Vol. 277, Issue 5, H1679-H1689, November 1999
Baroreflex stabilization of the double product
Bruce N.
van Vliet1 and
Jean-Pierre
Montani2
1 Faculty of Medicine, Memorial
University of Newfoundland, St. John's, Newfoundland, Canada A1B
3V6; and 2 Institute of
Physiology, University of Fribourg, CH-1700 Fribourg, Switzerland
 |
ABSTRACT |
We investigated whether the baroreflex control
of heart rate (HR) stabilizes the product of arterial pressure
(PA) and HR, called the double
product (DP), an indirect indicator of left ventricular oxygen
consumption. During pharmacological increases and decreases of
PA in conscious rabbits, the mean
(±SE) rate of change of the DP with respect to
PA
(dDP/dPA) was 
88 ± 36 and 20 ± 36 DP units/mmHg, respectively. Regression analysis of all peak responses obtained in individual rats produced a
dDP/dPA value of 15 ± 16 DP
units/mmHg. These estimates were significantly less than the
dDP/dPA value predicted if HR were
constant (184 ± 7 DP units/mmHg) and were not significantly
different from zero. We also compared values of baroreflex sensitivity
(BRS) from the literature with those calculated to provide ideal
stabilization of the DP. BRS values were significantly correlated with
the calculated ideal values (R = 0.95;
n = 14). BRS averaged 128 ± 24%
of the ideal value in all species and 148 ± 28% in mammals and
birds. Our results suggest that stabilization of the DP is a common
consequence of the baroreflex control of heart rate.
baroreceptors; cardiac metabolism; left ventricular oxygen
consumption; heart rate regulation; pressure-rate product
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INTRODUCTION |
IN 1969, Smyth et al. (66) introduced a
simple method for quantifying baroreflex sensitivity (BRS) as the slope
of the relationship between cardiac period and systolic pressure during
the pressor response to an infusion of angiotensin II.
Subsequent adaptations of this approach have been widely used to
investigate baroreflex function in a variety of animals including
humans. In many cases, measurement of BRS has been used to demonstrate
the effect of a treatment or pathology on baroreflex. Although reported
BRS values tend to be consistent within a species, the absolute value of BRS is known to vary considerably between species (6). However, to
the best of our knowledge, no physiological significance has previously
been attributed to the absolute value of BRS.
In this study, we address the hypotheses
1) that the inverse relationship
between heart rate and the mean arterial pressure (PA) imposed by the baroreflex
acts to stabilize the heart
rate-PA product, the so-called
double product, a determinant and correlate of left ventricular oxygen
consumption (8, 43, 46, 62, 63, 77), and
2) that among different species with
widely different values of BRS, the BRS value of a given species is of
an ideal magnitude to stabilize the double product. Our results, based on an analysis of the baroreflex control of heart rate in conscious rabbits and an analysis of BRS values from the literature, suggest that
in a variety of disparate species ranging from toads to humans the
baroreflex control of heart rate is a quantitatively important stabilizer of the double product. This conclusion may have important implications concerning the dynamics of cardiac metabolism and blood
flow, particularly in disease states in which the baroreflex control of
heart rate is known to be impaired and in which coronary reserve may be limited.
Predicted behavior of a system in which adjustments of heart rate
maintain the double product constant despite arterial pressure
perturbations.
The inverse relationship between heart rate and
PA imposed by the arterial
baroreflex will tend to attenuate
PA-induced changes in the heart
rate-PA product, the double
product. If the baroreflex control of heart rate were to function as an
ideal stabilizer of the double product, then the rate of
change of the double product with respect to
PA
(dDP/dPA) should equal zero;
that is, the double product should remain constant despite changes in
PA. In contrast, if heart rate
were fixed at a constant value (i.e., no baroreflex stabilization of
the double product), the double product would increase linearly with
PA and
dDP/dPA would have a value equal to that of the initial heart rate (see APPENDIX
A). In the first part of our results, we use the
relative change in double product with respect to
PA to evaluate the extent to which
the baroreflex stabilizes the double product.
