exponent determined in each of these
portions and in the original data set were compared. The determinations
of correlation dimension and greatest Lyapunov exponent were made in
subsets (1024 peak intervals each) of the original data set as well as
the original data set. For the chaos detection algorithm, the original
data set was divided into 10 subsets of 1000 peak intervals each. The
original data set size of 12 000 agrees well with estimates of the
minimal number of data points necessary to identify nonlinear
structures21 22 23 24 :
102+0.4d or 10d,
where d is the dimension of the structure under
study.
Correlation Dimension
The Grassberger-Procaccia algorithm was used to
determine the correlation dimension, defined as a dimension with
noninteger
values.25 26 The
correlation dimension is an estimate of the least number of independent
variables that characterize the system (given sufficient fine-scale
resolution). With each pass through the data, a new data point is
taken, and a hyperdimension sphere of embedding dimension D and radius
r is centered on that point. The fraction of subsequent data points in
the record within that sphere [C(r)] is then calculated for
various values of r (length scale), and a plot is made of the log C(r)
versus the log r for a range of embedding dimensions. The slope of this
relationship is the correlation dimension. These slopes were plotted
against r to identify values of the correlation dimension that were
independent of both r and the embedding dimension. The correlation
dimension was calculated over a wide range of embedding dimensions
(1–15) to enable the detection of a plateau of the values of the
calculated correlation dimension with increasing values of the
embedding dimension. The time delay was determined from the first zero
of the autocorrelation
function27 28 29
or from the minimum of the time delayed mutual
information,27 28 29
which were in close agreement for all data sets. The minimal sufficient
embedding dimension was determined by the false nearest neighbor
method.27 28 29
The length scale and its upper and lower limits were kept constant for
the analysis of control and experimental original data sets as
well as the matched surrogate data sets.
Lyapunov Exponent
The Lyapunov exponent is a measure of the exponential
rate at which nearby trajectories in phase space diverge (given
sufficient fine-scale resolution). The Lyapunov exponent, 
, is
directly related to the magnitude of chaos in the system. Periodic
processes have 
0, wherein trajectories eventually converge, while
uncorrelated random data (ie, noise) have =
. Chaotic systems have
0<<, indicating that the trajectories diverge; ie,
insignificant differences in the initial conditions become significant
over time, which is a defining feature of chaos. The greatest Lyapunov
exponent was estimated by the fixed evolution time program of Wolf et
al30 and the algorithm of
Kantz27 28 29
(lyap_k program27 ) over the
ranges of embedding dimensions similar to those used for determination
of correlation dimension. The length scale and its upper and lower
limits were kept constant for the analysis of control and
experimental original data sets as well as the matched surrogate data
sets.
Chaos Detection Algorithm
This algorithm detects nonlinear determinism in a
time series by iteratively generating a family of polynomial
autoregressive models. The null hypothesis (ie, that the time series is
stochastic with linear dynamics) is rejected if there is at least one
nonlinear model that provides a significantly better fit to the data in
a parsimonious manner than linear autoregressive models of all dynamic
orders. The statistical test is highly robust and sensitive, in that it
is resistant to noise contamination and is applicable to short
time series (<1000 data points). The technique provides a highly
specific test for deterministic chaos in that the null hypothesis is
not readily rejected in the presence of random noise unless the
underlying system is chaotic. The level of noise corruption that can be
tolerated is directly related to the magnitude of the greatest positive
Lyapunov exponent, a measure of the degree of chaos in the underlying
noise-free data. The best linear and nonlinear models are obtained for
both the original and the surrogate data series. This is defined as the
model that minimizes the cost function,
C(p)=loge
(p)+p/N, where (p) is the
residual error, p is the number of polynomial terms, and N is the
length of the time series. Chaos is established when the best nonlinear
model from the original data series is significantly more predictive
than both the best linear model from the original data series and the
best linear and nonlinear models obtained from the surrogate data
series. This is determined by statistical comparison of the residual
errors for the models using the F-ratio test at the 1% significance
level. The algorithm was applied to each of the 1000 data point subsets
of the original data set, and the frequency of linear and nonlinear
model selection was tabulated.
Surrogate Data
Iterative fast Fourier transform surrogate data
sets31 32 were
generated27 28 29 31 32
(surrogates program27 ) with
the use of a subsequence of the original data set with negligible end
point mismatch and minimal loss of data (end-to-end
program27 ). The surrogate
data sets have the same Fourier amplitudes and distribution of values.
