Spectral Analysis of Blood Pressure Variability in Heart Transplant Patients
Abstract The cardiac transplant patient provides a unique model for the study of blood pressure variability in the absence of heart rate variability. We examined the harmonic and fractal components of blood pressure variability in 14 heart transplant patients (12 men, 2 women; 21 to 62 years of age) and in age- and sex-matched control subjects during seated rest, supine rest, and supine rest with fixed-pace breathing (12 respirations per minute). Heart rate was faster in transplant patients than in control subjects, with much less heart rate variability (P<.0001). Spectral analysis of blood pressure variability revealed no difference in total power for either systolic or diastolic pressure, but transplant patients had less low-frequency (0 to 0.15 Hz) harmonic spectral power in both systolic (P<.01) and diastolic (P<.03) pressure and more high-frequency power (0.15 to 0.5 Hz) in diastolic pressure than control subjects. The ratio of high-frequency power in diastolic relative to systolic pressure was consistently higher (P<.0001) in the transplant patients (0.29 to 0.51) than in control subjects (0.11 to 0.13). The slope of the fractal component of systolic pressure was approximately 1.8 in both transplant patients and control subjects. This was greater than the slope for heart rate variability (approximately 1.1 in control subjects). These data provide clear evidence of independence of the fractal component of heart rate and blood pressure variabilities in both transplant patients and control subjects. The heart rate component of the arterial baroreflex minimized high-frequency diastolic pressure changes while contributing to low-frequency variations in both systolic and diastolic pressures.
Marked reduction of beat-by-beat heart rate variability (HRV) is well documented in human heart transplantation.1 2 3 4 5 6 7 8 This is a consequence of interruption of the parasympathetic and sympathetic neural activities to the sinoatrial node; however, some evidence of reinnervation has been presented.1 8 9 In terms of normal cardiovascular control, this functional denervation of the heart might be expected to affect blood pressure regulation as assessed by blood pressure variability (BPV). To date, there have been no reports of beat-by-beat BPV in posttransplant patients. Investigations of intermittent ambulatory blood pressure have shown return of overall circadian rhythm10 as well as greater overall variation in daytime, but not nighttime, systolic and mean arterial pressures in transplant patients than in hypertensive or normotensive subjects.11
In an effort to further our understanding of the physiological adaptations of the cardiovascular system in the presence of a functionally denervated heart, we studied 14 patients who had undergone heart transplantation between 1 year, 6 months and 7 years, 4 months before the experimentation. We used spectral analysis of HRV and BPV to explore the specific pattern of variability. For HRV with an intact nervous system, it has been shown that high-frequency oscillations (≥0.15 Hz) are mediated almost exclusively by the parasympathetic nervous system.12 13 In contrast, low-frequency variations (0 to 0.15 Hz) are mediated by both the sympathetic and parasympathetic nervous systems.12 13
Beat-by-beat BPV has not been extensively studied, even in healthy subjects. With respiration, arterial blood pressure typically falls on inspiration and rises on expiration.14 Respiration is a high-frequency (typically in the range of 0.2 to 0.4 Hz) modulator of cardiovascular function. Lower-frequency changes in blood pressure result from variations in sympathetic nervous system–mediated (α-receptor) vasoconstriction, as well as interaction of vasoactive agents and hormones with the autoregulatory processes. Thus, BPV has both high- and low-frequency variations resulting from mechanical and neural events. Normally, there is a high coherence between HRV and BPV.15 16 In transplant patients, this cannot occur.
Recent observations of both HRV and BPV have indicated that underlying the harmonic components of the spectral analysis is a pattern of fractal variability.17 18 19 20 A fractal process is self-similar, with a long-term correlation of the events within the time series data.18 19 It has been speculated that information encoded in this long-term correlation might be used in the maintenance of cardiovascular homeostasis.17 18 19 20 However, despite the known role of the arterial baroreflex, the regulation of the fractal components of HRV and BPV appear to be independent.18 This study of transplant patients, in whom HRV is almost nonexistent, could provide additional support for this hypothesis of independence of the fractal components.
