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1 Dipartimento di Fisica, Università di Trento, and Istituto Trentino di Cultura-ist, 38050 Povo, Trento; 2 Dipartimento Scienze Precliniche di Vialba, Università di Milano, 20157 Milano; and 3 Unità Operativa di Cardiologia, Ospedale S. Chiara, 38100 Trento, Italy
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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The interactions between
systolic arterial pressure (SAP) and R-R interval (RR) fluctuations
after acute myocardial infarction (AMI) were investigated by measures
of synchronization separating the feedback from the feedforward control
and capturing both linear and nonlinear contributions. The causal
synchronization, evaluating the ability of RR to predict SAP
(
s/t) or vice versa (t/s), and the global
synchronization () were estimated at rest and after head-up tilt in
35 post-AMI patients, 20 young and 12 old. Significance and
nonlinearity of the coupling were assessed by surrogate data analysis.
Tilting increased the number of young subjects in which RR-SAP link was
significant (from 17 to 19) and linear (from 11 to 18). In AMI, both
significance and linearity of the coupling were low at rest (26 significant and 24 nonlinear) and further reduced after tilt (17 significant and 16 nonlinear). Old subjects showed a partial recovery
of linearity after tilt (rest: 1 linear of 7 significant; tilt: 5 linear of 8 significant). In young subjects, the causal synchronization
indexes were balanced and increased from rest (t/s = 0.072 ± 0.037 and s/t = 0.054 ± 0.028) to tilt (t/s = 0.125 ± 0.071 and
s/t = 0.108 ± 0.053). On the contrary, in old
subjects and AMI patients, the feedforward was prevalent to the
feedback coupling at rest (old: t/s = 0.041 ± 0.023 and s/t = 0.069 ± 0.042; AMI:
t/s = 0.050 ± 0.030 and s/t = 0.089 ± 0.053). Tilting blunted the
unbalance in old subjects (t/s = 0.065 ± 0.052 and s/t = 0.069 ± 0.044) but not in AMI patients (t/s = 0.040 ± 0.019 and
s/t = 0.060 ± 0.040). Thus, after AMI,
nonlinear mechanisms are elicited in RR-SAP interactions. Furthermore,
the neural regulation of the cardiovascular system resulted in
imbalance as a consequence of impaired feedback and enhanced
feedforward control mechanisms.
causal analysis; nonlinear coupling; synchronization; baroreflex regulation
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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THE NEURAL REGULATION OF CIRCULATION is accomplished by the central control and the peripheral reflex mechanisms, which continuously interact in modulating the dynamics of heart rate and arterial blood pressure. A major role in the maintenance of a dynamic form of "homeostasis" is played by the arterial baroreflex (24). However, in humans, feedforward mechanisms of cardiovascular regulation operating through mechanically coupled changes in systolic arterial pressure (SAP) and R-R interval (RR) have been suggested (1, 27). Furthermore, it has been demonstrated that age and acute myocardial infarction (AMI) can strongly damage the cardiovascular performance by affecting the capability of the system to accomplish the beat-to-beat regulation of the heart rate (3, 5, 6, 13). Thus for describing the complex regulatory mechanisms appropriate causal models able to disentangle the causal verses of the RR-SAP regulation have been proposed (2, 18).
On the other side, the awareness of the complex interactions among hemodynamic, electrophysiological, and humoral variables makes inappropriate the assumption of pure linear dynamics in the genesis of cardiovascular fluctuations and of their interactions. The most common tools used for analyzing the variability of the cardiovascular signals fail in detecting couplings between rhythmicities occurring at different frequencies, suggesting the introduction of statistics able to characterize nonlinearity in time series (9). While several authors have provided evidence that nonlinear dynamics are present in the heart rate variability (8, 12, 26), recognizing also a role for predicting cardiac death after AMI (7), nonlinear approaches to the study of RR-SAP coupling have not been followed yet. Recently, cross-conditional entropy (CCE) measures were proposed for evaluating the coupling between short time variability series in biological systems (23).