As shown in APPENDIX B, the double
product can be held constant despite changes in
PA if the rate of change of the cardiac interval
(TC) with
respect to PA (i.e.,
dTC /dPA)
is equal to the initial ratio of
TC and
PA; that is, if
|
(1)
|
Because
dTC /PA
is a frequently reported form of BRS
(BRSTC; in ms/mmHg),
Eq. 1 provides a benchmark that we can
use to evaluate how well suited the baroreflex control of the heart is
to stabilize the double product. In the second part of our results, we
use Eq. 1 to evaluate the baroreflex
regulation of double product by comparing reported values of BRS with
the corresponding values of
TC /PA.
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METHODS |
Experiments were conducted using male lop-eared rabbits obtained from
local breeders. Rabbits were housed individually and maintained on a
12:12-h light-dark cycle with free access to water and 180 g/day of
commercial rabbit chow. All procedures were conducted with
the approval of the local animal care authorities.
Evaluation of the baroreflex stabilization of the double product in
rabbits.
The ability of the baroreflex control of heart rate to stabilize the
double product was assessed during pharmacological manipulations of
PA, which were also used to assess
baroreflex function. Ramplike increases and decreases of
PA were achieved by using
intravenous injections of phenylephrine hydrochloride (2-16
µg/kg) and glyceryl trinitrate (4-64 µg/kg), respectively. The
two drugs were given alternately after time was allowed for recovery
from the preceding dose. Drug dosages were prepared in a 0.5-ml volume
of saline, which was loaded into the 0.6-ml dead space of the venous
catheter. To inject the drugs, the catheter was flushed with 1 ml of
saline over a period of 10-20 s. Femoral arterial blood pressure
was measured with a pressure telemeter (Data Sciences International model TA11PA-C40) or a chronic catheter residing in the femoral artery.
Drugs were administered intravenously with the use of a chronic
indwelling femoral or jugular venous catheter or an acutely
catheterized marginal ear vein. Chronic catheters and pressure
telemeters were installed under halothane anesthesia at least 1 wk
before experimentation. PA data
were recorded on a computer at 500 Hz and analyzed off-line.
To estimate the BRS value associated with a single drug injection,
instantaneous heart rate was plotted against
PA so that the segment of the data
containing the linear inverse relationship between heart rate and
PA could be identified. In these
analyses, paired heart rate and PA
data represented concurrent values calculated from the same cardiac
interval. The beginning and end of the linear segment of the heart
rate-PA relationship were noted
for later use (see below). The BRS for heart rate
(BRSHR; in
beats · min
1 · mmHg1)
was estimated as the slope of the least-squares linear regression between heart rate and mean PA
over the linear segment of data. This process was repeated to estimate
the BRSTC (in ms/mmHg) from the
corresponding linear proportional relationship between
TC and mean
PA. In addition, the slope of a
linear least-squares regression between the double product and mean
PA was assessed over the same data
segment used in the preceding regressions. Although the units of this
slope can be reduced to beats/min, throughout this paper we present the
slope as double product (DP) units per millimeter of Hg to emphasize
that values of the slope represent the rate of change of the double
product with respect to PA (i.e.,
dDP/dPA).
Additional estimates of BRSHR,
BRSTC, and
dDP/dPA were calculated by using
the peak responses obtained from all injections of phenylephrine and
glyceryl trinitrate in each rabbit. In this case, estimates of
BRSHR,
BRSTC, and
dDP/dPA were determined as the
slope of a linear regression relating the pharmacologically manipulated
values of mean PA and the
corresponding values of heart rate,
TC, or double
product. Because the absolute peak value of
PA and the corresponding heart
rate and TC
values may reflect extreme responses well beyond the linear range of
the baroreflex control of the heart, calculations of
BRSHR,
BRSTC, and
dDP/dPA were based on peak values
of PA, heart rate, and
TC taken at the end of the linear segment of individual
PA ramps (see above). Control
values of PA, heart rate, and
TC for all
injections were averaged and included as a single additional data point
in the regressions. Thus the number of data points used in each
regression was equal to the number of experimental trials for that
rabbit, plus one.
Analysis of BRS values from the literature.
