INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Sympathetic nerve discharge (SND) contains a strong cardiac-related rhythm in baroreceptor-innervated cats. The cardiac-related discharges of different sympathetic nerves are highly correlated as indicated by ordinary coherence values approaching one (Barman et al. 1992; Gebber et al. 1990; Kocsis 1995). The tight linkage is manifested by a sharp peak at the cardiac frequency in the nerve to nerve coherence function (Coh_SND-SND) that rises above background. This peak is eliminated by surgical baroreceptor denervation (Gebber et al. 1994). Two studies in the cat (Gebber et al. 1994; Kocsis 1995) and one in man (Kocsis et al. 1999) have used a computational technique called partial coherence analysis to examine the mechanisms responsible for linkage of the cardiac-related discharges of pairs of sympathetic nerves. This method mathematically removes the portions of the cardiac-related SND that are coherent to the arterial pulse (AP). We assume that AP represents pulse-synchronous baroreceptor afferent nerve activity (Gebber et al. 1994; Kocsis 1995).

Theoretically, partialization of the nerve to nerve coherence function using AP (Coh_SND-SND/AP) will eliminate the peak at the cardiac frequency if the central circuits governing the discharges of the two nerves share baroreceptor inputs but are not otherwise connected and the relationship between AP and SND is strictly linear (Bendat and Piersol 1966; Rosenberg et al. 1998). Contrary to this model of baroreceptor-sympathetic interactions, there were numerous cases reported by Gebber et al. (1994), Kocsis (1995), and Kocsis et al. (1999) in which partialization reduced but did not eliminate the cardiac-related peak. This observation indicated that the cardiac-related discharges of sympathetic nerves pairs were not solely linearly correlated to pulse- synchronous baroreceptor inputs. Additional factors contributing to residual coherence may include coordination arising from physical interconnections of the central circuits generating the activities of different nerves (Gebber et al. 1994) and nonlinear relationships between pulse synchronous baroreceptor nerve activity and SND that are common to different sympathetic nerves (Kocsis 1995). There is evidence for some form of coupling between the central circuits generating SND in that after baroreceptor denervation, statistically significant Coh_SND-SND at frequencies near the heart rate is still observed (Gebber et al. 1994; Kocsis et al. 1990).

In the accompanying paper (Lewis et al. 2000), we observed two modes of coordination between AP and SND in the cardiac-related band, phase walk and phase-locking. The phase walk was characterized by a progressive cycle-by-cycle change in phase angle between peak systole and SND. This relationship may be viewed as nonlinear. In contrast, during phase-locking the range of phase angles is narrow, but the variation is apparently random. This relationship may be viewed as linear. On the basis of these observations, the current study was designed to answer two questions. First, what proportion of cardiac-related SND is the consequence of the nonlinear phase walk? Second, does the nonlinear phase-walk account for instances in which nerve-to-nerve coherence function partialized by AP (Coh_SND-SND/AP) contains a peak exceeding background at frequencies near the heart beat? To address the first question, we used partial spectral analysis, comparing the power in the autospectrum of SND before (AS_SND) and after partialization using AP (AS_SND/AP). To address the second question, we used partial coherence analysis as outlined in the preceding text.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Experimental subjects and anesthesia

Two groups of cats were used in this study. The first group of 24 cats of either sex (weight range 2.3-4.1 kg) were initially anesthetized with 2.5-3.5% isoflurane in oxygen. Following cannulation of a femoral vein, urethan (1.2-1.4 g/kg iv) was administered, and isoflurane inhalation was terminated. This dose range of urethan has been reported to maintain a surgical level of anesthesia for a period of 8-10 h (Flecknell 1987), which exceeded the duration of our experiments. Blood pressure was measured from a catheter inserted into the femoral artery. The cats were paralyzed and artificially ventilated with room air, and a bilateral pneumothoracotomy was performed. End tidal CO₂ was maintained between 3.5 and 4.0% by adjusting the parameters of ventilation. Rectal temperature was maintained near 38°C using a heat lamp. As previously described (Barman et al. 1992), potentials were monophasically recorded with bipolar platinum electrodes from the central ends of the cut postganglionic sympathetic inferior cardiac nerve (CN) and vertebral nerve (VN) near their exits from the left stellate ganglion and the left postganglionic sympathetic renal nerve (RN). Nerve recordings were made with a band-pass filter set at 1-1000 Hz (Grass Instruments 7P3 preamplifier), so that envelopes of multiunit spikes appeared as slow waves (Barman et al. 1992; Cohen and Gootman 1970). We recorded an 80-s epoch of data and then performed baroreceptor denervation by bilateral sectioning of the carotid sinus, aortic depressor and vagus nerves (Barman et al. 1992). Sectioning of these nerves eliminated the cardiac-related rhythm in SND and the inhibition of SND produced by raising blood pressure with a bolus intravenous injection of norepinephrine. Following baroreceptor denervation, we recorded a further 80-s epoch of data.

