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Am J Physiol Regul Integr Comp Physiol 288: R1339-R1346, 2005. First published March 3, 2005; doi:10.1152/ajpregu.00038.2004
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NEUROHUMORAL CONTROL OF CARDIOVASCULAR FUNCTION

Nonlinearities and asymmetries of the human cardiovagal baroreflex

Brian E. Hunt1,2 and William B. Farquhar1,3

1Research and Training Institute, Hebrew Rehabilitation Center for Aged, Boston; 2Department of Exercise Science, University of Massachusetts, Amherst, Massachusetts; and 3Department of Health, Nutrition, and Exercise Science, University of Delaware, Newark, Delaware

Submitted 20 January 2004 ; accepted in final form 24 December 2004


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
To determine whether an approach such as the modified Oxford technique can consistently produce data that reveal the nonlinear nature of the cardiovagal baroreflex and to ascertain whether the model parameters provide unique insight into baroreflex function, we retrospectively examined 91 baroreflex trials (38 subjects, 27 men and 11 women, ages 22–72 yr). The modified Oxford technique (bolus sodium nitroprusside followed by bolus phenylephrine) was used to perturb blood pressure, and the resulting systolic blood pressure-R-R interval responses were plotted and modeled using a linear, a four-parameter symmetric, and a five-parameter asymmetric model. Several issues, such as the effect of data averaging, various approaches to gain estimation, and the predictive value of model parameters, were examined during reflex modeling. Sigmoid models accounted for a greater amount of the variance than did the linear model: linear r2 = 0.81 ± 0.01, four-parameter r2 = 0.90 ± 0.08, and five-parameter r2 = 0.90 ± 0.08 (P < 0.05, linear vs. sigmoid models). Data averaging did not affect model fits. Although the four gain estimates (linear remodel, 1st derivative, peak, and set point) were statistically related, the set point gain was significantly lower than other estimates (P < 0.05). Subgroup comparisons between young and older healthy subjects revealed differences in all indexes of cardiovagal baroreflex gain, as well as R-R interval operating range and curvature parameters. In conclusion, the modified Oxford technique consistently reveals the nonlinear nature of the human cardiovagal baroreflex. Moreover, of the parameters produced by the symmetric sigmoid model, only the response range provides unique information beyond that of reflex gain.

sigmoid; mathematical modeling; autonomic nervous system; modified Oxford

ALTERATIONS IN CARDIOVAGAL baroreflex sensitivity are associated with many factors related to cardiovascular health, including advancing age (15), hormonal status (26), and cardiac arrhythmia risk (22). As a result, estimation of cardiovagal baroreflex sensitivity has become commonplace in the study of cardiovascular function, and a multitude of techniques and analytic approaches have been developed to estimate the sensitivity or gain of this reflex loop.

In humans, one of the earliest paradigms to examine baroreflex function was Valsalva's maneuver. However, this approach is relatively nonselective for engaging arterial baroreceptors (6). A more receptor-specific approach was developed by Smyth and colleagues (35): bolus infusions of a pressor agent were utilized to acutely increase blood pressure during recording of the reflex lengthening of the heart period. Termed the Oxford technique, this approach has become a "gold standard" for estimating cardiovagal baroreflex gain. Unfortunately, the relatively small changes in arterial pressure achieved by Valsalva's maneuver, the Oxford technique, and various spontaneous and frequency domain approaches limit analysis of the reflex to only a small portion of the entire sigmoid reflex arc, originally observed in animals and first described by Koch in 1931 (20). Thus only the average gain of the region examined can be derived. This and other shortcomings can be overcome by techniques such as the "modified Oxford" (5) and neck suction (7) techniques. Although both techniques can produce changes across a range of arterial pressures necessary to observe the nonlinear nature of the reflex, in contrast to research in animals, the range of pressure cannot be controlled in such a way as to ensure engagement of the reflex across the entire reflex range. Therefore, the first aim of this study was to determine whether the change in arterial pressure produced by the modified Oxford technique is sufficient to consistently reveal the nonlinear nature of the reflex arc in a broad range of subjects. To address this aim, we retrospectively examined data from 91 baroreflex trials from 38 human study subjects. The data were modeled using linear and symmetric sigmoid models to determine which model produced statistically better fits. However, responses to large perturbations are mediated through baroreceptors with high and low pressure thresholds. Therefore, the response may not be uniform throughout the entire reflex loop (4, 24). This may result in relatively poor data fits when a typical symmetric model is used. Therefore, we also applied a recently developed asymmetric sigmoid logistic model (32) to assess whether systematic asymmetries exist in the human arterial baroreflex arc.