The main objective of the literature review was to compile resting
values of the ratio of
TC to
PA
(TC /PA)
and BRSTC so that they might be
compared in the largest number of species possible. Because
methodology may have a large impact on the measurement of BRS, this
objective was balanced with the need to limit the review to studies
that used similar methodology. An initial review of the literature
suggested that the most common method of estimating BRS was based on
the cardiac response to an injection of a bolus of a selective
-adrenergic agonist such as phenylephrine. Therefore, a search for
literature concerning BRS published since 1973 was conducted using the
Medline database and the search terms "baroreflex sensitivity"
and "phenylephrine OR methoxamine." To include an additional
species, we also included a study in cats in which small doses of
norepinephrine (1-4 µg/kg) were used to raise
PA (58). To be included, studies
had to be performed in conscious subjects and include control values
for PA and heart rate or
TC so that
TC /PA
could be calculated. We included studies reporting the dynamic
component of BRS occurring during the ramp increase in
PA produced by the bolus or from
the peak response but not BRS estimates obtained from sustained
increases or decreases in PA. We
used BRS values irrespective of whether systolic or mean PA was used to estimate them,
because their relative change during a pressor response is not markedly
different (18) and the two produce similar BRS values (e.g., 1.84 ms/mmHg using mean PA vs. 1.76 ms/mmHg using systolic PA, Ref.
34). For species in which studies were plentiful (i.e., humans, rats,
dogs), we stopped compiling BRSTC
values when we reached a total of 10 acceptable studies. In compiling
these 10 studies, we favored those studies that reported the resting
level of mean PA, because in six
studies in which both the mean and systolic
PA were reported, the use of
systolic PA to calculate
TC /PA
tended to underestimate the ratio by 20-30%. To compare
BRSTC with
TC /PA,
our analysis required BRS to be expressed as
BRSTC. For studies that reported
BRSHR, we used the following
equation to estimate BRSTC from
the reported values of control heart rate
(HRC) and
BRSHR
![BRS<SUB>TC</SUB> = {(60,000 ms/s)/[HR<SUB>C</SUB> + (BRS<SUB>HR</SUB> ⋅ &Dgr;P<SUB>A</SUB>)]}](/content/vol277/issue5/fulltext/H1679/img002.gif)
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![− [(60,000 ms/s)/HR<SUB>C</SUB> ]](/content/vol277/issue5/fulltext/H1679/img003.gif)
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(2)
|
where 
PA = 1 mmHg, the interval of PA over
which BRSHR is usually expressed.
In the present study, for example, control heart rate was 184 ± 7 beats/min (Table 1) and
BRSHR for phenylephrine-induced increases in PA was 3.0 ± 0.5 beats · min1 · mmHg1
(Table 2). The use of Eq. 2 produced an estimate of
BRSTC of 5.4 ms/mmHg, a value 11%
lower than the average measured value of
BRSTC (6.0 ± 1.0, Table 2).
The errors introduced by such approximations and other inaccuracies
inherent in the compilation of control hemodynamic and
BRSTC values were considered to be acceptable relative to the wide range of BRS values compiled, which
varied >70-fold between species.
Statistical analysis.
Values are reported as means ± SE. Student's
t-tests were used to test for
significant differences between values.
P < 0.05 was used as the limit of
statistical significance.
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RESULTS |
BRS and stability of the double product during manipulations of
arterial pressure.
A summary of hemodynamic control values is presented in Table 1. Figure
1 illustrates an example of a pressor
response to phenylephrine (12 µg/kg) and the corresponding changes in
TC, heart rate,
and double product in a rabbit. The ramplike increase in
PA was closely matched by
proportional changes in
TC. These reflex
adjustments in heart rate and
TC resulted in
only a small change in double product despite the >70% increase in
PA (Figs. 1 and
2). An example of a response
to glyceryl trinitrate is also illustrated in Fig. 1.
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Fig. 1.
Example of hemodynamic responses to pharmacological manipulation of
mean arterial pressure (PA).
A-C: administration of
phenylephrine (12 µg/kg iv) in a representative rabbit. Cardiac
interval (TC;
 ) and PA are shown together in
A to illustrate their parallel
behavior. In this example, the reflex slowing of heart rate (HR) during
pressor response is sufficient to prevent increases in double product
(DP). D-F: response to
administration of glyceryl trinitrate (16 µg/kg iv). In this example,
a vigorous HR and
TC response
results in a slight increase in DP.