The aim of this study was to investigate the changes occurring after AMI in the synchronization between the spontaneous variabilities of the cardiac cycle length and the arterial pressure by disentangling the causal verses of their mutual relationship and without imposing any linear assumption. This approach made it possible to evaluate separately the feedback and feedforward regulation of RR and SAP and to verify the existence of nonlinear mechanisms originating the cardiovascular interactions.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Study populations. The study included 35 post-AMI patients (58.5 ± 10.2 yr), examined 10 ± 3 days after AMI and two control groups of healthy subjects: 20 young (25.0 ± 2.6 yr) and 12 old (63.1 ± 8.3 yr).
Post-AMI patients were part of larger database collected for a GISSI-3 arrhythmia substudy from February 1992 to July 1993 (16). According to the general study protocol, when present (8 patients),
-blocker therapy was discontinued two half-lives before the
recording session to avoid any interference with the autonomic and
cardiovascular systems. Eligible patients presented sinus rhythm and
were not taking antiarrhythmic drugs.
All control subjects were normotensive and free from any known disease
based on anamnesis and physical examination at the time of the study.
Experimental protocol and measurements. Cardiovascular signals were recorded in the electrophysiology laboratory in the morning, in comparably comfortable and quiet ambience conditions with subjects in sinus rhythm and breathing spontaneously. After a period of 15 min allowed for subject stabilization, electrocardiograms and arterial pressure signals were recorded for 10 min in a supine rest position, followed by 10 min of passive 60° head-up tilt. Arterial blood pressure was recorded at finger level by a photoplethysmographic Finapres device (Ohmeda 2300; Englewood, CO). All signals were digitized with a 1-kHz sampling rate.
RR and SAP values were automatically measured on digitized electrocardiogram and arterial blood pressure signal. The series were then cleaned up from artifacts, windowed to 300 points, and detrended by a high-pass filter to fulfill stationarity criteria (17). The normalized tachogram (t) and systogram (s) series were eventually obtained by subtracting the mean values and dividing by the SD.Causal nonlinear analysis of RR-SAP coupling.
Starting from the systogram series of N samples, s = {s(i), i = 1, ..., N}.
N 
L + 1 patterns
sL(i) of length L were extracted as [s(i), s(i 1), ...,
s(i L + 1)], and their Shannon entropy (SE) was estimated. By measuring the dispersion of the patterns
in the L-dimensional space, SE evaluates the amount of information carried by s given its partition in L-length
patterns. To consider the information lead from the systogram to the
tachogram, single samples of the series t = {t(i),
i = 1, ..., N} were jointed to the
patterns of s obtaining the mixed pattern [t(i),
sL(i)] (23). An example
with L = 3 is reported in Fig.
1. The CCE was then calculated as a
function of L as the difference between the SE of the mixed
patterns and the SE of the patterns of s. As shown in Fig.
2A, CCE quantifies the amount
of information carried by the tachogram that cannot be derived from the
systogram, i.e., the unpredictability of t(i) starting from
sL(i). To prevent the poor estimation
of SE due to the limited number of samples available for the
cardiovascular signals, in this study the corrected CCE introduced by
Porta et al. (23) was utilized. By normalizing (by the
division by the SE of t) and complementing to unity the corrected CCE
values, a measure of the predictability of the tachogram when
L-length patterns of the systogram are observed, the
synchronization function, was obtained (see Fig. 2B). The maximum over L of the synchronization function, quantifying
the maximum amount of information of t explained by s, was taken as the
causal synchronization index (t/s). In an analogous way, the predictability of the systolic pressure starting from the cardiac
period (s/t) was evaluated by inverting the role of the series s and t. The higher of t/s and s/t
was eventually assumed as the global synchronization (), indicating
the maximum amount of information exchanged by the two series. Because
the ith cardiac period cannot influence the ith
SAP value, the series s was one beat delayed before evaluating
t/s (17). We make reference to Ref.
23 for the methodological details and simulations.
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Surrogate data analysis. The method of surrogate data (19, 28) was applied to test 1) the significance and 2) the nonlinearity of the coupling between RR and SAP variability series. For this purpose, two types of surrogate data were generated according to the null hypothesis of 1) uncorrelated and 2) linearly correlated series. In the first case, the original RR and SAP series were Fourier transformed, and their Fourier phases were substituted with independent random numbers. After inverse Fourier transform was performed, two surrogate series (type I surrogates) having the same frequency distribution and power spectra as the original pair of signals, but completely uncoupled, were derived. The second type of surrogate data (type II surrogates) preserved not only the individual RR and SAP spectra but also the magnitude of their cross-spectrum. This was obtained by adding the same random number to the Fourier phases of the two series. In this way, the linear coupling was maintained, whereas nonlinear interactions were destroyed (19).
