Arterial baroreflex and spontaneously
dynamics in normotensive hypertensive rats
SEIKI HARADA, TSUTOMU IMAIZUMI, SHIN-ICHI YOSHITAKA HIROOKA, KENJI SUNAGAWA, AND Research Institute of Angiocardiology and Cardiovascular Kyushu University, Fukuoka 812, Japan Harada, Seiki, Tsutomu Imaizumi, Shin-ichi Ando, Yoshitaka Hirooka, Kenji Sunagawa, and Akira Takeshita. Arterial baroreflex dynamics in normotensive and spontaneously hypertensive rats. Am. J. Physiol. 263 (Regulatory Integrative Comp. Physiol. 32): R524-R528, 1992.-To investigate dynamic or frequency-dependent characteristics of arterial baroreflex control of efferent sympathetic nerve activity in spontaneously hypertensive rats (SHR) and Wistar-Kyoto rats (WKY), we assessed the transfer function from aortic pressure (AP) to renal sympathetic nerve activity (RSNA) using a “white-noise technique.” In pentobarbital sodium-anesthetized rats, we recorded RSNA as the output, while AP was randomly perturbed to impose input pressure changes with broad frequencies. We calculated the transfer function from AP to RSNA over the frequency range of 0.01-5 Hz through the spectral analysis of the input and output. The results indicated that the gain, phase shift, and coherence of the transfer function for SHR and for WKY were similar and statistically indistinguishable. The gain was relatively constant below 0.05 Hz but increased steadily by fivefold as frequency increased in the frequency range of 0.05-0.8 Hz. The phase was out of phase where coherence was high. The coherence was high (>0.5) in the frequency range of 0.04-0.8 and 1.00-1.03 Hz but was low in other frequencies. These results suggest that dynamic or frequency-dependent characteristics of arterial baroreflex control of RSNA were not altered in SHR as compared with WKY. sympathetic nerve activity; tics; hypertension; transfer Wistar-Kyoto rats
frequency-dependent function; white-noise
characteristechnique;
that the gain of arterial baroreflex control of heart rate in spontaneously hypertensive rats (SHR) is attenuated as compared with that in normotensive Wistar-Kyoto rats (WKY) (17, 18, 21). In contrast, conflicting results have been reported as to the gain of arterial baroreflex control of sympathetic nerve activity (SNA) in SHR. It has been reported that the gain of arterial baroreflex control of SNA is increased (17), equivalent (18, 20, 21), or decreased (7, 13, 14) as compared with that in WKY. Previous studies examined the gain of arterial baroreflex control of SNA under particular sets of arterial pressure (AP) change and assessedstatic characteristics of the arterial baroreflex mechanism in SHR (7, 13, 14, 17, 18, 20, 21). Dynamic or frequency-dependent characteristics of arterial baroreflex control of SNA in SHR and WKY are not completely known. Furthermore, in a conventional method, the extent to which changes in SNA can be attributable to changes in AP is not known. SNA is regulated by higher central nervous system as well as the baroreflex mechanism (12, 16, 27). Thus it is possible that the difference in the reflex gain assessedby the conventional method between SHR and WKY, if any, might result from the difference in the influence of the central nervous system on SNA. It has been sug-
IT HAS BEEN SHOWN
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ANDO, AKIRA TAKESHITA Clinic, Faculty of Medicine,
gested that control of SNA by the central nervous system is altered in SHR (6, 10, 13-15, 18, 20, 22, 25). Recently, we have reported the usefulness of the white-noise technique to identify dynamic transduction properties of aortic baroreceptors (24). Using the whitenoise technique, we can identify the unbiased linear properties in a nonlinear system and can determine dynamic properties of the arterial baroreflex system. The purpose of this study was to investigate dynamic characteristics of arterial baroreflex control of SNA in SHR and WKY by use of the white-noise technique. METHODS Animal
Preparation
Seven male 4- to 6-mo-old WKY (330-370 g) and seven agematched SHR (280-340 g) were used in this study. The rats were anesthetized with pentobarbital sodium (40 mg/kg ip), and supplementary doses (5 mg/kg iv) of the anesthetic were administered when necessary. The trachea was cannulated so as not to obstruct the airway. A polyethylene catheter (PE-50) was introduced into the aortic arch through the right carotid artery. The tip of the catheter was carefully positioned at the middle portion of the aortic arch. The proper position of the catheter was confirmed by palpation at the end of study in each rat. The arterial catheter was connected to a pressure transducer (Toyo Boldwin, TMI, Tokyo, Japan) for recording of AP. After the left flank was opened, the left renal nerve was identified, separated free, and cut under a dissecting microscope (OPMI 99, Zeiss). Multifiber nerve impulses were recorded by bipolar electrodes (silver/silver chloride) and preamplified with a high-gain difference amplifier (MEG-1100, Nihon-Kohden, Tokyo, Japan). A 2-Fr Fogarty catheter was introduced from the right femoral artery and positioned in the descending thoracic aorta. To perturb AP, the balloon of the catheter was inflated. Instantaneous AP and renal SNA (RSNA) were recorded simultaneously on a magnetic tape recorder using pulse code modulation (RD-IOlT, TEAC, Tokyo, Japan) for subsequent analysis. Data were also recorded on an eight-channel optical hardcopy recorder (8Ml4, San-ei, Tokyo, Japan) for monitoring the experimental conditions. Protocol Because AP and RSNA are interrelated through a feedback mechanism, external perturbation of AP with sufficient power was prerequisite to accurately estimate the transfer function by the frequency domain technique (see the DISCUSSION). To randomly perturb AP, we intermittently inflated and deflated the balloon in the descending aorta. Mean APs at a control condition was 123.3 t 6.2 (SE) mmHg for WKY and 184.1 t 5.5 mmHg for SHR (P < 0.001). AP varied, on the average, from 73.3 t 7.9 to 179.7 t 10.4 mmHg (5th and 95th percentile, respectively) in WKY and from 112.8 rfr 12.0 to 255.5 of: 8.5 mmHg in SHR. The inflation and deflation of the balloon was manually controlled according to a computer-generated random binary sequence (19). At every 1 s, inflation vs. deflation of the
0 1992 the American
Physiological
Society
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TRANSFER
FUNCTION
ANALYSIS
