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1 LaRC-Centro di Bioingegneria, Fondazione Don Carlo Gnocchi ONLUS and Politecnico di Milano, 20148 Milano; 2 Istituto Scientifico Ospedale San Luca, Istituto Auxologico Italiano, 20147 Milano; 3 Ospedale San Gerardo, Monza and Universita' degli Studi di Milano; and 4 Dipartimento di Bioingegneria, Politecnico di Milano, 20133 Milano, Italy
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ABSTRACT |
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In healthy subjects,
progressive beat-to-beat increases or decreases in systolic blood
pressure (SBP) ramps are not always accompanied by baroreflex-driven
lengthening or shortening in pulse interval (PI) ramps, respectively.
This phenomenon has been quantified by a new index, the baroreflex
effectiveness index (BEI), defined as the ratio between the number of
SBP ramps followed by the respective reflex PI ramps and the total
number of SBP ramps observed in a given time window. Specificity of BEI
was shown in eight cats by a
89% reduction of BEI after sinoaortic denervation. In 14 healthy humans, the 24-h average BEI value was 0.21, with a marked day-night modulation (
0.25 day,
0.15 night) in
counterphase with modulation of baroreflex sensitivity (BRS). Our
analysis indicates that 1) in normal subjects, arterial baroreflex can induce beat-by-beat PI changes in response to only 21%
of all SBP ramps, possibly because of central inhibitory influences or
of interferences at sinus node level by nonbaroreflex mechanisms and
2) BEI provides information on the baroreflex function that is complementary to BRS.
baroreceptor; blood pressure variability
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INTRODUCTION |
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THE SEQUENCE
TECHNIQUE (1) is a widely employed method to
investigate spontaneous baroreflex control of the heart. The popularity
of this procedure, as well as of other approaches proposed over the
years (5, 13, 16), is due to its capability to derive
information on baroreflex function through the analysis of systolic
blood pressure (SBP) and pulse interval (PI) beat-to-beat spontaneous
variability. The sequence technique is based on the identification of
sequences of consecutive beats in which progressive increases in SBP
are followed with a one-beat delay by a progressive lengthening in PI
(PI+/SBP+ sequences) or vice versa; progressive decreases in SBP are
followed by a progressive shortening in PI (PI
/SBP
sequences). The
slope of the regression line between the SBP and PI values included in
each sequence is taken as an index of the sensitivity of baroreflex
control of the heart, as done when SBP and PI changes are induced by
vasoactive drug injections (17). The baroreflex nature of
these PI/SBP sequences was demonstrated in a previous study by showing
that in cats their number markedly dropped (
86%) after surgical
baroreceptor denervation [sinoaortic denervation (SAD)]
(1), due to the resulting impairment of the
baroreceptor-reflex PI modulation.
In normal conditions, baroreflex PI/SBP sequences occur at a relatively high rate over the 24 h, about 80 sequences/h being typically observed in healthy ambulant subjects (15). These sequences, however, are often interspersed with progressive SBP changes that are not coupled with a progressive reflex PI modulation. The presence of these uncoupled SBP ramps might indicate that even in healthy subjects the baroreflex, although being continuously involved in cardiovascular homeostasis, may not be invariably effective in inducing reflex PI changes in response to short SBP transients.
In the present study, this so far unexplored aspect of the baroreflex control of the heart rate was pursued by proposing and applying a new index, the baroreflex effectiveness index (BEI), capable of quantifying the phenomenon in hand in a dynamic fashion.
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METHODS |
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The estimation of BEI was based on the analysis of beat-to-beat
series of SBP and PI recorded under spontaneous behavior. In the
assessment of such a new index, our analysis focused on the
identification of a specific pattern in the SBP series, which was taken
as a probe input to the baroreceptors, and on the quantification of how
many times this SBP input is followed by the expected PI reflex change.
