EVIDENCE OF UNBALANCED REGULATORY MECHANISM OF HEART RATE

AND SYSTOLIC PRESSURE AFTER ACUTE MYOCARDIAL INFARCTION

Giandomenico Nollo a, Luca Faes a, Alberto Porta b, Barbara Pellegrini a, Flavia Ravelli a,

Maurizio Del Greco c, Marcello Disertori c, Renzo Antolini a

a Dipartimento di Fisica, Università di Trento, INFM, and ITC-irst, via Sommarive, 38050

Povo, Trento, Italy

b DiSP LITA di Vialba, Università di Milano, 20157 Milano, Italy

c Unità Operativa di Cardiologia, Ospedale S. Chiara, 38100 Trento, Italy

Running title: Enhanced feedforward mechanism in post infarction

Corresponding author:

Giandomenico Nollo

Physics Department, University of Trento

Via Sommarive, 14

38050 Povo – Trento

Tel +39 0461 882041; Fax +39 0461 881696

nollo@science.unitn.it

Copyright 2002 by the American Physiological Society.

AJP-Heart Articles in PresS. Published on May 16, 2002 as DOI 10.1152/ajpheart.00882.2001

1

Abstract

The interactions between systolic arterial pressure (SAP) and RR interval 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 (χs/t) or

vice versa (χt/s), and the global synchronization (χ), 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, 24

nonlinear) and further reduced after tilt (17 significant, 16 nonlinear). Old showed a partial

recovery of linearity after tilt (rest: 1 linear out of 7 significant; tilt: 5 linear out of 8

significant). In Young, the causal synchronization indexes were balanced and increased from

rest (χt/s=0.072±0.037, χs/t=0.054±0.028) to tilt (χt/s=0.125±0.071, χs/t=0.108±0.053). On the

contrary, in Old and AMI the feedforward was prevalent to the feedback coupling at rest (Old:

χt/s=0.041±0.023, χs/t=0.069±0.042; AMI: χt/s=0.050±0.030, χs/t=0.089±0.053). Tilting

blunted the unbalance in Old (χt/s=0.065±0.052, χs/t=0.069±0.044) but not in AMI

(χt/s=0.040±0.019, χs/t=0.060±0.040). Thus, after AMI nonlinear mechanisms are elicited in

RR-SAP interactions. Further, the neural regulation of the cardiovascular system resulted

unbalanced as a consequence of impaired feedback and enhanced feedforward control

mechanisms.

Keywords: causal analysis; nonlinear coupling; synchronization; baroreflex regulation

2

Introduction

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 RR interval 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 between 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 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

3

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.

Methods

Study populations

The study included 35 post-AMI patients (58.5±10.2 years), examined 10±3 days after

acute myocardial infarction, and two control groups of healthy subjects: 20 Young (25.0±2.6

years) and 12 Old (63.1±8.3 years).

Post-AMI patients were part of larger database collected for GISSI-3 arrhythmias

substudy from February 1992 to July 1993 (16). According to the general study protocol,

when present (eight patients) beta-blocker therapy was discontinued 2 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 subjects

stabilization, ECG and arterial pressure signals were recorded for 10 minutes in supine rest

position, followed by 10 min of passive 60 degrees head-up tilt. Arterial blood pressure was

4

recorded at finger level by a photoplethysmographic Finapres device (Ohmeda 2300,

Englewood, CO). All signals were digitized with 1 KHz sampling rate.

RR intervals 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, in order 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 standard deviation.

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. In

order 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 patterns

(t(i),sL(i)) (23). An example with L=3 is reported in Figure 1. The cross-conditional entropy

(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 Figure 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 Figure 2b). The maximum over L of the synchronization function,

quantifying the maximum amount of information of t explained by s, was taken as causal

5

synchronization index, named χt/s. In an analogous way, the predictability of the systolic

pressure starting from the cardiac period, χs/t, was evaluated by inverting the role of the series

s and t. The higher of χt/s and χs/t was eventually assumed as the global synchronization χ,

indicating the maximum amount of information exchanged by the two series. Since the i-th

cardiac period cannot influence the i-th SAP value, the series s was one beat delayed before

evaluating χt/s (17). We make reference to (23) for the methodological details and simulations.