balloon was randomly determined. Probability for n-s sustained inflation would be l/Zn. Actual duration of inflation as well as deflation varied between 1 and 6 s. This guaranteed that the amplitude spectral density of AP was nearly flat up to 0.5 Hz if AP changes were made by step methods. We recorded instantaneous AP and RSNA for 20 min. If mean AP (average over 100 s) before and after perturbation of AP differed by >lO% during the experiment, the data were discarded. Data Analysis Envelope detection of nerve activity. The nerve impulse in a single fiber could be exactly quantified by firing frequency (i.e., counting the number of impulses per unit time). If the nerve impulse was obtained from multiple fibers, however, the firing frequency would not necessarily represent the overall nerve activity because of possible simultaneous firing of various fibers. To overcome this problem we measured the envelope of nerve impulse recording (24). We home-wired a specially designed circuit by which nerve impulse was fully rectified and smoothed (3). The corner frequency of the low-pass filter for the envelope detection was selected at 30 Hz (-3 dB). The bandwidth of the envelope detection was wide enough to cover the frequency of interest, that is, up to 5 Hz. In this paper this smoothed envelope of nerve impulse train is referred as “nerve activity” and is distinguished from raw “nerve impulse.” Because the absolute voltage value of nerve activity depends on various physical recording conditions, such as positioning of the electrodes,. the size of the electrodes, and so forth, we expressed the amplitude of nerve activity in an arbitrary unit. The zero level represented nerve activity at the noise level. The loo-unit level stood for nerve activity at the control condition. Identification of the transfer function. We digitized pretaped AP and the envelope of RSNA at 100 Hz (12-bit resolution) with an analog-to-digital converter (Canopus, ADX-98, Kobe, Japan). After removing high-frequency signals using a digital filter, we averaged those signals over 10 points, which effectively reduced the Nyquist frequency to 5.0 Hz. The 20-min data were subdivided into 20 overlapping (50%) segments. The length of each segment was 102.4 s. After applying the Blackman-Harris window (4 terms, -92 dB) (11) to minimize spectral leakage, we Fourier-transformed AP and RSNA to obtain their spectra [AP(f) and RSNA(f), respectively] using the fast Fourier transform (FFT) (2). We obtained the cross-power spectrum between AP and RSNA by multiplying the conjugate of AP(f) to RSNA(f). Similarly, we obtained the power spectra of AP and RSNA. We then ensembled those spectra across segments to reduce spectral variance (2, 19). The transfer function was obtained by dividing the ensembled cross-power spectrum by ensembled power spectrum of AP over the frequency range of 0.01-5 Hz, with a resolution of 0.01 Hz. In this paper, H(f) is the transfer function from AP to RSNA. We also obtained the amplitude spectra of AP and RSNA by computing the square root of the power spectra of AP and RSNA, respectively. To quantify the linear dependence of RSNA on AP, we estimated coherence function [C(f)] by dividing the squared magnitude of cross-power spectrum with the power spectra of AP and RSNA. The coherence attains a value between zero and unity. The unity coherence value implies that RSNA is linearly dependent on AP. The low coherence value indicates the nonlinear relationship between RSNA and AP, or the existence of input from other systems (e.g., higher central nervous systems) or the existence of contaminating noise. Statistical analysis. Unpaired Student’s t test was used to compare the mean AP of WKY vs. SHR at a control condition. Two-way analysis of variance was used to compare the gain of transfer function of WKY vs. SHR in the frequency range of 0.04-0.8 and 1.00-1.03 Hz. P < 0.05 was considered significant. All data are expressed as means rfr SE.
OF ARTERIAL
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RESULTS
Figure 1 shows actual recordings of AP and RSNA during random perturbation of AP. Figure 2 denotes the amplitude spectra of AP and RSNA during random perturbation of AP. As shown in Fig. 1, we were unable to step change AP. The time course of the AP change was rather exponential. Because of this distortion of AP, the amplitude spectral density of AP was not exactly flat up to 0.5 Hz, but it was nearly flat (i.e., within k3 dB) up to 0.4 Hz. The averaged H(f) and C(f) are shown in Fig. 3. As will be discussed, we estimated the H(f) for WKY [H,(f)] and that for SHR [H,(f)] in the frequency range of 0.01-0.8 Hz but compared them in the frequency range of 0.04-0.8 and 1.00-1.03 Hz. The averaged gain (moduli), phase shift, and coherence of transfer function over the frequency range examined were similar between SHR and WKY. In both SHR and WKY, the gain remained relatively constant below 0.05 Hz. In the frequency range of 0.05-0.8 Hz, the gain increased steadily by fivefold (P < 0.01). The gain in the investigated frequency range did not differ between SHR and WKY. The coherence was >0.5 in the frequency range of 0.04-0.8 and 1.00-1.03 Hz but was ~0.5 in other frequencies in both SHR and WKY. Coherence at each frequency did not differ between SHR and WKY. The phase was nearly out of phase in the frequency range with high coherence and did not differ between SHR and WKY. DISCUSSION
This study investigated transfer function of arterial baroreflex control of efferent SNA, using AP as the input and RSNA as the output, in SHR and WKY. Coherence was reasonably high (>0.5) in the frequency range of 0.04-0.8 and 1.00-1.03 Hz. The gain, phase shift, and coherence of transfer function in these frequency ranges were quite similar between SHR and WKY, which suggests that arterial baroreflex control of RSNA in response to AP changes is not altered in SHR as compared with that in WKY. However, baseline AP was higher in SHR than in WKY. Thus an operating pressure was higher in SHR than in WKY. Alterations in arterial baroreflex function in hypertension have been studied extensively (1, 4, 7-9, 13, 14, 17, 1821, 26). It has been consistently shown that the reflex gain of heart rate control is reduced in humans and animals with various forms of hypertension (1,4,8,9,17, 18, 21,26). In contrast, conflicting results have been reported as to the reflex gain of SNA control in hypertension. In
ILL Fig. 1. Original recordings of arterial thetic nerve activitv (RSNA) during
IOZC pressure (AP) and renal symparandom x>erturbation of AP.
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R526
TRANSFER
FUNCTION
ANALYSIS
OF ARTERIAL
BAROREFLEX
SHR 1
n
a Q) m 3 .m Q E a
01. 0.01
Fig. 2. Amplitude spectra of AP (top) and RSNA (bottom) during random perturbation of AP [pooled data; n = 7 for WKY (left), n = 7 for SHR (right)]. Note that power and frequency axes are logarithmically scaled. Solid lines represent mean and the 2 broken lines represent GE.
