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(Hypertension. 1995;25:1276-1286.)
© 1995 American Heart Association, Inc.

Articles

Spectral Analysis of Blood Pressure and Heart Rate Variability in Evaluating Cardiovascular Regulation

A Critical Appraisal

Gianfranco Parati; J. Philip Saul; Marco Di Rienzo; Giuseppe Mancia

From the Istituto Scientifico Ospedale S. Luca, Centro Auxologico Italiano, Milano (G.P., G.M.); Medicina Interna I, Ospedale S. Gerardo, Monza and Università di Milano (G.P., G.M.) (Italy); Children's Hospital, Department of Cardiology, Harvard Medical School, Boston (J.P.S.); Massachussetts Institute of Technology, Health Sciences and Technology, Cambridge (J.P.S.), Mass; and LaRC, Centro di Bioingegneria, Fondazione Pro Juventute, Milano, Italy (M. Di R.).

Correspondence to Gianfranco Parati, MD, Centro di Fisiologia Clinica e Ipertensione, Ospedale Maggiore and Università di Milano, via F. Sforza, 35 20122, Milano, Italy.

	Abstract

Top Abstract Introduction Rhythmic and Nonrhythmic Changes... Fast Fourier Transform Versus... Short- Versus Long-Lasting BP... Interpretation of Spectral Data Closing the Gaps BP and HR Variability... Conclusions Appendix A Appendix B References

 
Abstract Blood pressure variability includes rhythmic and nonrhythmic fluctuations that, with the use of spectral analysis, appear as clear peaks or broadband power, respectively. This review offers a concise and critical description of the spectral methods most commonly used (fast Fourier transform versus autoregressive modeling, time-varying versus broadband spectral analysis) and an evaluation of their advantages and disadvantages. It also provides insight into the problems that still affect the physiological and clinical interpretations of data provided by spectral analysis of blood pressure and heart rate variability. In particular, the assessment of blood pressure and heart rate spectra aimed at providing indexes of autonomic cardiovascular modulation is discussed. Evidence is given that multivariate models—which allow evaluation of the interactions between changes in blood pressure, heart rate, and other biological signals (such as respiratory activity) in the time or frequency domains—offer a more comprehensive approach to the assessment of cardiovascular regulation than that represented by the separate analysis of fluctuations in blood pressure or heart rate only.

Key Words: blood pressure • heart rate • autonomic nervous system • hypertension, essential • sequence analysis

	Introduction

Top Abstract Introduction Rhythmic and Nonrhythmic Changes... Fast Fourier Transform Versus... Short- Versus Long-Lasting BP... Interpretation of Spectral Data Closing the Gaps BP and HR Variability... Conclusions Appendix A Appendix B References

 
The regulation of blood pressure (BP) is traditionally described in terms of homeostasis.¹ This word comes from the Greek homeo (similar) and stasis (steady) and indicates that BP, although being continuously perturbed by external stimulations, always displays the tendency to come back toward a reference set point. This dynamic behavior of BP implies that attention should be directed not only to the average BP value, which can be regarded as the reference set point, but also to the BP and cardiovascular fluctuations occurring around this average. Data from a variety of sources indicate that these fluctuations are indeed much more than undesirable noise. On the contrary, they represent a rich source of information that can provide considerable insight into the mechanisms of cardiovascular control.^{2 3 4 5 6 7 8} Cardiovascular fluctuations can be studied through beat-to-beat BP and heart rate (HR) monitoring and calculation of the variance (or standard deviation) of their average values.^{2 3 9 10} Recently, however, frequency domain analysis has also been used to subdivide the variability of BP and HR into different frequency components and to quantify the variance or "power" at each specific frequency.^{11 12} A wide variety of algorithms and models have been proposed in this context to study spontaneous cardiovascular variability and to characterize the relation between the changes in HR, arterial BP, and respiration. However, the optimal methods for extracting such information and the most appropriate interpretations of the results obtained are still matters of considerable debate.¹³ This article will focus on these issues.

	Rhythmic and Nonrhythmic Changes in BP and HR

Top Abstract Introduction Rhythmic and Nonrhythmic Changes... Fast Fourier Transform Versus... Short- Versus Long-Lasting BP... Interpretation of Spectral Data Closing the Gaps BP and HR Variability... Conclusions Appendix A Appendix B References

 
Rhythmic BP and HR oscillations related to respiratory activity were first described by Hales¹⁴ and von Haller,¹⁵ and their observations were confirmed by Ludwig 80 years later.¹⁶ After a few decades, Mayer reported that BP also oscillates at frequencies slower than the respiratory rhythm, suggesting that these oscillations are related to vasomotor activity.^{16 17 18} More recently, technological progress in the field of data collection and analysis (continuous BP and HR recording, availability of low-cost computers, fast algorithms for data processing, etc) has led to more sophisticated approaches to rhythmic circulatory phenomena and to their more frequent investigation by power spectrum analysis. Originally, three BP and HR rhythmic oscillations were identified, all with a period shorter than 1 minute and with the appearance in the spectrum as individual peaks (Fig 1A). These peaks reflect (1) oscillations with a frequency around 0.2 to 0.4 Hz, a frequency similar to that of normal respiratory activity, defined as high-frequency (HF); (2) oscillations with a frequency of approximately 0.1 Hz, defined as mid-frequency (MF) and corresponding in the case of BP to the classic Mayer waves; and (3) oscillations with a frequency between 0.02 and 0.07 Hz, defined as low-frequency (LF) and probably related to a variety of cardiorespiratory phenomena and mechanisms.^{19 20 21 22} Subsequent studies, however, have made it clear that the amplitude and frequency of the above oscillations are by no means constant but vary as a function of different behavioral conditions. This is the case for the 0.3-Hz (HF) and 0.1-Hz (MF) oscillations. It is even more often the case for the 0.02 to 0.07–Hz oscillations (LF), which explains why investigators basing their analysis on peak detection models (see below) usually disregard these fluctuations and consider only two major components in the spectrum, around 0.1 and 0.3 Hz, defined as HF and LF, respectively.^{6 23}