Fourteen heart transplant patients (12 men and 2 women) were observed during part of their routine check-ups at the hospital. All were found to be in good health with no signs of rejection. Complete descriptive statistics are given in Table 1⇓. The patients ranged in age from 21 to 61 years. Control subjects were selected to match the patients in age and sex. Matching was done with the patient’s age rather than with the age of the donor,2 because the primary focus of this investigation was on BPV. Patients and subjects signed consent forms approved by the ethics committee of the institution.
HRV and BPV were recorded during a single session. Patients and subjects were first instrumented with electrocardiogram (ECG) electrodes and the finger cuff of a continuous noninvasive blood pressure monitor (Finapres 2300, Ohmeda). The blood pressure signal was allowed to stabilize for 3 to 5 minutes, then the servo reset mechanism was turned off to permit continuous measurement, although it was engaged between the individual collection periods. The ECG was monitored for the peak of the R wave as detected by a circuit that generated a pulse for each complex. A computer program determined the onset of the R wave to an accuracy of 1 millisecond. After detection of a heartbeat, the computer program searched the analog output from the blood pressure monitor for the subsequent highest and lowest values to represent systolic and diastolic pressure, respectively. All data were recorded on the computer for later analysis.
Each subject completed three separate 8- to 10-minute data collections within the single session. Testing was always in the order of seated rest, supine rest, and supine rest with breathing fixed in time with a signal at 12 breaths per minute (0.2 Hz). While subjects were in the seated and supine rest positions, breathing frequency was not controlled.
HRV and BPV were each evaluated by coarse graining spectral analysis.21 This method is a modification of the fast Fourier transform used by some investigators in previous studies of HRV. The rationale for using coarse graining spectral analysis as opposed to simple fast Fourier transform is that both HRV and BPV signals have been shown to be fractal17 18 22 23 ; that is, a broad-band, nonwhite signal underlies the high- and low-frequency variations that are normally taken for HRV to indicate parasympathetic and sympathetic neural activities.17 21 This fractal component is of itself very important to the understanding of the control of the cardiovascular system, as discussed below. However, it is important to isolate the fractal from the harmonic components, especially in the evaluation of parasympathetic and sympathetic activities for HRV. All spectra were calculated as the ensemble average of 256 beat sequences taken from a time series containing approximately 400 to 500 heartbeats. The 256-beat spectrum provides a good estimate of the fractal component of HRV.24 Consistent length spectra should be used for comparisons of spectral power distribution.24
Data are presented as the mean±SEM of 14 observations of patients and control subjects in each test condition. Tests for differences between groups were made by two-way ANOVA in which the main effects of patients compared with control subjects and of test condition were evaluated. Further analysis within a group (patients or control subjects) to determine the effect of test condition was completed by repeated-measures ANOVA. Statistical significance was accepted at a value of P<.05.
Transplant patients had a significantly shorter RR interval (higher heart rate) (P<.0001; Table 2⇓). In the control subjects, RR interval was significantly shorter when they were in the upright, seated position than when they were in either the supine rest or the supine plus fixed breathing position. In the transplant patients, RR interval was significantly shorter when they were in the upright, seated position than when they were in the supine rest position.
As anticipated, HRV in the transplant patients was markedly reduced (Table 2⇑). All patients but 1 (see “Discussion”) had a similar pattern, with only very low-amplitude, high-frequency variations (Fig 1⇓). Mean values of total spectral power (PTOT) were 39 to 72 ms2 in the patients, in contrast to 1210 to 1718 ms2 in control subjects. Between-group differences were also found for each of the components of spectral power (Table 2⇑). With the exception of less fractal power (PFrac) in the transplant patients in the seated position than in the supine position with fixed breathing, there were no between-position differences in spectral power distribution between the transplant and control groups.