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Fig. 2.
Relationships of
TC
(A), HR
(B), and DP
(C) with
PA during pressor response to
phenylephrine as illustrated in Fig. 1. Filled symbols represent points
considered to constitute the linear range of
HR-PA and
TC-PA
relationships. Dashed line in C
illustrates increase in DP that would have occurred in absence of a
change in HR.
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Figure 3 illustrates the extent of double
product stabilization that occurred during individual responses to
phenylephrine and glyceryl trinitrate in all rabbits. The extent of
double product stabilization was varied, with individual responses
being distributed on either side of the line representing ideal
stabilization (DP = 0). None of the responses closely approached the
line representing the absence of double product stabilization (DP = PA).
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Fig. 3.
Relationship between changes in DP and mean arterial blood pressure
(BP) plotted for individual responses to phenylephrine or glyceryl
trinitrate. Changes in DP (DP) and BP (BP) are expressed as
percent change from control values. Responses corresponding with ideal
stabilization of DP will lie on the abscissa (DP = 0), whereas those
corresponding with complete absence of DP stabilization will lie along
the line of unity (DP = BP).
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ANOVA revealed no effect of dose on regression results for
phenylephrine or glyceryl trinitrate. The results for all doses of a
given drug were therefore pooled and are summarized in Table 2.
dDP/dPA averaged 88 ± 36 DP units/mmHg (95% confidence interval: 176.8 to 1.1) during
ramp increases in PA and 20 ± 36 DP units/mmHg (95% confidence interval: 107.1 to 67.2)
during ramp decreases in PA.
Because the double product averaged 14,948 ± 839 mmHg/min during
the control period, these values of
dDP/dPA amount to a 0.6%
and 0.1% change in the double product for each 1-mmHg change in
PA. Results obtained
when regressions were performed on the peak responses to pressure ramps
are illustrated in Fig. 4 and summarized in
Table 3. With the use of this analysis
method, dDP/dPA averaged 15.3 ± 16.4 DP units/mmHg (95% confidence interval: 25.0 to
55.5), corresponding to a 0.1% increase in double product for each
1-mmHg change in PA. In the
absence of a cardiac response, the double product would be expected to
increase by 184 ± 7 mmHg/min (95% confidence interval: 166.7 to
202.0), or ~1.2% for each 1-mmHg increment in
PA.
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Fig. 4.
Relationships for changes in HR (A),
TC
(B), and DP
(C) with peak change in
PA during linear ramp increases
and decreases in PA produced by
injections of phenylephrine and glyceryl trinitrate, respectively. Each
filled symbol represents peak (linear) response to an individual
injection of phenylephrine or glyceryl trinitrate. Dashed line in
C represents change in DP that would
have occurred in absence of a change in HR. Open symbols represent mean
control values for all injections. In this rabbit, slopes of
regressions for HR,
TC, and DP were
2.01
beats · min1 · mmHg1
(R = 0.96), 5.04 ms/mmHg
(R = 0.98), and 27.5 DP
units/mmHg (R = 0.57);
n = 9 for all regressions.
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TC /PA
calculated from control data (Table 1) predicts that an ideal
baroreflex stabilization of the double product would require a
BRSTC value of 4.1 ± 0.3 ms/mmHg (Eq. 1). This value is
midway between the estimates of
BRSTC obtained from regressions based on peak responses to phenylephrine and glyceryl trinitrate (3.7 ± 0.9 ms/mmHg) and those based on individual up and down ramps (6.0 ± 1.0 and 4.6 ± 0.8 ms/mmHg, respectively).
Analysis of BRS values from the literature.
A survey of BRS values from the literature for 14 species is compiled
in Table 4.
BRSTC values varied >70-fold,
ranging from 1.3 ms/mmHg in rats to 93 ms/mmHg in turtles.
BRSTC was significantly correlated
with baseline values of
TC /PA
(R = 0.95, Fig.
5), TC
(R = 0.93, Fig.
6), and
PA
(R = 0.83). The negative
correlation with PA presumably
reflected the high BRS and low PA
values in frogs, toads, and turtles, because the correlation with
PA was no longer significant when
these species were excluded (R = 0.36). According to Eq. 1,
ideal baroreflex stabilization of the double product will occur when
the BRSTC value is equal to the
ratio TC /PA.