The linear properties (ie, mean, SD, power spectra, autocorrelation
function) of the surrogate data sets are identical to those of the
original data set. The null hypothesis being tested is that the
original data set arises from a stationary, possibly rescaled, linear
gaussian random (stochastic) process. As a measure of nonlinearity, a
nonlinear prediction error statistic (predict
program27 ) was used with
similar parameters of embedding dimension, time delay, and
radius for both the original and surrogate data sets. For a 1-sided
test to detect a significantly smaller error with a residual
probability 
of a false rejection, corresponding to a level of
significance of 100% (1-), then 1/1- surrogate data sets are
required; for =0.99, 100 surrogate data sets were constructed. The
assessment of nonlinearity is important because, while deterministic
chaos implies nonlinearity, the reverse is not true; thus, not all
nonlinear systems are chaotic.
Computer Software
Computer software programs were obtained from the
following sources: FFT,20 U.
Wittmann, University of Heidelberg (Germany); Chaos Data
Analyzer (professional
version),33 American
Institute of Physics, Physics Academic Software, North Carolina State
University, Raleigh; FET30
(a program that quantifies chaos in a time series); Chaos Detection
Algorithm34 (algorithm for
detection of nonlinear dynamics in short, noisy time series); and Time
Series Analysis
(TISEAN).27 28 29 32
Statistical Analysis
Statistical analyses were conducted with
ANOVA and Scheffé’s test for pairwise comparisons among means and
t test for comparison between
groups35 ; statistical
significance was taken at a value of
P<0.05. Statistical comparison
of the residual errors for the models in the Chaos Detection Algorithm
was performed with the F-ratio test, with statistical significance
taken at a value of P<0.01.
Data in text, tables, and figures are
mean±SE.
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Results |
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Conscious WKY and SHR
Compared with conscious WKY (n=6), conscious SHR (n=6) had higher MAP (153±4 versus 111±5 mm Hg), HR (400±10 versus 365±9 bpm), and RSNA (45.3±4.9 versus 30.1±3.1 mV/s · s) (all P<0.05). As seen in Figure 1, PAP (top) and RSNA spectral power (middle) were greater in SHR than in WKY. In SHR, both PAP and RSNA spectral power showed distinct peaks near 0.4 Hz, while PAP and RSNA spectral power in WKY at the same frequency were nearly 10-fold lower. Near 0.4 Hz frequency, coherence (Figure 1, bottom) was 0.932±0.031 in SHR (0.34 Hz) and 0.859±0.021 in WKY (0.39 Hz). Thus, as previously identified in conscious Sprague-Dawley rat,15 there is also a close coupling between RSNA and PAP at 0.4 Hz.
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Tests of Sinoaortic and Cardiac Baroreflex
Function
The results of serial testing of sinoaortic and cardiac
baroreflex function
(Table 1) showed that procedures used for isolation and
identification of the nerves required for sinoaortic and cardiac
baroreceptor denervation did not affect the renal
sympathoinhibitory responses to either
phenylephrine (sinoaortic) or
2-methyl-serotonin (cardiac), indicating preserved
sinoaortic and cardiac baroreceptor function. However, when sinoaortic
and cardiac baroreceptors were denervated, the renal
sympathoinhibitory responses to either
phenylephrine (sinoaortic) or
2-methyl-serotonin (cardiac) were abolished. These results
indicated effective sinoaortic and cardiac baroreceptor
denervation.
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Steady State Data
In the control period
(Table 2;
Figure 2A through 2D, top), basal values for MAP, HR, RSNA,
peak frequency, and peak amplitude were similar in Sprague-Dawley rats
and WKY but, except for peak frequency, were lower than those in SHR.
In all 3 strains, sinoaortic and cardiac baroreceptor denervation
increased MAP, HR, RSNA, and peak amplitude, while peak frequency was
unaffected. In the sinoaortic and cardiac baroreceptor denervation
period, values for MAP, HR, RSNA, and peak amplitude were greater in
SHR than in Sprague-Dawley rats and WKY, which were
similar.