The second group of 10 cats was used to compare AP-SND phase angles at different steady-state levels of blood pressure described in the accompanying paper (Lewis et al. 2000). These cats were anesthetized and ventilated as described in the preceding text, and the baroreceptor nerves were intact. Blood pressure was measured from the brachial artery, and the CN activity was recorded. Blood pressure was controlled at various steady-state levels by altering the parameters of a phenylephrine infusion.

The All-University Committee on Animal Use and Care of Michigan State University approved all protocols used in these experiments.

Data analysis

FREQUENCY DOMAIN ANALYSIS. Spectral analysis was performed using the fast Fourier transform (FFT) after SND had been low-pass filtered at 100 Hz. The sampling rate of 200 Hz gave a resolution of 0.2 Hz/bin. The power density spectra (autospectra) and ordinary coherence functions (normalized cross spectra) were averages of 32 5-s data windows, with a 50% overlap. The autospectrum of a signal shows how much power is present at each frequency and the coherence function measures the strength of correlation (scale 0-1.0) of two signals. The spectra are displayed over 0-10 Hz.

TIME SERIES ANALYSIS. Sympathetic nerve activity was digitally filtered (symmetric, nonrecursive band-pass filter with a Lanczos smoothing function, RC Electronics, Santa Barbara, CA), with a band-pass width of 4 Hz, and the center frequency was matched to that of the sharp peak at the frequency of the heart beat in the autospectrum of SND (Lewis et al. 2000). Following filtering we made cycle-by-cycle measurements of the interval (ms) between the peak of the AP and the next peak of sympathetic nerve activity as described in the accompanying paper (Lewis et al. 2000). The interval between the peak of the AP and the next peak of nerve activity was converted to a phase angle () in degrees using the formula
where t is the AP-SND interval (ms) and T is the interval (ms) between the peaks of the APs that immediately preceded and followed the nerve slow wave. The resolution of measurement of the phase angle was 5.4°/bin (sampling period was 5 ms) when the period of the cardiac cycle was 333 ms (heart rate, 3 Hz).

STATISTICAL ANALYSIS. Coherence values before and after partialization with AP and baroreceptor denervation and autospectral power in the cardiac-related band before and after partialization with AP were compared using a Student's paired t-test. Comparisons of values between groups were performed using unpaired t-test. Statistical tests were performed using Statview 5.0 (Abacus Concepts). Coherence values were Z-transformed before the statistical comparisons were made.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Figure 1 shows the relationships between CN, VN, and RN discharges and AP in a baroreceptor-innervated cat. The original recordings in Fig. 1 (top right) demonstrate that the discharges of CN, VN, and RN were related in a 1:1 fashion to AP. Consequently, most of the power in AS_SND was concentrated in a narrowband around the cardiac frequency, which is referred to as the cardiac-related band (see AS_SND Fig. 1, 2nd row). In AS_AP (Fig. 1 top left), and to a lesser extent in AS_SND (Fig. 1, 2nd row), in addition to the peak at the cardiac frequency, there are peaks at harmonics of the heart rate. The ordinary coherence functions demonstrate that there was significant coherence between SND and AP (Fig. 1, 3rd row) and between nerve pairs (Fig. 1, bottom row) at the frequency of the heart rate and at higher harmonics of the heart rate.