1
a z(0) 0.1 a
L
L
1
0.01
1
1
I~11111
11111111
0.1
I
1
IllI
I
1
I1111111
0.01
1
I11111~~
l
0.1
I11
1
Frequency particular, the decreased (7, 13, 14), equivalent (18, 20, 2l), or increased (17) gain of arterial baroreflex control of SNA has been reported in SHR as compared with that in WKY. In those previous studies, experimental conditions varied markedly so that comparisons of the results among those studies are not possible. Some studies were done in conscious animals (14, 17, 18, 21) and others under anesthesia (7, 13, 14, 20). Various methods were used to change AP, which included bolus injections or constant infusions of vasoactive drugs (17, 18, 21)) aortic constriction (13,14), hemorrhage (14), or electrical stimulation of hypothalamus (20). One study examined responses of
WKY
SNA to electrical stimulation of afferent aortic nerves in decerebrate rats (7). It should be noted that those previous studies have assessed ,the gain of reflex control of SNA by obtaining the slope of the regression line relating changes in SNA to those in AP under particular sets of AP changes. Thus they evaluated static characteristics of the arterial baroreflex mechanism in SHR. Dynamic or frequencydependent characteristics of the arterial baroreflex control of SNA have not been assessed in SHR. Moreover, there may be a possible risk for making an erroneous conclusion when the gain of arterial baroreflex control of
SHR
L-----l--
J :
_-. .
Moduli
------
.
I :,
__--.
_--_-_
._.
Fig. 3. Averaged transfer function from AP to RSNA for WKY (left; pooled data, n = 7) and for SHR (right; n = 7). Note that gain and frequency axes are logarithmically scaled to get a Bode plot. Solid lines represent mean, and the 2 broken lines represent ME.
1
0.01
Frequency
0.1
1
w z1
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TRANSFER
FUNCTION
ANALYSIS
SNA is assessed only by such a conventional method. First, the extent to which the output (changes in SNA) was attributable to the input (changes in AP) was not determined in previous studies. This was expressed in this study as coherence. SNA is regulated by the baroreflex mechanism and higher central nervous system. The difference in the reflex gain assessed by a conventional method between SHR and WKY might have resulted from the difference in the magnitude of the influence of the central nervous system on SNA. This consideration may be important particularly in studies in conscious animals (17, 18, 21) or with hypothalamic electrical stimulation (20). Second, as shown in Fig. 3, the reflex gain is frequency dependent. Thus, unless the speed of AP change is precisely controlled, the comparison of the reflex gain may not be valid. In most previous studies, the speed of AP change was not defined. Therefore, in this study, we determined the transfer function from AP to RSNA using the white-noise technique. The mathematical basis and the details of the white-noise technique were described in our previous publication (24) and, therefore, will be briefly discussed. There are two major reasons that made the white-noise approach essential. One is that we had to identify the transfer function from AP to RSNA in the presence of feedback coupling between these variables (23). In the presence of the feedback loop, accurate estimation of the transfer function through the conventional frequency domain technique becomes feasible only when the noise in the feedback loop (i.e., noise in RSNA) is insignificant. The fact that changes in RSNA are not always attributable to those in AP invalidates this assumption. If the natural noise in RSNA is much larger than that in AP, the estimated transfer function becomes identical to the reciprocal value of that from RSNA to AP. This is not the transfer function we would like to estimate. To avoid this serious problem, i.e., identification of transfer function of a closed-loop system, we imposed large perturbations in AP. With increases in the amplitude of perturbation, the estimated transfer function would asymptotically converge to its true value. In this experiment external perturbation of AP made its power 261 t 70 times larger than that of control. Thus we think that we sufficiently made the noise in AP larger than that in RSNA, which would guarantee an accurate estimation of the transfer function through the frequency domain approach. The other is the importance of the whiteness of external perturbation., Although we can separately impose thousands of different input sets of pressure at the expense of time, stability of the system under study would be in question. To circumvent this problem, we imposed input pressure changes over a broad frequency range and obtained output to get the general transduction properties. This was achieved by imposing random AP perturbation and by analyzing the output through a mathematical treatment (19). The “whiteness” is essential because it mathematically represents all pressure changes within the investigated frequency range. Figure 2 indicates that the whiteness of the input has been reasonably well accomplished up to 0.4 Hz. Furthermore, the white-noise technique can be applied to the nonlinear system because
OF ARTERIAL
R527
BAROREFLEX
the method allows us to estimate the linear kernel without distortion by the higher order kernels (19). The linearity of the systems is expressed as the coherence. Because the transfer function of the arterial baroreflex system is likely to be nonlinear, we applied the whitenoise technique to identify the system linear kernel. Theoretically, we could accurately estimate the transfer function up to 0.4 Hz, because the amplitude spectral density of input perturbation was reasonably high up to 0.4 Hz. However, we found that coherence functions of the systems [Cw(f) and C,(f)] remained relatively high (>0.5) up to 0.8 Hz and 1.00-1.03 Hz. The latter frequency range was that of respiratory cycle. On the contrary, in the frequency range of 0.01-0.04 Hz, C&f) and C,(f) were low (~0.5) despite high-amplitude spectral density of the input. Therefore, we decided to compare H,(f) and H,(f) in the frequency range of 0.04-0.8 and 1.00-1.03 Hz. In the frequency range in which coherence value was low, the estimated linear transfer function of arterial baroreflex system could not represent the system characteristics because the output unrelated to the input might be imposed. In this study, we defined the coherence above 0.5 as “high coherence” because they attained statistically highly significant values (i.e., P < 0.02) and were considered to be sufficient to represent the system characteristics. The results of this study indicate that Hs(f) and Hw(f) were quite similar (and statistically indistinguishable) in the frequency range examined (Fig. 3). In both Hs(f) and Hw(f), the gain was relatively constant in the frequency range co.05 Hz but increased steadily as frequency increased in the frequency range of 0.05-0.8 Hz. The phase shift and coherence function were also similar between SHR and WKY. These results strongly suggest that arterial baroreflex control of RSNA in anesthetized SHR is not altered as compared with that in WKY. However, resting AP was higher in SHR than in WKY. Thus the operating pressure was higher in SHR than in WKY. Brown et al. (5) have previously examined dynamic characteristics of aortic baroreceptors in SHR and WKY in the excised aortic arch preparation. They applied sinusoidal pressures at frequencies varying from 0.1 to 20 Hz while recording afferent aortic nerve activity. Dynamic characteristics of aortic baroreceptor responses to pressure changes were quite similar between SHR and WKY (5). Brown et al. (5) examined dynamic transduction properties of aortic baroreceptors from AP to afferent aortic nerve activity, while we investigated those of the entire baroreflex arc from AP to efferent SNA. In summary, the results of this study strongly suggest that dynamic characteristics of arterial baroreflex control of RSNA are similar between anesthetized SHR and WKY in the frequency range where coherence is high. We thank Mieko Itoyama for secretarial assistance. . This work was supported by Grants-in-Aid for Scientific Research from the Japanese Ministry of Education, Science, and Culture. Address for reprint requests: A. Takeshita, Research Institute of Angiocardiology and Cardiovascular Clinic, Faculty of Medicine, Kyushu University, 3-l-l Maidashi, Higashi-ku, Fukuoka 812, Japan. Received
28 January
1991; accepted
in final
form
7 February
1992.