The probe input to baroreceptors considered in our study was the
progressive increase or the progressive decrease in SBP occurring over
a run of three or more consecutive beats (in short a SBP+ or a SBP
ramp, respectively). The related progressive beat-to-beat PI
lengthening (PI+ ramps) or shortening (PI
ramps), respectively, was
taken as the expected reflex PI response. The coupling between a SBP
and a PI ramp obviously corresponds to a spontaneous PI/SBP baroreflex
sequence, as previously described. In our analysis, we considered SBP
and PI ramps coupled not only with a one-beat lag, as usually done in
the routine evaluation of baroreflex sensitivity (BRS) through the
sequence analysis, but also with 0- and 2-beat lags. This procedure was
based on 1) previously published reports showing the
presence of PI/SBP sequences with 0-, 1-, and 2-beat lags during
spontaneous behavior (4, 18); 2) the finding,
obtained by a surrogate data analysis, that these sequences are due to
a physiological rather than a chance coupling (3); and
3) the favorable results of an ancillary analysis of
experimental data, reported in the APPENDIX, showing also that the SBP
and PI ramps coupled with a 0- and 2-beat lag are under baroreflex
influence [the baroreflex nature of ramps with lag 1 has already been
shown elsewhere (1, 7)].
On the background of these observations, BEI was defined as the ratio between the number of SBP ramps followed within 0, 1, or 2 heart beats by reflex PI ramps (i.e., the number of PI/SBP sequences) and the total number of SBP ramps (independently on whether they are or are not accompanied by the corresponding reflex PI ramp) observed over a given time window.
In the present study, we have explored 1) the distribution and slope of the SBP ramps, as well as the magnitude of the overall blood pressure change within each ramp, throughout the 24 h; this was done to ensure that the SBP ramps occur during the day and night at a rate suitable for a dynamic estimation of BEI and to assess the possible modulation of the ramp features over time; 2) the specificity of BEI in reflecting the baroreflex function, which was done through the analysis of data collected before and after surgical baroreceptor denervation in cats; 3) the time course of BEI over the 24 h in normal humans under spontaneous behavior, which was done through the analysis of 24-h ambulatory intra-arterial recordings obtained in volunteers; and 4) the possible dependence of BEI on the characteristics of the input SBP ramps.
Data Collection
Cats. To verify the specificity of BEI, we analyzed continuous intra-arterial blood pressure tracings obtained in eight conscious and unrestrained cats. In each animal, blood pressure was recorded for about 180 min both in the intact condition and 1 wk after surgical denervation of arterial baroreceptors. The denervation was obtained by severing the afferent fibers stemming from the aortic arch and the carotid sinuses (SAD) after anesthesia with intraperitoneal injection of ketamine. Blood pressure was measured by a catheter positioned in the abdominal aorta and connected to a pressure transducer placed at the heart level. Each recording was performed with the animal in a Plexiglas box large enough to allow spontaneous activities such as walking, eating, stretching, and self-cleaning. Based on visual inspection, the behavior of the animals was not altered by SAD. Further details on the surgical procedure have been published elsewhere (1).
Humans. To evaluate the distribution of SBP ramps over the 24 h and the value of BEI in daily life, we made use of 24-h ambulatory intra-arterial recordings performed by the Oxford technique (2, 19) in 14 healthy volunteers [12 males and 2 females, 36 ± 3.7 (SD) yr]. Blood pressure was measured directly through a catheter percutaneously inserted into the brachial artery of the nondominant arm under previous local anesthesia with 2% lidocaine. The catheter was connected by a rigid-walled plastic tube to a polyethylene box placed on the chest at the heart level. The box contained the blood pressure transducer and a perfusing unit filled with heparinized saline solution aimed at keeping the catheter patent throughout the 24 h. The beat-by-beat blood pressure signal was then stored on a magnetic cassette recorder (Oxford Medilog) for subsequent analyses. During the recording, the subjects were free to move within the hospital area and to engage in the social activities of hospital inpatients (watching television, playing cards, walking in the hospital garden, visits from relatives, etc.). All subjects gave their informed consent to the procedure. Further details on the experimental set-up can be found elsewhere (9).
The protocols for both animals and humans were approved by the ethical committees of the clinical institutions involved.Data Analysis
Acquisition and preprocessing. The blood pressure signal was analog-to-digital converted with a 12-bit resolution at 200 Hz for the recordings performed in animals and at 165 Hz for the recordings performed in humans. SBP values were derived from each heart beat, and PI was computed as the interval between consecutive systolic peaks, after parabolic interpolation and resampling at 1,000 Hz of the apex of each pressure waveform.
Analysis of SBP ramps.