View larger version (33K): [in this window] [in a new window]   Fig. 1. Cardiac-related rhythm in sympathetic nerve discharge (SND) in a baroreceptor innervated cat. Top right: oscilloscopic records of arterial pulse (AP), and discharges (low-pass filtered at 100 Hz) of cardiac nerve (CN), vertebral nerve (VN), and renal nerve (RN). Top left: autospectrum (AS) of AP. Second row, left to right: ASCN, ASVN, and ASRN. Third row: ordinary coherence functions relating AP to CN, VN, and RN activities. Bottom: ordinary coherence functions relating CN and VN, CN and RN, and VN and RN discharges. Spectral analysis was performed on 32 5-s windows with 50% overlap, and have a frequency resolution of 0.2 Hz in this and subsequent figures.

Partialization of the autospectra of SND with AP removes the component of the AS_SND that is coherent with AS_AP. Two patterns of results were noted. The first of these is illustrated in Fig. 2. Here the AS_SND (top row) shows a major peak at the cardiac frequency. After partialization with AP (2nd row), a large portion, but not all, of the cardiac-related peak is removed for all three nerves. The residual peak in the AS_SND/AP indicates that there is activity in all three nerves in the cardiac-related band that was not coherent to activity in the AP. The residual power peaked at a lower frequency than in the original AS_SND (3.4 vs. 3.8 Hz). Power in the cardiac-related band of the AS_SND/AP represented 34, 37, and 40% of the original power in the cardiac-related band of AS_CN, AS_VN, and AS_RN, respectively. A residual peak containing >1% of the original cardiac-related power was observed in AS_SND/AP in 14 of 24 experiments for all three nerves.

View larger version (27K): [in this window] [in a new window]   Fig. 2. Partial spectral and coherence analysis of cardiac-related rhythm in discharges of CN, VN and RN. Top row, left to right: ASCN, ASVN, and ASRN. Second row: AS have been partialized using the AP, from left to right, ASCN/AP, ASVN/AP, and ASRN/AP. Third row: ordinary coherence functions are given, from left to right, CohCN-VN, CohCN-RN, and CohVN-RN. Bottom: partialized coherence functions are, from left to right, CohCN-VN/AP, CohCN-RN/AP, and CohVN-RN/AP.

In the example shown in Fig. 2, partialization of the nerve-nerve coherence functions with AP produced a small reduction in peak coherence within the cardiac-related band (compare 3rd and 4th rows) and moved the peak to the same frequency as peak residual power in the AS_SND/AP. The residual peak in Coh_SND-SND/AP exceeded background levels of coherence at frequencies >2 Hz.

The second type of outcome observed by partializing AS_SND with AP is shown in Fig. 3. In this case, cardiac-related power was almost completely removed in AS_SND/AP (residual cardiac-related power in AS_CN/AP, 0.1%; AS_VN/AP, 0.5%; and AS_RN/AP, 0.3%). In 10 of 24 experiments, partialization of AS_SND with AP removed >99% of the cardiac-related power for all three nerves.

View larger version (26K): [in this window] [in a new window]   Fig. 3. Partial spectral and coherence analysis of cardiac-related rhythm in discharges of CN, VN, and RN in a 2nd experiment. Top, left to right, ASCN, ASVN, and ASRN. Second row, left to right: ASCN/AP, ASVN/AP, and ASRN/AP. Third row, left to right: CohCN-VN, CohCN-RN, and CohVN-RN. Bottom row, left to right: CohCN-VN/AP, CohCN-RN/AP, and CohVN-RN/AP.

In the case shown in Fig. 3, there was no clear peak in Coh_CN-VN at the cardiac frequency (3rd row, left), due to the high level of coherence at all frequencies >2 Hz. It is important to note that since the coherence function is a normalized value it measures the correlation between the activity of two signals at a given frequency, independent of the magnitude of that activity (Bendat and Piersol 1966). Partialization with AP in this instance did not reduce coherence. For Coh_CN-RN and Coh_VN-RN, however, there was a peak in coherence at the frequency of the heart beat (3rd row), and this peak was substantially reduced by partialization with AP (bottom).