In contrast to the basic linear modeling approach that produces a single estimate of reflex gain, the somewhat more complex sigmoid models provide an opportunity to calculate various gain estimates, such as peak gain and gain at the set point of the reflex, in addition to the traditional gain estimated across the "linear" region of the relation. Moreover, sigmoid models produce several model parameters that have been reported to differentiate between cardiovascular states or subject populations (8, 12, 31). However, there are few data regarding the utility of these mathematical values to inform us regarding baroreflex function. Therefore, our second aim was to examine the ability of the various reflex gain estimates and model parameters to provide insight into baroreflex function. To accomplish this aim, average gain across the most linear portion of the relation was estimated. In addition, we estimated the peak gain and gain at the set point, because many spontaneous indexes are estimated from data within the set point. These gain estimates, along with the model parameters, were compared between groups of young and older adults. Our rationale was that baroreflex function declines with advancing age, and thus valid gain estimates and parameters linked to baroreflex function would be able to distinguish between these groups.


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Ninety-one baroreflex trials were randomly selected from previous studies examining age- and exercise-related differences in baroreflex function in men (15), the effects of estrogen replacement in healthy older women (16), and orthostatic intolerance (9). All study subjects were free of overt cardiovascular disease; they were not obese (body mass index <27 kg/m2), nor were they taking cardioactive medications. All studies were approved by the Institutional Review Board at the Hebrew Rehabilitation Center for Aged (15, 16) or Beth Israel Deaconess Medical Center (9). All subjects gave their written informed consent before participation. Twenty-seven men and 11 women were included in the analysis, and subjects ranged in age from 22 to 72 yr.

In all studies, supine subjects were instrumented with a three-lead ECG for R-R interval recording, finger photoplethysmography for measurement of beat-by-beat arterial pressure (Finapres, Ohmeda Medical, Baltimore, MD), an oscillometric arm cuff for standard brachial arterial pressure (Dinamap, GE Medical Systems, Mount Prospect, IL) for adjustment of Finapres pressures, elastic respiratory transducer bands for measurement of breathing frequency (Respitrace, NIMS, Miami Beach, FL), and an antecubital venous catheter for bolus drug infusions.

The modified Oxford technique was used to assess baroreflex function (5). A bolus injection of the vasodilator sodium nitroprusside (100 µg) was followed 60 s later by a bolus injection of the vasoconstrictor phenylephrine hydrochloride (150 µg) to induce a fall and a subsequent rise in arterial blood pressure of ~15 mmHg below and above baseline. In most subjects, this sequence was repeated two to three times, with 15 min of quiet rest between trials. All data were collected at 500 Hz. Beat-by-beat digitized systolic blood pressures from the original data recordings were associated with the appropriate R-R interval (14). To minimize the potential effects of hysteresis on reflex analysis, we used only data from the nadir to the peak blood pressure response for each trial (18).

To determine whether the modified Oxford technique consistently engages the baroreflex across a broad enough range to appreciate the nonlinear nature of the reflex loop, we used a linear (i.e., y = a + bx) and a symmetric sigmoid model (4, 13, 32) to model the data from each trial:

In this sigmoid model, P1 is the minimum R-R interval, P2 is the reflex response range (the predicted R-R interval range in response to changes in blood pressure), P3 is the curvature parameter, and P4 is the midpoint of the predicted pressure range. As with the linear model, the strength of the relation (r2) can be calculated. In addition, various estimates of reflex gain and model parameters can be calculated, allowing us to estimate the magnitude of the linear relation between model parameters, as well as gain estimates.

