Author + information
- Received June 2, 1997
- Revision received October 1, 1997
- Accepted October 13, 1997
- Published online February 1, 1998.
- Roberto Maestri, MSA,* (, )
- Gian Domenico Pinna, MSA,
- Andrea Mortara, MDA,
- Maria Teresa La Rovere, MDA and
- Luigi Tavazzi, MD, FACCA
- ↵*Roberto Maestri, Centro Medico di Montescano, 27040, Montescano (Pavia), Italy.
Objectives. This study sought to compare, in post-myocardial infarction patients, baroreflex sensitivity (BRS) measured by the phenylephrine method (Phe-BRS) with that estimated by the Robbe (Robbe-BRS) and Pagani (alpha-low frequency [LF] and alpha-high frequency [HF]) spectral techniques.
Background. BRS assessed by Phe-BRS has been shown to be of prognostic value in patients with a previous myocardial infarction, but the need for drug injection limits the use of this technique. Several noninvasive methods based on spectral analysis of systolic arterial pressure and heart period have been proposed, but their agreement with Phe-BRS has never been investigated in post-myocardial infarction patients.
Methods. The linear association and the agreement between each spectral measurement and Phe-BRS were assessed by correlation analysis and by computing the relative bias and the limits of agreement in 51 post-myocardial infarction patients.
Results. The correlation with Phe-BRS was r = 0.63 for Robbe-BRS, r = 0.62 for alpha-LF and r = 0.59 for alpha-HF. The relative bias was significant for alpha-LF (2.6 ms/mm Hg, p < 0.001) and alpha-HF (2.5 ms/mm Hg, p = 0.01) and not significant (−0.6 ms/mm Hg, p = 0.3) for Robbe-BRS. The normalized limits of agreement ranged from −98% to 95% for Robbe-BRS, from −67% to 126% for alpha-LF and from −108% to 143% for alpha-HF. When patients were classified according to left ventricular ejection fraction (LVEF, cutoff value 40%), the relative bias was higher in patients with a depressed LVEF, although statistical significance was high only for Robbe-BRS and was borderline for alpha-LF. The limits of agreement were similar in both groups of patients (p > 0.3).
Conclusions. Despite a substantial linear association, the agreement between spectral measurements and Phe-BRS in post-myocardial infarction patients is weak because the difference can be as large as the BRS value being estimated. Phe-BRS is the measurement most associated with hemodynamic impairment. Because several factors within each method contribute to the overall difference, neither method can be defined as being better than the other in estimating baroreflex gain, nor can one be used as an alternative to the other. Ad hoc studies are needed to assess which method provides the most useful physiologic or pathophysiologic information or the most accurate prediction of prognosis.
Baroreceptor reflex sensitivity (BRS) in humans has been mainly assessed by pharmacologic methods, administering agents that cause changes in blood pressure but do not directly affect heart rate [1–3]. These techniques measure the reflex heart rate response to a pharmacologic activation or deactivation of the arterial baroreceptors. It was recently demonstrated [4–6]that BRS as assessed by the phenylephrine method is of prognostic value in patients after myocardial infarction and adds information to that obtained from traditional measures such as left ventricular ejection fraction (LVEF) and ventricular arrhythmias . However, although the availability of noninvasive pressure monitors has greatly simplified the application of this technique , its widespread clinical use is somewhat limited by the need for drug injection.
In recent years there have been several proposals [8–12]to quantify BRS by using spectral techniques to analyze the relation between spontaneous beat to beat oscillations of systolic arterial pressure (SAP) and heart period (HP), on the basis that the baroreflexes not only control abrupt changes in arterial pressure, but are continuously activated by small variations of SAP around the set point for that particular patient or condition. These methods are very appealing as they do not require the use of drugs, allow continuous monitoring of the baroreflex gain and are simple and fast.
Despite substantial differences in the physiologic models on which the pharmacologic and spectral methods are based, several investigators [8, 10, 11, 13]have proposed that the spectral methods are reliable alternatives to the phenylephrine test, on the basis of correlation analysis. However, their highly promising results have been obtained only in small groups of normal subjects and hypertensive patients; no data have been reported for post-myocardial infarction patients.
The aim of this study was to analyze, in a sample of postmyocardial patients, the agreement between the baroreflex gain as assessed by two well established spectral techniques—those of Robbe et al. and Pagani et al. —and the value obtained by the vasoactive drug phenylephrine. Preliminary results have been presented . We also examined whether the agreement between the two techniques was dependent on the degree of impairment of left ventricular function. As each of these methods has important limitations and none can be considered the standard against which to compare the others, we used appropriate techniques to assess the agreement between observed measurements.