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ANALYSIS
REFERENCES 1. Angell-James, J. E., and M. J. George. Carotid sinus baroreceptor reflex control of the circulation in medial sclerotic and renal hypertensive rabbits and its modification by the aortic baroreceptors. Circ. Res. 47: 890-901, 1980. 2. Bendat, J. S., and A. G. Piersol. Random Data: Analysis and Measurement Procedures. New York: Wiley-Interscience, 1971. 3. Bishop, V. S., E. M. Hasser, and U. C. Nair. Baroreflex control of renal nerve activity in conscious animals. Circ. Res. 61, Suppl. I: 1-76-I-81, 1987. 4. Bristow, D., A. J. Honour, G. W. Pickering, P. Sleight, and H. S. Smyth. Diminished baroreflex sensitivity in high blood pressure. Circulation 39: 48-54, 1969. 5. Brown, A. M., W. R. Saum, and S. Yasui. Baroreceptor dynamics and their relationship to afferent fiber type and hypertension. Circ. Res. 42: 694-702, 1978. 6. Bunag, R. D., A. E. Eferakeya, and D. S. Langdon. Enhancement of hypothalamic pressor responses in spontaneously hypertensive rats. Am. J. Physiol. 228: 217-222, 1975. 7. Gonzalez, E. R., A. J. Krieger, and H. N. Sapru. Central resetting of baroreflex in the spontaneously hypertensive rat. Hypertension Dallas 5: 346-352, 1983. 8. Gordon, F. J., H. Matsuguchi, and A. L. Mark. Abnormal baroreflex control of heart rate in prehypertensive and hypertensive Dahl genetically salt-sensitive rats. Hypertension Dabs 3, Suppl. I: 1-135-I-141, 1981. 9. Guo, G. B., M. D. Thames, and F. M. Abboud. Arterial baroreflexes in renal hypertensive rabbits. Circ. Res. 53: 223-234, 1983. M., and B. Folkow. Cardiovascular responses to 10. Hallback, acute mental “stress” in spontaneously hypertensive rats. Acta Physiol. Stand. 90: 684-698, 1974. 11. Harris, F. J. On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66: 51-83, 1978. 12. Humphreys, P. W., and R. M. McAllen. Modification of the reflex response to stimulation of carotid sinus baroreceptors during and following stimulation of the hypothalamic defense area in the cat. J. Physiol. Land. 216: 461-482, 1971. 13. Judy, W. V., and S. K. Farrell. Arterial baroreflex control of sympathetic nerve activity in the spontaneously hypertensive rat. Hypertension Dallas 1: 605-614, 1979. 14. Judy, W. V., A. M. Watanabe, D. P. Henry, H. R. Besch, Jr., W. R. Murphy, and G. M. Hockel. Sympathetic nerve activity. Role in regulation of blood pressure in the spontaneously hvnertensive rat. Circ. Res. 38. Sud II: 11-21-11-29, 1976.
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BAROREFLEX
15. Juskevich, J. C., D. S. Robinson, and D. Whitehorn. Effect of hypothalamic stimulation in spontaneously hypertensive and Wistar-Kyoto rats. Eur. J. PharmacoZ. 51: 429-439, 1978. 16. Kumada, M., L. P. Schramm, R. A. Altmansberger, and K. Sagawa. Modulation of carotid sinus baroreceptor reflex by hypothalamic defense response. Am. J. Physiol. 228: 34-45, 1975, 17. Luft, F. C., G. Demmert, P. Rohmeiss, and T. Unger. Baroreceptor reflex effect on sympathetic nerve activity in strokeprone spontaneously hypertensive rats. J. Auton. New. Syst. 17: 199-209, 1986. 18. Lundin, S., S. E. Ricksten, and P. Thoren. Interaction between “mental stress” and baroreceptor reflexes concerning effects on heart rate, mean arterial pressure and renal sympathetic activity in conscious spontaneously hypertensive rats. Acta Physiol. Stand. 120: 273-281, 1984. P. Z., and V. Z. Marmarelis. Analysis of Phys19. Marmarelis, iological Systems: The White-Noise Approach. New York: Plenum, 1978. 20. Morrison, S. F., and D. Whitehorn. Baroreceptor reflex gain is not diminished in spontaneous hypertension. Am. J. PhysioZ. 243 (Regulatory Integrative Comp. Physiol. 12): R500-R505, 1982. 21. Ricksten, S. E., and P. Thoren. Reflex control of sympathetic nerve activity and heart rate from arterial baroreceptors in conscious spontaneous hypertensive rats. Clin. Sci. 61: 169s-172s, 1981. 22. Schramm, L. P., and G. N. Barton. Diminished sympathetic silent period in spontaneously hypertensive rats. Am. J. Physiol. 236 (Regulatory Integrative Comp. Physiol. 5): R147-R152, 1979. 23. Soderstrom, T., and P. Stoica. System Identification. Hertfordshire, UK: Prentice-Hall, 1989. 24. Sugimachi, M., T. Imaizumi, K. Sunagawa, Y. Hirooka, K. Todaka, A. Takeshita, and M. Nakamura. A new method to identify dynamic transduction properties of aortic baroreceptors. Am. J. Physiol. 258 (Heart Circ. Physiol. 27): H887-H895, 1990. 25. Takeda, K., and R. D. Bunag. Sympathetic hyperactivity during hypothalamic stimulation in spontaneously hypertensive rats. J. Clin.
Invest.
62: 642-648,
1978.
26. Takeshita, A., S. Tanaka, A. Kuroiwa, and M. Nakamura. Reduced baroreceptor sensitivity in borderline hypertension. Circulation 51: 738-742, 1975. 27. Wilson, M. F., I. Ninomiya, G. N. Franz, and W. V. Judy. Hypothalamic stimulation and baroreceptor reflex interaction on renal nerve activity. Am. J. Ph.ysiol. 221: 1768-1773, 1971.
