Analysis of blood pressure–heart rate feedback regulation under non-stationary conditions:

beyond baroreflex sensitivity

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Physiol. Meas. 30 (2009) 631–645 doi:10.1088/0967-3334/30/7/008

Analysis of blood pressure–heart rate feedbackregulation under non-stationary conditions: beyondbaroreflex sensitivity

Mikhail I Bogachev1,2,5, Oleg V Mamontov3, Alexandra O Konradi3,Yuri D Uljanitski2, Jan W Kantelhardt4 and Eugene V Schlyakhto3

1 Institut fur Theoretische Physik, Justus-Liebig-Universitat Giessen, Heinrich-Buff-Ring 16,35392 Giessen, Germany2 Radio Systems Department, St Petersburg State Electrotechnical University, Professor PopovStreet 5, 197376 St Petersburg, Russia3 Federal Almazov Heart, Blood, and Endocrinology Centre, Akkuratova Street 2, 197341 StPetersburg, Russia4 Institut fur Physik, Martin-Luther-Universitat Halle-Wittenberg, von-Seckendorff-Platz 1,06099 Halle/Saale, Germany

E-mail: Mikhail.Bogachev@physik.uni-giessen.de

Received 8 March 2009, accepted for publication 11 May 2009Published 5 June 2009Online at stacks.iop.org/PM/30/631

AbstractThe feedback regulation of blood pressure and heart rate is an importantindicator of human autonomic function usually assessed by baroreflexsensitivity (BRS). We suggest a new method yielding a higher temporalresolution than standard BRS methods. Our approach is based on a regressionanalysis of the first differences of inter-heartbeat intervals and blood pressurevalues. Data are recorded from 23 patients with hypertension and sleep apnoea,22 patients with diabetes mellitus and 23 healthy subjects. Using the proposedmethod for 3 min data segments, we obtain average regression coefficientsof 9.1 and 3.5 ms mmHg−1 for healthy subjects in supine and orthostaticpositions, respectively. In patients with hypertension, we find them to be 3.8 and2.6 ms mmHg−1. The diabetes patients with and without autonomic neuropathyare characterized by 3.1 and 6.1 ms mmHg−1 in the supine position comparedwith 1.7 and 3.3 ms mmHg−1 in the orthostatic position. The results are highlycorrelated with conventional BRS measures; we find r > 0.9 for the dualsequence method. Therefore, we suggest that the new method can quantifyBRS. It is superior in distinguishing healthy subjects from patients both insupine and orthostatic positions for short-term recordings. It is suitable for non-stationary data and has good reproducibility. Besides, we cannot exclude thatother regulatory mechanisms than BRS may also contribute to the regressioncoefficients between the first differences.

5 Author to whom any correspondence should be addressed.

0967-3334/09/070631+15$30.00 © 2009 Institute of Physics and Engineering in Medicine Printed in the UK 631

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Keywords: heartbeat intervals, blood pressure, tilt test, heart rate variability,baroreflex sensitivity, non-stationary conditions

(Some figures in this article are in colour only in the electronic version)

1. Introduction

The feedback regulation of blood pressure and heart rate is a major function of the centraland autonomous nervous system. Studying its dynamics improves understanding humanautonomic function and dysfunction. Several regulatory mechanisms act continuously andsimultaneously on heart rate and blood pressure. According to a simplified model (Paratiet al 1992), these mechanisms can be generally classified as feed forward and feedback. Thesimplest feed forward effect is the direct mechanical coupling, as increases (or decreases)in heart rate directly cause increases (or decreases) in blood pressure. In addition, centralmechanisms affect both heart rate and blood pressure. Sympathetic activation increases strokevolume and arterial stiffness leading to increased cardiac chronotropic function and bloodpressure. Parasympathetic influences affect heart rate and vessel tone, leading to decreasedheart rate and blood pressure. In addition, mechanisms such as statokinetic reflexes and reninextraction by the kidneys are involved in the orthostatic position.