View larger version (28K): [in this window] [in a new window]   Figure 1. Plots show respiratory and heart rate time series (left) and spectra (right) for one subject with "peaky" heart rate spectra (A) and one with broadband heart rate spectra (B).

Regardless of whether the spectrum is subdivided into two or three components, an important issue is whether power spectral analysis should exclusively focus on spectral peaks. The peak detection approach is supported by a number of investigators who believe that a peak may reflect a specific mechanism of cardiovascular control that can thus be quantitatively assessed by the power or area of the peak. However, other observations suggest that (1) a peak may originate from more than a single cardiovascular control mechanism, and (2) a single cardiovascular control mechanism may contribute to different peaks.^{4 22 24} In addition, recent studies have shown that BP and HR variability includes not only rhythmic oscillations but also nonrhythmic fluctuations that appear in the spectrum not as clearly defined peaks but as powers spread over a broad frequency region (Fig 1B). It is now clear that these nonrhythmic fluctuations are also relevant to cardiovascular control mechanisms. As an example, in unanesthetized cats under continuous BP and HR monitoring, removal of baroreceptor restraint of sympathetic activity by sinoaortic denervation is accompanied by systematic changes in nonpeaked BP and HR powers in several frequency regions²⁵ (Fig 2). Furthermore, in normotensive and hypertensive subjects, nonpeaked BP and HR powers are modified in a systematic fashion by a condition of reduced sympathetic and increased vagal activity such as sleep.^{26 27} Thus, consideration of broadband powers rather than peaks only may offer a broader description of cardiovascular regulation.

View larger version (17K): [in this window] [in a new window]   Figure 2. Plot shows broadband systolic blood pressure spectra obtained from a free-moving cat in the intact condition (dark line) and 3 weeks after sinoaortic denervation (SAD, light line). Blood pressure was continuously recorded for 3 hours by means of an intra-arterial catheter (abdominal aorta inserted through a femoral artery). Systolic pressure spectral components ranging from approximately 0.5 to 0.0001 Hz are considered. (Modified from Di Rienzo et al25 by permission.)

	Fast Fourier Transform Versus Autoregressive Methods

Top Abstract Introduction Rhythmic and Nonrhythmic Changes... Fast Fourier Transform Versus... Short- Versus Long-Lasting BP... Interpretation of Spectral Data Closing the Gaps BP and HR Variability... Conclusions Appendix A Appendix B References

 
The methods most commonly used for spectral analysis are based on (1) the discrete Fourier transform, usually implemented on the computer as the fast Fourier transform (FFT),²⁸ and (2) autoregressive (AR) modeling.^{12 29 30} The spectrum resulting from the FFT is derived from all the data present in the recorded signal; ie, it includes the entire signal variance, regardless of whether its frequency components appear as specific spectral peaks or as nonpeaked broadband powers. In contrast, with the AR procedure, the raw data are used to identify a best-fitting model from which the final spectrum, consisting of the DC component and a variable number of peaks, is derived. The components of the signal not fitting the model are treated as noise and partially or totally removed.^{12 29 30} The above considerations identify the most important differences between the two methods (Fig 3) and their advantages and disadvantages in different conditions. When attention is focused only on BP or HR rhythmic fluctuations driven by a fixed-rate oscillator, AR methods are suitable because of their ability to identify the central frequency of the oscillation in an analytic way. Furthermore, the AR approach is particularly appropriate when the number of samples available for the analysis is low, because the frequency resolution of the AR-derived spectrum is not as dependent as the FFT method on the length of the recording. On the other hand, when the analysis is focused on broadband powers, the AR method suitably describes the spectrum only if an appropriately high model order is used. Unfortunately, the criteria to automatically determine the model order usually lead to selection of an order that tends to be tendentially lower than that necessary to describe broadband spectra.^{12 31} Thus, the order so defined may need to be empirically corrected on the basis of the investigator's expertise. Under these conditions, the FFT method may be preferable. It should be emphasized that in several conditions, the results obtained by the FFT and AR methods may be very close to each other. This occurs when (1) the AR model order approaches the number of data points or (2) the FFT-derived spectrum is used with methodological manipulation (eg, the Blackman-Tukey method and a prewindowing and smoothing of the autocorrelation function³² ).

View larger version (20K): [in this window] [in a new window]   Figure 3. Plots show the same heart rate spectra of Fig 1A (right) and Fig 1B (left) obtained by means of different analysis methods. A, Data are plotted with an unsmoothed fast Fourier transform (FFT) algorithm; B, data are plotted with an autoregressive (AR) model, the order (=13) of which was determined by Akaike criteria; C, data are plotted with an FFT algorithm smoothed with a Gaussian window and appear like those obtained with the AR model having an order of 13 (B); D, data are plotted with an AR model with a high order (=30) and appear like those obtained with the unsmoothed FFT algorithm (A).