Fifteen independent pairs of type I and type II surrogate series were derived from each pair of original RR and SAP series. The synchronization index was then computed on the original and on the
set of surrogate series, and finding a statistical difference led to
rejection of the null hypothesis and thus to detection of the presence
of the searched property.
Statistical analysis.
An ANOVA test was used to assess the significance of the comparison
between all indexes across the three groups (unpaired data). The
differences between s/t and t/s within
groups were checked by Student's t-test (paired data) and
were considered statistically significant at P < 0.05.
distribution
evaluated on the surrogate pairs. The critical -value was obtained,
under the hypothesis of normal distribution, assuming a
P value of 0.05.
A chi-squared test for a 2 × 2 contingency table was performed to
assess the statistical difference of the significance and of the
nonlinearity of RR-SAP coupling between pairs of groups.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Table 1 reports the baseline
characteristics of the variability series measured in rest and tilt
conditions on patients belonging to the three populations. During
head-up tilt, all groups showed a significant decrease of the cycle
length along with a decrease of the total RR variability in old
subjects and AMI patients. In AMI patients, the tilt test determined
significant variations of the mean and SD of the systolic pressure. An
increase in variability of SAP series was also observed in young
subjects.
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Global coupling.
At rest, the resulted equal to 0.079 ± 0.037 in young
subjects, 0.070 ± 0.042 in old subjects, and 0.092 ± 0.053 in AMI patients. The three values were not statistically different
(ANOVA, P > 0.05). Figure
3 shows how the tilt testing pointed out
a differentiated response of for the three populations. Indeed,
after tilt, the synchronization was markedly increased in young
subjects ( = 0.139 ± 0.068) and was not significantly
changed in old subjects ( = 0.080 ± 0.048), whereas AMI
patients showed a significant decrease ( = 0.062 ± 0.039). The index increased in 16 of 20 young subjects (80%) and
decreased in 28 of 35 AMI patients (80%). As a result, the amount of
coupling measured by the synchronization index after the tilt maneuver
was higher for young than for old subjects (P < 0.05)
and AMI (P < 0.005) patients. The analysis of
significance of , performed by type I surrogate data, supported these results. Indeed, moving from rest to tilt, the number of subjects
showing uncoupling (solid circles in Fig. 3 and first row of Table
2) resulted slightly decreased in young
subjects, substantially unchanged in old subjects, and markedly
increased in AMI patients. As expected, the average value of the
synchronization index evaluated on type I surrogate series was
independent of groups and experimental conditions.
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resulted
significantly larger than zero. Table 2 and Fig.
4 evidence the number of subjects showing
nonlinear coupling for the three populations in both rest and tilt
conditions. At rest, this number was lower for young (6 of 17 cases)
than for old subjects (6 of 7 cases, P = 0.07) and AMI
(24 of 26 cases, P < 0.001) patients. After tilt, the
coupling resulted highly linear in young subjects (1 nonlinear of 19 significant) and remained highly nonlinear in post-AMI patients (16 nonlinear of 17 significant, P < 0.0001 vs. young
subjects), whereas old subjects showed a reduced number of nonlinearly
interacting series (3 nonlinear of 8 significant, P < 0.01 vs. AMI patients). On average, the synchronization evaluated on
type II surrogates approached the value obtained from the original RR
and SAP series, where the coupling resulted linear, and was substantially lower where the coupling was detected as nonlinear. AMI
subjects showed the lowest values of calculated on type II
surrogates.
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Causal coupling.
The results of the causal synchronization analysis are summarized in
Table 3 and Fig.
5. In young subjects, the two causal synchronization indexes s/t and t/s
measured a comparable coupling level either in the supine or
orthostatic positions. As shown for , the causal indexes also
augmented after the tilt maneuver. In old subjects, s/t
was significantly higher than t/s at rest, but this
difference was not maintained during tilt. No significant changes were
observed between the two indexes moving from supine to standing
position. In AMI patients, a marked unbalance between the causal
synchronization indexes was observed at rest and preserved during tilt.