The feedback mechanisms limiting fluctuations in blood pressure by rapidhaemodynamical changes are mainly represented by baroreflex components, for example,by the cardiochronotropic component of the arterial baroreflex. Mechanoreceptors activityfrom high blood pressure zones affects vessel tone and heart rate, leading to a decrease inblood pressure and a decrease in heart rate (i.e., lengthening the heartbeat intervals). The mainquantity characterizing the efficiency of this feedback mechanism is baroreceptor sensitivity,or baroreflex sensitivity (BRS). This indicator is widely used as a prognostic marker in clinicalsettings (Eckberg et al 1992, Schwartz et al 1992, Dawson et al 1997, La Rovere et al 2001,Nollo et al 2001). In particular, post-infarction patients with impaired BRS show highercardiac mortality than those with recovered BRS (Schwartz et al 1992). It was found thatthe level of BRS is essential for risk stratification in patients with life-threatening arrhythmias(La Rovere et al 2001). BRS decline was also shown to be an early indicator of transientautonomic dysfunction in patients with neuro-cardiogenic syncope (Freitas et al 1999). WhileBRS does not essentially react to mental stress (Adler et al 1991, Fauvel et al 2000), it changessignificantly under a variety of physical stressors, e.g. orthostatic pressure (Adler et al 1991,Julu et al 2003).

In this paper, we suggest a new method to quantify the efficiency of the feedback regulationof blood pressure and heart rate. The method is based on the first differences of systolic bloodpressure (SBP) values and following heartbeat intervals. It can be applied to short datasegments under non-stationary conditions. We calculate the regression coefficients betweenthe first differences during simultaneous increases (decreases) of the SBP and lengthenings(shortenings) of the following heartbeat interval. Since the feedback mechanisms are mainlyrepresented by the baroreflex components, we compare the calculated regression coefficientswith standard BRS estimates. Here, we compare with time-domain BRS methods and spectralBRS methods studying data measured during tilt tests in healthy subjects and in patients withimpaired autonomic regulation, including patients with hypertension and diabetes mellitus. Inthe supine position, we find high correlations of the quantities obtained with the new methodand the BRS values obtained with conventional techniques. In the orthostatic position, we

Analysis of blood pressure–heart rate feedback regulation under non-stationary conditions 633

Table 1. Description of the studied subject groups.

Normal Patients with Patients withsubjects hypertension diabetes mellitus

Age (mean ± SD) (year) 42.1 ± 7.2 45.3 ± 11.3 39.8 ± 8.7Male/female 10/13 9/14 10/12Body weight (kg) 63.9 ± 9.7 106.5 ± 18.4 70.6 ± 14.0Body mass index 22.1 ± 2.3 35.1 ± 5.9 23.1 ± 3.6Apnoea/hypopnoea index – 38.9 ± 13.7 –

find that the new method can better distinguish between healthy subjects and patients thanconventional BRS estimates. In addition, it yields significantly lower variations within thesubject groups under non-stationary conditions. In patients with diabetes mellitus, the newmethod successfully distinguishes between patients with and without autonomic neuropathy.Finally, we show that the new method is able to quantify dynamically the changes in theautonomic regulation status during a tilt test. We believe that the regression slope calculatedwith our method mainly represents the baroreceptor sensitivity. However, this is currentlya result of statistical considerations, and we cannot exclude that changes related to otherautonomic and central mechanisms during the tilt test also partially contribute to the quantity.

2. Subjects and methods

2.1. Subjects and experimental protocol

We studied 23 patients with essential hypertension (level II, moderate) accompanied by sleepapnoea syndrome, 22 patients with diabetes mellitus (type I) and 23 healthy volunteers. Meanage and gender ratio as well as the values characterizing their pathologies are given in table 1for all groups.

Prior to their inclusion into the study, all subjects gave an informed consent about theprotocol which was approved by the local ethical committee. After an initial recording in thesupine position, head-up tilt table testing (tilt test) was performed under identical laboratoryconditions between 10 am and 1 pm. Tilt tests were run in accordance with the Westminsterprotocol (table tilt: 60◦, maximal duration of the orthostatic position: 45 min) (Brignole et al2004). Pre-tilt supine phase duration was around 10 min. We neither used any pharmacologicalstimulation to elicit syncope nor included patients with any therapy that could influence theautonomic regulation status. Some patients with diabetes mellitus demonstrated positive tilttest responses according to the criteria adopted (Brignole et al 2004), so that the diabetesgroup was subdivided into two subgroups according to their autonomic regulation status.To achieve this, the following six established autonomic neuropathy markers from formerclinical investigations of the same patients have been used: Valsalva ratio, total power of HBinterval fluctuation, cold-pressure vasoconstriction, 30:15 ratio, orthostatic hypotension andparadoxical dynamic of the lower frequency component of HB intervals during orthostasis(see Brignole et al (2004), Clarke et al (1979), Malik et al (1996), Rothschild et al (1987) andVictor et al (1987) for the definitions). The 12 patients who demonstrated at least two positivemarkers out of these six markers were classified as patients with autonomic neuropathy, whilethe 10 remaining diabetic patients were classified as patients without autonomic neuropathy.