The fractal component of HRV was evaluated by the fractal power and by the slope of the log power–log frequency relationship. PFrac was markedly reduced in the transplant patients but was significantly higher when expressed as a percentage of PTOT (Table 2⇑). The slope of the fractal component was slightly but not significantly (P=.058) greater in the transplant patients than in the control subjects. The slope for the control subjects (1.09 to 1.16) was close to the value found in younger resting subjects.17
Mean values of systolic pressure did not differ significantly between the transplant patients and control subjects (Table 3⇓). Systolic pressure was higher for the control subjects during supine fixed breathing than while they were in the supine rest condition.
Systolic pressure variability in the two groups was not different in terms of the overall spectral power, but the distribution of the power was significantly different (Table 3⇑, Fig 2⇓). Transplant patients had a significantly smaller amount of low-frequency spectral power (PLO) (P<.01) and harmonic power (P<.03) than the control subjects. Between–test position differences were found for high-frequency spectral power (PHI) in the transplant patients (greater in the supine plus fixed breathing position than in either the supine rest or the seated rest position) and for PLO in the control subjects (greater in the supine rest position than in the supine plus fixed breathing position).
The percent fractal component in the systolic pressure signal did not differ between the transplant patients and control subjects. The slope of the fractal component was not different between the two groups. There was a significant position effect (P<.004). In the control subjects, this was evident as a greater slope in the supine rest position than in the seated rest or the supine plus fixed breathing position.
An overall elevation in diastolic pressure was found in transplant patients compared with the control subjects (P<.0004). There were significant between–test position differences in diastolic pressure. In the transplant patients, diastolic pressure was higher in the seated position than in the supine plus fixed breathing position. In the control subjects, diastolic pressure was lower in the supine rest position than in either the seated rest or the supine plus fixed breathing position (Table 4⇓).
Although there were no differences in PTOT for diastolic pressure between groups, there were several differences in the distribution of the variability (Table 4⇑). PLO was smaller and PHI was greater in the transplant patients than in the control subjects (Figs 2⇑ and 3⇓). The only between–test position differences observed were for the greater PHI in the transplant patients in the supine plus fixed breathing position than in either the seated position or the supine rest position.
There was considerable between-subject variation in PFrac for diastolic pressure. As a consequence, there were no significant between-group or between–test position differences for PFrac or percent fractal (Table 4⇑). However, there was a significant between-group difference for the slope of the fractal component (P<.04). Additional analysis showed that slope was less in the transplant patients when they were in the supine plus fixed breathing position than when they were in either the seated or the supine rest position, and it was greater in the control subjects when they were in the supine rest position than when they were in the seated rest position (Table 4⇑).
Diastolic and Systolic Pressure Interactions
A ratio of PHI in the diastolic pressure with PHI in the systolic pressure can provide an indicator of the relative contributions to the dynamic response of arterial blood pressure made by stroke volume changes and the interaction between peripheral vascular resistance and modulation of RR interval. This ratio was 0.35±0.04, 0.29±0.04, and 0.51±0.09 for the transplant patients in the seated rest, supine rest, and supine plus fixed breathing positions, respectively. For the control subjects, the corresponding values were significantly less (0.12±0.03, 0.13±0.04, and 0.11±0.02; P<.0001). This analysis emphasizes the important role of beat-by-beat changes in RR interval in the normal diastolic pressure response.
A similar comparison of the ratio of PLO in the diastolic pressure to PLO in the systolic pressure showed no significant between-group difference. Values for transplant patients were 0.55±0.04, 1.06±0.34, and 0.37±0.05 in the seated rest, supine rest, and supine plus fixed breathing positions, respectively, and the corresponding values for control subjects were 0.58±0.07, 0.41±0.03, and 0.54±0.04 (P>.05).
Heart transplantation represents a major challenge to the multiple neural and humoral interactions on the heart and peripheral vasculature that are involved in the maintenance of relative stability or homeostasis. Indeed, it has been frequently observed that HRV is greatly diminished in transplant patients.1 2 3 4 5 6 7 8 Intermittent 24-hour recordings of arterial pressure have shown greater variability of blood pressure in awake and ambulatory transplant patients than in a control group.11 The first observations of beat-by-beat changes in arterial pressure in patients with heart transplant have only recently been reported by Macor et al.25 There are several differences between the results of their study and the current data discussed below. The major findings of the present study were reduced PLO in both systolic and diastolic pressures in the transplant patients, greater PHI in diastolic pressure in the transplant patients, and a greater ratio of PHI in diastolic pressure to PHI in systolic pressure in the transplant patients. Furthermore, there were similarities in the long-term BPV (slope [β] of the fractal component) between transplant and control groups despite marked differences in HRV. Each of these findings provides clues that will allow us to explore the normal interactions between heart rate and blood pressure. Our observations will be used in a critique of models that might explain the complex interactions of beat-by-beat cardiovascular control.