Surrogate data analysis

The method of surrogate data (19, 28) was applied to test (i) the significance and (ii)

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 (i) uncorrelated and

(ii) 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 performing the inverse Fourier Transform, 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, while 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 χ was then computed on the

original and on the set of surrogate series, and finding a statistical difference leaded to reject

the null hypothesis and thus to detect the presence of the searched property.

6

Statistical Analysis

ANOVA test was used to assess the significance of the comparison between all

indexes across the three groups (unpaired data). The differences between χs/t and χt/s within

groups were checked by the Student t-test (paired data), and were considered statistically

significant at P<0.05.

The significance and the nonlinearity of RR-SAP coupling were verified by the

hypothesis testing included in the method of surrogate data. The null hypothesis was rejected

when the synchronization of the original series was higher than the critical value of the χ

distribution evaluated on the surrogate pairs. The critical χ value was obtained, under the

hypothesis of normal distribution, assuming a P-value of 0.05.

The Chi square test for 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.

Results

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 and AMI. In AMI patients the tilt test determined significant variations of

mean and standard deviation of the systolic pressure. An increase in variability of SAP series

was also observed in Young.

7

Global coupling

At rest, the global synchronization index χ resulted equal to 0.079±0.037 in Young,

0.070±0.042 in Old, and 0.092±0.053 in AMI. The three values were not statistically different

(ANOVA, P>0.05). Figure 3 shows how the tilt testing pointed out a differentiated response

of χ for the three populations. Indeed, after tilt the synchronization was markedly increased in

Young (χ=0.139±0.068) and was not significantly changed in Old (χ=0.080±0.048), while

AMI show a significant decrease (χ=0.062±0.039). The index increased in 16 out of 20 young

subjects (80%), and decreased in 28 out of 35 AMI patients (80%). As a result, the amount of

coupling measured by the synchronization index after the tilt manoeuvre was higher for

Young than for Old (P<0.05) and AMI (P<0.005). The analysis of significance of χ,

performed by type I surrogate data, supported these results. Indeed, moving from rest to tilt

the number of subjects showing uncoupling (filled circles in Figure 3 and first row of Table 2)

resulted slightly decreased in Young, substantially unchanged in Old, and markedly increased

in AMI. As expected, the average value of the synchronization index evaluated on type I

surrogate series was independent of groups and experimental conditions.

The presence of nonlinear features underlying the interactions between RR and SAP

was investigated by means of type II surrogate data analysis on subjects for which the

synchronization χ resulted significantly larger than zero. Table 2 and Figure 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 out of 17 cases) than for Old (6 out of

7 cases, P=0.07) and AMI (24 out of 26 cases, P<0.001). After tilt, the coupling resulted

highly linear in young subjects (1 nonlinear out of 19 significant) and remained highly

nonlinear in post-AMI patients (16 nonlinear out of 17 significant, P<0.0001 vs. Young),

while elderly showed a reduced number of nonlinearly interacting series (3 nonlinear out of 8

8

significant, P<0.01 vs. AMI). 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 χ calculated on type II surrogates.

Causal coupling

Results of the causal synchronization analysis are summarized in Table 3 and Figure 5.

In Young, the two causal synchronization indexes χs/t and χt/s measured a comparable

coupling level either in the supine or in the orthostatic position. As shown for the global

synchronization, also the causal indexes augmented after tilt manoeuvre. In Old, χs/t was

significantly higher than χt/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 χt/s and χs/t were reduced by the tilt

manoeuvre.

As reported in Table 3, at rest χt/s was reduced in Old and AMI in comparison with

Young. During tilt, this index resulted lower in AMI than in Old and Young, and lower in Old

than in Young. At rest χs/t was significantly increased for AMI with respect to Young and after

tilt was lower in Old and AMI than in Young.