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dynamics in normotensive hypertensive rats
SEIKI HARADA, TSUTOMU IMAIZUMI, SHIN-ICHI YOSHITAKA HIROOKA, KENJI SUNAGAWA, AND Research Institute of Angiocardiology and Cardiovascular Kyushu University, Fukuoka 812, Japan Harada, Seiki, Tsutomu Imaizumi, Shin-ichi Ando, Yoshitaka Hirooka, Kenji Sunagawa, and Akira Takeshita. Arterial baroreflex dynamics in normotensive and spontaneously hypertensive rats. Am. J. Physiol. 263 (Regulatory Integrative Comp. Physiol. 32): R524-R528, 1992.-To investigate dynamic or frequency-dependent characteristics of arterial baroreflex control of efferent sympathetic nerve activity in spontaneously hypertensive rats (SHR) and Wistar-Kyoto rats (WKY), we assessed the transfer function from aortic pressure (AP) to renal sympathetic nerve activity (RSNA) using a “white-noise technique.” In pentobarbital sodium-anesthetized rats, we recorded RSNA as the output, while AP was randomly perturbed to impose input pressure changes with broad frequencies. We calculated the transfer function from AP to RSNA over the frequency range of 0.01-5 Hz through the spectral analysis of the input and output. The results indicated that the gain, phase shift, and coherence of the transfer function for SHR and for WKY were similar and statistically indistinguishable. The gain was relatively constant below 0.05 Hz but increased steadily by fivefold as frequency increased in the frequency range of 0.05-0.8 Hz. The phase was out of phase where coherence was high. The coherence was high (>0.5) in the frequency range of 0.04-0.8 and 1.00-1.03 Hz but was low in other frequencies. These results suggest that dynamic or frequency-dependent characteristics of arterial baroreflex control of RSNA were not altered in SHR as compared with WKY. sympathetic nerve activity; tics; hypertension; transfer Wistar-Kyoto rats
frequency-dependent function; white-noise
characteristechnique;
that the gain of arterial baroreflex control of heart rate in spontaneously hypertensive rats (SHR) is attenuated as compared with that in normotensive Wistar-Kyoto rats (WKY) (17, 18, 21). In contrast, conflicting results have been reported as to the gain of arterial baroreflex control of sympathetic nerve activity (SNA) in SHR. It has been reported that the gain of arterial baroreflex control of SNA is increased (17), equivalent (18, 20, 21), or decreased (7, 13, 14) as compared with that in WKY. Previous studies examined the gain of arterial baroreflex control of SNA under particular sets of arterial pressure (AP) change and assessedstatic characteristics of the arterial baroreflex mechanism in SHR (7, 13, 14, 17, 18, 20, 21). Dynamic or frequency-dependent characteristics of arterial baroreflex control of SNA in SHR and WKY are not completely known. Furthermore, in a conventional method, the extent to which changes in SNA can be attributable to changes in AP is not known. SNA is regulated by higher central nervous system as well as the baroreflex mechanism (12, 16, 27). Thus it is possible that the difference in the reflex gain assessedby the conventional method between SHR and WKY, if any, might result from the difference in the influence of the central nervous system on SNA. It has been sug-
IT HAS BEEN SHOWN
R524
0363-6119/92
$2.00
Copyright
ANDO, AKIRA TAKESHITA Clinic, Faculty of Medicine,
gested that control of SNA by the central nervous system is altered in SHR (6, 10, 13-15, 18, 20, 22, 25). Recently, we have reported the usefulness of the white-noise technique to identify dynamic transduction properties of aortic baroreceptors (24). Using the whitenoise technique, we can identify the unbiased linear properties in a nonlinear system and can determine dynamic properties of the arterial baroreflex system. The purpose of this study was to investigate dynamic characteristics of arterial baroreflex control of SNA in SHR and WKY by use of the white-noise technique. METHODS Animal
Preparation
Seven male 4- to 6-mo-old WKY (330-370 g) and seven agematched SHR (280-340 g) were used in this study. The rats were anesthetized with pentobarbital sodium (40 mg/kg ip), and supplementary doses (5 mg/kg iv) of the anesthetic were administered when necessary. The trachea was cannulated so as not to obstruct the airway. A polyethylene catheter (PE-50) was introduced into the aortic arch through the right carotid artery. The tip of the catheter was carefully positioned at the middle portion of the aortic arch. The proper position of the catheter was confirmed by palpation at the end of study in each rat. The arterial catheter was connected to a pressure transducer (Toyo Boldwin, TMI, Tokyo, Japan) for recording of AP. After the left flank was opened, the left renal nerve was identified, separated free, and cut under a dissecting microscope (OPMI 99, Zeiss). Multifiber nerve impulses were recorded by bipolar electrodes (silver/silver chloride) and preamplified with a high-gain difference amplifier (MEG-1100, Nihon-Kohden, Tokyo, Japan). A 2-Fr Fogarty catheter was introduced from the right femoral artery and positioned in the descending thoracic aorta. To perturb AP, the balloon of the catheter was inflated. Instantaneous AP and renal SNA (RSNA) were recorded simultaneously on a magnetic tape recorder using pulse code modulation (RD-IOlT, TEAC, Tokyo, Japan) for subsequent analysis. Data were also recorded on an eight-channel optical hardcopy recorder (8Ml4, San-ei, Tokyo, Japan) for monitoring the experimental conditions. Protocol Because AP and RSNA are interrelated through a feedback mechanism, external perturbation of AP with sufficient power was prerequisite to accurately estimate the transfer function by the frequency domain technique (see the DISCUSSION). To randomly perturb AP, we intermittently inflated and deflated the balloon in the descending aorta. Mean APs at a control condition was 123.3 t 6.2 (SE) mmHg for WKY and 184.1 t 5.5 mmHg for SHR (P < 0.001). AP varied, on the average, from 73.3 t 7.9 to 179.7 t 10.4 mmHg (5th and 95th percentile, respectively) in WKY and from 112.8 rfr 12.0 to 255.5 of: 8.5 mmHg in SHR. The inflation and deflation of the balloon was manually controlled according to a computer-generated random binary sequence (19). At every 1 s, inflation vs. deflation of the
0 1992 the American
Physiological
Society
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TRANSFER
FUNCTION
ANALYSIS