Heart Rate Variability
In the healthy human heart, beat-by-beat HRV is almost exclusively a consequence of variation in parasympathetic and sympathetic nervous system activities to the sinoatrial node. It has been shown, by study of the actions of atropine, that most of the variability is mediated by the parasympathetic nervous system across both the low- and high-frequency regions of the power spectrum.12 In the transplanted heart, complete and lasting denervation has been observed in most patients studied to date.1 2 3 4 9 However, evidence for both parasympathetic1 9 and partial sympathetic8 reinnervation has been presented. In our study, patient 9 displayed a high-frequency but not a low-frequency HRV and a notably slower heart rate than any of the other patients (Fig 4⇓). This also suggests that parasympathetic reinnervation might have occurred. Absence of low-frequency HRV in this patient indicates that neural control had not returned completely to that expected in healthy subjects. Parasympathetic activity normally contributes to low-frequency as well as high-frequency variability.12
In all transplant patients, heart rate varied slightly in phase with respiration. However, the magnitude of the high-frequency variation (2% to 7% of control; Table 2⇑, Fig 1⇑) indicates that this was probably not neurally mediated. Small-amplitude HRV in transplant patients has been attributed to varying stretch of intrinsic pacemaker tissues in phase with the respiration effect on venous return.1 2 3
Blood Pressure Variability
To date, there have been few investigations of BPV from beat-to-beat data. The need for intra-arterial measurement of blood pressure has recently been obviated by use of the continuous, noninvasive blood pressure monitor. Omboni et al26 concluded that the finger monitor could be used for spectral analysis of beat-by-beat BPV but that some caution was needed in the interpretation of the low-frequency region in comparisons between finger pressure and intra-arterial measurements. It was not clear to them, however, whether the problem was one of error or of amplification with the finger pressure monitor. In the present study, we used the same measurement device to make comparisons between transplant patients and control subjects. There should not be any reason to doubt the validity of these between-group comparisons.
Fractal Nature of Blood Pressure Variability
In a recent comparison between levels of lower body negative pressure, we found that systolic pressure exhibited a large percentage of fractal component in its variability signal.18 An observation by Parati et al22 and data from other research with dogs3 also support the concept of fractal variability of BPV. Mathematically, this means that the BPV signal is self-similar21 ; it can be viewed over a range of time scales and still appear to have a similar pattern. The physiological significance of this finding is that blood pressure variability has correlated information that is encoded over both the short-term and the long-term. We17 18 and others19 20 have previously speculated on the importance of this information in the maintenance of cardiovascular homeostasis. The complexity of the overall BPV can be appreciated by determination of the slope of the fractal component.