9

Discussion

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 cross-conditional entropy allows 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, then looking for statistical differences in the

synchronization index. Nonlinear mechanisms in 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 about 0.03 the synchronization level of completely uncoupled series,

while the χ value for type II surrogates resulted dependent on the nature of RR-SAP

interactions. Indeed, after type II surrogates 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 vs.

nonlinear components of the coupling. Thus, the fact that in AMI patients the synchronization

10

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.

Although in resting condition the average coupling strength was not significantly

different among the three groups, the presence of nonlinear dynamics in RR-SAP interactions

was found in much more post-AMI patients than Young subjects. Differences across groups

became more evident after sympathetic stimulation as synchronization increased in Young,

was substantially unchanged in Old, and decreased in AMI group. In physiological condition,

tilting is supposed to reduce the complexity of RR and SAP, entraining all the operating

mechanisms in the LF band (15, 22) and increasing the number of correlated sequences

between the two series (11). In our study, this tilt-induced simplification of the coupling was

documented in Young by the increase of the synchronization index and of the number of

patients showing pure linear RR-SAP interactions. This feature was partially verified also in

elderly that after tilt showed a prevalence of linear interactions between RR and SAP

fluctuations. Differently, in AMI the synchronization index was reduced after tilt, the number

of subjects showing uncoupled RR and SAP dynamics was doubled, and where the coupling

was significant its nature resulted non linear in all but 1.

Thus, the dumping of the coupling strength documented by the synchronization index

confirms the complex response of post-AMI patients to tilt-induced sympathetic activation

and vagal deactivation, also previously demonstrated by spectral analysis (13). Moreover,

results of surrogate data analysis demonstrate that in this class of patients the use of nonlinear

measures of coupling adds new knowledge on the study of RR-SAP dynamic interactions.

Indeed, the demonstrated marked prevalence of non linear links at rest and its persistence

during orthostatic stimulation suggest that after myocardial infarction mechanisms of genesis

11

of cardiovascular oscillations are tightly complicated by the rise non linear features otherwise

not evidenced in basal physiological condition (22).

Unbalanced RR-SAP regulation

As demonstrated by Young, in physiological conditions the coupling strength

evaluated on the two regulatory pathways is substantially balanced and preserved also after the

sympathetic activation. In elderly, 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

two weeks 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, that favors the

mechanical matching between the left ventricle and the vasculature.

By the passive assumption of the orthostatic position the unbalance was reduced in Old

through a partial recovery of the coupling on the baroreflex path, while it was kept in AMI. It

has been suggested that the alterations in the sympathovagal balance at sinus node present at

rest after AMI prevent its further modifications after the tilt manoeuvre (13). In the same way,

tilt seems able neither to improve the synchronization in both arms of the RR-SAP regulatory

mechanism, as happen in Young, nor to recover the balancing between the two causal

regulations, as happens in Old.

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

12

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 condition, the synchronization causal index indicated in elderly 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 χt/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 group.

Again, the continuous interaction between excitatory and inhibitory feedback

mechanisms should be considered to explain the different effects of the tilt manoeuvre on the

causal measure of coupling across the three groups. While it has been demonstrated that the

baroreflex gain is reduced when subjects change from lying to standing position (4, 25), in

Young we found a consistent increase of coupling. Thus, it seems that in physiological

condition the tilt-induced increase in sympathetic activity overwhelms the vagal deactivation

and determines the observed growth of χt/s. On the other side, the smoothed response of

13

elderly to the assumption of the orthostatic position, documented by a lower shortening of RR

interval length, was reflected also by the poor increase of the synchronization measure.

Finally, the decrease of this index observed in AMI 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 an

impairment of mechanisms regulating heart rate with a depressed negative feedback and 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 AMI group were recorded at pre-

discharge time on patients in pharmacological washout. Due to this constraint, only patients

able to support without appreciable risk the suspension of beta-blockers treatment and no

taking antiarrhythmic drugs were enrolled for the study. This criterion of selection, based on

the demonstration of both preserved ventricular function and absence of myocardial

ischaemia, characterized a subgroup of very-low-risk post-AMI patients. Thus, 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 non linear 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 is comparable to that of a large part

of post-MI patients characterized by positive prognosis as it has been recently shown that after

myocardial infarction more than 50% of patients had heart rate ranging from 50 to 69 beats

per minute 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

14

ours study for age and pathology may suggest a further raise of complexity in patients with

complicated MI and poor prognosis.