The cardiovagal baroreflex has been reported to be asymmetric in some animals (32). Therefore, to maximize our ability to see the sigmoid nature of this reflex loop, we also applied a sigmoid model that includes two curvature parameters:

In this model, P1–P4 are the same as described for the symmetric model, and P5 represents the second curvature parameter, allowing for different curvature above and below the midpoint of the predicted curve. As with the symmetric model, initial parameter values were set as suggested by Ricketts and Head (32), with iterative increments of 1 and maximal iterations of 100 using SigmaPlot 8.0 commercial software.

We presumed that valid model estimates would encompass the set point of the reflex. Therefore, we considered the mean ± SD of the beat-by-beat systolic blood pressure and R-R interval during the 60 s immediately preceding each baroreflex trial to represent the set point of the reflex. The model was considered to adequately encompass the set point if there was overlap between the model's 95% confidence intervals (CIs) and the set point (Fig. 1).



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  		Fig. 1. Systolic blood pressure (SBP)-heart period (R-R interval) relation in 1 trial. A linear and a symmetric sigmoid model are applied to the data. Dashed lines, 95% confidence intervals (CIs) for the sigmoid relation. Set fell within 95% CIs of the symmetric sigmoid model.

 
Almost all analytic approaches to determining baroreflex gain typically average (i.e., bin) the data across some pressure range (5, 14, 18, 36). However, this form of data processing may systematically, or "artificially," improve the model's fit. To determine whether binning systematically increased the magnitude of the relation between variables (r2), the raw, 1-mmHg, 2-mmHg, and 3-mmHg binned data were independently modeled using a symmetric sigmoid logistic function in a random subsample of 30 trials.

Several approaches were used to estimate the gain of the blood pressure-heart period relation. Typically, the gain of this relation is estimated from the slope of the linear region of the reflex arc, but how does one determine the linear portion of a nonlinear response? We attempted to objectively delineate the most linear region of the reflex using the second derivative of the blood pressure-heart period relation. The most linear region of the reflex was defined as the data points that fell between the peak and the nadir of the second-derivative curve (see Fig. 3B).



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  		Fig. 3. A: typical symmetric sigmoid relation (2-mmHg pressure bins) between SBP and heart period. B: 2nd-derivative curve of the sigmoid model. C: "remodeling" approach to determining gain, where data in the linear region, determined from the 2nd-derivative curve in B, are reanalyzed using a linear model. D: 1st-derivative curve of the sigmoid relation from which mean gain (termed "1st-derivative gain"), peak gain, and set point gain are derived.

 
Once the linear region of the reflex was determined, several approaches were used to estimate reflex gain. In the study of human physiology, the data within this region are typically reanalyzed using a linear model ("remodeled gain"). An alternative approach is to directly calculate the average gain across the linear region directly from the first derivative of the logistic function ("1st-derivative gain"). The first derivative can also be used to determine the gain at a single point, such as the maximal or "peak gain" of the relation, as well as the gain at the set point of the reflex ("set point gain").

Finally, to test the utility of the various model parameters and gain estimates produced by the sigmoid models, we compared parameter values between two subgroups known to have different baroreflex function. Previous data clearly demonstrate lower cardiovagal baroreflex gain in older adults than in their younger counterparts (15, 27), so we hypothesized that parameter values that provide physiological information related to baroreflex function would also differ between age groups. Thus gains and parameters derived from the symmetric sigmoid model were compared between younger subjects (16 trials, age 22–38 yr) and older healthy subjects (25 trials, age 53–72 yr).

Statistical analysis. Correlation coefficient (r), 95% CI, and F statistic were calculated for each fit. To determine whether the data produced by the modified Oxford technique consistently fit the sigmoid models better than a linear model, we performed ANOVA for paired data on the r- to z-transformed correlation coefficients (10) due to the positive skewness of correlation coefficients followed by the Newman-Keuls method for multiple comparisons if indicated. The same approach was used to determine whether data averaging systematically produced a better model. The various estimates of baroreflex gain were also compared by ANOVA with Newman-Keuls post hoc analysis, Pearson-product correlation, and Bland-Altman plots. Differences in reflex gain and parameters between younger and older healthy adults were examined via ANOVA for unpaired data. P < 0.05 was considered statistically significant.