SBP time series were scanned to identify SBP+ and SBP
ramps of three
or more consecutive beats characterized, respectively, by a progressive
increase or reduction of 1 mmHg/beat, regardless of the possible
occurrence of concomitant reflex changes in PI. For each ramp, two
structural features have been considered: 1) its slope and
2) the overall blood pressure change (hereafter termed blood
pressure swing). The ramp slope was estimated by computing the modulus
of the slope of the regression line between the SBP values included in
the ramp and time. The magnitude of the SBP swing within the ramp was
estimated as the difference between the highest and the lowest SBP
value occurring in the ramp.
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/SBP
sequences with a 0-, 1-, and 2-beat lags and the total
number of SBP ramps is the sum of all SBP+ and SBP
ramps observed in
a given time window.
The PI+/SBP+ and PI
/SBP
spontaneous sequences required for the
computation of BEI were identified as the SBP+ and SBP
ramps (defined
as above) followed, with a delay of 0, 1, or 2 heart beats, by PI+ or
PI
ramps, respectively. PI ramps were characterized by progressive PI
lengthening or shortening of at least 5 ms/beat. For each sequence, the
regression line between the SBP and PI values of the sequence was also
estimated. In the eight cats in our study, average correlation
coefficients were 0.94 ± 0.02 and 0.95 ± 0.03 for PI+/SBP+
and PI
/SBP
sequences, respectively. In the 14 subjects, the
corresponding correlation coefficients were 0.94 ± 0.008 and
0.95 ± 0.005. The slope of each regression line was then taken as
an index of BRS.
BEI was additionally subdivided into two subtypes to evaluate the
"selective" responsiveness of the baroreflex to SBP+ and SBP
ramps, i.e.
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BEI vs. features of the SBP ramps. To verify whether BEI is influenced by the rate of change of the SBP input, the SBP ramps observed in each subject also have been classified according to their slope. BEI was then separately estimated for each slope class.
Similarly, the possible influence on BEI of the magnitude of the SBP swing within the input ramp was estimated by grouping the SBP ramps on the basis of their pressure swing and by computing BEI separately for each SBP swing class.Statistical analysis. In humans, the above parameters were averaged over 24 h, over day (8 AM to 12 PM) and night (0 AM to 4 AM) subperiods, and hourly. In cats, BEI values were computed over the whole blood pressure recording period. The Student's t-test was used to assess the significance of the differences between 1) intact and SAD conditions in cats and 2) day and night subperiods in humans. P < 0.05 was taken as the level of statistical significance. Unless otherwise stated, "±" refers to SE.
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RESULTS |
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SBP Ramps Over 24 h
In the 14 subjects in our study, we observed an average of 363 ± 18 SBP ramps/h (obtained by pooling SBP+ and SBP
ramps). As shown in Fig. 1, top, the
hourly number of SBP ramps was modulated over the 24 h, with the
maximum occurring during the day and the minimum at night. A parallel
day-night modulation was observed also for the structural
characteristics of the ramps, i.e., for their slope and their pressure
swing magnitude (Fig. 1, middle and bottom,
respectively). Similar profiles were obtained from the separate
analysis of the SBP+ and SBP
ramps. Details of the day vs. night
changes in number, slope, pressure swing, and duration of the SBP ramps
are shown in Fig. 2. At night, a
significant reduction in the absolute number of ramps (
45%) was
observed. The number of ramps still was significantly reduced (
23%)
at night even after normalization for the reduced number of beats caused by the nocturnal lengthening of PI (the average number of beats
fell during the night with respect to the day from 4,651 to 3,757 beats/h). It should be noted, however, that despite the above
reduction, a noticeable number of ramps (>200 ramps/h) was still
present at night. Significant nocturnal reductions were observed also
for slope (
28%) and pressure swing magnitude (
14%) of the ramps.
No day-night change was observed for the ramp duration.
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BEI Specificity
Figure 3 shows the average values of BEI computed in the eight cats before and after SAD. In the intact condition, BEI was 0.33. After baroreceptor denervation, BEI dropped to a negligible value of 0.04. Similar findings were obtained from the separate analysis of BEI+ and BEI
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BEI Time Course Over the 24 h
In our 14 subjects, the average value of BEI throughout the 24 h was 0.21, indicating that in healthy humans the baroreflex can respond to a SBP ramp with a progressive modulation of PI approximately one of five times. The hourly profile of BEI averaged for the whole group of subjects is illustrated in Fig. 4. BEI is characterized by a pronounced day-night modulation, ranging from about 0.15 at night to more than 0.25 during the day. A similar behavior characterized BEI+ and BEI
when separately considered.