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When we used the absolute value of the standard deviation (SDxxx) as a measure of variability (Figure 2A through 2D, bottom), in all 3 strains sinoaortic and cardiac baroreceptor denervation increased the variability of MAP and decreased the variability of HR, RSNA, and peak amplitude, while the variability of peak frequency was unaffected (not shown).
Power Spectral Analysis and Transfer
Function
Sprague-Dawley Rats
In the control period
(Figure 3, top), RSNA spectral power was greater than PAP
spectral power. The PAP spectra showed low frequency power at <0.1 Hz
and a broad respiratory oscillation near 1.0 Hz. The RSNA
spectra showed multiple oscillations at frequencies <1.0
Hz and a distinct respiratory oscillation near 1.0 Hz.
Strong oscillations in the vicinity of 0.4 Hz were not
seen. When we used RSNA as the input signal and PAP as the output
signal
(Figure 4, left), coherence was 0.5 to 0.8 over the
entire frequency range, except for lower values at 0.7 and >1.1 Hz;
the largest value was at the respiratory oscillation
frequency near 1.0 Hz. The transfer gain showed higher values at 0.2,
0.7, and 0.9 Hz (clearly less than the respiratory
oscillation frequency near 1.0 Hz). The phase angle was
variably positive and negative, with prominent negative values at 0.15,
0.6, and >1.0 Hz and prominent positive values at 0.8, 1.0 (the
respiratory oscillation frequency), and 1.35 Hz. At
frequencies <0.6 Hz, time delays were small and variable. At the
respiratory oscillation frequency near 1.0 Hz, the change
in PAP preceded the change in RSNA by 220 ms.
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After sinoaortic and cardiac baroreceptor denervation (Figure 3, bottom), spectral power increased more in RSNA than in PAP. The PAP spectra showed low frequency power at <0.1 Hz, a small oscillation near 0.4 Hz, and a more narrow respiratory oscillation near 1.15 Hz. The RSNA spectra again showed multiple oscillations, with a more prominent oscillation near 0.4 Hz (same frequency as the oscillation in the PAP spectra) that had a coherence of 0.7. Transfer gain was slightly less than during control. Phase angle was positive over the entire frequency range, indicating that changes in PAP preceded changes in RSNA, with the maximum time delay of 140 ms occurring at 1.15 Hz.
Wistar-Kyoto Rats
In all respects, the data on WKY were not significantly
different from those on Sprague-Dawley rats (not
shown).
Spontaneously Hypertensive Rats
In the control period
(Figure 5, top), RSNA power was greater than PAP power except
at frequencies <0.1 Hz. The PAP spectra showed low frequency power at
<0.1 Hz and a broad respiratory oscillation near 1.2 Hz.
The RSNA spectra showed multiple oscillations at
frequencies <1.0 Hz and a distinct respiratory oscillation
near 1.2 Hz. Strong oscillations in the vicinity of 0.4 Hz
were not seen. With the use of RSNA as the input signal and PAP as the
output signal
(Figure 4, right), coherence was 0.5 to 0.8 over the entire
frequency range, except for lower values at 0.7 and 0.9 Hz; the largest
value was at the respiratory oscillation frequency near 1.2
Hz. The transfer gain showed higher values at 0.34, 0.44, and near 1.2
Hz (respiratory oscillation frequency). The phase angle was
variably negative and positive. At frequencies >0.4 Hz, time delays
were small and variable.
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After sinoaortic and cardiac baroreceptor denervation (Figure 5, bottom), power increased more in RSNA than in PAP. The PAP spectra showed low frequency power at <0.1 Hz and a respiratory oscillation near 1.15 Hz. The RSNA spectra again showed multiple oscillations, with a respiratory oscillation near 1.15 Hz. Strong oscillations in the vicinity of 0.4 Hz were not seen. Coherence was 0.5 to 0.8 over the entire frequency range, with the highest value at the respiratory oscillation frequency near 1.15 Hz. Transfer gain was slightly less than during control, with a larger value near the respiratory oscillation frequency. Phase angle was variably positive and negative over the entire frequency range. At frequencies >0.4 Hz, time delays were small and variable.
Nonlinear Dynamic Analysis
As previously
reported,7 the values for the
greatest Lyapunov exponent determined by the algorithm of Wolf (FET),
the algorithm of Kantz, and Chaos Data Analyzer were within 8%
of each other with the use of 2 benchmark data series. In addition, the
Chaos Detection Algorithm also showed a significant nonlinear component
in both benchmark data series.