   RESULTS
TOP
 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 GRANTS
 REFERENCES
 
Linear vs. sigmoid modeling. A linear model fit the data well across all trials (r2 = 0.81 ± 0.11; Fig. 1). However, the symmetric sigmoid model fit the data somewhat better (r2 = 0.90 ± 0.08, P < 0.05 vs. linear model). In 25% of the trials, the data did not encompass the entire sigmoid relation (threshold, dynamic, and saturation regions), as demonstrated in Fig. 5. Arbitrary cutoff criteria are often used to aid in assessing whether a particular model adequately fits the data. When an arbitrary standard of r2 > 0.70 was used, the linear model met this criterion 84% of the time, whereas 98% of the sigmoid fits met or exceeded this value. The use of the asymmetric model did not provide a better fit of the data (r = 0.90 ± 0.08 vs. 0.90 ± 0.08, P = 0.77) or different model parameters compared with the symmetric sigmoid model (see Table 3). The sigmoid models encompassed the set point in 79% of the trials. Although the set points were evenly distributed at (n = 26), above (n = 23), and below (n = 23) the midpoint of the reflex relation in these trials, a large proportion of set points were near the threshold region in older adults (11 of 25), whereas none of the set points in the younger subjects fell in this region. In those trials where the estimated set point was not encompassed by the model, set points were evenly distributed at (n = 6), above (n = 5), and below (n = 8) the midpoint of the relation.



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  		Fig. 5. Set points not included within the 95% CI of the symmetric sigmoid model. A: trial in which the set point appears shifted to lower blood pressure and, perhaps, higher R-R intervals. B: trial in which the set point is also shifted to the left of data that do not encompass the entire sigmoid relation.

 

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  		Table 3. Age-related differences in model parameters

 
Data averaging. Because of various technical or physiological considerations, data are often averaged, or "binned," when the baroreflex is modeled. When we binned our data on the basis of arterial pressure, we found that increasing bin size was associated with an apparent improvement in model fit (Fig. 2). However, when comparisons of r- to z-transformed data (z-scores) or F statistics were made, binning did not significantly increase the model's predictive power. Because data binning did not affect the model fit and most studies regarding baroreflex function utilize some form of data averaging, all subsequent analyses are based on data averaged over 2-mmHg bins.



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  		Fig. 2. "Binning" of SBP-heart period data. Raw data show no binning.

 
Gain estimates. Figure 3A shows a typical symmetric sigmoid relation between arterial pressure and heart period where gain changes very little at low (threshold) and high (saturation) pressures. The most linear region was selected as the peak to the nadir of the second-derivative curve, where the gain changes precipitously (Fig. 3B). The typical approach, where the data within the linear region of the reflex are reanalyzed using a linear model (the "remodeling" approach), is depicted in Fig. 3C, and Fig. 3D demonstrates gain derived from the first derivative of the sigmoid model. Although remodeling produced robust estimates of reflex gain in the majority of trials, some estimates were based on models with low regression coefficients (Fig. 3C) or only two data points. Nonetheless, we found that the remodeled gain (20 ± 3 ms/mmHg) did not differ from gains calculated from sigmoid model parameters (1st-derivative gain = 20 ± 2, peak gain = 28 ± 2 mmHg), whereas set point gains were significantly lower (13 ± 1, P < 0.05) than all other gains. Although all gain estimates were related to one another (Table 1), there is a fixed and proportional bias in peak gain (Fig. 4).


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  		Table 1. Association between estimates of baroreflex gain

 


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  		Fig. 4. Bland-Altman plots depicting agreement between estimates of baroreflex gain.