balloon was randomly determined. Probability for n-s sustained inflation would be l/Zn. Actual duration of inflation as well as deflation varied between 1 and 6 s. This guaranteed that the amplitude spectral density of AP was nearly flat up to 0.5 Hz if AP changes were made by step methods. We recorded instantaneous AP and RSNA for 20 min. If mean AP (average over 100 s) before and after perturbation of AP differed by >lO% during the experiment, the data were discarded. Data Analysis Envelope detection of nerve activity. The nerve impulse in a single fiber could be exactly quantified by firing frequency (i.e., counting the number of impulses per unit time). If the nerve impulse was obtained from multiple fibers, however, the firing frequency would not necessarily represent the overall nerve activity because of possible simultaneous firing of various fibers. To overcome this problem we measured the envelope of nerve impulse recording (24). We home-wired a specially designed circuit by which nerve impulse was fully rectified and smoothed (3). The corner frequency of the low-pass filter for the envelope detection was selected at 30 Hz (-3 dB). The bandwidth of the envelope detection was wide enough to cover the frequency of interest, that is, up to 5 Hz. In this paper this smoothed envelope of nerve impulse train is referred as “nerve activity” and is distinguished from raw “nerve impulse.” Because the absolute voltage value of nerve activity depends on various physical recording conditions, such as positioning of the electrodes,. the size of the electrodes, and so forth, we expressed the amplitude of nerve activity in an arbitrary unit. The zero level represented nerve activity at the noise level. The loo-unit level stood for nerve activity at the control condition. Identification of the transfer function. We digitized pretaped AP and the envelope of RSNA at 100 Hz (12-bit resolution) with an analog-to-digital converter (Canopus, ADX-98, Kobe, Japan). After removing high-frequency signals using a digital filter, we averaged those signals over 10 points, which effectively reduced the Nyquist frequency to 5.0 Hz. The 20-min data were subdivided into 20 overlapping (50%) segments. The length of each segment was 102.4 s. After applying the Blackman-Harris window (4 terms, -92 dB) (11) to minimize spectral leakage, we Fourier-transformed AP and RSNA to obtain their spectra [AP(f) and RSNA(f), respectively] using the fast Fourier transform (FFT) (2). We obtained the cross-power spectrum between AP and RSNA by multiplying the conjugate of AP(f) to RSNA(f). Similarly, we obtained the power spectra of AP and RSNA. We then ensembled those spectra across segments to reduce spectral variance (2, 19). The transfer function was obtained by dividing the ensembled cross-power spectrum by ensembled power spectrum of AP over the frequency range of 0.01-5 Hz, with a resolution of 0.01 Hz. In this paper, H(f) is the transfer function from AP to RSNA. We also obtained the amplitude spectra of AP and RSNA by computing the square root of the power spectra of AP and RSNA, respectively. To quantify the linear dependence of RSNA on AP, we estimated coherence function [C(f)] by dividing the squared magnitude of cross-power spectrum with the power spectra of AP and RSNA. The coherence attains a value between zero and unity. The unity coherence value implies that RSNA is linearly dependent on AP. The low coherence value indicates the nonlinear relationship between RSNA and AP, or the existence of input from other systems (e.g., higher central nervous systems) or the existence of contaminating noise. Statistical analysis. Unpaired Student’s t test was used to compare the mean AP of WKY vs. SHR at a control condition. Two-way analysis of variance was used to compare the gain of transfer function of WKY vs. SHR in the frequency range of 0.04-0.8 and 1.00-1.03 Hz. P < 0.05 was considered significant. All data are expressed as means rfr SE.
OF ARTERIAL
R525
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RESULTS
Figure 1 shows actual recordings of AP and RSNA during random perturbation of AP. Figure 2 denotes the amplitude spectra of AP and RSNA during random perturbation of AP. As shown in Fig. 1, we were unable to step change AP. The time course of the AP change was rather exponential. Because of this distortion of AP, the amplitude spectral density of AP was not exactly flat up to 0.5 Hz, but it was nearly flat (i.e., within k3 dB) up to 0.4 Hz. The averaged H(f) and C(f) are shown in Fig. 3. As will be discussed, we estimated the H(f) for WKY [H,(f)] and that for SHR [H,(f)] in the frequency range of 0.01-0.8 Hz but compared them in the frequency range of 0.04-0.8 and 1.00-1.03 Hz. The averaged gain (moduli), phase shift, and coherence of transfer function over the frequency range examined were similar between SHR and WKY. In both SHR and WKY, the gain remained relatively constant below 0.05 Hz. In the frequency range of 0.05-0.8 Hz, the gain increased steadily by fivefold (P < 0.01). The gain in the investigated frequency range did not differ between SHR and WKY. The coherence was >0.5 in the frequency range of 0.04-0.8 and 1.00-1.03 Hz but was ~0.5 in other frequencies in both SHR and WKY. Coherence at each frequency did not differ between SHR and WKY. The phase was nearly out of phase in the frequency range with high coherence and did not differ between SHR and WKY. DISCUSSION
This study investigated transfer function of arterial baroreflex control of efferent SNA, using AP as the input and RSNA as the output, in SHR and WKY. Coherence was reasonably high (>0.5) in the frequency range of 0.04-0.8 and 1.00-1.03 Hz. The gain, phase shift, and coherence of transfer function in these frequency ranges were quite similar between SHR and WKY, which suggests that arterial baroreflex control of RSNA in response to AP changes is not altered in SHR as compared with that in WKY. However, baseline AP was higher in SHR than in WKY. Thus an operating pressure was higher in SHR than in WKY. Alterations in arterial baroreflex function in hypertension have been studied extensively (1, 4, 7-9, 13, 14, 17, 1821, 26). It has been consistently shown that the reflex gain of heart rate control is reduced in humans and animals with various forms of hypertension (1,4,8,9,17, 18, 21,26). In contrast, conflicting results have been reported as to the reflex gain of SNA control in hypertension. In
ILL Fig. 1. Original recordings of arterial thetic nerve activitv (RSNA) during
IOZC pressure (AP) and renal symparandom x>erturbation of AP.
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R526
TRANSFER
FUNCTION
ANALYSIS
OF ARTERIAL
BAROREFLEX
SHR 1
n
a Q) m 3 .m Q E a
01. 0.01
Fig. 2. Amplitude spectra of AP (top) and RSNA (bottom) during random perturbation of AP [pooled data; n = 7 for WKY (left), n = 7 for SHR (right)]. Note that power and frequency axes are logarithmically scaled. Solid lines represent mean and the 2 broken lines represent GE.