The values of correlation dimension and greatest Lyapunov exponent calculated for each half of the original record agreed with each other and with the values calculated from the entire original record to within 5%. This was the case for each rat strain before and after sinoaortic and cardiac baroreceptor denervation.
Figure 6 (top) shows the relation between the logarithm of
the correlation sums, C(r), and the logarithm of the radius, r, for a
Sprague-Dawley rat after sinoaortic and cardiac baroreceptor
denervation. Each curve signifies a different embedding dimension
(from 6 to 15) whereby the correlation dimension, D(r), is given
by the slope of the linear segment in these curves:
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It can be seen that the curves contain a linear segment
in which the slope converges to a constant value as the embedding
dimension increases.
Figure 6 (bottom) shows the relation between the correlation
dimension, D(r), and r for the same range of embedding dimensions. A
plateau (ie, scaling range) is identified around a value of r1e+1,
where the correlation dimension, D(r), is independent of changes in
either the embedding dimension or r. For values of r greater or less
than this scaling range, the correlation dimension, D(r), shows
dependence on both the embedding dimension and r. In the vicinity of
r1e+1, D(r)=2.09±0.07 (averaged over the 10 embedding
dimensions). The nonlinear prediction error for the original data set
was 1.9104, while those for the 100 surrogate data sets ranged from
2.0943 to 2.1339, so that the null hypothesis that the original data
set arises from a stationary, possibly rescaled, linear gaussian random
process was rejected at the 99% level of significance. The correlation
dimension for the original data set, 2.09, was outside the range of
correlation dimensions for the 100 surrogate data sets, 3.21 to 5.68.
The greatest Lyapunov exponent for the original data set, 0.065, was
outside the range of greatest Lyapunov exponents for the 100 surrogate
data sets, 0.074 to 0.099.
Figure 7 (top) shows the correlation dimension calculated as a function of embedding dimension before and after sinoaortic and cardiac baroreceptor denervation for Sprague-Dawley rats, WKY, and SHR. The mean correlation dimension approached a plateau (ie, converged) at increasing values of the embedding dimension. The mean correlation dimensions over the plateau range of embedding dimension of 10 to 15 for Sprague-Dawley rats, WKY, and SHR before and after sinoaortic and cardiac baroreceptor denervation are shown in Table 3. Before sinoaortic and cardiac baroreceptor denervation, correlation dimension was similar in Sprague-Dawley rats, WKY, and SHR. After sinoaortic and cardiac baroreceptor denervation, correlation dimension decreased by 11% in Sprague-Dawley rats and by 4% in WKY and was unchanged in SHR. Figure 7 (bottom) shows the greatest Lyapunov exponents before and after sinoaortic and cardiac denervation for each of the Sprague-Dawley rats, WKY, and SHR; mean data are presented in Table 3. Before sinoaortic and cardiac denervation, the greatest Lyapunov exponent was similar in Sprague-Dawley rats and WKY but significantly less in SHR. After sinoaortic and cardiac denervation, the greatest Lyapunov exponent decreased similarly in Sprague-Dawley rats (35%) and WKY (31%) and significantly less in SHR (14%).
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In each of the Sprague-Dawley rats, WKY, and SHR, both before and after sinoaortic and cardiac baroreceptor denervation, the values of the nonlinear prediction error, the correlation dimension, and the greatest Lyapunov exponent for the original data set were compared with those values calculated for 100 surrogate data sets. In each case, the values for the original data set were outside the range of values obtained for the surrogate data sets. In addition, the plots of correlation dimension versus embedding dimension for the surrogate data sets, in comparison with the original data set, did not exhibit plateaus (ie, convergence).
In each of the Sprague-Dawley rats, WKY, and SHR, both before and after sinoaortic and cardiac baroreceptor denervation, the frequency of linear versus nonlinear model detection by the chaos detection algorithm was calculated for the 1000 point data subsets. As shown in Table 4, during the control period, the nonlinear model predominated in Sprague-Dawley rats and WKY, with a slightly lower level in SHR. During the sinoaortic and cardiac baroreceptor denervation period, the linear and nonlinear models were equal in Sprague-Dawley rats and WKY, while the linear model predominated in SHR.