BRSTC and
TC /PA
values were not significantly different (P = 0.60), although several species
had reported BRSTC values that
were well above or well below the calculated
TC /PA
value: BRSTC ranged from 39% of
TC /PA
in frogs to 341% of
TC /PA
in sheep. On average, the BRSTC
amounted to 128 ± 24% of
TC /PA
in all species (95% confidence interval: 76.2 to 179.8) and 148 ± 28% in mammals and birds (95% confidence interval: 85.0 to
209.4). Regressions of BRSTC
against
TC/PA
for all species produced a slope of 0.55 (P < 0.001). A value of 0.60 (P < 0.001) was obtained when the
regressions were forced to pass through the origin. When regressions
were restricted to data from mammals and birds, the regression slope
was 1.79 (P = 0.03). A value of 1.67 (P < 0.001) was obtained when
regressions were forced to pass through the origin.
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Fig. 5.
Relationship between baroreflex control of cardiac interval
(BRSTC) and resting ratio of
TC to
PA
(TC /PA)
in various species. A: relationship
for mammals and birds. Dashed line represents the regression BRS = 1.79(TC /PA) 0.923 (R = 0.64, n = 11).
B: relationship for all 14 species,
including 3 cold-blooded vertebrates. Dashed line represents the
regression BRS = 0.55(TC /PA) + 5.13 (R = 0.95, n = 14). In
A and
B, solid line represents the
relationship BRS = TC /PA,
which provides ideal stabilization of DP. Data are from Table
4.
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Fig. 6.
Relationship between BRSTC and
resting TC in
various species. A: relationship for
mammals and birds. Dashed line represents the regression BRS = 0.012(TC) 1.89 (R = 0.49, n = 11).
B: relationship for all 14 species,
including 3 cold-blooded vertebrates. Dashed line represents the
regression BRS = 0.030(TC) 7.24 (R = 0.93, n = 14). Data are from Table 4.
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DISCUSSION |
A main objective of the present study was to test the hypothesis that a
consequence of the inverse relationship between heart rate and
PA imposed by the baroreflex is
the stabilization of the heart
rate-PA product, the double
product. This objective was addressed by directly evaluating the rate
of change of the double product with respect to
PA during pharmacological
manipulations of PA in conscious
rabbits. The relative consistency of the double product despite large
changes in PA was evident after
most injections of phenylephrine or glyceryl trinitrate (Fig. 3).
During ramp increases and decreases in
PA, the rate of change of the
double product amounted to 88 ± 36 and 20 ± 36 mmHg/min for each 1-mmHg increment in
PA, values that were not
significantly different from zero. The corresponding value produced by
regression of peak responses amounted to 15 ± 16 DP units/mmHg,
which was also not significantly different from zero. In contrast to
these estimates, the double product would be expected to vary by 186 DP
units/mmHg in the absence of a heart rate change. Our data therefore
suggest that the baroreflex control of the heart tends to stabilize,
and may even reverse, PA-induced
increases in the double product in conscious rabbits.
The second objective of our study was to test the hypothesis that among
different species with widely different values of BRS, the BRS value of
a given species is of an appropriate magnitude to completely stabilize
the double product. To test this hypothesis, we utilized
Eq. 1, which predicts that ideal
baroreflex stabilization of the double product will occur when
BRSTC is equal to the resting TC /PA
value (Eq. 1;
APPENDIX B). In the rabbit,
TC /PA (4.1 ± 0.3) was of a magnitude similar to that of the
BRSTC value, lying midway between
estimates of BRSTC produced by
regressions of peak responses to pressure ramps (3.7 ± 0.9) and
those produced by regression during individual up (6.0 ± 1.0) and
down ramps (4.6 ± 0.8). However, the results of our analysis of
data in the literature were far more striking. Even though
BRSTC varied >70-fold among the
14 species for which data were available, there was approximate
agreement between
TC /PA
and the BRSTC value in most species. BRSTC averaged 128 ± 24% of the
TC /PA
value in all species and 148 ± 28% of that in mammals and birds.