The data from 14 experiments in which the AS_SND/AP contained >1% residual cardiac-related power (group 1) and from the 10 experiments in which the AS_SND/AP contained <1% residual cardiac-related power (group 2) are summarized in Table 1. There was no significant difference between these two groups with respect to mean arterial pressure, cardiac frequency, Coh_AP-SND, or peak Coh_SND-SND within the cardiac-related band. Coh_AP-SND values were not significantly different for the three nerves, and there was no difference between the Coh_SND-SND values for the three nerve pairs. For each of the three nerve pairs in both groups, Coh_SND-SND in the cardiac-related band was significantly reduced by partialization with AP. However, the reduction was significantly less for group 1 than for group 2 for each of the nerve pairs.

Figure 4 shows nerve to nerve coherence functions for the three nerves following baroreceptor denervation (Coh_SND-SND(Den)) superposed on to the same scale as Coh_SND-SND/AP. In Fig. 4A, which is from the same experiment as Fig. 2, Coh_SND-SND(Den) is lower than the Coh_SND-SND/AP at most frequencies and particularly within the cardiac-related band due to the elimination of the peak above background following sectioning of the baroreceptor nerves. Coh_SND-SND(Den) at the cardiac frequency was significantly lower than peak Coh_SND-SND/AP within the cardiac-related band in group 1 for each of the nerve pairs (Table 1). In Fig. 4B, which is from the same experiment as Fig. 3, there was little difference between Coh_SND-SND(Den) and Coh_SND-SND/AP. In group 2, statistically significant differences were not detected between Coh_SND-SND(Den) and Coh_SND-SND/AP at the cardiac frequency (Table 1).

View larger version (17K): [in this window] [in a new window]   Fig. 4. Comparison of effects of partialization using AP and baroreceptor denervation on coherence functions relating the discharges of sympathetic nerve pairs. Data in A and B are from the experiments illustrated in Figs. 2 and 3, respectively. Left to right: the partialized (dark line) and baroreceptor denervated (light line) coherence functions are superposed on the same scale for CohCN-VN, CohCN-RN, and CohVN-RN pairs.

We used time series analyses to investigate the mode of relationship between AP and SND in all 24 baroreceptor-innervated cats. In the 14 cases in which we found residual cardiac-related power in the AS_SND/AP (group 1), phase walk was the predominant mode of coordination between AP and SND. In the 10 cases in which residual cardiac-related power in AS_SND/AP was <1% of control (group 2), phase-locking was the predominant mode of AP-SND relationship. Figure 5, A and B, illustrates a time series for 20-s data epochs taken from the experiments shown in Figs. 2 and 3, respectively. Positive and negative values of phase angle refer to lags and leads of activity in the second signal relative to the first. From top to bottom, the time series in Fig. 5, A and B, show the phase angle between peak systole and CN, VN, and RN activities. In Fig. 5A a phase walk was observed for all three nerves, occurring over a portion of the cardiac cycle, with a period of ~3.3 s. The range of the walk was 170, 160, and 220° for AP-CN, AP-VN, and AP-RN, respectively. For all three nerves, the timing of the cardiac-related slow wave was progressively delayed relative to peak systole from heart beat to heart beat until reaching maximal values (AP-CN, 110°; AP-VN, 95°; and AP-RN, 175°) at which point a transition back to the starting values (AP-CN, 50°; AP-VN, 55°; and AP-RN, 45°) occurred more rapidly, generally within a few heart beats. In this experiment, the walk was less regular for RN than for the other two nerves. Heart rate was constant over this data epoch (240 beats/min), and the blood pressure was stable (130/100 mmHg). In Fig. 5B, strong phase-locking was observed between each nerve and the AP. The bands of phase angles were restricted to 55° for AP-CN, 50° for AP-VN, and 55° for AP-RN. Heart rate (210 beats/min) and blood pressure (190/145 mmHg) were stable over the recorded epoch.

View larger version (16K): [in this window] [in a new window]   Fig. 5. Time series showing cycle-by-cycle measurements of phase angles between peak systole (AP) and peak of cardiac related slow waves in CN (top), VN (middle), and RN (bottom). Data in A are from the experiment illustrated in Figs. 2 and 4A. Data in B are from the experiment illustrated in Figs. 3 and 4B. Positive and negative phase angles denote, respectively, lags and leads of the slow wave relative to AP.