	Short- Versus Long-Lasting BP and HR Recordings

Top Abstract Introduction Rhythmic and Nonrhythmic Changes... Fast Fourier Transform Versus... Short- Versus Long-Lasting BP... Interpretation of Spectral Data Closing the Gaps BP and HR Variability... Conclusions Appendix A Appendix B References

 
Most studies on spectral analysis of BP and HR variability make use of data segments 3 to 5 minutes long derived from recordings obtained under standardized laboratory conditions after removal of possible artifacts (an issue briefly dealt with in Appendix A). This provides reliable results when spectral components with periods shorter than 1 minute are being considered, regardless of whether the subject has a low or high basal HR. On the other hand, such a spectral analysis cannot be appropriately performed if the recording segments are shorter than 3 minutes (J.P.S., unpublished data, 1994) unless the analysis focuses on components with frequencies equal to or greater than 0.1 Hz only. In the latter case, even a window of 1 minute in length may suffice, although in a bradycardic subject this would result in a low number of points available for the analysis and thus in a critical reduction of the frequency resolution of the spectral estimate if the FFT method is used.

Data collected in laboratory conditions, however, cannot reflect what happens in daily life, and to this aim, 24-hour BP and HR recordings performed in ambulant subjects have to be considered. Analysis of these recordings may provide a description of the day-night modulation of fast (ie, >0.025 Hz) BP and HR spectral components. This can be obtained by time-varying spectral analysis techniques, such as the sequential spectral approach or the Wigner-Ville technique,^{26 27 33 34 35 36 37} all of which track the time-varying features of BP and HR over the recording period. Use of these techniques allows the BP and HR spectral responses to behavioral and environmental factors to be identified (Fig 4). Through the analysis of 24-hour ambulatory BP and HR recordings, information on slower components of BP and HR variability can also be obtained. This can be achieved by using spectral techniques that provide a single spectrum from the entire 24-hour recording, thereby estimating spectral components over a broad range of frequencies (broadband spectral analysis, Fig 5).^{25 38 39 40} This allows one to collect information on ultraslow HR and BP changes and on their potential relevance to cardiovascular control mechanisms. The broadband approach, for example, has led to the important finding that 24-hour BP and HR spectra are characterized by a 1/f trend^{38 39 41 42} ; ie, the amplitudes of BP and HR fluctuations increase progressively with the reduction in the frequency of such fluctuations. This spectral characteristic indicates that overall 24-hour BP and HR variabilities depend more on very low than on higher frequency components. The 1/f trend of BP and HR spectra has also been shown to undergo marked changes in different pathophysiological conditions.⁴³

View larger version (46K): [in this window] [in a new window]   Figure 4. Plots show sequential power spectrum densities (PSD) of low-frequency (0.025 to 0.07 Hz), mid-frequency (0.07 to 0.14 Hz), and high-frequency (0.14 to 0.35 Hz) systolic blood pressure (SBP) oscillations computed over consecutive segments of 256 beats throughout a 24-hour period in a representative subject. SBP mean values and standard deviations for each half hour of the recording are also shown. Data are derived from a 24-hour intra-arterial ambulatory blood pressure recording of a representative subject. Dotted lines in the right panel refer to segments in which PSD could not be estimated because of nonstationarities in the recorded signal. (From Parati et al27 by permission.)

View larger version (15K): [in this window] [in a new window]   Figure 5. Plot shows broadband spectrum of systolic pressure obtained from the analysis of a 24-hour ambulatory intra-arterial blood pressure recording performed in a normotensive volunteer. Spectral components with frequencies ranging from 1 to approximately 0.000023 Hz (ie, with periods ranging from 1 second to 12 hours) are considered. The continuous line refers to the actual spectra; the discontinuous line is the 1/f line modeling the spectrum in the frequency region where the 1/f model is suitably applicable.

	Interpretation of Spectral Data

Top Abstract Introduction Rhythmic and Nonrhythmic Changes... Fast Fourier Transform Versus... Short- Versus Long-Lasting BP... Interpretation of Spectral Data Closing the Gaps BP and HR Variability... Conclusions Appendix A Appendix B References

 
Spectral analysis techniques used to quantify BP and HR variability usually focus on the variability components with frequencies ranging between 0.025 and 0.50 Hz, based on the evidence that in these frequency regions, BP and HR spectra are at least in part modulated by neural autonomic influences.^{4 5 6 44 45 46} Despite the large number of studies available on this issue, however, the interpretation of the BP and HR spectra in this frequency region is still a matter of some debate.