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BEI vs. Features of the SBP Ramps
The curves representing the relationships between BEI and the SBP ramp slope and between BEI and SBP swing magnitude are illustrated in Fig. 5. Results are averaged over the whole group of subjects and refer to the entire 24 h (Fig. 5, A and C) and to the day and night subperiods (Fig. 5, B and D). In each panel, the number of SBP ramps observed for each slope class (Fig. 5, A and B) or for each pressure swing magnitude class (Fig. 5, C and D) is also reported for reference.
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A progressive increase of BEI as a function of the slope and pressure swing is evident both when the complete 24 h are considered or when the day and night subperiods are considered separately. It should be noted, however, that the relationships between BEI and slope and between BEI and pressure swing are not constant over the 24 h. In particular, for any given value of slope or pressure swing, the BEI value is invariably lower at night than during the day.
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DISCUSSION |
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Our study represents the first attempt to quantify a yet unexplored aspect of spontaneous baroreflex control of the heart, i.e., the rate at which the baroreflex can modulate progressively PI in response to short progressive SBP changes. This was done through the computation of a new index (BEI), which derives information on the effectiveness of the cardiac baroreflex from the analysis of PI responses to a probe SBP input (the SBP ramps) spontaneously occurring in daily life.
SBP Ramps
Our study shows that in humans a large number of SBP ramps occur over the 24 h. The number of the SBP ramps is greater during the day than at night, indicating, as expected, that the occurrence of this pressure pattern may be influenced directly by the level of physical and emotional challenges associated with daily activities. However, our data also show that >200 SBP ramps/h are still present during the night. Thus even in a condition characterized by a reduced behavioral activity, such as night sleep, the hourly number of SBP ramps, although reduced with respect to the daytime, remains remarkably high. This means that the specific SBP pattern we used to evaluate BEI does actually represent a frequent stimulation to the arterial baroreceptors throughout the 24 h and thus appears to be a suitable probe input for investigating the arterial baroreflex in a dynamic fashion with a time resolution in the order of tens of seconds.Moreover, a significant day-night modulation also was observed in the structure of the ramps as quantified by their slope and their pressure swing, namely, their overall pressure change. For both these characteristics, the maximal value was observed during the day, thus suggesting that the daily activity may influence not only the number of the SBP ramps but also their structure. The possible influence of these characteristics on the BEI value will be addressed separately in the next section.
Finally, before using SBP ramps as a probe input for BEI estimation, a
further issue related to the intermittent occurrence of these ramps
over time needs to be discussed. It is very likely that periods
characterized by the absence of SBP ramps correspond to periods when
stimulations capable of inducing these SBP transients are absent.
However, it could be alternatively speculated that when the SBP ramps
are absent, this is because the efficiency of the baroreflex in
buffering blood pressure is temporarily increased to such an extent
that any SBP change is quickly buffered in less than three beats. We
explored this hypothesis in the eight cats of our study by evaluating
the effects of SAD on the number of SBP ramps. Obviously, if the above
hypothesis holds true, the number of observed SBP ramps should increase
after SAD because of the removal of baroreflex-buffering action. This
does not seem to be the case, however, because SAD-induced opening of
the baroreflex loop did not result in any significant increase in the
number of spontaneous SBP ramps (710 ± 79 vs. 739 ± 88 SBP+
ramps/h and 627 ± 85 vs. 691 ± 110 SBP
ramps/h before and
after SAD, respectively). These experimental results are thus in
contrast with the hypothesis that the absence of SBP ramps might depend
on an increase in the efficiency of the baroreflex and rather suggest
that the occurrence of SBP ramps is a phenomenon somewhat unrelated
with the baroreflex.
BEI
The different features of BEI investigated in our study will be addressed separately hereafter.Specificity.
The striking reduction (
89%) in BEI value observed in cats after
surgical baroreceptor denervation compared with the intact condition
demonstrates the specificity of BEI in reflecting baroreflex function.
This finding represents an important experimental support to the use of
this new index.