1.1 Subjects and Protocol
We studied 60 patients who had been consecutively admitted to the Montescano Rehabilitation Center after myocardial infarction. All patients had sinus rhythm without evidence of peripheral neuropathy. The rate of ectopic beats was ≤5% in each recording analyzed. All subjects gave informed consent to the study, which was approved by the local ethics committee. Nine patients were excluded from analysis because one or more spectral indexes were not computable because of a lack of coherence between SAP and HP. This led to a final group of 51 patients with an average time from myocardial infarction of 42 days (range 20 to 146). Patients were classified into two groups according to the median value of LVEF: In 25 patients, LVEF was depressed (≤40%) and in 26 it was preserved (>40%).
The experimental sessions for the spectral measurement of the baroreflex gain and for the phenylephrine test were carried out in the morning. After instrumentation (electrocardiographic [ECG] monitor and the Finapres device), patients were asked to lie supine. After a 15-min period for patient and signal stabilization, the Finapres self-adjustment was disconnected and an 8-min recording of ECG and blood pressure signals was performed.
After Finapres recalibration, the self-adjustment was switched off once more and the phenylephrine test was performed according to the Oxford technique as previously described . Briefly, phenylephrine (2 μg/kg body weight) was given as an intravenous bolus to raise SAP by 15 to 40 mm Hg. When the pressure did not increase sufficiently, additional injections were made with increments of 25 μg of phenylephrine. At least three bolus injections were made at 10-min intervals at the dose that caused the desired increase in SAP.
1.2 Signal Acquisition
All analog signals were digitized with a sampling rate of 250 Hz and stored in a personal computer for subsequent analysis. The HP and SAP time series were computed. A resolution of 1 ms was obtained for the HP time series by using a linear interpolation algorithm on the filtered first derivative of the ECG signal.
1.3 Spectral Techniques
The 8-min HP and SAP time series were then plotted together, and the longest portion of signals free from artifacts or large transients having a minimal length of 4.5 min was selected. This choice was a compromise between the length used in the technique of Robbe et al. (4.5 min) and that used in the method of Pagani et al. (512 beats) .
Correction of ventricular premature complexes is mandatory when using spectral techniques to avoid spurious spectral details while preserving the continuity of cardiovascular rhythms . In our software this was performed by means of a semiautomated procedure that substituted each couple of aberrant beats with their average. According to the technique of Robbe et al., bivariate spectral analysis between SAP and HP time series was first performed (we used the Blackman-Tukey approach with a Parzen window having a bandwidth of 0.015 Hz). The transfer function modulus and the coherence function were also computed. The mean value of the transfer function modulus in the frequency band 0.07 to 0.14 Hz, considering only those points where the coherence was ≥0.5, was taken as the measure of the baroreflex gain. We will refer to this index as the Robbe-BRS.
To implement the method of Pagani et al., univariate and bivariate spectral analysis was performed by using the autoregressive approach and related spectral decomposition techniques . The baroreflex gain was quantified by performing the following steps: 1) estimation of the spectrum of HP and SAP and computation of spectral components in the low frequency (LF) band (from 0.04 to 0.15 Hz) and in the high frequency (HF) band (from 0.15 to 0.45 Hz); 2) estimation of the coherence function; and 3) computation of the square root of the ratio between the HP and the SAP spectral components in both bands, provided that the coherence between these components was >0.5. These two indexes are usually called alpha-LF and alpha-HF, respectively. An example of the computation of the spectral indexes of Robbe and Pagani et al. is shown in Fig. 1.
1.4 Analysis of the Phenylephrine Test Data
Ectopic beats were first removed from raw recordings of HP and SAP. Each systolic pressure peak was associated with the subsequent RR interval. The time series of HP and SAP changes with respect to the corresponding median values during the preinjection phase were then plotted together, and the analysis window was defined as the interval between the beginning and the end of the first increase in SAP ≥15 mm Hg. The slope of the regression line relating HP changes to SAP changes in the analysis window was automatically computed. Only regression lines with a statistically significant slope (p < 0.05) were accepted for analysis. A final slope was obtained by calculating the mean value of at least three measurements. This index will be referred to as Phe-BRS.