1
a z(0) 0.1 a
L
L
1
0.01
1
1
I~11111
11111111
0.1
I
1
IllI
I
1
I1111111
0.01
1
I11111~~
l
0.1
I11
1
Frequency particular, the decreased (7, 13, 14), equivalent (18, 20, 2l), or increased (17) gain of arterial baroreflex control of SNA has been reported in SHR as compared with that in WKY. In those previous studies, experimental conditions varied markedly so that comparisons of the results among those studies are not possible. Some studies were done in conscious animals (14, 17, 18, 21) and others under anesthesia (7, 13, 14, 20). Various methods were used to change AP, which included bolus injections or constant infusions of vasoactive drugs (17, 18, 21)) aortic constriction (13,14), hemorrhage (14), or electrical stimulation of hypothalamus (20). One study examined responses of
WKY
SNA to electrical stimulation of afferent aortic nerves in decerebrate rats (7). It should be noted that those previous studies have assessed ,the gain of reflex control of SNA by obtaining the slope of the regression line relating changes in SNA to those in AP under particular sets of AP changes. Thus they evaluated static characteristics of the arterial baroreflex mechanism in SHR. Dynamic or frequencydependent characteristics of the arterial baroreflex control of SNA have not been assessed in SHR. Moreover, there may be a possible risk for making an erroneous conclusion when the gain of arterial baroreflex control of
SHR
L-----l--
J :
_-. .
Moduli
------
.
I :,
__--.
_--_-_
._.
Fig. 3. Averaged transfer function from AP to RSNA for WKY (left; pooled data, n = 7) and for SHR (right; n = 7). Note that gain and frequency axes are logarithmically scaled to get a Bode plot. Solid lines represent mean, and the 2 broken lines represent ME.
1
0.01
Frequency
0.1
1
w z1
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TRANSFER
FUNCTION
ANALYSIS
SNA is assessed only by such a conventional method. First, the extent to which the output (changes in SNA) was attributable to the input (changes in AP) was not determined in previous studies. This was expressed in this study as coherence. SNA is regulated by the baroreflex mechanism and higher central nervous system. The difference in the reflex gain assessed by a conventional method between SHR and WKY might have resulted from the difference in the magnitude of the influence of the central nervous system on SNA. This consideration may be important particularly in studies in conscious animals (17, 18, 21) or with hypothalamic electrical stimulation (20). Second, as shown in Fig. 3, the reflex gain is frequency dependent. Thus, unless the speed of AP change is precisely controlled, the comparison of the reflex gain may not be valid. In most previous studies, the speed of AP change was not defined. Therefore, in this study, we determined the transfer function from AP to RSNA using the white-noise technique. The mathematical basis and the details of the white-noise technique were described in our previous publication (24) and, therefore, will be briefly discussed. There are two major reasons that made the white-noise approach essential. One is that we had to identify the transfer function from AP to RSNA in the presence of feedback coupling between these variables (23). In the presence of the feedback loop, accurate estimation of the transfer function through the conventional frequency domain technique becomes feasible only when the noise in the feedback loop (i.e., noise in RSNA) is insignificant. The fact that changes in RSNA are not always attributable to those in AP invalidates this assumption. If the natural noise in RSNA is much larger than that in AP, the estimated transfer function becomes identical to the reciprocal value of that from RSNA to AP. This is not the transfer function we would like to estimate. To avoid this serious problem, i.e., identification of transfer function of a closed-loop system, we imposed large perturbations in AP. With increases in the amplitude of perturbation, the estimated transfer function would asymptotically converge to its true value. In this experiment external perturbation of AP made its power 261 t 70 times larger than that of control. Thus we think that we sufficiently made the noise in AP larger than that in RSNA, which would guarantee an accurate estimation of the transfer function through the frequency domain approach. The other is the importance of the whiteness of external perturbation., Although we can separately impose thousands of different input sets of pressure at the expense of time, stability of the system under study would be in question. To circumvent this problem, we imposed input pressure changes over a broad frequency range and obtained output to get the general transduction properties. This was achieved by imposing random AP perturbation and by analyzing the output through a mathematical treatment (19). The “whiteness” is essential because it mathematically represents all pressure changes within the investigated frequency range. Figure 2 indicates that the whiteness of the input has been reasonably well accomplished up to 0.4 Hz. Furthermore, the white-noise technique can be applied to the nonlinear system because
OF ARTERIAL
R527
BAROREFLEX
the method allows us to estimate the linear kernel without distortion by the higher order kernels (19). The linearity of the systems is expressed as the coherence. Because the transfer function of the arterial baroreflex system is likely to be nonlinear, we applied the whitenoise technique to identify the system linear kernel. Theoretically, we could accurately estimate the transfer function up to 0.4 Hz, because the amplitude spectral density of input perturbation was reasonably high up to 0.4 Hz. However, we found that coherence functions of the systems [Cw(f) and C,(f)] remained relatively high (>0.5) up to 0.8 Hz and 1.00-1.03 Hz. The latter frequency range was that of respiratory cycle. On the contrary, in the frequency range of 0.01-0.04 Hz, C&f) and C,(f) were low (~0.5) despite high-amplitude spectral density of the input. Therefore, we decided to compare H,(f) and H,(f) in the frequency range of 0.04-0.8 and 1.00-1.03 Hz. In the frequency range in which coherence value was low, the estimated linear transfer function of arterial baroreflex system could not represent the system characteristics because the output unrelated to the input might be imposed. In this study, we defined the coherence above 0.5 as “high coherence” because they attained statistically highly significant values (i.e., P < 0.02) and were considered to be sufficient to represent the system characteristics. The results of this study indicate that Hs(f) and Hw(f) were quite similar (and statistically indistinguishable) in the frequency range examined (Fig. 3). In both Hs(f) and Hw(f), the gain was relatively constant in the frequency range co.05 Hz but increased steadily as frequency increased in the frequency range of 0.05-0.8 Hz. The phase shift and coherence function were also similar between SHR and WKY. These results strongly suggest that arterial baroreflex control of RSNA in anesthetized SHR is not altered as compared with that in WKY. However, resting AP was higher in SHR than in WKY. Thus the operating pressure was higher in SHR than in WKY. Brown et al. (5) have previously examined dynamic characteristics of aortic baroreceptors in SHR and WKY in the excised aortic arch preparation. They applied sinusoidal pressures at frequencies varying from 0.1 to 20 Hz while recording afferent aortic nerve activity. Dynamic characteristics of aortic baroreceptor responses to pressure changes were quite similar between SHR and WKY (5). Brown et al. (5) examined dynamic transduction properties of aortic baroreceptors from AP to afferent aortic nerve activity, while we investigated those of the entire baroreflex arc from AP to efferent SNA. In summary, the results of this study strongly suggest that dynamic characteristics of arterial baroreflex control of RSNA are similar between anesthetized SHR and WKY in the frequency range where coherence is high. We thank Mieko Itoyama for secretarial assistance. . This work was supported by Grants-in-Aid for Scientific Research from the Japanese Ministry of Education, Science, and Culture. Address for reprint requests: A. Takeshita, Research Institute of Angiocardiology and Cardiovascular Clinic, Faculty of Medicine, Kyushu University, 3-l-l Maidashi, Higashi-ku, Fukuoka 812, Japan. Received
28 January
1991; accepted
in final
form
7 February
1992.