Figure 6, A and B, illustrates the nerve to nerve relationships for the same 20-s epochs that are shown in Fig. 5, A and B, respectively. From top to bottom, time series in Fig. 6, A and B, show the CN-VN, CN-RN, and VN-RN phase relationships. Phase-locking was the predominant mode of coordination between the cardiac-related slow waves for the three nerve pairs in both experiments. The CN-VN phase angles were largely restricted to a band from 20 to 20° in Fig. 6A and from 5 to 15° in Fig. 6B. In both experiments, phase-locking of the cardiac-related slow waves of CN and VN was tighter than that observed for the other two nerve pairs as might be expected from the higher Coh_CN-VN within the cardiac-related band and at all frequencies >2 Hz (Figs. 2 and 3).

View larger version (16K): [in this window] [in a new window]   Fig. 6. Time series showing cycle-by-cycle measurements of phase angles between peaks of cardiac related slow waves in activities of, top to bottom, CN-VN, CN-RN, and VN-RN pairs. Data in A and B are from the experiments illustrated in Figs. 2 and 3, respectively.

For the experiments in group 1, on average, there were no significant differences in the percentages of residual cardiac-related power for the three nerves (AS_CN/AP, 25 ± 13% of control; AS_VN/AP, 23 ± 11% of control; and AS_RN/AP, 22 ± 11% of control). Nevertheless, there were individual cases in which partialization differentially reduced cardiac-related power. An example of this is shown in Fig. 7. On the left, from top to bottom, the time series show the phase angle between peak systole and cardiac-related slow waves of CN, VN, and RN discharges. The AP-CN and AP-VN time series show phase walk starting at approximately 10°, with progressive phase delays of the slow waves in SND relative to systole, up to a maximum phase angle of ~100° before rapidly returning to 10° (range 110°). The AP-RN phase walk started at around 30° and consisted of progressive delays of RN to a maximal value of 40° (range 70°). The walk was less regular for AP-RN than for the other two nerves. The AS_SND and the AS_SND/AP for the three nerves are given on the right of the corresponding time series. Residual cardiac-related power in AS_CN/AP and AS_VN/AP was 31 and 28% of control respectively, but the AS_RN/AP contained only 15% residual cardiac-related power. This suggests that the range of the phase walk may be related to the amount of residual cardiac-related power in AS_SND/AP.

View larger version (18K): [in this window] [in a new window]   Fig. 7. Relationship between magnitude of AP-SND phase walk and reduction in cardiac related power in ASSND produced by partialization using AP. Left: time series showing cycle-by-cycle measurements of, top to bottom, AP-CN, AP-VN, and AP-RN phase angles. Middle: ASCN, ASVN, and ASRN. Right: ASCN/AP, ASVN/AP, and ASRN/AP.

For the 14 experiments in which AS_SND/AP contained residual cardiac-related power (group 1), there was a statistically significant correlation between the range of the phase walk, measured as the standard deviation of the phase angles between AP and SND, and the residual cardiac-related power in AS_SND/AP (percent of control) for each of the three nerves (CN, r = 0.72, P = 0.002; VN r = 0.70, P = 0.003; RN r = 0.70, P = 0.004). In addition, there was a significant inverse correlation between Coh_AP-SND at the cardiac frequency and the residual cardiac-related power in AS_SND/AP (CN r = 0.72, P = 0.002; VN r = 0.69, P = 0.004; RN r = 0.83, P = 0.0001). Neither the range of the phase walk nor the Coh_AP-SND at the cardiac frequency was correlated significantly with MAP (range 110-195 mmHg). The relationships between residual power and Coh_AP-SND and range of the phase walk suggest that Coh_AP-SND and range of phase angles may be negatively correlated. In fact, Fig. 8 illustrates that the inverse relationship between Coh_AP-SND and range of phase angles was very similar for both the 14 cases in which the predominant mode of coordination was phase walk (group 1) and the 10 cases in which phase-locking (group 2) was observed. This observation that Coh_AP-SND was dependent on the range of AP-SND phase angles independent of the mode of coordination is explained in the APPENDIX.