1.5 Data Analysis
The linear association between spectral and phenylephrine measurements was assessed by correlation analysis. The agreement of the two measurements was assessed by analyzing the differences between them (spectral measurement − phenylephrine measurement). A statistical model of observed measurements was assumed in which both the phenylephrine and the spectral measurements are supposed to be corrupted by two independent components of error: a systematic component (commonly called “bias”) and a random component (see Appendix A). Hence, when the difference between the two measurements is considered, it is also constituted by a systematic term (called “relative bias”) and by a random term that accounts for the random error of both methods.
Following a well established and efficient approach , we plotted the individual differences (for instance, the differences between the Robbe-BRS and Phe-BRS measurements) as a function of the average of the two measurements. The average of the two measurements is the best estimate we can have of the “true” value of the baroreflex gain of each subject. We also computed the mean and the 95% confidence intervals of the differences (the so-called limits of agreement ). The mean difference estimates the relative bias or constant offset between the two methods. The limits of agreement, in contrast, give a realistic picture of the range of values within which 95% of individual differences between the spectral and standard measurements lie. The limits of agreement were also computed on the normalized difference, obtained by dividing the difference between two measurements by their mean value and multiplying by 100. Hypothesis testing for the bias (null hypothesis: bias = 0) was performed by the one-sample ttest; testing for differences between groups was performed by the ttest for independent samples. Comparisons of the width of limits of agreement were performed by the F test.
The agreement between the spectral and phenylephrine measurements was also assessed by computing quartiles of the variables and measuring the proportion of patients ranked within the same quartiles by the two methods.
A p value ≤ 0.05 was considered statistically significant. When multiple comparisons were performed, the Bonferroni correction was applied; for a family of three comparisons, this implies a significance level of 0.014.
The clinical characteristics of the patients are given in Table 1.
2.1 Measurements by Individual Methods
Descriptive statistics of the four BRS measurements for all patients and for patients with depressed and preserved LVEF are reported in Table 2. Although all BRS measures were lower in patients with impaired than with preserved LVEF, only phenylephrine measurements changed significantly, with a mean value in the latter group being about twice that in the former. Alpha-LF and alpha-HF data showed a higher value of mean BRS with respect to Phe-BRS both in the overall group and in the two subgroups. Moreover, these measurements were characterized by a larger spread of the data among patients.
2.2 Agreement between Measurements
2.2.1 Overall Study Group
The scatterplots of each spectral estimate of BRS versus phenylephrine measurements are shown in Fig. 2. The identity lines are also plotted. There is a substantial linear association for all comparisons, as assessed by the correlation coefficient (r ≈ 0.6). However, several points in all three plots lie far from the line of identity, and all the spectral indexes tend to overestimate low Phe-BRS values. Fig. 3a displays the Bland-Altman plot of the difference against the mean for the comparison between the Robbe-BRS and the Phe-BRS measurements. Differences as great as −10 ms/mm Hg can be observed over a baroreflex gain ranging from ∼1 to 25 ms/mm Hg. This high dispersion of values is made evident by the limits of agreement, which span from −9.0 to 7.7 ms/mm Hg. Hence, 95% of observed differences between the two methods are expected to lie within this range, in other words, the Robbe-BRS measure may underestimate the Phe-BRS by as much as 9 ms/mm Hg or overestimate it by as much as 7.7 ms/mm Hg. The slight bias between the two measurements, which is estimated by the mean difference, is not significant. Detailed results are given in Table 3.
It is clear from Fig. 3a that, owing to the lack of homogeneity of the distribution of the differences over the observed range of baroreflex gain, the computed limits of agreement tend to be overestimated for low gain values and underestimated for high values.
When the normalized difference (Fig. 4a) is considered, the distribution becomes much more uniform. The corresponding limits of agreement range from −98% to 95%. Hence, one can expect the difference between the two measurements to be almost as large as the baroreflex gain being estimated. Similar considerations can be drawn from Fig. 3bFig. 4b and Fig. 3cFig. 4c, for the comparison, respectively, of alpha-LF and alpha-HF with Phe-BRS. For these measurements, however, a highly significant positive bias and larger limits of agreement can be observed. When subjects were ranked by quartiles, <50% were equally classified by the two methods (45% for Robbe-BRS, 45% for alpha-LF, 35% for alpha-HF, all with respect to Phe-BRS).
2.2.2 Depressed and Preserved LVEF
The results for patients with reduced and preserved LVEF are given in Table 3. Correlation coefficients between spectral measurements and Phe-BRS were higher in the patients with LVEF >40% than in those with LVEF ≤40%. However, none of these differences was statistically significant (p > 0.1 for all comparisons).