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Conscious Versus Anesthetized Rats During Control State
The design of these experiments permitted an analysis of the immediate responses of MAP, HR, and RSNA to sinoaortic and cardiac baroreceptor denervation, with each rat serving as its own control. This design minimized the variability between rats, which is generally larger than the variability within each rat. This is of special importance for RSNA, wherein it is not possible to keep the number of renal sympathetic nerve fibers on the recording electrode and their contact with the recording electrode constant between rats. This design required the use of anesthesia, which may have multiple effects on cardiovascular reflex behavior. However, given the time limit for reliable RSNA recordings in conscious rats, avoiding the effects of anesthesia by using conscious rats resulted in the comparison of 2 different groups of rats: intact versus sinoaortic and cardiac baroreceptor denervated. In this case, there was a greater degree of between-rat variability, albeit without the potentially confounding aspects of anesthesia.
Because an aim of the study was to examine the immediate
response to sinoaortic and cardiac baroreceptor denervation, the
experiments were conducted under anesthesia to permit a
rapid denervation procedure with continuous recording. From
previous studies in Sprague-Dawley
rats,15 it was known that
pentobarbital anesthesia (as used herein) had substantial
but different effects on basal values of MAP, HR, and RSNA and the
spectral power of PAP, HR, and RSNA. Anesthesia, while not
affecting MAP, decreased HR by 8% and RSNA by 15%. However,
anesthesia markedly decreased maximum spectral power of PAP
(-90%), HR (-96%), and RSNA (-66%), while not affecting the
frequency at which the maximum spectral power occurred.
Anesthesia did not affect the maximum coherence between PAP
and RSNA or the frequency at which this maximum coherence occurred. In
these conscious SD, the maximum peak spectral power for PAP was at 0.08
Hz, while that for RSNA was at 0.4 Hz. However, there was an 70%
smaller peak in spectral power for PAP that was also located at 0.4 Hz.
The maximum coherence between PAP and RSNA of 0.9 occurred at 0.4
Hz.
To examine whether the effects of anesthesia on basal values of MAP, HR, and RSNA and on the spectral power of PAP, HR, and RSNA in WKY and SHR were different from those previously reported in Sprague-Dawley rats,15 groups of conscious WKY and SHR were studied so that their results could also be compared with those from anesthetized WKY and SHR. Conscious WKY and SHR had similar basal MAP and HR but higher basal RSNA than anesthetized WKY and SHR. Power spectral analysis in conscious WKY and SHR showed spectral power in both PAP and RSNA at 0.4 Hz that was stronger in SHR than in WKY; there was strong coherence between PAP and RSNA spectral power at 0.4 Hz in both WKY and SHR. These results are similar to those in conscious Sprague-Dawley rats15 and indicate a coupling between RSNA and PAP at 0.4 Hz.
However, during the control period in anesthetized SHR, both PAP and RSNA spectral power were markedly decreased compared with that in conscious SHR; this was the case for WKY as well (data not shown). Anesthetized Sprague-Dawley rats and WKY did not display prominent PAP or RSNA spectral power at 0.4 Hz, while SHR showed RSNA but not PAP spectral power at 0.4 Hz. Coherence values were relatively low at 0.4 Hz (0.617±0.031 in Sprague-Dawley rats, 0.512±0.029 in WKY, and 0.306±0.021 in SHR). Thus, the suppressive effect of anesthesia on PAP and RSNA spectral power in WKY and SHR was similar to that previously reported for Sprague-Dawley rats.15
Immediate Effect of Sinoaortic and Cardiac
Baroreceptor Denervation
Absolute Values and Variability
Immediately after sinoaortic and cardiac baroreceptor
denervation, MAP, HR, RSNA, and the peak amplitude of synchronized RSNA
were increased in Sprague-Dawley rats, WKY, and SHR; the peak
frequency of synchronized RSNA was unchanged. In synchronized RSNA,
peak amplitude reflects the number of active renal nerve fibers, and
peak frequency reflects the activity of central rhythm oscillators,
which may be influenced by afferent input from peripheral
reflex mechanisms. Thus, these results indicate that the immediate
response of synchronized RSNA to sinoaortic and cardiac baroreceptor
denervation involves an increase in the number of active renal nerve
fibers rather than an increase in the frequency of central rhythm
oscillators. Since the number of fibers on the recording
electrode is unchanged, this indicates that there is recruitment of
previously silent fibers to begin firing. Since the renal nerves are a
heterogeneous population with respect to effects on various
renal
functions,36 37 38 39 40
this makes possible the engagement of functionally specific renal
sympathetic nerve fibers after sinoaortic and cardiac baroreceptor
denervation. Variability, as reflected by SDxxx,
was increased in MAP and HR but decreased in RSNA and peak
amplitude.