During all the tests, pulse intervals and beat-to-beat SBP values were recorded non-invasively with Finometer (TNO, The Netherlands), and ECG was recorded with cardiograph

634 M I Bogachev et al

Cardio-8 (APRY, St Petersburg, Russia). The results of several previous studies show explicitlythat both the blood pressure values and the conventional BRS estimates obtained using the non-invasive volume-clamp method originally introduced by Penaz (1973) are in a good agreementwith those obtained from invasive ones (Pinna et al 1996, 2000). We confirmed very highcorrelations of the pulse intervals with the R–R intervals obtained from the ECG in our study(r > 0.98), consistent with previously reported results (Low et al 1997). Further processingof the recorded data was performed offline. We applied the first differences method and theconventional BRS estimation techniques to the data as described below.

First, we studied segments of 3 min duration, both for the last minutes of the supineposition and after the (relative) stabilization in the orthostatic position. However, in manyrecords, the second segment could not be regarded as stationary (while checking by the runtest), especially for the SBP in those patients who demonstrated later a positive response to thetilt test. The main goal was to demonstrate the performance of the novel first differences methodin comparison with conventional BRS estimation techniques described below in quantifyingthe autonomic regulation and in distinguishing between the subjects with normal and impairedautonomic function.

Finally, we have applied the same methods to shorter data fragments in short time windowsrunning over the whole tilt test record to show the consecutive changes in the autonomic statusin the orthostatic position.

2.2. Conventional time-domain approach for measuring BRS

The most widely applied time-domain method is the sequence method (Bertinieri et al 1985,Malberg et al 2002). In this study, we use the dual sequence method denoted by M2.Sequences of at least three consecutive SBP values and three following heartbeat intervalswith unidirectional behaviour are selected, separately for increases in SBP and lengtheningsin heartbeat intervals (‘brady’, SBP↑), and for decreases in SBP and shortenings in heartbeatintervals (‘tachy’, SBP↓). Changes of at least 1 mmHg in SBP and of at least 4 ms in heartbeatintervals are assumed to be over the noise threshold. Then the slopes of the regression linesbetween SBP values and heartbeat interval values are calculated for each sequence. Slopesare averaged separately in each 3 min segment to be used as a measure of BRS.

The most important advantage of the time-domain method for our tests under stressconditions is the fact that heartbeat intervals and SBP time series need not be stationary. Adisadvantage of the time-domain methods is the usage of information only from segmentsdemonstrating consistent behaviour, disregarding most of the measured data.

2.3. Conventional frequency-domain (spectral) approaches for measuring BRS

The second group of BRS estimation methods consists of algorithms operating in the frequencydomain (De Boer et al 1985, Robbe et al 1987, Cerutti et al 1987, Badra et al 2001,Pinna et al 2002). Although spectral BRS estimations were reported to be slightly morerepresentative than those performed by time-domain techniques (Dawson et al 1997), thereare also several limitations. Firstly, high coherence between heartbeat intervals and SBPoscillations is required. Recently, it has been reported that this requirement can be neglectedto improve statistics at least for the transfer function method (Pinna et al 2002), see also Laudeet al (2004). A second limitation regards all spectral methods. They need at least 5 minrecordings under stationary conditions to yield BRS values comparable for different methods(Clayton et al 1995). There is no evidence of the methods’ performances for shorter data

Analysis of blood pressure–heart rate feedback regulation under non-stationary conditions 635

segments. A third limitation of spectral techniques lies in the inability of providing separateinformation about bradycardiac and tachycardiac effects in BRS.

In this study we use the following two frequency-domain approaches.

The power spectral density method (M3). Equidistant datasets are generated by cubic splineinterpolation of the measured data series followed by resampling at 5 Hz sampling frequency.Power spectral densities are calculated for both the supine and for the orthostatic recordsegments by Thomson’s multi-taper method (Marple 1987). The analysis is performedseparately in the low-frequency (LF) band (0.04–0.16 Hz) and the high-frequency (HF) band(0.16–0.4 Hz). The square root of the quotient of the integrals from the individual powerspectral densities of the heartbeat intervals and the SBP values is calculated for all frequencies(Cerutti et al 1987) (see also Parati et al (1992)), where the local coherence of both signals(defined as the quotient of the squared absolute value of the cross-spectral density and theproduct of the individual power spectral densities (Bendat and Piersol 1986)) exceeds 0.5. Theaverage of these square roots for each of the 3 min segments is used as a measure of BRS.