Neither value was significantly different from 100%, which represents
ideal stabilization of the double product. It should be noted that
these mean figures include values for species in which
BRSTC was well above or below the
TC /PA
value. The lowest values of BRSTC
relative to
TC /PA occurred in toads, frogs, and turtles and may reflect a common property
of the baroreflex among ectothermic vertebrates or the occurrence of a
high
TC /PA
in species in with remarkably low PA. Although
BRSTC was well above
TC /PA
in dogs, sheep, and humans, BRSTC
and
TC /PA
were within 30% of each other in 8 of 11 mammalian species for which
data were available.
In the three species in which
BRSTC exceeded
TC /PA
by >30%, the baroreflex control of heart rate would be expected to
overcompensate for the effect of increases in
PA on the double product. In the case of overcompensation, the double product would actually fall below
control levels during an increase in
PA. Although this would be
effective in averting PA-induced
increases in the double product that would otherwise occur, a similarly
vigorous reflex response to a fall in
PA would be counterproductive,
raising the double product above control levels (e.g., Fig. 1).
However, overcompensation during falls in
PA is unlikely to be common or
severe because the BRSTC values
for decreases in PA are generally
less than those for increases in
PA. In the present study, the
BRSTC for down ramps (4.6 ± 0.8 ms/mmHg) was considerably less than that for up ramps (6.0 ± 1.0 ms/mmHg). In both humans and dogs, the BRS measured during a fall
in PA has also been reported to be
considerably less than that during increasing
PA (60% less, Ref. 60; 64% less,
Ref. 36; 69% less, Ref. 23; 48% less, Ref. 22).
At least two possible mechanisms may explain why
BRSTC tends to approximate
TC/PA
in different species. First, a match between BRSTC and
TC/PA
would be advantageous in that it results in stabilization of the double
product and therefore cardiac metabolism. Natural selection may be
expected to favor this arrangement, and, as a consequence, the double
product may tend to be stabilized in most species. Second, it is
additionally possible that baroreflex stabilization of the double
product is promoted by a negative feedback mechanism. It is clear that
baroreceptors are capable of encoding heart rate because they increase
the level of their discharge per unit of time as cardiac frequency is
increased (1). More importantly, direct evidence of the ability of the
baroreflex to both sense and respond to heart rate has been obtained in
subjects with complete atrioventricular conduction block. In these
experiments, increasing the rate of ventricular pacing results in a
slowing of the atrial rate that is not attributable to changes in the
PA level (61). Such responses can
be blocked with atropine and are also observed during spontaneous
ventricular tachycardias in subjects with atrioventricular conduction
block. Because the baroreflex is capable of responding to both
PA and heart rate, it must also be
capable of sensing their product. However, the variable extent to which
the double product was stabilized in rabbits (Fig. 3) suggests that
negative feedback regulation of the double product, if present, must be relatively weak.
The main significance of the ability of the baroreflex control of the
heart to stabilize the double product is that it suggests that the
baroreflex will also tend to stabilize left ventricular oxygen
consumption during changes of PA.
This conclusion is dependent on the ability of the double product to
reflect underlying changes in left ventricular oxygen consumption. A
linear relationship between left ventricular oxygen consumption and
pressure (left ventricular developed pressure) was first described by
Rohde (62) in the isolated isometrically beating cat heart.
Subsequently, a strong linear correlation between the product of heart
rate and mean or systolic PA has
been confirmed by a number of investigators (8, 43, 46, 63, 77).
Although the double product is based on only two of the many factors
influencing left ventricular oxygen consumption, it is a remarkably
robust correlate of left ventricular oxygen consumption under a variety
of conditions (4, 8, 43, 44, 57, 63). One exception occurs during
-adrenergic stimulation of ventricular metabolism, which increases
the ratio of left ventricular oxygen consumption to the double product
(77). This effect on ventricular metabolism is unlikely to have
significantly influenced our present results because the baroreflex is
thought to have relatively modest effects on the sympathetic control of the left ventricle in conscious resting animals (72), and dynamic testing of baroreflex sensitivity occurs over brief periods of time in
which large shifts in cardiac sympathetic tone are not otherwise
expected. Thus the double product is likely to provide a good
indication of the underlying changes in left ventricular oxygen
consumption during the assessment of baroreflex sensitivity. In
addition, our present conclusions based on the use of the double product are consistent with those of a preliminary investigation (70)
in anesthetized dogs in which we demonstrated that increases in direct
measurements of left ventricular oxygen consumption produced by
phenylephrine-induced pressor responses in dogs with paced hearts were
prevented or reversed when the baroreflex slowing of the heart was
allowed to occur. When combined, our results provide strong support for
the concept that the baroreflex regulation of heart rate functions as a
stabilizer of left ventricular oxygen consumption in the face
of changing PA.