We chose to analyze our data by coarse graining spectral analysis.21 The advantage of this method over other techniques of spectral analysis is its ability to extract the fractal components from the harmonic components.17 21 This is achieved by a type of rescaling of the data. The algorithm has been described in detail, along with a demonstration of its efficiency in separating harmonic from fractal components.21 In brief, the data are rescaled in two steps (in one by sampling every second data point, in the other by sampling each point twice) before cross-correlation with the original data. In the cross correlations, only fractal components are retained, because of their property of being self-similar across a range of scales, while the harmonic components are lost. Therefore, a subtraction of this rescaled cross-correlation from an autocorrelation of the original data yields the harmonic-only spectral power. The fractal component has linear scaling across a wide range of frequencies when the data are plotted as log spectral power versus log frequency, in what is commonly called the 1/fβ relationship.9 10 11 12 13 14 15 16 17 18 19 20 21 The β value is the slope of the linear regression applied to these data. When the value of β is close to 1, there is a high level of complexity because the data frequently change direction toward or away from the mean. In contrast, for β close to 2, there are longer, less complex excursions of the measured data in one direction before a change.18 19 21
In a previous study,18 we did not have the opportunity to examine BPV in the absence of HRV as we did in this study of transplant patients. However, we concluded that the overall regulatory mechanisms for HRV and BPV must be independent because the slope of the fractal component for BPV remained constant, while that for HRV increased as the level of lower body negative pressure increased.18 In the current study, we can reach a similar conclusion for systolic pressure because there were no differences between the transplant patients and the control subjects for the percent fractal power or the slope of the fractal component. There were small differences in the slope of the spectral component for diastolic pressure, with smaller slopes for the transplant patients in the two supine positions but a greater slope in the seated rest position (Table 4⇑). That is, BPV was largely independent of HRV. As we previously concluded,18 the baroreflex influence on HRV does not appear to be linked to overall BPV.
Mechanisms of Blood Pressure Variability
There was a clear difference between transplant patients and control subjects in the relationship of the ratio of PHI in the diastolic pressure to PHI in the systolic pressure. High-frequency power is introduced to the blood pressure signal by the mechanical effects of respiration. With inspiration, blood pressure decreases and heart rate normally increases, whereas the opposite effects are observed with expiration.14 Exactly how the HRV occurs (whether it is due to baroreflex27 28 or central respiratory pattern generator influence on the vagal motor nucleus27 29 ) is not resolved, but the outcome of this research would not influence the present discussion. The important point is that there was tachycardia with inspiration and bradycardia with expiration in the healthy subjects. Therefore, as blood pressure increased with expiration, heart rate slowed simultaneously. This gave increased filling time that might, through the Starling mechanism, have caused increased stroke volume and higher systolic pressure. Simultaneously, there was a greater time for run-off, such that diastolic pressure might not have increased to the same extent. Thus, from the beginning to the end of expiration, the relative increase in systolic pressure might be greater than that of diastolic pressure. In contrast, the transplant patient, or healthy subjects taking atropine to block vagal activity,28 experienced very little modification of heart rate, so that any effects on systolic and diastolic pressures might be expected to be more linear functions of the mechanical effects of respiration. At odds with these data and this theory is the recent finding by Macor et al25 that there was no difference in the high-frequency component of either systolic or diastolic pressure between transplant patients and control subjects. Although Macor et al confined their study to recent transplant recipients (16 to 23 days after surgery), this should not be a reason for the difference between the studies. Indeed, the total variances in systolic and diastolic pressures were similar in the study by Macor et al and the present one; it was the pattern of variability that differed.
It has also been suggested that heart transplantation interrupts afferent fibers from the ventricles that are involved in the cholinergic vasodilator response.30 However, we believe that the above description of blood pressure and heart rate interactions can account for the modified systolic and diastolic pressure responses. Thus, it might not be necessary to speculate about the existence of cholinergic vasodilator fibers.
An interesting observation made in the present study was the significantly smaller PLO in both systolic and diastolic pressures in the transplant patients than in the control subjects. PLO for HRV has been proposed to originate with low-frequency oscillations in arterial blood pressure.12 13 Thus, absence of neural input to the heart would not be expected to cause a reduction in PLO for BPV. In fact, one would expect that the baroreflex would minimize any low-frequency variations in blood pressure. On the contrary, examination of the simultaneous beat-by-beat patterns of HRV and BPV indicated that nonbaroreflex events could contribute to low-frequency variations in blood pressure. That is, slow changes in RR interval were associated with directionally opposite changes in systolic pressure (Fig 5⇓). Saul et al15 suggested, on the basis of the phase relationship between HRV and BPV, that low-frequency variations resulted from both heart rate effects on blood pressure and blood pressure effects on heart rate. The reduction in PLO for systolic and diastolic pressures in the transplant patients also supported the concept that heart rate contributes importantly to PLO.