The transfer function method (M4). Equidistant datasets are prepared in the same way as forM3. The transfer function, i.e. the ratio of the cross-spectral density of heartbeat intervals andSBP values and the spectral density of SBP values, is calculated (Robbe et al 1987, Badraet al 2001). The average absolute value of the transfer function in the selected frequencyband is used as a measure of BRS. Again, LF and HF bands are considered separately, but nolimitation on the coherence between signals is applied.

2.4. The first differences method (M1)

To overcome the limitations of the time-domain and frequency-domain methods discussedabove, an alternative method is proposed here. To eliminate trends occurring both in heartbeatintervals and SBP values during functional tests (e.g. during the orthostatic tilt test), weemploy the simplest detrending procedure: studying differences of consecutive SBP valuesand differences of following heartbeat intervals. Generally, information on the short-timedynamics is provided by the combined probability density function of the first differencesof heartbeat intervals (�HBI) and SBP values (�SBP). Regulatory responses with prevalentinfluence of the feedback mechanisms (mainly represented by the baroreflex mechanism) arelocalized in the quadrants with �SBP > 0 and �HBI > 0 as well as �SBP < 0 and �HBI < 0.On the other hand, regulatory responses with dominating feed forward mechanisms (like directmechanical coupling) are localized in the quadrants with �SBP < 0 and �HBI > 0 as well as�SBP > 0 and �HBI < 0. A separate estimation of bradycardiac (�SBP > 0, �HBI > 0) andtachycardiac (�SBP < 0, �HBI < 0) regulation is achieved. For each 3 min data segment,all points with �SBP > 0 and �HBI > 0 are selected for the ‘brady’ feedback (SBP↑), andall points with �SBP < 0 and �HBI < 0 are selected for the ‘tachy’ feedback (SBP↓). Wecalculated the regression coefficients between �HBI and �SBP in both quadrants. We callthis approach the ‘first differences method’ in the following.

To disregard uncertain changes, a minimum threshold value for �SBP and �HBI shouldbe applied. Moreover, we suggest disregarding very fast changes (that are often measurementartefacts) by setting an upper limit for the first differences. Both limit values should be selectedsuch that only physiologically feasible changes in SBP and heartbeat intervals are regarded.In this study, beat-to-beat changes of less than 1 mmHg in SBP or less than 3 ms in heartbeatintervals and more than 20 mmHg in SBP or more than 100 ms in heartbeat intervals wereignored. We also considered higher thresholds for the SBP values up to 4 mmHg and comparedthe results.

636 M I Bogachev et al

The main advantage of the suggested method is that information on many more datapoints can be used than in the classical sequence method, since the condition of at least threeconsecutive pairs of measured values with unidirectional behaviour is dropped. This improvesthe statistics for short data recordings and—particularly important—the time resolution in longrecordings (providing reliable estimations in short time windows). However, the advantage isclosely associated with a disadvantage, i.e. the inability of the suggested method to disregardHF oscillations commonly associated with mechanisms of autonomic regulation other thanthe baroreflex, e.g. with respiratory modulation. Moreover, the method studies series offirst differences rather than the original time recordings. It is thus difficult to comparestraightforwardly the values obtained by this technique with the BRS values estimated byother methods.

2.5. Statistical analysis

To quantify the statistical significance of our results, we apply a three-factor analysis of variance(ANOVA), considering initial classification into the groups as an among-subject factor andposition and quantification method applied as two within-subject factors. For checking thenormality of the distribution of calculated BRS values, we applied the Shapiro–Wilk test. Wefound that normality generally holds in healthy subjects in the supine position (except forthe results of M4), while it was often violated in the orthostatic position and in groups withpathologies. Therefore, Student’s t-test was applied for M1–M3 only to check reproducibility,while we used the Wilcoxon sign-rank test for independent samples for all methods M1–M4.For pairwise comparisons between values obtained for the same subjects in the supine and inthe orthostatic position, the Wilcoxon sign-rank test for paired samples has been applied. TheBonferroni correction was used for the probability threshold values (originally 0.05).