Both t/s and s/t were reduced by the tilt
maneuver.
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t/s was reduced in old
subjects and AMI patients compared with young subjects. During tilt, this index resulted lower in AMI patients than in old and young subjects and lower in old than in young subjects. At rest,
s/t was significantly increased for AMI with respect to
young subjects and after tilt was lower in old subjects and AMI
patients than in young subjects.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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This work points out that the study of the complex cardiovascular regulation in impaired conditions can be improved by considering the causal dependencies between cardiac cycle length and systolic pressure and without a priori assuming the linearity of their coupling. In particular, the use of CCE allows us to incorporate both linear and nonlinear contributions into a quantitative measure of RR-SAP coupling. Moreover, the introduction of causality leads to the simultaneous and separate evaluation of feedback and feedforward mechanisms, quantifying their relative contribution to the overall cardiovascular regulation.
Nonlinearity in RR-SAP dynamic interaction.
The presence of significant coupling was verified by generating a set
of pairs of surrogate series (type I surrogates) in which any link was
totally destroyed by randomizing the phase spectra of original RR and
SAP series and then looking for statistical differences in the
synchronization index. Nonlinear mechanisms in the RR-SAP link were
then assessed with the same methodology by generating a new set of
pairs of surrogate series (type II surrogates) in which the linear
coupling was maintained and nonlinear coupling canceled by conserving
phase differences between RR and SAP randomized phase spectra. Analysis
of type I surrogates assessed at ~0.03 the synchronization level of
completely uncoupled series, whereas the value for type II
surrogates resulted dependent on the nature of RR-SAP interactions.
Indeed, after type II surrogate generation, the synchronization level
was unchanged for linearly coupled series and was blunted when
nonlinearities significantly affected the coupling. Moreover, when
nonlinearity is detected, the synchronization gap between original and
surrogate series may provide information about the extent of linear
versus nonlinear components of the coupling. Thus the fact that in AMI
patients the synchronization of type II surrogates resulted very low,
approaching the uncoupling level, indicates the predominance of
nonlinear features with respect to linear ones in determining the
coupling between cardiac period and arterial pressure fluctuations.
Unbalanced RR-SAP regulation. As demonstrated by young subjects, in physiological conditions the coupling strength evaluated on the two regulatory pathways is substantially balanced and preserved also after the sympathetic activation. In old subjects, our results showed an unbalanced RR-SAP regulation with increased feedforward and a decreased feedback mechanism, thus confirming a recent study pursued by linear cross-spectral analysis (21). This unbalancing was more marked in patients 2 wk after the infarction, mostly due to an increase of coupling on the feedforward regulatory pathway. Previous studies based on the analysis of the concurrent changes in RR and SAP demonstrated a dependence of the balancing between feedforward and feedback mechanisms on the efficiency of the neural control (11, 20). In our study, the increased extent of coupling on the feedforward arm could be explained by considering the passive behavior of the vascular bed due to the arterial stiffening induced by age and disease, which favors the mechanical matching between the left ventricle and the vasculature.
By the passive assumption of the orthostatic position, the imbalance was reduced in old subjects through a partial recovery of the coupling on the baroreflex path, whereas it was kept in AMI patients. It has been suggested that the alterations in the sympathovagal balance at the sinus node present at rest after AMI prevent its further modifications after the tilt maneuver (13). In the same way, tilt seems able to neither improve the synchronization in both arms of the RR-SAP regulatory mechanism, as happens in young subjects, nor to recover the balancing between the two causal regulations, as happens in old subjects. The results of previous (11, 18, 27) and present investigations assess the importance of separately investigate the two arms of the regulatory loop, indicating a possible differentiate capability of one cardiovascular variable to affect the other. The increased strength of coupling on the nonbaroreflex path found in the present study for AMI patients supports the concept that feedforward mechanisms play a dominant role in the control of circulation in impaired pathological conditions. As the nonbaroreflex coupling does not merely reflect a mechanical matching but can be mediated by the autonomic nervous system (11), the measure of the balancing between feedback and feedforward mechanisms could provide a new perspective for evaluating the neural regulation of the cardiovascular function.Impairment of heart rate regulation.