Average level. A challenging finding of our study concerns the average value of BEI computed during spontaneous behavior. In humans, over the 24 h the average BEI was 0.21 (in cats being only slightly higher). Such a low value of BEI, observed in healthy subjects during spontaneous behavior, indicates that the arterial baroreflex can respond to progressive SBP changes with concordant changes in PI only in a minor fraction (21%) of cases. Although a certain amount of noise in baroreflex PI modulation was in part expected on the basis of current physiological knowledge, the observation that the baroreflex is able to produce a progressive PI modulation in response to SBP ramps at such a limited rate is an intriguing result. A possible explanation for this finding may come from the observation that in physiological conditions the cardiac rhythm is controlled not only by the baroreflex but also by other nonbaroreflex mechanisms (central neural influences directed to the heart, respiratory activity, modulations by humoral substances, etc.). It may happen that the action exerted by these nonbaroreflex mechanisms on the sinus node is strong enough to mask the baroreflex influence on heart rate. Moreover, the baroreflex itself is known to be affected at variable degrees by central inhibitory influences (20), which may also contribute to a temporary reduced efficiency in the baroreflex control of the heart. Thus the effectiveness of the arterial baroreflex quantified by BEI in healthy subjects, where the baroreflex itself can be assumed to be properly functioning, is likely to reflect the level of both the above interferences, i.e., those exerted by nonbaroreflex factors on the baroreflex beat-to-beat control of the sinus node and those exerted by inhibitory influences at a central level. It should be considered, however, that the baroreflex effectiveness in controlling the heart rate does not necessarily mirror the ability of the baroreflex to achieve an efficient blood pressure buffering. Indeed, in our healthy subjects, the relatively low value of BEI is physiologically compatible with an efficient baroreflex-mediated blood pressure homeostasis. This apparent contradiction may be explained by considering that the interactions reflected by BEI are those affecting the short-term baroreflex control of PI in response to fast SBP transients, whereas the baroreflex modulation of PI over longer time scales and the baroreflex control of the peripheral vessels may be largely unaffected by these "physiological" interferences (8, 10).
The 24-h behavior. An additional point worth mentioning refers to the observation that in our human subjects, BEI values are modulated over time and display a minimum at night. The observed similarity between the 24-h profile of BEI and that of the pressure swing of the SBP ramps (cf. Figs. 1 and 4) raises the possibility that the time modulation of BEI might simply reflect the time modulation of the characteristics of the input SBP stimulus. Data shown in Fig. 5 allow us to clarify this issue. Actually, on one side the results obtained by considering the whole 24-h period clearly show the existence of a direct relationship between BEI and ramp slope and between BEI and ramp pressure swing magnitude, thus indicating that BEI is in part related to the strength of the input stimulus. On the other side, however, results obtained from the separate analysis of day and night subperiods also clearly indicate that at night there is a marked downward shift of the curves representing the relationship between BEI and the characteristics of the SBP ramps. This means that the observed marked nocturnal reduction of BEI may only be partially caused by the nocturnal reduction in the average values of the slope and pressure swing (which shifted from 5.6 mmHg/s and 14.7 mmHg during the day to 4 mmHg/s and 12.6 mmHg at night, respectively). Indeed, most of the nocturnal drop in BEI seems to be caused by a systematic downward shift of the curve, representing the link between BEI and slope of the SBP ramps (presumably due to agents not related to the characteristics of the input SBP stimulus). A number of factors might be responsible for the nocturnal reduction in BEI. These include the occurrence of short-lasting arousals during stage 2 sleep observed in concomitance with the appearence of the so-called K-complexes in the EEG signal; they also include the frequent occurrence of phasic bursts of nonreflex tachycardia during rapid eye movement sleep (17). They may finally include the increased contribution at night of the central component of respiratory sinus arrhythmia that is known to favor the occurrence of opposite changes in SBP and PI and thus contrasting the occurrence of the PI/SBP sequences (which are based on concordant changes).