In prior studies comparing groups of conscious Sprague-Dawley rats,1 those studied 1 day after sinoaortic baroreceptor denervation showed increases in MAP, HR, and RSNA. As a measure of variability, sinoaortic baroreceptor denervation increased SDMAP but decreased SDHR and SDRSNA. In the group studied 14 days after sinoaortic baroreceptor denervation, MAP, HR, and RSNA had returned to normal, as had SDHR and SDRSNA, while the SDMAP remained increased. At both 1 and 14 days after sinoaortic baroreceptor denervation, the correlations between MAP and RSNA were negative (ie, RSNA inversely related to MAP) in 30% to 40% of the cardiac cycles (compared with 90% in control rats) and were positive (ie, RSNA directly related to MAP) in 30% of the cardiac cycles (compared with 0% in control rats).
Frequency Domain Analysis
In prior studies comparing groups of conscious
Sprague-Dawley rats, the magnitude of PAP spectral power in the 0.3- to
0.5-Hz frequency range was reduced when examined at both
741 (-50%) and
1442 (-75%) days after
sinoaortic baroreceptor denervation. The effect of sinoaortic
baroreceptor denervation on RSNA spectral power was not reported in
those studies.
Herein, under anesthesia, before sinoaortic and
baroreceptor denervation, prominent PAP spectral power at 0.4 Hz was
not identified in Sprague-Dawley rats, WKY, or SHR, while RSNA spectral
power at 0.4 Hz was greater in SHR than either Sprague-Dawley rats or
WKY. With the large increase in RSNA after sinoaortic and cardiac
baroreceptor denervation in Sprague-Dawley rats, WKY, and SHR,
prominent RSNA spectral power was identified at 0.4 to 0.5 Hz, which
showed high coherence (0.7) with smaller oscillations in
PAP spectral power at the same frequency.
It appears that the absence of prominent PAP or RSNA spectral power at 0.4 Hz during the control period likely reflects the marked suppressive effect of pentobarbital anesthesia on both PAP and RSNA spectral power. However, with the increase in MAP and RSNA after sinoaortic and cardiac baroreceptor denervation, these suppressive effects of pentobarbital anesthesia were partially offset by the increases in RSNA spectral power. Under these conditions, prominent RSNA spectral power and residual PAP spectral power were seen at 0.4 to 0.5 Hz with increased (compared with control period) coherence values of 0.71±0.02 in Sprague-Dawley rats, 0.70±0.03 in WKY, and 0.71±0.02 in SHR.
When the results from conscious and anesthetized studies ranging from immediate (seconds) to longer-duration (1 to 2 weeks) responses to sinoaortic and/or cardiac baroreceptor denervation in normotensive and hypertensive rats are synthesized, it appears that there are immediate increases in MAP, HR, and RSNA that are accompanied by increased variability in MAP but decreased variability in HR and RSNA. These effects are sustained for at least 1 day, but by 14 days the only residual alteration is an increase in MAP variability. Despite different baseline levels of MAP, HR, and RSNA between Sprague-Dawley rats, WKY, and SHR, the immediate responses to sinoaortic and cardiac baroreceptor denervation are qualitatively similar. Power spectral analysis shows a strong coupling between RSNA and PAP near 0.4 Hz, which is qualitatively similar between normotensive (Sprague-Dawley rats and WKY) and hypertensive rats; it is readily detected in the conscious state but is substantially depressed by anesthesia and appears to be related to sinoaortic (and possibly cardiac) baroreceptor-dependent mechanisms.