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FUNCTION
ANALYSIS
REFERENCES 1. Angell-James, J. E., and M. J. George. Carotid sinus baroreceptor reflex control of the circulation in medial sclerotic and renal hypertensive rabbits and its modification by the aortic baroreceptors. Circ. Res. 47: 890-901, 1980. 2. Bendat, J. S., and A. G. Piersol. Random Data: Analysis and Measurement Procedures. New York: Wiley-Interscience, 1971. 3. Bishop, V. S., E. M. Hasser, and U. C. Nair. Baroreflex control of renal nerve activity in conscious animals. Circ. Res. 61, Suppl. I: 1-76-I-81, 1987. 4. Bristow, D., A. J. Honour, G. W. Pickering, P. Sleight, and H. S. Smyth. Diminished baroreflex sensitivity in high blood pressure. Circulation 39: 48-54, 1969. 5. Brown, A. M., W. R. Saum, and S. Yasui. Baroreceptor dynamics and their relationship to afferent fiber type and hypertension. Circ. Res. 42: 694-702, 1978. 6. Bunag, R. D., A. E. Eferakeya, and D. S. Langdon. Enhancement of hypothalamic pressor responses in spontaneously hypertensive rats. Am. J. Physiol. 228: 217-222, 1975. 7. Gonzalez, E. R., A. J. Krieger, and H. N. Sapru. Central resetting of baroreflex in the spontaneously hypertensive rat. Hypertension Dallas 5: 346-352, 1983. 8. Gordon, F. J., H. Matsuguchi, and A. L. Mark. Abnormal baroreflex control of heart rate in prehypertensive and hypertensive Dahl genetically salt-sensitive rats. Hypertension Dabs 3, Suppl. I: 1-135-I-141, 1981. 9. Guo, G. B., M. D. Thames, and F. M. Abboud. Arterial baroreflexes in renal hypertensive rabbits. Circ. Res. 53: 223-234, 1983. M., and B. Folkow. Cardiovascular responses to 10. Hallback, acute mental “stress” in spontaneously hypertensive rats. Acta Physiol. Stand. 90: 684-698, 1974. 11. Harris, F. J. On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66: 51-83, 1978. 12. Humphreys, P. W., and R. M. McAllen. Modification of the reflex response to stimulation of carotid sinus baroreceptors during and following stimulation of the hypothalamic defense area in the cat. J. Physiol. Land. 216: 461-482, 1971. 13. Judy, W. V., and S. K. Farrell. Arterial baroreflex control of sympathetic nerve activity in the spontaneously hypertensive rat. Hypertension Dallas 1: 605-614, 1979. 14. Judy, W. V., A. M. Watanabe, D. P. Henry, H. R. Besch, Jr., W. R. Murphy, and G. M. Hockel. Sympathetic nerve activity. Role in regulation of blood pressure in the spontaneously hvnertensive rat. Circ. Res. 38. Sud II: 11-21-11-29, 1976.
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15. Juskevich, J. C., D. S. Robinson, and D. Whitehorn. Effect of hypothalamic stimulation in spontaneously hypertensive and Wistar-Kyoto rats. Eur. J. PharmacoZ. 51: 429-439, 1978. 16. Kumada, M., L. P. Schramm, R. A. Altmansberger, and K. Sagawa. Modulation of carotid sinus baroreceptor reflex by hypothalamic defense response. Am. J. Physiol. 228: 34-45, 1975, 17. Luft, F. C., G. Demmert, P. Rohmeiss, and T. Unger. Baroreceptor reflex effect on sympathetic nerve activity in strokeprone spontaneously hypertensive rats. J. Auton. New. Syst. 17: 199-209, 1986. 18. Lundin, S., S. E. Ricksten, and P. Thoren. Interaction between “mental stress” and baroreceptor reflexes concerning effects on heart rate, mean arterial pressure and renal sympathetic activity in conscious spontaneously hypertensive rats. Acta Physiol. Stand. 120: 273-281, 1984. P. Z., and V. Z. Marmarelis. Analysis of Phys19. Marmarelis, iological Systems: The White-Noise Approach. New York: Plenum, 1978. 20. Morrison, S. F., and D. Whitehorn. Baroreceptor reflex gain is not diminished in spontaneous hypertension. Am. J. PhysioZ. 243 (Regulatory Integrative Comp. Physiol. 12): R500-R505, 1982. 21. Ricksten, S. E., and P. Thoren. Reflex control of sympathetic nerve activity and heart rate from arterial baroreceptors in conscious spontaneous hypertensive rats. Clin. Sci. 61: 169s-172s, 1981. 22. Schramm, L. P., and G. N. Barton. Diminished sympathetic silent period in spontaneously hypertensive rats. Am. J. Physiol. 236 (Regulatory Integrative Comp. Physiol. 5): R147-R152, 1979. 23. Soderstrom, T., and P. Stoica. System Identification. Hertfordshire, UK: Prentice-Hall, 1989. 24. Sugimachi, M., T. Imaizumi, K. Sunagawa, Y. Hirooka, K. Todaka, A. Takeshita, and M. Nakamura. A new method to identify dynamic transduction properties of aortic baroreceptors. Am. J. Physiol. 258 (Heart Circ. Physiol. 27): H887-H895, 1990. 25. Takeda, K., and R. D. Bunag. Sympathetic hyperactivity during hypothalamic stimulation in spontaneously hypertensive rats. J. Clin.
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26. Takeshita, A., S. Tanaka, A. Kuroiwa, and M. Nakamura. Reduced baroreceptor sensitivity in borderline hypertension. Circulation 51: 738-742, 1975. 27. Wilson, M. F., I. Ninomiya, G. N. Franz, and W. V. Judy. Hypothalamic stimulation and baroreceptor reflex interaction on renal nerve activity. Am. J. Ph.ysiol. 221: 1768-1773, 1971.
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