Interpretation of HR Spectra
Vagal cardiac control operates like a low-pass filter with a relatively high cutoff frequency, effectively modulating HR up to 1.0 Hz, while sympathetic cardiac control operates as a low-pass filter with a much lower cutoff frequency, capable of significantly modulating HR only at frequencies below 0.15 Hz. The results of a number of studies support this view. In dogs, broadband electrical stimulations of the vagus are followed by HR changes with minimal dampening up to at least 0.7 Hz, whereas broadband electrical stimulation of the right stellate ganglion is followed by HR changes with a delay of approximately 2 seconds and a dampening that leads to a minimal response above 0.15 Hz.^{22 23 24} Second, in dogs and humans, parasympathetic blockade by atropine eliminates most HR fluctuations above 0.15 Hz, while leaving those below 0.15 Hz partly unaffected.^{22 47 48 49} Third, cardiac sympathetic blockade with propranolol reduces HR fluctuations below 0.15 Hz, while leaving those above 0.15 Hz largely unaffected.^{22 24 50} Thus, HR changes at frequencies above 0.15 Hz seem to be primarily caused by modulation of cardiac vagal efferent activity. Also, since respiration usually occurs at frequencies greater than 9 breaths per minute (0.15 Hz), respiratory fluctuations in HR are likely to be mediated primarily by parasympathetic efferent pathways. These observations explain the use of respiratory sinus arrhythmia as a measure of cardiac vagal modulation.^{23 48 49} However, they also explain why respiratory sinus arrhythmia may not accurately reflect only vagal HR modulation, since sympathetic modulation of respiratory-induced HR changes occurs when the respiratory activity is below 0.15 Hz. Finally, even at frequencies above 0.15 Hz, not all HR modulation is parasympathetically mediated. A small respiratory sinus arrhythmia postulated to be caused by mechanical modulation of sinus rate by stretch persists after combined pharmacological sympathetic and parasympathetic blockade and after cardiac transplantation.^{22 51 52 53 54 55} One can thus conclude that HR power in the HF band, above 0.15 Hz, is a satisfactory but incomplete measure of vagal cardiac control.

The specificity of LF and MF HR powers for a single control mechanism is even lower because (1) in animals, HR fluctuations at frequencies below 0.15 Hz are affected by electrical stimulation of both vagal and sympathetic cardiac nerves^{22 24} ; (2) in humans, HR powers between 0.03 and 0.15 Hz are reduced by either parasympathetic or sympathetic pharmacological blockade^{22 50} ; and (3) HR fluctuations in this region have been associated with a wide variety of stimuli, including thermoregulation, periodic breathing, and hemodynamic instability.^{56 57 58} Thus, HR spectra in the MF or LF regions are not invariably a specific sympathetic marker, as it has been suggested,^{6 23} but may also depend on vagal influences and other mechanisms. The reliability of these spectral indexes in reflecting cardiac sympathetic modulation can be enhanced, however, in a number of behavioral or experimental conditions in which the sympathetic system can be selectively activated.^{23 44}

Interpretation of BP Spectra
The observation that HF BP power is not substantially modified in patients with denervated donor hearts^{51 54 55} has led to the suggestion that this power is mainly caused by the mechanical effects of respiration on the pressure gradients, size, and functions of the heart and large thoracic vessels.^{22 52 53 54 55} There are, however, conflicting findings on this issue. Actually, it has also been suggested that vagally mediated changes in HR and cardiac output play a role in determining HF BP powers.²² However, the influence of vagal modulation on HF BP powers may be different in different species because in conscious cats, sinoaortic denervation, ie, an intervention that markedly impairs cardiac vagal drive, markedly reduces HF HR powers with only a minor and nonsignificant reduction in HF BP powers.²⁵

Autonomic modulation of HR is an even less important determinant of BP powers in the LF and MF regions because cardiac autonomic blockade by the combined administration of atropine and propranolol eliminates only a fraction of BP variability at frequencies lower than 0.15 Hz.²² It thus seems likely that LF and MF BP powers are predominantly caused by fluctuations in vasomotor tone and systemic vascular resistance. At frequencies between 0.025 and 0.07 Hz, the factors involved in this vascular modulation have been regarded as being the renin-angiotensin system, endothelial factors, local influences related to thermoregulation, and others.^{21 59 60 61} However, their precise role remains largely speculative. In contrast, evidence has been collected that in the frequency region between 0.07 and 0.15 Hz (or between 0.05 and 0.15 Hz according to other authors), BP powers increase with laboratory stimuli that increase sympathetic cardiovascular influences (eg, head-up tilting, mental stress) and decrease with conditions that decrease sympathetic cardiovascular influences (eg, sleep and -adrenergic blockade).^{6 26 27 33} Thus, the hypothesis has been advanced that the BP spectral powers between 0.07 (or 0.05) and 0.15 Hz (defined as LF or MF by different investigators) represent a marker of sympathetic vasomotor tone. As mentioned above, the same type of evidence (increase and decrease in power during increase and decrease in sympathetic drive) has been used to conclude that HR powers in the same frequency region represent a marker of sympathetic cardiac drive.^{6 44} However, as is the case with HR, LF (or MF) BP power may not invariably be a consistent marker of sympathetic vasomotor regulation.

