## Abstract

We investigated whether the baroreflex control of heart rate (HR) stabilizes the product of arterial pressure (P_{A}) and HR, called the double product (DP), an indirect indicator of left ventricular oxygen consumption. During pharmacological increases and decreases of P_{A} in conscious rabbits, the mean (±SE) rate of change of the DP with respect to P_{A}(dDP/dP_{A}) was −88 ± 36 and −20 ± 36 DP units/mmHg, respectively. Regression analysis of all peak responses obtained in individual rats produced a dDP/dP_{A} value of 15 ± 16 DP units/mmHg. These estimates were significantly less than the dDP/dP_{A} 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

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 (P_{A}) imposed by the baroreflex acts to stabilize the heart rate-P_{A} 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 P_{A} imposed by the arterial baroreflex will tend to attenuate P_{A}-induced changes in the heart rate-P_{A} 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 P_{A}(dDP/dP_{A}) should equal zero; that is, the double product should remain constant despite changes in P_{A}. 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 P_{A} and dDP/dP_{A} would have a value equal to that of the initial heart rate (see appendix
). In the first part of our results, we use the relative change in double product with respect to P_{A} to evaluate the extent to which the baroreflex stabilizes the double product.

As shown in appendix
, the double product can be held constant despite changes in P_{A} if the rate of change of the cardiac interval (*T*
_{C}) with respect to P_{A} (i.e., d*T*
_{C} /dP_{A}) is equal to the initial ratio of*T*
_{C} and P_{A}; that is, if
Equation 1Because d*T*
_{C} /P_{A}is a frequently reported form of BRS (BRS_{TC}; 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*T*
_{C} /P_{A}.

## 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 P_{A}, which were also used to assess baroreflex function. Ramplike increases and decreases of P_{A} 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. P_{A} 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 P_{A} so that the segment of the data containing the linear inverse relationship between heart rate and P_{A} could be identified. In these analyses, paired heart rate and P_{A}data represented concurrent values calculated from the same cardiac interval. The beginning and end of the linear segment of the heart rate-P_{A} relationship were noted for later use (see below). The BRS for heart rate (BRS_{HR}; in beats ⋅ min^{−1} ⋅ mmHg^{−1}) was estimated as the slope of the least-squares linear regression between heart rate and mean P_{A}over the linear segment of data. This process was repeated to estimate the BRS_{TC} (in ms/mmHg) from the corresponding linear proportional relationship between*T*
_{C} and mean P_{A}. In addition, the slope of a linear least-squares regression between the double product and mean P_{A} 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 P_{A} (i.e., dDP/dP_{A}).

Additional estimates of BRS_{HR}, BRS_{TC}, and dDP/dP_{A} were calculated by using the peak responses obtained from all injections of phenylephrine and glyceryl trinitrate in each rabbit. In this case, estimates of BRS_{HR}, BRS_{TC}, and dDP/dP_{A} were determined as the slope of a linear regression relating the pharmacologically manipulated values of mean P_{A} and the corresponding values of heart rate,*T*
_{C}, or double product. Because the absolute peak value of P_{A} and the corresponding heart rate and *T*
_{C}values may reflect extreme responses well beyond the linear range of the baroreflex control of the heart, calculations of BRS_{HR}, BRS_{TC}, and dDP/dP_{A} were based on peak values of P_{A}, heart rate, and*T*
_{C} taken at the end of the linear segment of individual P_{A} ramps (see above). Control values of P_{A}, heart rate, and*T*
_{C} 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*T*
_{C} to P_{A}(*T*
_{C} /P_{A}) and BRS_{TC} 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 α-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 P_{A} (58). To be included, studies had to be performed in conscious subjects and include control values for P_{A} and heart rate or*T*
_{C} so that*T*
_{C} /P_{A}could be calculated. We included studies reporting the dynamic component of BRS occurring during the ramp increase in P_{A} produced by the bolus or from the peak response but not BRS estimates obtained from sustained increases or decreases in P_{A}. We used BRS values irrespective of whether systolic or mean P_{A} 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 P_{A} vs. 1.76 ms/mmHg using systolic P_{A}, Ref.34). For species in which studies were plentiful (i.e., humans, rats, dogs), we stopped compiling BRS_{TC}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 P_{A}, because in six studies in which both the mean and systolic P_{A} were reported, the use of systolic P_{A} to calculate*T*
_{C} /P_{A}tended to underestimate the ratio by 20–30%. To compare BRS_{TC} with*T*
_{C} /P_{A}, our analysis required BRS to be expressed as BRS_{TC}. For studies that reported BRS_{HR}, we used the following equation to estimate BRS_{TC} from the reported values of control heart rate (HR_{C}) and BRS_{HR}
Equation 2where ΔP_{A} = 1 mmHg, the interval of P_{A} over which BRS_{HR} is usually expressed. In the present study, for example, control heart rate was 184 ± 7 beats/min (Table 1) and BRS_{HR} for phenylephrine-induced increases in P_{A} was −3.0 ± 0.5 beats ⋅ min^{−1} ⋅ mmHg^{−1}(Table 2). The use of *Eq.2
* produced an estimate of BRS_{TC} of 5.4 ms/mmHg, a value 11% lower than the average measured value of BRS_{TC} (6.0 ± 1.0, Table 2). The errors introduced by such approximations and other inaccuracies inherent in the compilation of control hemodynamic and BRS_{TC} 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.