Chaos Analysis
Interruption of afferent input from the sinoaortic and
cardiac baroreceptors resulted in a decrease in the correlation
dimension and the greatest Lyapunov exponent of the nonlinear dynamic
characteristics of synchronized RSNA that was different among
Sprague-Dawley rats, WKY, and SHR. In Sprague-Dawley rats, the
immediate responses to sinoaortic and cardiac baroreceptor denervation
were qualitatively similar to those seen in previous
studies7 in which 60 minutes
was allowed to elapse between the completion of the denervation
procedure and the collection of the experimental data. However, there
are important quantitative differences in that the decrease in the
correlation dimension was less in the present study (immediate,
2.42 versus 2.16, -11%) than in the previous study (60 minutes, 2.65
versus 1.64, -38%), while the situation was opposite for the
greatest Lyapunov exponent (immediate, 0.199 versus 0.130, -35%; 60
minutes, 0.201 versus 0.177, -12%). With respect to central nervous
system control mechanisms, it seems likely that multiple adaptive and
compensatory adjustments occur in the first 60 minutes after sinoaortic
and cardiac baroreceptor denervation.
Compared with Sprague-Dawley rats, the immediate effect of sinoaortic and cardiac baroreceptor denervation in normotensive WKY was a lesser decrease in the correlation dimension with a similar decrease in the greatest Lyapunov exponent, whereas SHR showed no change in the correlation dimension and a lesser decrease in the greatest Lyapunov exponent. The chaotic behavior of synchronized RSNA discharge in normotensive Wistar rats and SHRSP has been examined with the use of another reflex stimulus, brachial nerve stimulation (simulate somatic afferent stimulation).12 Somatic afferent stimulation decreased both correlation dimension and greatest Lyapunov exponent in Wistar rats but did not affect these measurements in SHRSP. These studies concur in the view that, in the SHR genetic model of hypertension, the correlation dimension and the greatest Lyapunov exponent are unaffected by 2 different maneuvers that alter afferent neural input to the brain. Thus, the agreement of these studies reinforces the notion that the normal control mechanisms within the brain that determine the pattern of RSNA are different in SHR (and SHRSP) from those in WKY (and Wistar rats). It is likely that reflex alterations in central neural input have limited effects on the chaotic behavior of synchronized RSNA in SHR. Because somatic afferent stimulation involves an increase in central input of both excitatory and inhibitory signals, while sinoaortic and cardiac baroreceptor denervation involves a decrease in central input of predominantly inhibitory signals, it is speculated that the central neural mechanisms governing the chaotic behavior of synchronized RSNA in SHR might be somewhat rigid and inflexible, ie, uninfluenced by bidirectional afferent inputs from a variety of different peripheral receptor stations. This may be of potential significance in terms of the generation and maintenance of the increased level of single fiber renal sympathetic nerve activity known to be present in SHR.43
In summary, conscious WKY and SHR, like conscious Sprague-Dawley rats, exhibit a strong coupling between arterial pressure and RSNA at 0.4 Hz. Under anesthesia, the immediate response of Sprague-Dawley rats, WKY, and SHR to sinoaortic and cardiac baroreceptor denervation involves increases in MAP, HR, and RSNA, with the increase in RSNA derived from an increase in peak height (but not peak frequency) of synchronized RSNA discharge. There is increased variability in MAP but decreased variability in HR, RSNA, and peak height. Before sinoaortic and cardiac baroreceptor denervation, the suppressive effect of anesthesia on PAP and RNSA spectral power obscures the 0.4-Hz coupling that is readily observed in the conscious state. After sinoaortic and cardiac baroreceptor denervation, the overall increases in MAP and RSNA, and especially RSNA spectral power, enable the 0.4-Hz coupling to be observed even under anesthesia. In Sprague-Dawley rats and WKY, sinoaortic and cardiac baroreceptor denervations decrease 2 indices of chaotic behavior of synchronized RSNA discharge, the correlation dimension and the greatest Lyapunov. In contrast, in SHR these indices were unchanged (correlation dimension) or decreased to a lesser extent (greatest Lyapunov exponent), indicating that the central neural mechanisms that regulate RSNA in response to alterations in cardiovascular reflex inputs are different in SHR from those in Sprague-Dawley rats and WKY.
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Acknowledgments |
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This work was supported by National Institutes of Health grants DK-15843, DK-52617, and HL-55006 and by a Department of Veterans Affairs Merit Review Award.
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Footnotes |
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Reprint requests to Gerald F. DiBona, MD, Department of Internal Medicine, University of Iowa College of Medicine, 200 Hawkins Dr, Iowa City, IA 52242.
Received June 30, 2000; first decision August 23, 2000; accepted September 19, 2000.
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