A comparison of the two recordings in the supine position available for healthy subjectsand patients with hypertension (before and after a tilt test) was used to quantify thereproducibility of the methods. To assess the reproducibility, we applied a complex proceduretesting both for possible systematic differences and for the random fluctuations in the values.Where normality held we used Student’s t-test to check for systematic differences. To cover thecases without a normal distribution of the values, we used the Wilcoxon sign-rank test suitablefor comparing paired samples and for detecting random changes. Finally, we calculatedthe correlation coefficients between the values obtained within both groups in the first and inthe second supine recording to see if the within-group deviations were systematic and repeatedin the second recording. We consider a method to have good reproducibility if the p-values inthe t-test and the Wilcoxon sign-rank test exceed 0.1 (for the cases without normality Wilcoxonsign-rank only) and the correlation coefficient exceeds 0.5.

3. Results

Significant changes in SBP up to the third minute in the orthostatic position were registeredin both, normal subjects (105 ± 10 mmHg versus 119 ± 6 mmHg) and diabetic patientswith concomitant autonomic neuropathy (134 ± 41 mmHg versus 155 ± 35 mmHg). Inthe other groups, non-significant changes were found (137 ± 32 mmHg versus 144 ±18 mmHg in hypertensive patients with sleep apnoea and 133 ± 18 mmHg versus 137 ±16 mmHg in diabetic patients without concomitant autonomic neuropathy). However, insome of the patients in each group, trendy behaviour of SBP and heartbeat intervals wasregistered. The feedback regulation of SBP and heartbeat intervals was quantified by the newfirst differences method M1 and the three conventional BRS methods M2–M4 described in

Analysis of blood pressure–heart rate feedback regulation under non-stationary conditions 637

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Figure 1. (a) Heartbeat intervals (in s), (b) systolic blood pressure values (in mmHg) and(c–e) local BRS coefficients (in ms mmHg−1) obtained with the first differences method M1(triangles), the dual sequence method M2 (circles), the spectral method M3 (squares) and thetransfer function method M4 (diamonds) in non-overlapping windows of length (c) 64, (d) 32 and(e) 16 data points for a representative healthy subject. Panels (f)–(j) show the same quantities fora patient with diabetes mellitus and concomitant autonomic neuropathy.

subsections 2.2–2.5. The detailed results for 3 min data segments for each patient group andmethod are summarized in table 2.

Both the new and the conventional time-domain methods have shown good reproducibilityaccording to a three-method criterion (see section 2). In addition, M4 being applied in the LFband also demonstrated good reproducibility. However, in patients with hypertension, onlythe new first differences method M1 yielded reproducible values during the second supinemeasurement. In addition, M1 calculated significantly different values in normal subjectsand patients in all cases except for the orthostatic recording for patients without autonomicneuropathy. M1 thus seems to be a sensitive tool for quantifying the autonomic regulationstatus and detecting autonomic neuropathy in the supine and orthostatic position.

In the following, we study BRS estimators for short data windows in order to quantify itsdynamical changes during functional tests. Figure 1 shows the data from two representativesegments of tilt test recordings including the last 3 min of the supine position, the transition tothe orthostatic position, and the following 3 min of the orthostatic position, one record froma healthy subject and one from a patient suffering from diabetes mellitus with concomitantautonomic neuropathy. In addition to the heartbeat interval and the SBP series, the localestimates of the first differences regression coefficients (M1) and the conventional BRSestimates (M2–M4) are shown for three different lengths of running windows: 64, 32 and 16data points. To improve statistics, the ‘brady’ and the ‘tachy’ values have been averaged forboth time-domain methods. Only the LF band has been considered in the spectral methods,disregarding frequencies with coherence below 0.5 in M3. Since the lowest frequency in theLF band is 0.04 Hz, we could not consider window sizes of 16 data points in M3 and M4. The

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Table 2. Regression coefficients (in ms mmHg−1) characterizing feedback regulation of SBP and heartbeat intervals obtained with the first differences method (M1) and the dualsequence method (M2) for ‘brady’ (SBP↑) and ‘tachy’ (SBP↓) feedback, as well as BRS values obtained with spectral methods (M3 and M4) within the low-frequency (LF) and thehigh-frequency (HF) bands for 3 min fragments in the supine and in the orthostatic position. All the data are presented in the format of the median ± interquartile range; the mediansand the interquartile ranges of the ratios of orthostatic values and supine values are reported in the lines ‘Orthostatic/supine’.