View larger version (9K): [in this window] [in a new window]   Fig. 8. Relationship between CohAP-SND and the standard deviation of the phase angles between AP and SND during phase walk () and phase-locking (). The slopes of the fitted lines for the 2 groups were not significantly different, and for both modes of coordination the relationship was highly significant (P = 0.0001).

In 12 of the 14 experiments in group 1, residual power in AS_SND/AP peaked at a frequency 0.4 Hz below that of the original cardiac-related peak in the AS_SND. This observation may be related to the fact that in most cases, the phase walks were asymmetric, showing slow progressive delays of nerve slow waves relative to timing of systole (Figs. 5A and 7). In such cases, the slow-wave-to-slow-wave intervals during most of the phase walk were of longer duration (and thus at a lower frequency) than the systole-systole intervals. There were two instances in which residual power in AS_SND/AP consisted of two distinct peaks, one below and one above the cardiac frequency. One of these cases is illustrated in Fig. 9. In this experiment, the initial peak in AS_SND was at a frequency of 3.0 Hz, and the AS_SND/AP show two clear peaks, one at 2.6 Hz, the other at 3.4 Hz. The larger of the two peaks was at the lower frequency. Figure 10 shows a 20-s time-series plot of AP-SND for the three nerves from this experiment. In this case, the phase walk involves progressive delays to a maximal phase angle followed by progressive shortening to a minimal phase angle for each of the three nerves and is therefore more symmetrical than the examples shown in Figs. 5A and 7. As a consequence, the intervals between successive peaks of cardiac-related slow waves in SND were longer than the AP-AP intervals in approximately the first half of the walk (as phase angle is increasing) and shorter in the second half (as phase angle is decreasing), resulting in residual power in AS_SND/AP at frequencies both lower and higher than the heart rate. In this case, Coh_SND-SND/AP contained two peaks within the cardiac-related band at the frequencies of the two peaks in AS_SND/AP (Fig. 9).

View larger version (28K): [in this window] [in a new window]   Fig. 9. Partial spectral and coherence analysis of cardiac-related rhythm in CN, VN, and RN discharges. Top row, left to right: ASCN, ASVN, and ASRN. Second row, left to right: ASCN/AP, ASVN/AP, and ASRN/AP. Third row, left to right: CohCN-VN, CohCN-RN, and CohVN-RN. Bottom row, left to right: CohCN-VN/AP, CohCN-RN/AP, and CohVN-RN/AP.

View larger version (12K): [in this window] [in a new window]   Fig. 10. Time series showing cycle-by-cycle measurements of, top to bottom, AP-CN, AP-VN, and AP-RN phase angles. Data are from the experiment illustrated in Fig. 9.

Steady-state blood-pressure changes

From the steady-state blood-pressure experiments in the accompanying paper (Lewis et al. 2000), we examined 18 epochs from 7 animals in which phase walk was the predominant mode of AP-SND coordination, and 18 epochs from 10 animals in which strong phase-locking was the predominant mode. In all 18 cases of phase walk, AS_CN/AP contained a residual cardiac-related peak, with residual power ranging from 7 to 69% (mean 33%) of that in the control autospectrum, AS_CN. In all of the 18 epochs of strong phase-locking, AS_CN/AP contained <1% residual cardiac-related power. Figure 11 shows the data from one experiment at three steady-state blood pressures. These data are from the example shown in Fig. 5 of the accompanying paper. In Fig. 11, A-C, the plots are, from left to right, time series of cycle-by-cycle measurements of the phase angle of CN relative to peak systole, AS_CN, and AS_CN/AP. In Fig. 11A, recorded with a systolic blood pressure near 114 mmHg, values of AP-CN phase angles were scattered over 360°, and there is no evidence of a peak in AS_CN at the cardiac frequency, although a clear peak is seen at 10 Hz. The emergence of a 10-Hz rhythm in SND at low blood pressures has been well characterized (Barman et al. 1992). Because there was no discernable cardiac-related power, partialization of AS_CN with AP had no effect. In Fig. 11B, the systolic blood pressure was raised to near 200 mmHg, and at this level of blood pressure, phase-locking was predominant. The values of AP-CN phase angles were restricted to a band from 0 to 90°. Under these conditions, there was a sharp cardiac-related peak in AS_CN, which was almost completely removed by partialization with AP. In Fig. 11C, the systolic blood pressure was raised to near 280 mmHg, and under these conditions, a phase walk between 0 and 210° with a period of ~3.8 s was observed. Note that in this case the phase walk consists of progressive delays in AP-CN phase angle followed by progressive advances. There is a sharp peak at the cardiac frequency (3.4 Hz) in AS_CN and considerable residual cardiac-related power is apparent in AS_CN/AP (59% of control). Note also that the residual power consists of two peaks, one at 3.0 Hz, the other at 3.4 Hz, consistent with a phase walk involving both progressive delays and progressive advances in AP-CN phase angle.