In patients with impaired LVEF all spectral methods gave higher estimates of BRS than did phenylephrine, but this positive relative bias reached statistical significance only for alpha-LF and alpha-HF. In patients with preserved LVEF, the positive relative bias between alpha-LF and alpha-HF versus Phe-BRS was lower than in patients with depressed LVEF. However, this difference was not significant for alpha-HF (p = 0.40) and was borderline for alpha-LF (p = 0.033). Conversely, it was negative and highly significant for Robbe-BRS (p < 0.001). Concerning the width of the limits of agreement, the two groups showed substantially similar results (p > 0.30 for all three comparisons), indicating an equivalent magnitude of the random component of the difference.
The present investigation shows that in a group of patients with previous myocardial infarction, despite a substantial linear association, the agreement between BRS obtained by spectral techniques and by the phenylephrine test is rather weak, as the difference between the two measurements can be as large as the baroreflex gain being estimated.
The alpha-LF and alpha-HF indexes showed a positive systematic offset with respect to Phe-BRS in patients with depressed or preserved LVEF. The Robbe index, in contrast, showed a positive offset in patients with depressed LVEF and a negative offset in the other group. The limits of agreement were similar in the two groups.
Several theoretic and methodologic factors may account for the observed lack of agreement between spectral and phenylephrine measurements: different physiologic conditions under which the gain of the baroreflex is measured, differences in the models of cardiovascular regulation on which each method is based and measurement error due to signal conditioning, processing algorithms and analysis criteria.
3.1 Disagreement due to Physiologic Difference
There are four major differences in the physiologic conditions under which the phenylephrine and spectral measurements of baroreflex gain are taken. 1) The pressure change induced during the phenylephrine test basically overrides both the pressure to pressure reflexes (through changes in peripheral resistance, arterial and venous compliance, heart contractility and other factors) and the heart rate-pressure feedforward mechanism, thus approximating an open loop condition. Spectral measurements, in contrast, are based on spontaneous fluctuations of SAP and heart rate and are taken with all reflexes and control mechanisms fully active, that is, in a closed loop condition. Hence, significant differences in the relation between SAP and HP in the two conditions are likely. 2) The phenylephrine method requires a ramp increase of SAP of ≥15 mm Hg, giving rise to a certain degree of baroreceptor “stretching,” whereas spontaneous oscillations of systolic pressure usually span a few mm Hg around its set point. 3) The ramp increase in pressure associated with phenyleprine injection is a different stimulus for the baroreceptors than the “oscillatory” stimulus that is implicitly assumed by spectral techniques. These methods, in fact, are all based on the notion of “spectral component” or “cardiovascular rhythm,” in both the LF and HF bands, which is based on the experimental observation of quasi-periodic oscillations in these bands . 4) The peripheral vasoconstriction induced by phenylephrine may cause the activation of other receptors like cardiopulmonary mechanoreceptors (as a result of increased afterload) and exert a direct effect on the vessel walls of carotid and aortic arteries, which might in turn modify their firing rate. The former effect may be more pronounced in patients with left ventricular dysfunction, thus acting as a potential confounder on HP changes induced by the drug.
3.2 Differences in Modeling Assumptions
Each of the four techniques considered in this study (Phe-BRS, Robbe-BRS, alpha-LF and alpha-HF) implicitly assumes a model of short-term pressure regulation . Depending on the appropriateness of these models to the underlying physiologic mechanisms, the estimated BRS will be more or less accurate, adding further variability to the differences among the considered methods. The phenylephrine method, for instance, assumes that each HP value is related to the previous SAP peak and that this relation is linear . However, it has been suggested that a more accurate model should represent each RR interval as a function of at least a few preceding beats, to take into account the slower sympathetic influences as well. The method of Robbe et al. basically assumes an open loop model relating SAP to HP even though signals, as noted, are actually analyzed in a closed loop condition. Finally, the spectral method for baroreflex gain estimation proposed by Pagani et al. assumes a closed loop model, where changes in SAP induce changes in HP and these, in turn, affect SAP , but a few major simplifications are made to allow for mathematic solution. In fact external disturbances are supposed to affect only SAP, which is equivalent to assuming that fluctuations in HP are almost entirely driven by blood pressure fluctuations alone through the baroreceptors (i.e., all other central or reflex influences on the sinoatrial node are negligible) . Baselli et al. showed elegantly from a mathematic point of view that the application of this model simplification is the cause of a positive bias (up to 41%) in alpha-LF and alpha-HF indexes compared with Robbe-BRS. Our study results confirm these theoretic expectations as the relative bias of alpha-LF and alpha-HF is consistently greater than that of Robbe-BRS (see Table 3).