Note. Black cells with white text indicate significant differences between initial (supine) and orthostatic values (Wilcoxon’s sign-rank test for paired samples, Bonferroni’s correctionwith initial p < 0.05). Bold font indicates good reproducibility during the repeated supine position (assessed using complex criteria described in section 2.5). Grey cells mark all caseswith significantly different values for controls and patients with different pathologies (Wilcoxon’s rank-sum test for the independent samples, Bonferroni’s correction with initial p < 0.05).

Analysis of blood pressure–heart rate feedback regulation under non-stationary conditions 639

figure shows that M3 and M4 are characterized by a significantly higher number of anomalousmeasurements in comparison with M1 and M2.

For all time-domain methods, we have calculated the fraction of considered data points,i.e. the quotient of the number of SBP values used in the analysis over their total number. Thisindicator is closely related with the capability of the techniques to provide statistically validestimations from short-term recordings. The first differences method M1 used 55 ± 10% ofall data points, while the dual sequence method M2 used only 33 ± 13% for 3 min segments.The sequence method was not able to calculate any estimate in several windows of length 32or 16, since no sequences with unidirectional behaviour were found therein.

Figure 2 shows quantitative statistics of the short-time estimates for the same methodsand window sizes as in figure 1, over 3 min segments in the supine and in the orthostaticposition for each cohort. One can see that both frequency-domain methods are characterizedby significantly broader interquartile ranges, in comparison with the time-domain methods.The transfer function method, based on the Fourier transform, yields the most fluctuatingquantity, especially for small window lengths. The most stable estimates are provided by thefirst differences method M1. Overall, M1 yields the lowest average interquantile variations ofthe measurements in different windows, both in the supine and in the orthostatic position forall three window lengths considered.

In addition, we used a three-factor ANOVA for 3 min data segments of all subject groupsconsidering both supine and orthostatic position. We found that all factors (group, positionand method) as well as all possible interaction between these factors are significant. For amore detailed analysis, we focused on pairwise comparisons.

While all methods yielded at least comparable results for the supine position, the spectralmethod M3 failed in detecting a significant reaction to the orthostatic load in both normalsubjects and patients with hypertension, while M4 failed only in patients with hypertension.This is mainly due to the large deviations caused by several anomalous BRS values, indicatinga weak robustness of spectral methods under non-stationary conditions in several patientsdemonstrating a prolonged progressive decline in SBP. Another problem with spectral methodsin the HF band is that they probably put more emphasis on physiological effects different fromthe baroreflex mechanism. Both the new and the conventional time-domain methods (M1 andM2), on the other hand, recognized a significant decline in the regression coefficients as areaction to the orthostatic load (medians of the declines between 21 and 60% were registered).The first differences method shows a consistent decline in both, the ‘brady’ and the ‘tachy’regression coefficients with lowest interquartile ranges in most cases (see table 2). Besides,the coefficients calculated with M1 are in nearly quantitative agreement with the BRS valuesobtained using M2.

While there are many failures in distinguishing between patients with diabetes mellituswithout autonomic neuropathy and normal subjects, both with and without orthostatic load, allmethods yield significantly reduced BRS in the diabetic patients with autonomic neuropathy(see table 2). However, reduced BRS in patients with hypertension and concomitant sleepapnoea is found only in the supine position by all conventional methods. Just the dual sequencemethod M2 for the ‘tachy’ sequences can detect the reduction of BRS also under the non-stationary conditions of orthostatic load in these patients. The first differences method M1yielded significantly different values in normal subjects and patients in all cases except forthe orthostatic recording for the patients without autonomic neuropathy. Thus it seems tobe a sensitive tool for quantifying the autonomic regulation status and detecting autonomicneuropathy in the supine and orthostatic position.

Table 3 reports the correlations between BRS values estimated by different methods,showing a matrix of correlation coefficients calculated for all healthy subjects in the supine

640 M I Bogachev et al

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Figure 2. Median values and interquartile ranges for the BRS estimates (in ms mmHg−1) obtainedby methods M1 to M4 applied in non-overlapping windows of (a) 64, (b) 32 and (c) 16 data points.