## RESULTS

#### BRS and stability of the double product during manipulations of arterial pressure.

A summary of hemodynamic control values is presented in Table 1. Figure1 illustrates an example of a pressor response to phenylephrine (12 μg/kg) and the corresponding changes in*T*
_{C}, heart rate, and double product in a rabbit. The ramplike increase in P_{A} was closely matched by proportional changes in*T*
_{C}. These reflex adjustments in heart rate and*T*
_{C} resulted in only a small change in double product despite the >70% increase in P_{A} (Figs. 1 and2). An example of a response to glyceryl trinitrate is also illustrated in Fig. 1.

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 (ΔDP = 0). None of the responses closely approached the line representing the absence of double product stabilization (ΔDP = P_{A}).

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/dP_{A} averaged −88 ± 36 DP units/mmHg (95% confidence interval: −176.8 to 1.1) during ramp increases in P_{A} and −20 ± 36 DP units/mmHg (95% confidence interval: −107.1 to 67.2) during ramp decreases in P_{A}. Because the double product averaged 14,948 ± 839 mmHg/min during the control period, these values of dDP/dP_{A} amount to a −0.6% and −0.1% change in the double product for each 1-mmHg change in P_{A}. 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/dP_{A} 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 P_{A}. 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 P_{A}.

*T*
_{C} /P_{A}calculated from control data (Table 1) predicts that an ideal baroreflex stabilization of the double product would require a BRS_{TC} value of 4.1 ± 0.3 ms/mmHg (*Eq. 1
*). This value is midway between the estimates of BRS_{TC} 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. BRS_{TC} values varied >70-fold, ranging from 1.3 ms/mmHg in rats to 93 ms/mmHg in turtles. BRS_{TC} was significantly correlated with baseline values of*T*
_{C} /P_{A}(*R* = 0.95, Fig.5),*T*
_{C}(*R* = 0.93, Fig.6), and P_{A}(*R* = −0.83). The negative correlation with P_{A} presumably reflected the high BRS and low P_{A}values in frogs, toads, and turtles, because the correlation with P_{A} 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 BRS_{TC} value is equal to the ratio*T*
_{C} /P_{A}. BRS_{TC} and*T*
_{C} /P_{A}values were not significantly different (*P* = 0.60), although several species had reported BRS_{TC} values that were well above or well below the calculated*T*
_{C} /P_{A}value: BRS_{TC} ranged from 39% of*T*
_{C} /P_{A}in frogs to 341% of*T*
_{C} /P_{A}in sheep. On average, the BRS_{TC}amounted to 128 ± 24% of*T*
_{C} /P_{A}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 BRS_{TC}against*T*
_{C}/P_{A}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.

## DISCUSSION

A main objective of the present study was to test the hypothesis that a consequence of the inverse relationship between heart rate and P_{A} imposed by the baroreflex is the stabilization of the heart rate-P_{A} product, the double product. This objective was addressed by directly evaluating the rate of change of the double product with respect to P_{A} during pharmacological manipulations of P_{A} in conscious rabbits. The relative consistency of the double product despite large changes in P_{A} was evident after most injections of phenylephrine or glyceryl trinitrate (Fig. 3). During ramp increases and decreases in P_{A}, the rate of change of the double product amounted to −88 ± 36 and −20 ± 36 mmHg/min for each 1-mmHg increment in P_{A}, 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, P_{A}-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 BRS_{TC} is equal to the resting*T*
_{C} /P_{A}value (*Eq. 1
*;appendix
). In the rabbit,*T*
_{C} /P_{A}(4.1 ± 0.3) was of a magnitude similar to that of the BRS_{TC} value, lying midway between estimates of BRS_{TC} 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 BRS_{TC} varied >70-fold among the 14 species for which data were available, there was approximate agreement between*T*
_{C} /P_{A}and the BRS_{TC} value in most species. BRS_{TC} averaged 128 ± 24% of the*T*
_{C} /P_{A}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 BRS_{TC} was well above or below the T_{C} /P_{A}value. The lowest values of BRS_{TC}relative to*T*
_{C} /P_{A}occurred in toads, frogs, and turtles and may reflect a common property of the baroreflex among ectothermic vertebrates or the occurrence of a high*T*
_{C} /P_{A}in species in with remarkably low P_{A}. Although BRS_{TC} was well above*T*
_{C} /P_{A}in dogs, sheep, and humans, BRS_{TC}and*T*
_{C} /P_{A}were within 30% of each other in 8 of 11 mammalian species for which data were available.