3.3 Measurement Error
The lack of agreement between Phe-BRS and spectral indexes of baroreflex gain is partly dependent on measurement error of both quantities. Although the design of this study does not allow for the estimation of the magnitude of measurement error, its possible sources can be discussed. One source could be related to the fact that spectral indexes of baroreflex gain are obtained from recordings different from those used to estimate Phe-BRS. We have previously shown that the precision of Finapres measurements is lower in the postinjection phase than in stationary condition. Well recognized sources of variability in the phenylephrine method are mainly due to the rate of injection, the steepness of arterial pressure increase and the subjective choice of the window for the analysis . Accordingly, averaging the results of at least three consecutive responses has been proposed in order to increase measurement precision.
Two main sources of measurement error are relevant in the estimation of spectral indexes: the statistical instability of spectral estimates, due to the finite record length of the time series analyzed , and the signal to noise ratio of the signals within the frequency bands in which the indexes are computed. Concerning the first issue, although increasing the record length increases statistical stability, in practical analysis there are two main limitations: 1) the stationarity requirement for spectral estimation (which is difficult to satisfy in long records), and 2) the need for periodic readjustment of the Finapres device. On the basis of results of a previous investigation , we argue that the record length selected for this study, which is a reasonable compromise between the Robbe-BRS Pagani-BRS methods, is an adequate choice. Concerning the second issue, reduced power of the LF and HF bands, has been associated with patients with left ventricular dysfunction, thus implying a lower level of the signals of interest (i.e., spontaneous LF and HF oscillations) with respect to contaminating noise. This in turn would give rise to lower coherence values and a related higher positive bias of alpha-LF and alpha-HF indexes (see previous paragraph).
The accuracy of BRS estimates also depends on the computation criteria adopted in the application of each method. In estimating Phe-BRS, for instance, the algorithm used is unique (i.e., simple linear regression) and the acceptance of each computed slope depends solely on its statistical significance. In spectral methods, in contrast, results are dependent on the spectral algorithm used and on related analysis criteria (such as type and width of the spectral window, order of the autoregressive model, threshold for coherence).
Although several drugs are known to affect the autonomic balance, for patients under treatment the medication schedule did not differ between the times of phenylephrine and spectral BRS assessment.
3.4 Previous Studies
Spectral estimation of baroreflex gain has been validated in small samples of normal subjects or hypertensive patients [8, 10, 13]. These studies have shown that the different methods are significantly related.
We obtained a correlation coefficient between alpha-LF and Phe-BRS of 0.62 and between alpha-HF and Phe-BRS of 0.59; both values are quite similar to those Pagani et al. obtained for the same indexes in 11 hypertensive subjects. Our correlation coefficient of 0.63 between Robbe-BRS and Phe-BRS is slightly higher than that (r = 0.48) obtained by Watkins et al. using a similar methodology in 42 normotensive and borderline hypertensive subjects. Conversely, Robbe et al. observed an excellent correlation coefficient of 0.94 in eight healthy volunteers. The reasons for these discrepancies are not clear, but we can speculate that they might depend on the lower coherence we found in our patients (median coherence 0.6, range 0.5 to 0.8) compared with that in the normal subjects studied by Robbe et al. (median coherence 0.8, range 0.4 to 0.95); the different sample size (51 subjects vs. 8); and the different range of the baroreflex sensitivity taken into consideration (1 to 27 ms/mm Hg in our study, 7 to 27 ms/mm Hg in the study of Robbe et al.).
However, use of the correlation coefficient to assess the agreement between two measurement methods has been criticized . For example, this value depends on the range of observed measurements and is unable to distinguish between linear relations lying along the line of identity and any other kind of linear relation . To overcome these limitations we adopted the simple and powerful technique of computing the bias and the limits of agreement. Manually deriving these parameters from the scatterplot shown in the report of Watkins et al. , we found a larger bias with an opposite sign (≈−8.1 ms/mm Hg) to that found in our study, and a similar magnitude of limits of agreement (≈−153% to 31%).
3.5 Role of Ventricular Dysfunction
The average value of Phe-BRS was significantly different between patients with reduced and preserved LVEF, whereas this difference was no longer significant for spectral indexes, thus suggesting a greater dependence of Phe-BRS on the degree of ventricular dysfunction.