The concept that adjustments in heart rate might stabilize the rate of
cardiac energy utilization was originally suggested by Marey (51, 52),
who in 1859 was the first to report the reciprocal relationship between
heart rate and PA. Because the existence of baroreceptors and the concept of the baroreflex regulation of heart rate or PA were not then
known, Marey attributed this response to the heart itself. Although
others have demonstrated that stimulation of carotid sinus
baroreceptors leads to a reduction in left ventricular oxygen
consumption (29, 41), and electrical activation of the carotid sinus
baroreceptors has been used to alleviate symptoms of angina in humans
(19, 28, 30), to the best of our knowledge a role for the baroreflex
control of the heart in stabilizing left ventricular oxygen demand has
not otherwise been addressed.
Because increases in ventricular oxygen demand are generally thought to
be well met with corresponding increases in coronary blood flow and
oxygen delivery by the processes of metabolic autoregulation, the
question remains: Why should the double product be stabilized? One
reason is that because autoregulatory adjustments require ~10 s to be
complete (13, 56), they are not fast enough to cope well with sudden
large changes in PA. This is
supported by the observation that in paced and isolated canine heart
preparations in which the baroreflex control of heart rate is absent,
step increases in afterload cause transient subendocardial
ischemia, tissue hypoxia, and myocardial dysfunction (31, 33,
74). The normal presence of a rapid reflex slowing of the heart may be
expected to attenuate the development of myocardial hypoxia and
dysfunction by preventing
PA-induced increases in left
ventricular oxygen demand. In addition, by increasing the diastolic
time available for coronary blood flow (42), reductions in heart rate
are known to cause marked and immediate increases in coronary perfusion (37, 47). In this manner, reflex adjustments of heart rate may be
anticipated to attenuate or prevent
PA-induced disturbances in
myocardial oxygen balance and performance. These considerations suggest
that the baroreflex control of the heart may be especially important in
compensating for sudden or transient changes in
PA, because the baroreflex control
of heart rate may be the only mechanism capable of influencing
myocardial oxygen balance on a rapid, and in some cases beat-to-beat,
time scale.
Baroreflex stabilization of the double product is not expected to occur
during all hemodynamic disturbances. In many situations including
exercise and arousal, the baroreflex does little to oppose the
pronounced increases in arterial pressure and heart rate that may
occur, and the double product may rise markedly. The baroreflex may be
expected to stabilize the double product during hemodynamic
disturbances that are not directly caused by the autonomic nervous
system, such as those that may be associated with the Valsalva maneuver
or pharmacological manipulations of arterial pressure. The main
mechanism by which the baroreflex may act to stabilize the double
product and cardiac metabolism may simply be through the reflex
regulation of arterial pressure. By stabilizing arterial pressure, the
baroreflex will greatly attenuate hemodynamically mediated changes in
cardiac metabolism that might otherwise occur. However, because the
baroreflex is an imperfect regulatory system and can only attenuate,
not prevent, arterial pressure perturbations, the baroreflex regulation
of arterial pressure alone would not completely stabilize cardiac metabolism. As shown in the present study, disturbances in arterial pressure that occur despite the operation of the baroreflex are accompanied by corresponding reflex changes in
TC that tend to stabilize the double product. Thus the reflex control of cardiac interval (or heart rate) provides a means of stabilizing cardiac metabolism over and above the stabilization provided by the baroreflex control of arterial pressure.
If stabilization of ventricular energy expenditure is a normal
consequence of the baroreflex control of the heart, then impairment of
cardiac baroreflex sensitivity by cardiovascular disease may introduce
an additional strain on myocardial energy balance. It is interesting to
consider that a modest reduction of BRS in hypertension may be
appropriate with respect to stabilization of the double product,
because
TA/PA
is reduced by the elevation of PA.