 
Model parameters. As expected, all estimates of reflex gain were different between younger and older adults (Table 2). Although all model parameters were significantly related to one another (all P < 0.05), when model parameters were compared between the age groups, we found that only R-R interval range (P2) and curvature (P3 and P5) parameters were different between groups (Table 3). As one would expect, there is a significant relation between curvature parameters and reflex gain in symmetric (r = 0.80) and asymmetric models (r = 0.67 and 0.58 for P3 and P5, respectively), whereas R-R interval range was not correlated with reflex gain (r = 0.08) or other parameters.


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  		Table 2. Age-related differences in estimated baroreflex gain derived from sigmoid model

 

   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
GRANTS
 REFERENCES
 
The present study examined several issues pertaining to cardiovagal baroreflex analysis in humans. 1) We determined that the modified Oxford technique engages the reflex across a range of pressures sufficient to consistently model the nonlinear nature of this relation in a diverse group of subjects. 2) The cardiovagal baroreflex arc does not appear to exhibit obvious asymmetries in humans. 3) We established that data averaging has little impact on the modeling of this reflex arc. 4) We determined that all estimates of reflex gain are related to one another and that, other than gain, the only model parameter that revealed age-related differences in reflex function was the R-R interval range.

Over the range of pressures induced by the pharmacological approach used in this study, we found that the relation between systolic blood pressure and R-R interval was best described by a nonlinear (i.e., sigmoid) function. Although the sigmoid models resulted in smaller errors of estimate, the linear correlation coefficients were always statistically significant, and many (76 of 91 trials) met or exceeded an arbitrary r2 of 0.70. On the basis of this finding, one may be tempted to conclude that linear models are adequate for characterizing the cardiovagal baroreflex arc in humans. Although this is true for a small range in pressure, a linear model would contain increasing estimate error as the pressure range increases. Perhaps this contributes to the poor relation between dynamic estimates of baroreflex gain and spontaneous indexes of autonomic function (23).

Responses to pressure perturbations are mediated through receptors with high and low pressure thresholds. The interaction of these receptors has been proposed to result in asymmetries in baroreflex-mediated responses (4). Therefore, it is plausible that the cardiovagal baroreflex may be better characterized using an asymmetric sigmoid model. However, our analysis indicates that humans do not exhibit systematic asymmetries in the cardiovagal baroreflex relation. Kingwell and colleagues (19) reported a similar finding in seven healthy young adults. However, the approach they employed was to apply separate symmetric sigmoid functions to pressure changes above and below resting pressures, presuming that resting blood pressure (i.e., set point) would occur at the midpoint of the reflex curve. This led to a discontinuity of blood pressure and R-R intervals at the midpoint, requiring various manipulations of the data to compare gains derived from symmetric and asymmetric models. Moreover, because of the assumption regarding set point, this algorithm has little utility when resting pressure is near the threshold or saturation, as has been shown to occur in dogs and hypertensive rats, as well as in some subjects in the present data set. To overcome these possible limitations, we chose to examine 91 sets of baroreflex data from 38 men and women across a broad age range. Furthermore, we applied a single asymmetric logistic model that makes no assumptions regarding set point position. This model has been applied in experimental rabbits and dogs, where approximately one-third of the data demonstrate an improved fit with the asymmetric model (32). This may be due to the fact that we limited our analysis to unidirectional changes in pressure, whereas the data used by Ricketts and Head (32) included data from falling and rising pressure; thus their data may reflect a greater reflex hysteresis in dogs than in rabbits.

The estimated set point was encompassed by the symmetric sigmoid model in ~80% of the reflex trials. This is in agreement with the findings of Ricketts and Head (32), who found that forcing the model to intersect the set point did not improve model fit in most cases. In the few data sets where the set point was not included within the model, a few set points were shifted to the right of the reflex curve, suggestive of a mild anticipatory, or stress, response, whereas several appeared to the left of the predicted reflex curve (Fig. 5), suggestive of resetting during reflex engagement. However, the relatively ramplike engagement of the reflex and the moderate change in arterial pressure make this unlikely. Classic data from Landgren (21) show that ramp changes in arterial pressure, and thus carotid diameter, do not result in baroreceptor resetting. Moreover, changes in barosensory vessel pressure must be >20–60 mmHg. In addition, the preponderance of trials displayed no such apparent shift; therefore, we do not believe that resetting of the reflex is likely. The more likely explanation may be that 60 s of data immediately before reflex engagement can be inadequate to estimate set point in some subjects. Others using similar pharmacological approaches have used the preceding 5 min of data from which to estimate the set point (9), and this may provide a more robust estimate. Most interesting, we found that across all subjects the set point was evenly distributed above, below, and at the midpoint of the reflex relation. However, in ~45% of the older healthy subjects, set points were near the threshold of the reflex, whereas none of the younger adults had set points in this region. This is not surprising, given our understanding that vagal tone declines in older adults. Moreover, this may play a role in the discrepancy often seen between spontaneous indexes of autonomic function and gains derived from the most linear portion of the reflex relation assessed from dynamic perturbations of the receptors.