View larger version (18K): [in this window] [in a new window]   Fig. 11. Time series and spectral analysis from 1 baroreceptor-innervated cat at 3 steady-state levels of blood pressure. A-C, left to right: time series showing cycle-by-cycle measurements of AP-CN phase angles, ASCN, and ASCN/AP. A: systolic blood pressure was 114 mmHg; there is no coordination between AP and CN and no cardiac-related power in ASCN. B: systolic blood pressure was 200 mmHg and phase-locking was observed. Cardiac-related power in ASCN was almost completely removed by partialization with AP (ASCN/AP). C: at a systolic pressure of 280 mmHg, phase walk was observed, and cardiac-related power in ASCN/AP was only slightly reduced from control (ASCN). The data shown here are from the experiment shown in Fig. 5 in the accompanying paper (Lewis et al. 2000).

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

In the accompanying paper, we have described two modes of baroreceptor-sympathetic nerve coordination, phase walk and phase-lock, as reflected by the temporal relationship between SND and AP. The former mode represents a nonlinear interaction of AP and SND, while the latter represents a linear interaction (Lewis et al. 2000). In this study, we have demonstrated that partialization of the autospectrum of SND with AP leaves considerable residual cardiac-related power when the predominant mode of coordination is phase walk but removes virtually all cardiac-related power during phase-locking. Residual cardiac-related power in AS_SND/AP results from activity in the cardiac-related band of SND that is not coherent with the AP (Jenkins and Watts 1968; Rosenberg et al. 1998). Thus while virtually all the cardiac-related SND is coherent to AP during phase-locking, this is not the case during phase walk.

In the accompanying paper, the phase walk has been described in terms of relative coordination, which is a characteristic feature of forced nonlinear oscillators. We have suggested that the phase walk is caused by the influence of a third factor on the AP-SND relationship, such as blood pressure oscillations or an interaction with the respiratory system (Lewis et al. 2000), although such interactions remain to be fully characterized and were not investigated in this study. Whatever the mechanism generating the phase walk, the result is a tendency for a significant portion (as much as 69%) of cardiac-related SND to occur at a frequency distinct from that of the heart rate. In most cases in the present study, cardiac-related activity was attracted to a lower frequency, evidenced by a residual peak in AS_SND/AP at a frequency lower than that of the heart rate. Such peaks are consistent with phase walk characterized by progressive delays of cardiac-related sympathetic slow waves relative to the timing of systole with abrupt snap backs from a point of maximal delay.

Theoretically, relative coordination between two signals does not result in any linear coherence (Hoyer et al. 1997) because one signal is attracted to, but never quite achieves, the frequency of the other. Under these circumstances the phase walk is through 360° (Kelso 1995). In this sense, the AP-SND phase walks that we have described do not fit the classical definition of relative coordination since during phase walk there was still high Coh_AP-SND at frequencies within the cardiac-related band, and the phase walk occurred over <360°. Thus it is probable that we never saw pure phase walk but rather a mixture of phase walk and phase-locking. This may reflect the fact that our system was never truly at a "steady state" in that the excitability of the central sympathetic oscillator(s), and/or the strength of the pulse synchronous baroreceptor input was continually changing in a cyclic fashion.

The range of phase angles during phase walk was found to be predictive of the amount of residual cardiac-related power observed in AS_SND/AP. When the phase angle between AP and SND changes progressively from one cycle to the next, then the frequency of SND is different from the heart rate (which in our experiments was essentially constant due to the vagolytic actions of gallamine and the sectioning of one cardiac sympathetic nerve). Thus the range of the phase angles in the phase walk is proportional to the time that the frequency of SND is divergent from the frequency of AP and therefore should be proportional to the amount of residual power in AS_SND/AP in the cardiac-related band.