Resting systolic pressure tended to be higher, and resting diastolic pressure was higher, in the transplant patients than in the control subjects. Such an increase in blood pressure has been noted before and is often attributed to the effects of immunosuppressive therapy.10 31
Model of Heart Rate–Blood Pressure Interactions
Several authors have recently proposed different schemes in which heart rate and blood pressure interact with normal respiration. There are two possible scenarios. In the first, respiration acts primarily on heart rate through a central respiratory pattern generator gating29 of the vagal output to the sinoatrial node.15 In the second, respiration acts as a mechanical modulator of cardiac output,28 and therefore of blood pressure, which then acts on heart rate through the arterial baroreflex.27 The modulation of blood pressure in the transplant patients showed clearly that there was a direct effect of respiration on the high-frequency component of blood pressure variability. This observation and the resultant conclusion are in direct contrast to the results of recent experiments with dogs in which the high-frequency blood pressure variability was attributed to effects of heart rate modulation,32 but this might reflect a simple species difference. We also observed a low-frequency component that was independent of heart rate in the transplant patients. Recently, Seals et al33 observed no systematic variation in systolic or diastolic pressure with respiration in either control subjects or heart-lung transplant patients when they analyzed their data by pooling over a number of breaths. This latter method fails to treat the low-frequency variability independently of the high-frequency variability, as is done in the spectral analysis approach of the present and other studies.25 28
The data further indicated the importance of heart rate in blood pressure variability. In control subjects with intact innervation, PLO for systolic and diastolic pressures was increased and PHI for diastolic pressure was reduced compared with values in transplant patients. We take these data to support the hypothesis that respiration plays an important role in influencing heart rate through the arterial baroreflex response to the mechanical effects of respiration on blood pressure.27 The data also support a limited contribution of heart rate to variations in blood pressure.
We have demonstrated important differences between control subjects and transplant patients without intact neural control of heart rate in the way arterial blood pressure is regulated. Although there were no significant differences in the total variability of systolic and diastolic pressures between the groups, there were differences in the distribution of the harmonic components of the variability. We observed that important roles of heart rate were to act as a damper of high-frequency variability associated with respiration and to contribute to the low-frequency variability of systolic and diastolic pressures. The fractal components of HRV and BPV were examined separately to provide an understanding of the overall complexity of the cardiovascular control processes.17 18 20 The clear difference in the control subjects between the fractal component β for HRV and the β for BPV showed that these two cardiovascular variables were regulated independently.18 This was confirmed by data from transplant patients in whom, in the absence of significant HRV, the β of systolic pressure was not different from that of control subjects.
This research was supported by the Heart and Stroke Foundation of Ontario, the Natural Sciences and Engineering Research Council of Canada, the Centre Nationale d’Etudes Spatiales, G.I.P. Exercice, and Région Rhône-Alpes. R.L.H. was an MRC/INSERM/CNRS Visiting Scientist.
- Received May 19, 1994.
- Revision received September 21, 1994.
- Accepted November 15, 1994.
Bernardi L, Keller F, Sanders M, Reddy PS, Griffith B, Meno F, Pinsky MR. Respiratory sinus arrhythmia in the denervated human heart. J Appl Physiol. 1989;67:1447-1455.
Bernardi L, Salvucci F, Suardi R, Solda PL, Calciati A, Perlini S, Falcone C, Ricciardi L. Evidence for an intrinsic mechanism regulating heart rate variability in the transplanted and the intact heart during submaximal dynamic exercise? Cardiovasc Res. 1990;24: 969-981.
Sands KE, Appel ML, Lilly LS, Schoen FJ, Mudge GH Jr, Cohen RJ. Power spectrum analysis of heart rate variability in human cardiac transplant recipients. Circulation. 1989;79:76-82.
Zbilut JP, Murdock DK, Lawson L, Lawless CE, Von Dreele MM, Porges SW. Use of power spectral analysis of respiratory sinus arrhythmia to detect graft rejection. J Heart Transplant. 1988;7: 280-288.