In basal conditions, the synchronization causal index indicated in old
subjects and post-AMI patients a reduction in the ability of the
systolic pressure changes to drive heart rate variability. This finding
agrees with others demonstrating a decrease of baroreflex sensitivity
with age and coronary disease (6, 10). However, in the
regulation of the heart rate, two opposite feedback mechanisms, the
vagally mediated arterial baroreflex (negative feedback) and the
excitatory sympathetic efferent discharge (positive feedback), are
involved (14). The causal synchronization index
t/s, accounting for both these mechanisms, cannot be
strictly related to the baroreflex gain. Hence, in post-AMI patients,
the reduced vagal activity could be counterbalanced by the enhanced
sympathetic activity, thus explaining the comparable values found in
patients and healthy age-matched control groups.
t/s.
On the other hand, the smoothed response of old subjects to the
assumption of the orthostatic position, documented by a lower
shortening of RR length, was reflected also by the poor increase of the
synchronization measure. Finally, the decrease of this index observed
in AMI patients can be attributed to the inability of these patients to
respond to tilt-induced changes in cardiac output by further
sympathetic activation (13). Therefore, the
reduction of causal synchronization after tilt demonstrated in AMI
patients an impairment of mechanisms regulating heart rate with a
depressed negative feedback and a not-responding overloaded positive
feedback. This uncoupling could also contribute to the lack of
the cardiac output documented by the lowering of SAP during standing position.
Potential limitations.
According to the study protocol, cardiovascular signals of the AMI
group were recorded at predischarge time on patients in pharmacological
washout. Because of this constraint, only patients able to support
without appreciable risk the suspension of -blocker treatment and no
taking of antiarrhythmic drugs were enrolled for the study. This
criterion of selection, based on the demonstration of both preserved
ventricular function and absence of myocardial ischemia,
characterized a subgroup of very low-risk post-AMI patients. Thus the
results of our study cannot be generalized to the whole post-AMI
population. Furthermore, the lower heart rate shown by AMI patients
could affect part of findings of the study. In fact, high vagal tone
has been previously associated to nonlinearity in the dynamic of the
cardiovascular variables (8); thus one cannot exclude that
the nonlinear nature of coupling mechanisms elicited in AMI could be
attributable to the vagal tone predominance rather than to the
underlying pathology. However, the mean heart rate shown by AMI
patients is comparable with that of a large part of post-MI patients
characterized by positive prognosis, as it has been recently shown that
after myocardial infarction >50% of patients had heart rates ranging
from 50 to 69 beats/min and higher heart rate was associated to
increased risk of death (29). Furthermore, the increase of
nonlinearity and unbalancing in the regulatory mechanism demonstrated
by our study for age and pathology may suggest a further raise of
complexity in patients with complicated myocardial infarction and poor prognosis.
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FOOTNOTES |
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Address for reprint requests and other correspondence: G. Nollo, Physics Dept., Univ. of Trento, Via Sommarive, 14 38050 Povo-Trento, Italy (E-mail: nollo{at}science.unitn.it).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
May 16, 2002;10.1152/ajpheart.00882.2001
Received 10 October 2001; accepted in final form 1 May 2002.
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TOP
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METHODS
RESULTS
DISCUSSION
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  M Di Rienzo, G Parati, A Radaelli, and P Castiglioni Baroreflex contribution to blood pressure and heart rate oscillations: time scales, time-variant characteristics and nonlinearities Phil Trans R Soc A, April 13, 2009; 367(1892): 1301 - 1318. [Abstract] [Full Text] [PDF]
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G. Nollo, L. Faes, R. Antolini, and A. Porta Assessing causality in normal and impaired short-term cardiovascular regulation via nonlinear prediction methods Phil Trans R Soc A, April 13, 2009; 367(1892): 1423 - 1440. [Abstract] [Full Text] [PDF]
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G. Nollo, L. Faes, A. Porta, R. Antolini, and F. Ravelli Exploring directionality in spontaneous heart period and systolic pressure variability interactions in humans: implications in the evaluation of baroreflex gain Am J Physiol Heart Circ Physiol, April 1, 2005; 288(4): H1777 - H1785. [Abstract] [Full Text] [PDF]
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) in A and is reported after
normalization in B. The maximum of the synchronization
function (
in B) represents the causal
synchronization 