Coh_AP-SND was inversely related to the range of AP-SND phase angles irrespective of whether phase walk or phase-locking was the predominant mode of coordination between the two signals. In fact, the slopes describing these relationships were the same for both modes of coordination (see Fig. 8). The range of phase angles between AP and SND observed during phase-locking is proportional to the amount of random perturbation of the 1:1 relationship between the two signals. As mathematically derived in the APPENDIX, such randomness is as effective in reducing coherence between AP and SND as a nonlinearity producing a phase walk with a similar range of phase angles.

Given that phase walk and phase-locking with equivalent ranges of phase angles result in the same Coh_AP-SND and that the Coh_AP-SND determines the portion of AS_SND that is removed by partialization using AP, then why is it that a phase walk resulted in considerable residual cardiac-related power, while the random fluctuations that occur in phase-locking did not? The phase walk alters the frequency of SND slightly from that of the heart rate but in a structured manner, and this activity therefore rises above background to form part of the cardiac-related band that is seen in AS_SND/AP. Random perturbations of the AP and SND relationship should be as effective in producing residual power as a nonlinearity (Bendat and Piersol 1966). However, due to the apparently random fluctuations in AP-SND phase angles during phase-locking the power in AS_SND/AP at any given frequency within the cardiac-related band would be indistinguishable from background activity.

Gebber et al. (1994) and Kocsis (1995) have previously reported that Coh_SND-SND/AP remains high within the cardiac-related band. Kocsis (1995) commented on the possibility of a nonlinearity contributing to residual coherence but did not elaborate on the nature of the nonlinearity. Gebber et al. (1994) proposed that physical interconnection (coupling) of the central circuits governing discharges of different sympathetic nerves might also lead to residual Coh_SND-SND/AP in the cardiac-related band. We have demonstrated that a nonlinearity is present in the relationship between AP and SND and that this nonlinearity results in residual cardiac-related power in AS_SND/AP. The interpretation of Coh_SND-SND/AP in the cardiac-related band needs to be reexamined in this light.

The phase walk that produces residual cardiac-related power in AS_SND/AP is also responsible for the peak in the residual Coh_SND-SND/AP within the cardiac-related band in group 1. It would seem logical to assume that the nonlinear AP-SND relationship is the result of central circuits for all three nerves responding similarly to their baroreceptor inputs. However, commonality of response to shared baroreceptor inputs cannot be the only factor involved in generating residual Coh_SND-SND/AP because significant coherence remains following baroreceptor denervation (Gebber et al. 1994; Kocsis et al. 1990; also Table 1). This would require either some other form of shared input (noise) or physical interconnections to be present generating some coherence between nerve pairs.

There is evidence for some noise affecting the relationship between SND and AP, particularly during phase-locking, in that there are apparent random variations in phase angles. However, nerve-to-nerve phase angles appear less disrupted by these random variations between SND and AP. This suggests that either the source of noise is common or that there are physical interconnections between the nerves leading to less apparent noise in the nerve-to-nerve relationship, either of which would produce residual Coh_SND-SND/AP. The relationship between these three factors may be very complex. For example, any nonlinearity in the AP-SND relationship may be shared not only because of common responses to similar inputs to the central circuits for different nerves but also because of physical interconnections between these circuits, therefore the extent to which each mechanism contributes to residual Coh_SND-SND/AP in the cardiac-related band cannot be stated.

In conclusion, there are two predominant modes of coordination between AP and SND, phase-locking and phase walk. To an extent, these two modes may always be coexistent. The effect of phase walk is to move a considerable portion of the cardiac-related activity to frequencies other than that of the heart rate, such that residual peaks are seen in AS_SND/AP and in Coh_SND-SND/AP. However, during both modes of coordination, other factors must be involved in generating Coh_SND-SND/AP because there is still significant coherence at frequencies near the heart rate after sectioning of the baroreceptor nerves. Such factors may include physical interconnections between central circuits generating SND and common inputs of nonbaroreceptor origin.