Kaye DM, Esler M, Kingwell B, McPherson G, Esmore D, Jennings G. Functional and neurochemical evidence for partial cardiac sympathetic reinnervation after cardiac transplantation in humans. Circulation. 1993;88:1110-1118.
Giorgi DMA, Bortolotto LA, Seferian P, Bocchi EA, Bernardes-Silva H, Pereira-Barretto AC, Bellotti G, Pileggi F, Jatene AD. Twenty-four-hour monitoring of blood pressure and heart rate in heart transplant patients. J Hypertens. 1991;9(suppl 6):S340-S341.
Pomeranz B, Macauley RJB, Caudill MA, Kutz I, Adam D, Gordon D, Kilborn KM, Barger AC, Shannon DC, Cohen RJ, Benson H. Assessment of autonomic function in humans by heart rate spectral analysis. Am J Physiol. 1985;248:H151-H153.
Kitney RI. Beat-by-beat interrelationships between heart rate, blood pressure, and respiration. In: Kitney RI, Rompelman O, eds. The Beat-by-Beat Investigation of Cardiovascular Function: Measurement, Analysis and Applications. Oxford, UK: Clarendon Press; 1987:146-178.
Rowell LB. Human Cardiovascular Control. New York, NY: Oxford University Press; 1993:30-33.
Saul JP, Berger RD, Albrecht P, Stein SP, Chen MH, Cohen RJ. Transfer function analysis of the circulation: unique insights into cardiovascular regulation. Am J Physiol. 1991;261:H1231-H1245.
Pagani M, Lombardi F, Guzzetto S, Rimoldi O, Furlan R, Pizzinelli P, Sandrone G, Malfatto G, Dell’Orto S, Piccaluga E, Turiel M, Baselli G, Cerutti S, Malliani A. Power spectral analysis of heart rate and arterial pressure variabilities as a marker of sympathovagal interaction in man and conscious dog. Circ Res. 1986;59:178-193.
Butler GC, Yamamoto Y, Xing HC, Northey DR, Hughson RL. Heart rate variability and fractal dimension during orthostatic challenges. J Appl Physiol. 1993;75:2602-2612.
Butler GC, Yamamoto Y, Hughson RL. Fractal nature of short term systolic blood pressure and heart rate variability during lower body negative pressure. Am J Physiol. 1994;267:R26-R33.
Lipsitz LA, Mietus J, Moody GB, Goldberger AL. Spectral characteristics of heart rate variability before and during postural tilt: relations to aging and risk of syncope. Circulation. 1990;81: 1803-1810.
Parati G, Di Rienzo M, Omboni S, Castiglioni P, Frattola A, Mancia G. Spectral analysis of 24 h blood pressure recordings. Am J Hypertens. 1993;6(suppl):188S-193S.
Marsh DJ, Osborn JL, Cowley AW Jr. 1/f fluctuations in arterial pressure and regulation of renal blood flow in dogs. Am J Physiol. 1990;258:F1394-F1400.
Yamamoto Y, Hughson RL. On the fractal nature of heart rate variability in humans: effects of data length and β-adrenergic blockade. Am J Physiol. 1994;266:R40-R49.
Macor F, Fagard R, Vanhaecke J, Amery A: Respiratory-related blood pressure variability in patients after heart transplantation. J Appl Physiol. 1994;76:1961-1962.
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.
DeBoer RW, Karemaker JM, Strackee J. Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model. Am J Physiol. 1987;253:H680-H689.
Kaye D, Thompson J, Jennings G, Esler M. Cyclosporine therapy after cardiac transplantation causes hypertension and renal vasoconstriction without sympathetic activation. Circulation. 1993;88: 1101-1109.
Hedman AE, Hatikainen JEK, Tahyanainen KUO, Hakumaki MOK. Power spectral analysis of heart rate and blood pressure variability in anaesthetized dogs. Acta Physiol Scand. 1992;146: 155-164.
Seals DR, Suwarno O, Joyner MJ, Iber C, Copeland JG, Dempsey JA. Respiratory modulation of muscle sympathetic nerve activity in intact and lung-denervated humans. Circ Res. 1993;72:440-454.