In the three species in which BRS_{TC} exceeded*T*
_{C} /P_{A}by >30%, the baroreflex control of heart rate would be expected to overcompensate for the effect of increases in P_{A} on the double product. In the case of overcompensation, the double product would actually fall below control levels during an increase in P_{A}. Although this would be effective in averting P_{A}-induced increases in the double product that would otherwise occur, a similarly vigorous reflex response to a fall in P_{A} would be counterproductive, raising the double product above control levels (e.g., Fig. 1). However, overcompensation during falls in P_{A} is unlikely to be common or severe because the BRS_{TC} values for decreases in P_{A} are generally less than those for increases in P_{A}. In the present study, the BRS_{TC} 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 P_{A} has also been reported to be considerably less than that during increasing P_{A} (60% less, Ref. 60; 64% less, Ref. 36; 69% less, Ref. 23; 48% less, Ref. 22).

At least two possible mechanisms may explain why BRS_{TC} tends to approximate*T*
_{C}/P_{A}in different species. First, a match between BRS_{TC} and*T*
_{C}/P_{A}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 P_{A} 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 P_{A} 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 P_{A}. 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 P_{A} 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 β-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 P_{A}.

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 P_{A}. Because the existence of baroreceptors and the concept of the baroreflex regulation of heart rate or P_{A} 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 P_{A}. 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 P_{A}-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 P_{A}-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 P_{A}, 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*T*
_{C} 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 T_{A}/P_{A}is reduced by the elevation of P_{A}. 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 P_{A} imposed by the arterial baroreflex results in a stabilization of the heart rate-P_{A} 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 P_{A}-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.

## Acknowledgments

We thank A. Tempini and L. L. Chafe for expert technical assistance.

## Appendix

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 ⋅ P_{A})/dP_{A}= HR ⋅ d(P_{A})/dP_{A}= HR, where HR is heart rate, P_{A}is arterial pressure, HR ⋅ P_{A} is the double product, and d(HR ⋅ P_{A})/dP_{A}represents the rate of change of the double product with respect to arterial pressure.

## Appendix

Because d(*u*/*v*)/d*x*= 1/*v*(d*u*/d*x*) −*u*/*v*
^{2} ⋅ (d*v*/d*x*), where *u* and*v* are functions of*x* (Ref. 48), the following relationship between P_{A} and cardiac interval (*T*
_{C} = 1/HR) can be established: d(P_{A}/*T*
_{C})/d*t*= (1/*T*
_{C}) ⋅ (dP_{A}/d*t*) − [P_{A}/(*T*
_{C})^{2}] ⋅ (d*T*
_{C} /d*t*).

In situations in which the product of heart rate and arterial pressure remains constant, HR ⋅ P_{A} =*k*, where*k* is a constant. Therefore, P_{A}/*T*
_{C}= *k*, dP_{A}/d*T*
_{C}= 0, and (1/T_{C}) ⋅ (dP_{A}/d*t*) = [P_{A}/(T_{C})^{2}] ⋅ (d*T*
_{C} /d*t*). Rearrangement leads to d*T*
_{C} /dP_{A}=*T*
_{C} /P_{A}.

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 (d*T*
_{C} /dP_{A}) is equal to the initial ratio of the cardiac interval and arterial pressure (*T*
_{C} /P_{A}). Because BRS_{TC} is defined as d*T*
_{C} /dP_{A}during a blood pressure perturbation, the double product will remain constant despite changes in arterial pressure when BRS_{TC} =*T*
_{C} /P_{A}.

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 BRS_{HR} = HR/(P_{A} + ΔP_{A}), where ΔP_{A} is the size of the perturbation in P_{A} used to measure BRS_{HR}. According to this equation, the ideal value of BRS_{HR} will depend on the size of the pressure perturbation. Thus the solution is much simpler in the case of BRS_{TC}, for which a single ideal value of BRS_{TC} is predicted from the control values of*T*
_{C} and P_{A}.

## Footnotes

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).

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.

- Copyright © 1999 the American Physiological Society