The correlation coefficients between phenylephrine and spectral indexes tended to be lower in patients with depressed LVEF, indicating a higher proportion of uncorrelated information between the two measurements in this subgroup of patients. This would suggest that impaired LVEF might emphasize the different physiologic conditions under which BRS is assessed (see earlier). Indeed, in the presence of an increased sympathetic drive as observed in patients with depressed LVEF, small changes in HP induced by small changes in SAP (as quantified by spectral techniques) are likely to be preserved, whereas a greater increase of HP after a phenylephrine-induced increase in SAP (>15 mm Hg) may be limited. Moreover, in the presence of left ventricular dysfunction a significant increase in afterload by causing a further hemodynamic impairment, may activate other mechanisms (reduction in rate of rise of left ventricular pressure [dP/dt] of the pulse waveform, cardio-cardiac reflexes) which interfere with the reflex bradycardia induced by phenylephrine, ultimately leading to an underestimation of BRS. This hypothesis is consistent with our data as shown by the higher relative bias for alpha-LF and alpha-HF and by the change from negative to positive in the bias of Robbe-BRS. However, the possibility that the model simplifications applied for alpha-LF and alpha-HF spectral measurements overestimate the baroreflex gain to a greater extent in patients with a more impaired LVEF has also to be taken into account.
Nevertheless, despite a different bias, the random component of measurement error, as shown by the limits of agreement, is similar in patients with preserved and depressed LVEF, confirming that spectral indexes and Phe-BRS cannot be used as alternatives in either patient groups.
The relation between BRS and the function of the left ventricle (in patients with a previous myocardial infarction) is of particular interest. Because the derangement in neural endings at the infarct site associated with changes in left ventricular geometry and myocardial contractility are the likely causes of the impaired baroreflex gain after myocardial infarction, a logical expectation would be that the larger the infarct size (and, accordingly, the greater the left ventricular dysfunction), the lower the baroreflex gain. Although a previous report found no linear association between Phe-BRS and LVEF in patients without clinical signs of heart failure after myocardial infarction, in a larger series of postmyocardial infarction patients Phe-BRS was significantly lower among subjects with more severe ventricular dysfunction. However, even in the present larger series, the lack of a significant linear relation between Phe-BRS and LVEF did not allow us to consider BRS after phenylephrine injection as an index of the status of ventricular function.
3.6 Clinical Implications and Conclusions
As several factors within each method contribute to the overall difference (systematic and random) between Phe-BRS and spectral indexes, neither method can be considered better than the other in estimating baroreflex gain nor used alternatively to the other without a great chance of marked errors. Further investigations are needed to assess which method provides the most useful physiologic or pathophysiologic information or the most accurate prediction in prognosis. Our data and data from other studies suggest that the agreement between the pharmacologic and spectral techniques and their applicability may depend on the patient group considered. In postmyocardial infarction patients we found a weak agreement between the indexes in patients with depressed and more preserved LVEF. Lower values of baroreflex gain were observed when using the phenylephrine technique as compared to spectral measures in patients with impaired LVEF.
A.1 The Statistical Model
The basic statistical model assumed for the measurement of baroreflex sensitivity has the form: (1)where xikis the measurement taken on subject iwith the kth method (k= 1, 2, 3, where 1 represents phenylephrine, 2 the method of Robbe et al. and 3 the method of Pagani et al.); αkis the bias of the kth method; πiis the true value (also called “true score” or “steady state value”) of the baroreflex sensitivity of the subject; and ϵikrepresents a random contribution due to the measurement process that is supposed to be independent of πi, have zero mean and fixed variance.
To study the agreement between the kth spectral method (k = 2, 3) and the phenylephrine method, their difference is first computed: (2)where Δαkrepresents the relative bias and can be easily estimated by computing the mean d̄kof the observed differences between the two measurements. The standard deviation of the ηikterm can be estimated by the sample standard deviation skof the same differences.
Assuming δikto be normally distributed, the 95% limits of agreement are defined as : (3)
- baroreflex sensitivity measured by the high frequency spectral method of Pagani et al. in the high frequency band
- baroreflex sensitivity measured by the low frequency spectral method of Pagani et al. in the low frequency band
- baroreflex sensitivity
- high frequency (0.15 to 0.45 Hz)
- heart period
- low frequency (0.04 to 0.15 Hz)
- left ventricular ejection fraction
- baroreflex sensitivity measured by the phenylephrine method
- baroreflex sensitivity measured by the spectral method of Robbe et al. 
- systolic arterial pressure
- Received June 2, 1997.
- Revision received October 1, 1997.
- Accepted October 13, 1997.
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