However, individuals in which the cardiac baroreflex sensitivity is
severely impaired (as may occur in some patients with hypertension,
heart failure, myocardial infarction, and autonomic neuropathies) may be exposed to greater fluctuations in cardiac energy expenditure, even
in association with normal daily activities (e.g., the Valsalva maneuver). This may be particularly damaging in patients with coronary
artery disease in which the effects of existing myocardial ischemia and reduced baroreflex sensitivity may be additive.
Perspectives
The results of the present study demonstrate that the reciprocal
relationship between heart rate and
PA imposed by the arterial baroreflex results in a stabilization of the heart
rate-PA product, the double
product. Because the double product is highly correlated with left
ventricular oxygen consumption, the baroreflex control of the heart may
attenuate or prevent PA-induced
increases in ventricular oxygen demand that might otherwise lead to
myocardial hypoxia and dysfunction. In addition to suggesting a new
interpretation of the physiological significance of the baroreceptor
control of heart rate, our results also raise the question of what
impact reduced baroreflex sensitivity may have on myocardial oxygen
balance. This may be of particular concern in patients with coronary
artery disease in which the effects of existing myocardial
ischemia and reduced baroreflex sensitivity may be additive.
| |
APPENDIX A |
When heart rate is fixed at a constant value, the rate of change of the
double product with respect to arterial pressure is necessarily equal
to the value of the heart rate. This can be shown formally as follows.
When heart rate is constant, then
d(HR · PA)/dPA = HR · d(PA)/dPA = HR, where HR is heart rate, PA
is arterial pressure,
HR · PA is the
double product, and
d(HR · PA)/dPA represents the rate of change of the double product with respect to
arterial pressure.
| |
APPENDIX B |
Because
d(u/v)/dx = 1/v(du/dx) u/v2 · (dv/dx),
where u and
v are functions of
x (Ref. 48), the following
relationship between PA and
cardiac interval
(TC = 1/HR) can
be established:
d(PA/TC)/dt = (1/TC) · (dPA/dt) [PA/(TC)2] · (dTC /dt).
In situations in which the product of heart rate and arterial pressure
remains constant,
HR · PA = k, where
k is a constant. Therefore,
PA/TC = k,
dPA/dTC = 0, and
(1/TC) · (dPA/dt) = [PA/(TC)2] · (dTC /dt).
Rearrangement leads to
dTC /dPA = TC /PA.
Thus the double product remains constant in the face of changing
arterial pressure when the rate of change of cardiac interval with
respect to arterial pressure
(dTC /dPA)
is equal to the initial ratio of the cardiac interval and arterial
pressure
(TC /PA). Because BRSTC is defined as
dTC /dPA
during a blood pressure perturbation, the double product will remain
constant despite changes in arterial pressure when
BRSTC = TC /PA.
It is also possible to define the conditions required to stabilize the
double product in terms of the required reflex changes in heart rate,
but the solution is more complex. It can be shown that a constant
double product will occur when
BRSHR = HR/(PA + PA), where
PA is the size of the
perturbation in PA used to measure
BRSHR. According to this equation,
the ideal value of BRSHR will
depend on the size of the pressure perturbation. Thus the solution is
much simpler in the case of BRSTC,
for which a single ideal value of
BRSTC is predicted from the
control values of
TC and
PA.
| |
ACKNOWLEDGEMENTS |
We thank A. Tempini and L. L. Chafe for expert technical assistance.
| |
FOOTNOTES |
This work was supported by grants from the Medical Research Council of
Canada (to B. Van Vliet), the Heart and Stroke Foundation of New
Brunswick (to B. Van Vliet), the Swiss National Science Foundation (to
J.-P. Montani), and the Swiss Foundation of Cardiology (to J.-P. Montani).
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. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: B. N. Van Vliet,
Faculty of Medicine, Memorial Univ. of Newfoundland, St. John's,
Newfoundland, Canada A1B 3V6 (E-mail: vanvliet{at}morgan.ucs.mun.ca).
Received 13 October 1998; accepted in final form 24 May 1999.
| |
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ABSTRACT
INTRODUCTION