BP and HR Spectral Powers as Indexes of Autonomic Cardiovascular Modulation
Markers capable of dynamically assessing sympathetic vasomotor and cardiac drive in daily life conditions would be important diagnostic tools.⁶² However, the reliability of BP (or HR) powers around 0.1 Hz as specific sympathetic markers has recently been questioned by several investigators. Their data come not only from animal experiments, which have the problem of a safe extrapolation to humans, but also from healthy subjects and patients with cardiovascular disease. For example, Cohen et al⁶³ reported that in healthy volunteers a reflex increase in sympathetic nerve traffic (measured directly by microneurography) and in vascular resistance (measured by forearm venous occlusion plethysmography) induced by lower body negative pressure was not accompanied by a similar consistent increase in 0.1-Hz HR power. Saul et al⁴⁴ found that in normotensive humans the reflex increase in sympathetic nerve traffic (microneurography) induced by intravenous infusion of nitroprusside was associated with an increased 0.1-Hz HR power but that no reduction in the 0.1-Hz HR power occurred during the reduction in sympathetic nerve traffic reflexly induced by intravenous infusion of phenylephrine. Kingwell et al⁶⁴ showed that although in some clinical conditions (early heart transplantation and pure autonomic failure) cardiac norepinephrine spillover and 0.1-Hz HR power were concordantly reduced, in other clinical conditions (late heart transplantation, aged individuals, and congestive heart failure) they showed discordant changes. Kienzle et al⁶⁵ observed that in heart failure patients there was an inverse correlation between different measures of HR variability, including 0.1- and 0.3-Hz powers, and indexes of sympathoexcitation such as muscle sympathetic nerve activity and plasma norepinephrine—ie, the higher the sympathoexcitation, the lower the powers of 0.05 to 0.15– and 0.2 to 0.5–Hz HR spectral components and the HR standard deviation. Daffonchio et al⁶⁶ observed that in conscious rats destruction of the peripheral sympathetic nerves by 6-hydroxydopamine reduced the 0.2 to 0.8–Hz BP powers (ie, the powers corresponding to the powers around 0.1 Hz in humans) by 65% in normotensive rats and by only 20% in hypertensive rats, the remaining power being unaffected by the elimination of residual sympathetic activity and adrenal gland influences via additional -adrenergic blockade. Finally, Adamopoulos et al⁶⁷ also showed that in patients with congestive heart failure, spectral indexes of autonomic activity correlate poorly with other measures of autonomic function.

The important conclusion that can be drawn from these observations is that the level of sympathetic cardiovascular modulation cannot always be specifically reflected by the power of HR and BP spectral components around 0.1 Hz.

A further important issue to be considered is the reproducibility of these spectral indexes. Although some studies have reported that, in standardized conditions, 0.1- and 0.3-Hz powers of BP and HR have a good reproducibility,^{68 69 70} other studies have emphasized the possible occurrence of a high random variability in BP and HR spectral powers even when derived from standardized recordings.^{71 72} Reproducibility of BP and HR spectral powers in the 0.025 to 0.5–Hz region is an even more complex problem when these spectral components are quantified, in individual subjects, from the analysis of short-lasting segments derived from 24-hour ambulatory BP and HR recordings because of the influence of varying behavioral conditions.^{26 27 73}

Other more general problems related to the use of spectral powers as tools for selective quantification of autonomic cardiac or vascular influences are worth mentioning. First, neural modulation of both HR and BP is influenced by a large number of input signals and a diversified interaction of central command and reflexes at various brain levels. Thus, it may be that an approach which assumes that these complex mechanisms can be described by considering only BP and HR spectral powers within the narrow frequency regions around 0.1 and 0.3 Hz is too simplistic. It is more likely that a much wider frequency region, containing rhythmic and nonrhythmic fluctuations, is under the modulation of these neural mechanisms, a hypothesis that has some support in the literature. When broadband spectral analysis has been used for the assessment of BP and HR variability in conscious cats and dogs, arterial baroreflex regulation of BP and HR fluctuations has been found to occur at all frequencies, from the very low to the very high.^{25 40 74}

Second, the current interpretation of spectral data relies on the assumption that the responses of the system under evaluation are approximately linear. Yet, neural regulation of the cardiovascular system is characterized by at least two orders of nonlinearity. There are system nonlinearities, present regardless of the operating point, such as the nonadditive nature of the interactions of cardiac sympathetic and parasympathetic responses,⁷⁵ the cardiac phase–dependent response of the slope of phase 4 depolarization to vagal stimuli,⁷⁶ and the possible nonlinear gating of vagal and sympathetic neural outflow by respiration.⁷⁷ In addition, there are nonlinearities that may originate in specific behavioral and experimental conditions, driving the cardiovascular system control mechanisms to operate out of their linear range. Virtually every physiological control system has steady-state responses that are sigmoidal and include a threshold, a saturation point, and in between, a linear operating regime⁷⁸ (Fig 6A and 6B). A typical example of this is represented by the arterial baroreflex control of HR, which has a sigmoidal stimulus (BP)–response (RR interval) curve. In this instance, both the steady-state and dynamic responses of the system are a function of the BP level. The dynamic response can be thought of as continuously moving up and down the sigmoid curve that describes the steady-state baroreflex gain, with a maximal gain usually equal to the instantaneous slope of the sigmoid curve (Fig 6C and 6D). In addition, the system gain at any one mean operating point might depend on other factors, such as the frequency with which the input varies (eg, low-pass filter responses to sympathetic modulation) or the rate of change of the input (eg, high-pass differentiator properties of the arterial baroreceptors to phasic inputs).⁷⁸ Fig 6C shows clearly that an increase in the mean operating point of the input may be associated with an increase, decrease, or no change in the dynamic gain of the system, depending on the initial operating point, a parameter that cannot be determined by means of a simple frequency domain analysis. This implies that changes in the activity of cardiovascular control mechanisms (which, as already mentioned, are often intrinsically nonlinear) may not be linearly related to changes in BP or HR variability. Thus, a measure of BP or HR fluctuations may fail to quantify alterations of autonomic cardiovascular influences in several instances. Of course, this may be a problem of all measures of autonomic tone in relation to its modulating influences and to its effect on receptor, cardiac, and vascular responses.