Furthermore, it should be considered that the above nighttime reduction of BEI occurs in concomitance with an increase in BRS (15) (compare Fig. 4A with Fig. 4B, which shows the 24-h behavior of BRS estimated in the same 14 subjects of our study through the sequence technique). All of these findings might be justified by the fact that the central inhibitory influences (see above) that during sleep simultaneously reduce blood pressure and PI oppose at a presynaptic level the central integration of baroreceptor influences (11, 20), thus resulting in a reduction of the number of times the baroreflex control of the heart responds to SBP ramps, i.e., in a reduction of BEI. At the same time, however, the same inhibitory influences remove other mechanisms (hypothalamic influences involved in emotional behavior, somatic afferent influences stimulated by muscle contraction, etc.) that normally oppose postsynaptically the baroreflex effects (6, 8, 12), thus resulting in an increased BRS.Information conveyed by BEI and BRS. The discrepant behavior of BEI and BRS observed over the 24 h in our subjects indicates that BEI and BRS may provide data on different aspects of baroreflex control of the heart. This means that the information provided by the two indexes is not redundant but is rather complementary, and thus the joint estimation of BEI and BRS may offer a more comprehensive picture of reflex cardiovascular regulation in daily life. The complementary nature of these indexes is also evident if one considers that BEI quantifies the number of times the baroreflex is effective in driving the sinus node, whereas BRS quantifies, only when this drive is effective, the magnitude of the reflex PI response with respect to the amplitude of the input SBP change.
Applicability in pathological conditions. In pathological conditions associated with a dysfunction of the cardiac baroreflex, BEI conceivably reflects not only the interference by nonbaroreflex mechanisms, as done in normal subjects, but also the degree of the baroreflex impairment. Thus a reduction of BEI directly related to the level of the baroreflex dysfunction would be expected in these instances. In our study, we explored the behavior of this new index in two opposite extreme situations: 1) in healthy subjects and intact cats on one side and 2) in cats after complete abolition of baroreflex control of circulation on the other side. What might actually happen to BEI in a condition of partial impairment of the baroreflex should be assessed in future analyses.
Perspectives
BEI estimates the effectiveness of baroreflex control of the heart in daily life by focusing on the reflex PI response to a specific probe SBP input. This index should be considered as a first approach to a complex and mostly unexplored aspect of the baroreflex function, namely, the interaction between the arterial baroreflex and other nonbaroreflex mechanisms in controlling the sinus node. The application of this new index in healthy subjects has shown that when the arterial baroreflex is triggered by SBP ramps, i.e., by transients with a nonnegligible pressure change of 12-15 mmHg, nonbaroreflex mechanisms largely prevail in driving heart rate and let the baroreflex control of the sinus node be effective on average only in one of five cases. To what extent the level of effectiveness of the baroreflex observed by using SBP ramps as a probe input to the baroreceptors can reflect also the effectiveness in response to different and more complex SBP input patterns remains to be investigated in future studies.| |
APPENDIX |
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To decide whether to include also the sequences displaying a SBP-PI lag of 0 and 2 beats in the estimation of BEI, we had to test the baroreflex involvement in their genesis.
For this analysis, we considered the same set of 3-h blood pressure intra-arterial recordings performed in the group of eight cats before and 7 days after SAD that has been used in the main study (see METHODS for the experimental details). On each recording, we searched for the spontaneous sequences (runs of 3 or more heart beats in which SBP and PI progressively increased or decreased) characterized by a SBP-PI lag of 0, 1, and 2 heart beats.
Figure 6 shows the hourly number of
sequences observed before and after denervation in the whole group of
cats as a function of the lag. In intact animals, during
spontaneous behavior most of the sequences are characterized by a
one-beat lag [201 ± (SE) 50] as expected. However, a
nonnegligible number of sequences with lags 0 and 2 (104 ± 34 and
115 ± 34, respectively) are also present. SAD produced a marked
drop in the hourly number of all these sequences regardless of the
value of the lag (
80% for lag 0,
86% for lag 1, and
90% for
lag 2).
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Such a drastic reduction in the number of sequences after denervation, observed for all the three lags considered, not only confirms the baroreflex nature of the sequences with lag 1 (as already demonstrated) but also provides evidence of the major role played by the baroreflex also in the genesis of the sequences with a SBP-PI lags of 0 and 2 heart beats.
From the practical point of view, this finding provides an experimental validation to the inclusion of PI/SBP sequences with lags 0 and 2 in the evaluation of BRS and in the estimation of BEI.
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FOOTNOTES |
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Address for reprint requests and other correspondence: M. Di Rienzo, LaRC-Centro di Bioingegneria, Fondazione Don Carlo Gnocchi and Politecnico di Milano, Via Capecelatro 66 20148 Milano, Italy (E-mail: dirienzo{at}mail.cbi.polimi.it).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 4 January 2000; accepted in final form 2 October 2000.
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