Most approaches to baroreflex assessment require data averaging. Various spontaneous approaches (1, 2, 33), as well as steady-state infusion protocols (34), average data across some period of time. Even neck suction typically combines the responses from several trials (36). Using the modified Oxford technique, we (14) and others (5, 11) generally binned the blood pressure and R-R interval responses before modeling. Our rationale has been that binning minimizes non-baroreflex-mediated changes in pressure and R-R interval, such as those that occur with ventilation and variability due to measurement error (particularly when the variable of carotid diameter is added to the analysis, as is routinely done in our laboratories). However, as noted by Hunt et al. (14), data binning often appears to decrease the linear fit and improve the sigmoid fit. Contrary to this prior anecdotal evidence, the present analysis showed that data binning had no systematic effect. Thus estimates of cardiovagal baroreflex function should be comparable between models derived from raw or averaged data. Although it is not necessary, data averaging can have advantages when relations between baroreflex function and other physiological variables are examined. For example, recent studies have examined the role of dynamic carotid vascular function in baroreflex control (15, 25). In this case, when estimates of arterial diameter, which likely have greater measurement error than blood pressure or R-R interval, are included in the analysis, data averaging can reduce the error of estimate. Similarly, modeling of the sympathetic limb of the reflex arc, where each cardiac cycle may not have a corresponding sympathetic burst, may require data averaging.

Typically, gain is derived from the slope of the relation between pressure and heart period across the most linear region of the reflex. It is not uncommon for investigators to subjectively define this region through visual inspection (11, 14). More objective, although arbitrary, approaches have been used, such as excluding 5–20% of the upper and lower portions of the reflex response and modeling the remaining data (19, 36). However, this approach does not necessarily exclude only data in and around the threshold and saturation regions, particularly when pressure does not move through either or both of these portions of the reflex arc. Therefore, we chose to use the second derivative of the sigmoid function to guide us in determining the most linear region of the reflex, that portion of the relation where changes in R-R interval are most strongly associated with concurrent changes in pressure (Fig. 3). This approach objectively demarcates the most linear portion of the reflex arc.

As is common, we applied a linear model to the data bins within the linear region of each trial and used the slope of the relation as an estimate of reflex gain (remodeled gain) (11, 14, 23). Although this approach produced gain estimates similar to other approaches, some estimates were based on models with low regression coefficients or only two data points. To overcome these limitations, we simply calculated the mean gain across this region of the sigmoid function on the basis of the first derivative of sigmoid function (Fig. 3D). Across all trials, this approach produced gain estimates similar to the conventional remodeling approach (Tables 1 and 2), without the need to eliminate trials due to low correlation coefficients or minimal data within the linear region. An alternative is to use less strict criteria to delineate the linear region. For example, when the dynamic region of the reflex was defined as that portion of the reflex with gain greater than zero in the trials with questionable remodeled gain estimates, 95% met the arbitrary criterion of r2 > 0.70. Thus the second derivative of the relation between heart period and arterial pressure can be used in numerous ways to objectively define the linear or dynamic region of the reflex relation.