View larger version (27K): [in this window] [in a new window]   Figure 6. Schematic drawing shows different features of the sensitivity (gain) of baroreflex heart rate control. A, Sigmoid curve describing the relationship between changes in the input (blood pressure, BP) and reflex changes in the output (RR interval). As BP increases, RR interval also increases, approximating a sigmoidal relationship with threshold and saturation values at either end of the curve. The gain of the heart rate baroreflex is defined as the slope at any given point on the response curve. Administration of vasoactive agents (nitroprusside [NP] or phenylephrine [PE]) induces changes in mean arterial pressure, moving the normal baroreflex operating point (baseline) into a different operating range. This potentially may lead to different gains. B, Plot of baroreflex steady-state gain as a function of BP. As the baroreflex stimulus-response curve is sigmoidal, maximal gain is observed in the linear portion of the curve, occurring at intermediate BP values. At more extreme BP values, steady-state gain is diminished. C, Dynamic (or "beat-to-beat") baroreflex gain as measured by the autoregressive moving average (ARMA) the spectral and the sequence techniques at the mean operating point in A may be higher or lower than the steady-state gain, depending on the characteristics of the BP signal. D, In particular, the dynamic gain will probably depend on the frequency content of the input signal because of either inherent filtering characteristics of the baroreflex response (ie, low-pass, high-pass, band-pass) or dependence on a signal derived from the input, such as the derivative or rate of change of the input signal. In this case, maximal gain is found to occur around 0.15 Hz, with decreased gain at both ends of the frequency range, suggesting band-pass characteristics.

As a somewhat separate issue, frequency domain techniques are particularly suitable for the measurement of dynamic responses. Thus they may not be appropriate for the assessment of mean operating conditions in the system under evaluation. This is particularly the case in the evaluation of the sympathetic or parasympathetic modulation of HR or BP, in which spectral analysis is unlikely to provide a measure of mean neural activity. This point is graphically demonstrated by the response of respiratory sinus arrhythmia to an elevation of mean arterial pressure induced by an infusion of phenylephrine (Fig 7). In this case, mean vagal activity almost certainly increases (HR decreases by approximately 18 beats per minute), but respiratory sinus arrhythmia disappears, probably secondary to the saturation of either the vagal responses or the response of the heart to vagal activity (J.P.S., G.P., unpublished observations, 1994).⁷⁹

View larger version (19K): [in this window] [in a new window]   Figure 7. Plots show time series of respiratory volume (top), heart rate (middle), and mean blood pressure (bottom) in one subject. Data were obtained in control conditions (left) and during intravenous phenylephrine infusion (right), which determined an increase in blood pressure and a reflex bradycardia. Note that at the time of maximal reflex cardiac vagal stimulation under phenylephrine infusion, respiratory sinus arrhythmia disappeared.

Finally, two further methodological issues deserve to be discussed in this context. First, proper interpretation of power spectra is highly dependent on the presence of signal stationarity.¹¹ This issue is more than a theoretical requirement for the use of spectral analysis any time the attention is focused on specific spectral peaks because the dynamic characteristics of the system are likely to be different during changes in the mean operating point. Second, interpretation of the spectra also depends on the occurrence of an appropriate degree of spontaneous fluctuations of the parameters that influence the signal under evaluation so that the risk of having no input data in the frequency range of interest is avoided.^{22 49 80 81} A proper degree of variability in the input data can be obtained by recording the signal under changing external stimulations. As an example, this can be done by using paced breathing over a wide frequency range as a means to elicit variations in the cardiovascular signals and in the engaged control mechanisms.

	Closing the Gaps

Top Abstract Introduction Rhythmic and Nonrhythmic Changes... Fast Fourier Transform Versus... Short- Versus Long-Lasting BP... Interpretation of Spectral Data Closing the Gaps BP and HR Variability... Conclusions Appendix A Appendix B References

 
The most common attempt for improving the assessment of autonomic cardiovascular modulation by the spectral analysis approach is to couple the information obtained from the recorded biological signal with the information derived from physiological and mathematical models. This may help the interpretation of the results, provided that the model (1) is used when its assumptions fit with the biological data and (2) is validated at least in part by experimental data independently obtained. An example is a model based on the assumption that sympathetic and vagal cardiac influences are normally altered in opposite directions and that thus one can improve on the limited sensitivity of 0.1-Hz (LF or MF, according to different authors' definitions) and 0.3-Hz (HF) powers as respective markers of sympathetic and vagal cardiac drive by using their ratio as an index of sympathovagal balance. Such a model may provide useful information in a number of instances.²³ However, there may be conditions (eg, exercise, diving) in which these two spectral components undergo not discordant but concordant changes of similar or different magnitude. In the latter case, the resulting changes in the LF-HF ratio may be misinterpreted as indicating opposite changes in sympathetic and vagal drive.

Other more complex examples are the modeling approaches that consider the relationship between fluctuations of two or more cardiovascular signals physiologically related to each other. To date, these multivariate models have allowed evaluation of the baroreceptor-HR reflex using both time domain and frequency domain approaches.⁸² A time domain method described in the 1980s^{83 84 85} is based on computer identification of sequences of three or more consecutive beats characterized either by a progressive increase in systolic BP followed by a linearly related lengthening in pulse interval or by a progressive reduction in systolic BP followed by a linearly related shortening in pulse interval. The slope of the regression line between systolic BP and pulse interval changes is taken as an index of baroreflex sensitivity. A frequency domain method also used to assess baroreflex sensitivity is based on the computation of the squared ratio between the spectral powers of RR interval and systolic BP⁸⁶ or of the modulus of the cross-spectrum between systolic BP and RR interval⁸⁷ in the frequency regions (0.07 to 0.35 Hz) where these two signals show a significant coherence.⁸² The validity of either approach has been independently verified by the striking changes in the outputs of these models produced by sinoaortic denervation in animals,^{82 84} which allows their use as a reliable index of baroreflex sensitivity in daily life.