Analysis of blood pressure–heart rate feedback regulation under non-stationary conditions 641

Table 3. Correlation matrix of BRS estimates, obtained with different methods for all healthysubjects in the supine position. Grey backgrounds mark low correlation coefficients (r < 0.60).

position. The values obtained with M4 in the HF band demonstrated the lowest correlationswith the other methods. This can be explained by different physiological effects emphasizedwhen studying rhythms in the HF band, rather related to sympathetic and vagal activity as wellas respiratory modulation effects than to baroreceptor activity. In the LF band, significantlyhigher correlation coefficients with the time-domain methods indicate more similarity. Thefirst differences method M1 yields very high correlations with the dual sequence method M2(r > 0.9), and relatively high correlations (r > 0.65) with the spectral method M3 andthe transfer-function method M4, the latter two applied in the LF band. On the other hand,correlations with the estimations obtained for the HF band with M4 are significantly lower. Thisprovides us with evidence that—despite the absence of Fourier filtering—the first differencesmethod emphasizes rather the physiological effects related with the baroreflex mechanismthan those related with sympathetic or vagal activity, respiratory modulation of physiologicalrhythms, etc.

To find out the prevalence of feedback effects (mainly represented by the baroreflexregulatory mechanism) and feed forward effects (mechanical coupling), we have studied thecombined distribution of �SBP and �HBI for each individual subject; see figure 3 for anexample. As explained in section 2.4, feedback effects are located in quadrants B and D, whilefeed forward effects are located in quadrants A and C. We disregard all points with |�SBP| or|�HBI| below the noise level. We find that the combined distribution is quite independent ofpathology and/or condition. In all subjects, 20–24% of the total time was under prevalence ofstraightforward mechanical coupling, when the heartbeat interval increases (decreases) causedSBP decreases (increases). However, 50–60% of time a clear prevalence of the feedbackeffects was observed, since heartbeat interval increases (decreases) followed SBP increases(decreases). A slight imbalance observed between quadrants B and D, as well as A and C isdue to the difference between the initial and the final conditions of the test, and should not playa significant role when studying longer recordings. Increasing the lower �SBP threshold to4 mmHg yielded only 9% of total time with feedback coupling and increased the fluctuationsof the estimated regression coefficients. However, comparable median values were obtainedfor all BRS quantities.

Figure 3 also shows that the combined probability density function of the first differencesof heartbeat intervals and SBP values is more spread along the SBP axis for the patientscompared with healthy subjects. This effect can be quantified by the square root of the sum ofvariances of the first differences in quadrants B and D. Significantly lower values were foundin patients with diabetes mellitus compared with healthy volunteers (15.3 ± 7.1 and 23.3 ±10.6 ms mmHg−1, respectively; p < 0.01). In the orthostatic position, both values significantly

642 M I Bogachev et al

(a) (b)

Figure 3. Representative examples of combined probability density functions for the firstdifferences of heartbeat intervals (�HBI, in ms) and SBP values (�SBP, in mmHg) in supinepositions for (a) a healthy subject and (b) a patient suffering from diabetes mellitus with concomitantautonomic neuropathy.

decreased further (13.2 ± 5.8 and 17.7 ± 10.4 ms mmHg−1; p < 0.05). We suggest that thesechanges are due to the total reduction in heart rate variability as a reaction to the orthostaticload, demonstrating less reserve of the autonomic nervous system capability for adaptation tospontaneous changes in SBP.

4. Discussion

Studying the combined distribution of the first differences of SBP values and followingheartbeat intervals, we found that feedback-dominated situations are nearly three times morefrequent than feed forward-dominated situations. This clearly shows that the feedbackmechanisms play a major role in the regulation of SBP and heart rate. There was practically nocontinuous prevalence of one mechanism for more than ten consecutive data points, showingthat both mechanisms are always active and compensating each other. Applying four differentmethods to quantify the feedback regulation of SBP values and heartbeat as well as BRS(as dominant mechanism of the feedback regulation), we found a significant decrease in allfeedback parameters under the orthostatic condition in most healthy subjects and patients withautonomic disorders.

We suggest that the first differences method should be chosen for studying data in shortmoving time windows, since it allows characterizing the autonomic regulation status withhighest resolution in time dynamically during functional tests. In addition, it yields the bestrobustness and reproducibility in analysing non-stationary segments of physiological records.Besides, it is superior to the conventional methods in distinguishing autonomic regulationpathologies from normal regulation, especially when only short data segments are available.

The reproducibility of different BRS methods has been studied before by Dawson et al(1997), who reported slightly better reproducibility for spectral methods. However, the studyconsidered only healthy subjects and supine recordings, selecting 5 min segments with stableSBP (<10 mmHg fluctuations) and regular breathing. In our study, lower reproducibility wasobserved for the spectral methods since we included data from the orthostatic position notfulfilling these criteria for blood pressure stability. Under our conditions, the first differencesmethod yielded the most representative quantity characterizing the feedback regulation of SBPand heartbeat interval values in both normal subjects and patients.