In addition to estimates of gain across a range of the reflex relation, gains can be estimated for any given point within the reflex. In those studies that characterize the entire baroreflex relation, it is not unusual to report the peak gain of the relation (28, 32). By definition, this gain should be greater than those derived across a broad range of pressures. Indeed, peak gain across all trials was greater than all other estimates of gain (Fig. 4) and was significantly associated with all other estimates. Another point estimate of reflex function, the gain at the set point, is not typically calculated or reported. A plethora of techniques have arisen that attempt to exploit the inherent rhythmicity within the set point to estimate autonomic function. Some of these spontaneous estimates have been reported to be clinically relevant; thus set point gain could potentially provide important information regarding reflex function. The set point is generally assumed to lie near the middle of the linear region of the reflex (19, 30, 32) and, thus, should produce estimates of gain similar to peak gain or the mean across the linear region. However, set point gain was significantly lower than all other estimates of gain. This could occur only if the set point was not always near the midpoint of the reflex. We found that it was not uncommon for the set point to lie near the ends of the linear region as previously explained by Eckberg and Sleight (6). This heterogeneity is depicted in the large scatter shown in Fig. 4, C, E, and F. Although the physiological significance of this finding is not clear, it may help explain the poor relations between spontaneous indexes of autonomic function and more robust estimates of baroreflex gain (23). However, one must consider, on the basis of the fact that ~20% of the estimated set points were not encompassed by the models, some inaccurate set point gains were included in our analysis. When we examined the associations between gain estimates only for those trials in which the set point was included within the 95% CI of the model, there was no significant increase in these relations (Table 1).

In his provocative article, Dickinson suggested that it was time to move beyond simply estimating baroreflex gain and examine other, more mechanistic, aspects of baroreflex physiology (3). Perhaps related to this perspective, several authors have begun to report group or state differences in various sigmoid model parameters, the implication being that these mathematical values provide some insight into baroreflex physiology. However, few data exist that can directly inform us regarding the utility of these parameters to provide unique information about reflex function. Ludwig and Convertino (25) used a multidimensional covariance analysis to examine the redundancy of various characteristics of the baroreflex-mediated response. Their analysis suggested that the nine characteristics fell into four classifications, and characteristics within the same classification could be considered to provide redundant information. Although insightful, it was clear that "further work was needed on the quantification of the slope [to determine if other estimates of gain] accurately reflect the response from both a physiological and mathematical perspective" (25). Moreover, the physiological insight that can be gained from various characteristics of the reflex response remains unclear. Therefore, we compared the parameter estimates between groups known to have different reflex function to determine which parameters could differentiate between these groups. Only the curvature (P3 and P5) and R-R interval range (P2) parameter values were different between older and younger adults, suggesting that these values may provide unique physiological insight into baroreflex function in humans. However, because the curvature parameter is highly related to the gain estimate, it is unlikely that this parameter provides any information beyond that found in the gain estimate. Although others have reported differences in the reflex response range (P2), its physiological significance is unclear. In our data, we observed a greater response range (R-R interval) and reflex gain in the healthy younger individuals than in the older adults (Table 3). This is not surprising, given that, in our experience, those with higher reflex gain tend to demonstrate large changes in heart period in response to a challenge to pressure homeostasis, thereby blunting the fall or rise in pressure, although there was not a significant relation between response range and reflex gain. This is somewhat in contrast to the findings of Head and Burke (12), who reported that rabbits induced to hypertension show an increase in their reflex response range (P2), whereas reflex gain declined. This apparent contradiction may be partially explained by the different metrics used for heart period. We used R-R interval, which is linearly related to cardiac vagal neural outflow (17, 29), whereas Head and Burke used heart rate, which is linearly related to blood pressure. When the response range is recalculated using R-R interval, no differences appear to exist between normotensive and hypertensive rabbits.


   GRANTS
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
REFERENCES
 
This work was supported by National Heart, Lung, and Blood Institute Grants HL-59332 and HL-59459 and a generous contribution from the Hinda and Fred Shuman Charitable Foundation (Boston, MA).


   FOOTNOTES
 

Address for reprint requests and other correspondence: B. E. Hunt, Dept. of Exercise Science, Totman 110, 30 Eastman Ln., Amherst, MA 01003 (E-mail: bhunt{at}excsci.umass.edu)

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.


   REFERENCES
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 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 

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