Other multivariate models are (1) those addressing the relationships between BP and HR in a closed-loop fashion, by means of either autoregressive moving average techniques (ARMA models)⁸⁸ or Fourier-based transfer function techniques, and (2) those quantifying the relations between respiration and either BP or HR fluctuations using the same techniques.^{22 89} In the former instance, ARMA models have been used to study not only the reflex effects of BP alterations on HR changes (reflex feedback) but also the direct mechanical effects of alterations in HR on BP changes (mechanical feedforward). On the other hand, with either technique, the evaluation of the relation between respiratory activity and BP or HR changes can be used to provide a quantification of the gain and phase relationship between respiration and its cardiovascular effects as a function of the frequency of these changes. This approach may be further improved if the analysis is not limited to spontaneous respiratory activity (which may have a limited frequency content) but makes use of a paced breathing pattern to obtain a broadband or "whitened" input respiratory signal that contains all physiologically relevant frequencies simultaneously (see above).⁹⁰

	BP and HR Variability in Essential Hypertension

Top Abstract Introduction Rhythmic and Nonrhythmic Changes... Fast Fourier Transform Versus... Short- Versus Long-Lasting BP... Interpretation of Spectral Data Closing the Gaps BP and HR Variability... Conclusions Appendix A Appendix B References

 
Using short-lasting BP and HR recordings obtained in the laboratory environment, Guzzetti et al⁹¹ reported that, compared with normotensive subjects, patients with essential hypertension are characterized by a greater LF power (defined as the power around 0.1 Hz) and a smaller HF power of RR interval during supine rest. They also reported that these powers showed a smaller increase and decrease, respectively, during passive tilting. These observations were interpreted as indicating that cardiac sympathetic tone is increased and cardiac vagal tone and modulation are decreased in essential hypertension, a conclusion in line with the previous studies in which autonomic cardiac modulation was investigated by different techniques.^{92 93} They also concluded, however, that sympathetic cardiac modulation may be impaired in hypertension, which is not entirely in agreement with previous reports showing unchanged and even enhanced HR responses to exercise, stress, and other behaviors modifying autonomic cardiac drive.⁹⁴

Comparison data are also available on BP and HR variability of normotensive and essential hypertensive subjects throughout the 24 hours. In a study that made use of 24-hour intra-arterial ambulatory BP recording, the standard deviation of 24-hour mean BP values (obtained by beat-to-beat analysis) increased progressively from normotensive subjects to patients with borderline, mild, and more severe essential hypertension.² The HR standard deviation was similar in normotensive subjects and in borderline and mildly hypertensive patients and decreased in severely hypertensive patients.²

Further results were obtained in additional studies in which the 24-hour intra-arterial BP and HR signals of normotensive and hypertensive subjects were divided into contiguous segments of 5 to 6 minutes, and power spectral analysis was performed on all segments characterized by a stationary signal.^{26 27} In all subjects, spectral powers displayed a large segment-to-segment variability over the entire frequency region considered, presumably because of the effect of the changing behavioral pattern. Spectral powers, however, also showed systematic fluctuations, which consisted of (1) a pronounced nocturnal reduction of the systolic and diastolic BP powers around 0.1 Hz and (2) a more slight nocturnal increase in the 0.3-Hz (HF) power of pulse interval. With the exception of a smaller nighttime increase in the HF power of pulse interval, average powers and power changes were similar in the normotensive and mildly hypertensive subgroups.^{26 27}

Finally, the time domain and frequency domain techniques for computer evaluation of the arterial baroreflex described above^{82 85 86} have shown that the sensitivity of the baroreceptor-HR reflex is much lower in essential hypertensive than in normotensive subjects for each hour of the 24 hours, thereby confirming previous conclusions obtained by studying the baroreflex with laboratory techniques.⁹⁵ Dynamic analysis of the baroreflex, however, has also shown that although in normotensive subjects baroreflex sensitivity shows a marked nocturnal increase, this feature is much less evident in hypertensive patients.

Thus, data obtained by quantification of BP and HR fluctuations in hypertensive patients emphasize that, although interpretation of the results may not always be easy (mainly because of the composite nature of spectral powers), time domain and frequency domain analysis of HR and BP variability can provide interesting new insights into the daily life alterations of autonomic cardiovascular modulation in hypertension. A striking finding appears to be a daily life impairment of the baroreceptor-HR reflex. There are also an increase in BP variability and to a lesser extent a reduction in HR variability. These alterations are more evident when overall measures of BP and HR variability rather than specific components of these phenomena are considered.

	Conclusions

Top Abstract Introduction Rhythmic and Nonrhythmic Changes... Fast Fourier Transform Versus... Short- Versus Long-Lasting BP... Interpretation of Spectral Data Closing the Gaps BP and HR Variability... Conclusions Appendix A Appendix B References

 
Available data unequivocally indicate that analysis of BP and HR variability by the spectral approach, as well as by time domain techniques, may provide interesting information and represent a useful tool for the study of the mechanisms involved in cardiovascular regulation in both normal and diseased conditions. The potential importance of these techniques is in particular related to the possibility they offer for information to be obtained on cardiovascular regulation in real life conditions, ie, in conditions free from artificial laboratory stimulations. However, interpretation of BP and HR spectra is sometimes controversial, particularly when signals recorded outside of a standardized laboratory environment are considered, and there is evidence that specific spectral components may be related to different mechanisms in different conditions. In particular, although sympathetic vascular and cardiac modulation appears to be reflected by BP and HR powers around 0.1 Hz, the specificity, sensitivity, and reproducibility of these powers as indexes of mean sympathetic activity in different conditions are not always optimal. Progress in the field is now offered by multivariate models that allow interactions between BP, HR, and other biological signals to be evaluated in the time or frequency domain. Application of some of these models to the analysis of long-lasting BP and HR recordings obtained in ambulant subjects will also allow the problems arising from the use of laboratory data to predict what happens in daily life to be overcome.