We like to note that the first differences method is robust to single artefacts occurring inthe recordings. Examples of such artefacts (spikes or outliers) can be seen in figures 1(a), (b)

Analysis of blood pressure–heart rate feedback regulation under non-stationary conditions 643

and (f). Such spikes cause changes exceeding the maximal �HBI or �SBP limits. They arethus automatically eliminated from the analysis. In spectral methods, on the other hand, suchartefacts must be removed beforehand. The same feature makes the first differences methodmore suitable to analyse data from non-invasive measurements assessed with the volume-clamp method realized in Finometer. The periodical self-recalibration procedure required bythis technique results in the absence of SBP values during several heartbeats; a new value isprovided later. Since �SBP = 0 during recalibration, the calibration points are automaticallyeliminated from further analysis. In spectral methods, the spline interpolation of the data usedwhile creating equidistant sequences reduces (but not eliminates) the recalibration problem.

Since the proposed method deals with the regression analysis of first difference values ofSBP and heartbeat intervals, it is hard to give a physiological proof that this is straightforwardlymeasuring BRS. However, the baroreflex mechanism is the most important contribution to thefeedback regulation of SBP and heart rate. There is thus no doubt that the baroreflex contributessignificantly to our suggested regression coefficient. There is also strong statistical support forthis suggestion, since the correlations between the values of the first differences method and thedual sequence method as well as the two frequency-domain methods are very high for supinerecordings. The latter three methods are typical tools to quantify BRS under spontaneousblood pressure fluctuations. On the other hand, there is a systematic difference between thevalues calculated by the new and the conventional methods, at least in the supine position.The first differences method yields slightly lower values than the conventional ones. Possiblya certain correction is needed to make direct comparison of these values with conventionalBRS measures from previous studies. Besides, we cannot exclude the possible contribution ofother autonomic regulation mechanisms to the values obtained by the first differences methodon the basis of our physiological knowledge.

5. Summary, conclusion and outlook

To summarize, we have suggested a new method to quantify the feedback regulation of bloodpressure and heart rate, the easily implemented first differences method. We have comparedit with three well-established methods quantifying arterial BRS. According to our findings,the first differences method is a sensitive tool in quantifying the feedback regulation, robustagainst measurement artefacts and suitable for non-stationary conditions. It yields betterreproducibility than all three standard methods when applied to data of the same subjectsin the supine position before and after a tilt test. In addition, reliable estimations with lowvariance can be obtained from much shorter data segments, allowing observing dynamicalchanges in the SBP—heart rate feedback regulation.

In most cases, the first differences method also distinguished between healthy andpathological subject groups studied under similar conditions, showing its efficiency in detectingautonomic disorders. For long data segments, its parameter is highly correlated with the BRSvalue obtained from the most established BRS method in healthy subjects in the supine position.Therefore, it most likely characterizes BRS effects of autonomic regulation. However, possiblecontributions of other regulatory mechanisms cannot be excluded.

Analysing tilt test recordings can quantify changes in the autonomic regulation status inthe orthostatic position in comparison with the supine position. For all (patho-) physiologicalgroups, we observed a significant decline in both the first differences regression coefficientsand their standard deviations with tilt. This decline seems to be characteristic of the orthostaticposition.

In this study, we relied explicitly upon results obtained from clinical recordings of realheartbeat intervals and SBP values. However, this is not fully sufficient for a quantitative

644 M I Bogachev et al

characterization of the methods and their performance for data with strong trends, high noiselevels, missing points (e.g. missed R peaks in the ECG or missed pulse peaks), very shortdata, etc. Such problems are rather common in data recorded from subjects under stress-testconditions. To quantify their consequences, we are currently testing the BRS estimationmethods on surrogate data, simulating the behaviour of heartbeat intervals and SBP valuesunder various conditions. To generate such data, we use existing models and take into accountlong-term correlations in physiological rhythms (Buldyrev et al 1994, Bunde et al 2000, Losaet al 2005, Bogachev et al 2009). The results of these studies will be published separately.

Acknowledgments

We thank our colleagues Armin Bunde, Georg Schmidt, Eugene Nifontov, Igor Kireenkov,Alexei Nevorotin and Aicko Schumann for discussions. We would like to acknowledge partialsupport of this work from the European Community (project DAPHNet) and the DeutscheForschungsgemeinschaft (DFG) as well as from the grants awarded by the Ministry of theScience and Education of Russia and by the Government of St Petersburg.

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