	Appendix A

Top Abstract Introduction Rhythmic and Nonrhythmic Changes... Fast Fourier Transform Versus... Short- Versus Long-Lasting BP... Interpretation of Spectral Data Closing the Gaps BP and HR Variability... Conclusions Appendix A Appendix B References

 
Removal of Artifacts
Recordings of BP, electrocardiographic, and other biological signals may include artifacts, such as dampening of the BP signal, distortion of the pulse waveform by movements, premature beats, etc. The likelihood of these artifacts being found in the recorded signals is obviously higher when long-lasting recordings are being considered, particularly if these recordings are obtained in ambulant subjects.

A high frequency of artifacts also must be expected when long-lasting recordings obtained by a Finapres measuring device (Finapres 2300, Ohmeda) or by its portable version (Portapres, TNO) are considered because the site of BP measurement, at the finger level, is associated with a high rate of movement artifacts^{96 97} and because the continuous BP recording is periodically interrupted by automatic calibration signals.^{98 99 100}

These artifacts must be removed to obtain reliable spectral estimation, and signal editing is particularly crucial to avoid errors in the quantification of faster HR and BP spectral components.

Occasional ectopic beats can be removed by means of several procedures: (1) Interpolated ectopic beats can be directly removed, and the RR interval corresponding to the missing beat will then be the sum of the intervals preceding and following the ectopic beat; (2) if a delay follows the ectopic beat, the RR interval considered for analysis might be the mean of the intervals preceding and following the removed ectopic beat. Such a procedure is particularly suitable for ectopic beats followed by a compensatory delay. Obviously, recordings without arrhythmias should generally be preferred. In case of long-lasting recordings (eg, 24-hour Holter tracings), an acceptable criterion might be to consider for spectral analysis only subperiods during which the frequency of ectopic beats is less than 1% of total beats.

The editing task can be efficiently performed through computer identification of aberrant waveforms. This is commonly obtained (1) by setting threshold values for specific fiducial points on the recorded waveform (eg, in the case of BP recordings, the maximal and minimal values for systolic and diastolic BPs, the maximal and minimal time lengths of a given waveform, rate of change of BP within the waveform, etc) and (2) by matching each recorded waveform with a template.

Once detected, artifacts can be either automatically deleted by the computer or visualized on a screen and interactively deleted by the operator.

	Appendix B

Top Abstract Introduction Rhythmic and Nonrhythmic Changes... Fast Fourier Transform Versus... Short- Versus Long-Lasting BP... Interpretation of Spectral Data Closing the Gaps BP and HR Variability... Conclusions Appendix A Appendix B References

 
Essential Glossary
Autoregressive (AR) Modeling
Technique for the mathematical modeling of signals. This approach is based on the assumption that the value of a signal depends only on the previous values of the same signal plus "noise." Once the AR model of a signal is estimated, the spectrum of the input signal can be computed from a manipulation of the mathematical model.

Autoregressive Moving Average (ARMA) Modeling
Technique for the mathematical modeling of signals. It is based on the assumption that the value of the output signal depends on either the previous values of the same signal (autoregressive component) and on the present and previous values of a different input signal (moving average component), with the addition of a "noise" factor.

Broadband Spectral Analysis
Spectral analysis providing a spectral estimation over a wide range of frequencies. By this approach, a single spectrum is obtained from a relatively long-lasting input data record.

Fourier Transform
Decomposition of a given signal into a series of sine and cosine waves having frequencies that are multiples of the fundamental frequency (the reciprocal of the time length of the input data record). The spectral power of the input signal can be derived from the magnitude of these sine and cosine waves.

Fast Fourier Transform
Algorithm for the fast estimation of the Fourier transform. It requires that the number of samples derived from the input signal be powers of 2.

Set Point
The specific value of the controlled variable that should be maintained by a given control mechanism (eg, the arterial baroreflex).

Time-Varying Spectral Analysis
A set of analysis procedures that describes how the spectral characteristics of the input signal change as a function of time.

Transfer Function
Mathematical relationship between the input and output of a system as a function of the frequency.

Received September 8, 1994; first decision October 25, 1994; accepted February 16, 1995.

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98. Wesseling KH, de Wit B, Settels JJ, Klawe WH. On the indirect registration of finger blood pressure after Penaz. Funkt Biol Med. 1982;1:245-250.

99. Parati G, Casadei R, Groppelli A, Di Rienzo M, Mancia G. Comparison of finger and intra-arterial blood pressure monitoring at rest and during laboratory testing. Hypertension. 1989;13:647-655. [Abstract/Free Full Text]

100. Omboni S, Parati G, Frattola A, Mutti E, Di Rienzo M, Castiglioni P, Mancia G. Spectral and sequence analysis of finger blood pressure variability: comparison with analysis of intra-arterial recordings. Hypertension. 1993;22:26-33.[Abstract/Free Full Text]

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