Conclusion

In summary, our study emphasizes the importance of considering nonlinearity and

causality for investigating on the interactions between spontaneous fluctuations of the

cardiovascular parameters in nonphysiological conditions. Indeed, while in healthy young

subjects the coupling between heart rate and arterial pressure occurs mainly through linear

interactions, in elderly and post-AMI patients the presence of nonlinear mechanisms was

found to play an important role. Further, differently from physiological conditions two weeks

after AMI the baroreflex feedback regulation seems to be deeply damaged as its capability to

respond to sympathetic stimulation was denied, while the strength of feedforward regulation

was markedly enforced. This finding supports the concept that a balance between the two

arms of the regulatory mechanism is essential to achieve the most adequate regulation of

cardiovascular system.

15

References

1. Akselrod S, Gordon D, Madwed JB, Snidman NC, Shannon DC, and Cohen RJ.

Hemodynamic regulation: investigation by spectral analysis. Am J Physiol 249: H867-

H875, 1985.

2. Baselli G, Porta A, Rimoldi O, Pagani M, and Cerutti S. Spectral decomposition in

multichannel recordings based on multivariate parametric identification. IEEE Trans

Biomed Eng 44: 1092-1101, 1997.

3. Bigger JTJ, Fleiss JL, Steinman RC, Rolnitzky LM, Kleiger RE, and Rottman JN.

Frequency domain measures of of heart period variability and mortality after myocardial

infarction. Circulation 85: 164-171, 1992.

4. Cooke WH, Hoag JB, Crossman AA, Kuusela TA, Tahvanainen KUO, and

Eckberg DL. Human response to upright tilt: a window on central autonomic

integration. J Physiol 517: 617-628, 1999.

5. Craft N and Schwartz JB. Effects of age on intrinsic heart rate, heart rate variability,

and AV conduction in healthy humans. Am J Physiol 268: 1441-1452, 1995.

6. Gribbin B, Pickering TG, Sleight P, and Peto R. Effect of age and high blood

pressure on baroreflex sensitivity in man. Circ Res 29: 424-431, 1971.

7. Huikuri HV, Makikallio TH, Peng CK, Goldberger AL, Hintze U, and Moller M.

Fractal correlation properties of R-R interval dynamics and mortality in patients with

depressed left ventricular function after an acute myocardial infarction. Circulation 101:

47-53, 2000.

16

8. Kanters JK, Hojgaard MV, Agner E, and Holstein-Rathlou NH. Short- and long-

term variations in non-linear dynamics of heart rate variability. Cardiovasc Res 31: 400-

409, 1996.

9. Kaplan DT. The analysis of variability. J Cardiovasc Electrophysiol 5: 16-19, 1994.

10. La Rovere MT, Bigger JTJ, Marcus FI, Mortara A, and Schwartz PJ. Baroreflex

sensitivity and heart-rate variability in prediction of total cardiac mortality after

myocardial infarction. Lancet 351: 478-484, 1998.

11. Legramante JM, Raimondi G, Massaro M, and Iellamo F. Positive and negative

feedback mechanisms in the neural regulation of cardiovascular function in healthy and

spinal cord-injured humans. Circulation 103: 1250-1255, 2001.

12. Lombardi F, Sandrone G, Mortara A, Torzillo D, La Rovere MT, Signorini MG,

Cerutti S, and Malliani A. Linear and nonlinear dynamics of heart rate variability after

acute myocardial infarction with normal and reduced left ventricular ejection fraction.

Am J Cardiol 77: 1283-1288, 1996.

13. Lombardi F, Sandrone G, Pernpruner S, Sala R, Garimoldi M, Cerutti S, Baselli

G, Pagani M, and Malliani A. Heart rate variability as an index of sympathovagal

interaction after acute myocardial infarction. Am J Cardiol 60: 1239-1245, 1987.

14. Malliani A. Homeostasis and instability: the hypothesis of tonic interaction in the

cardiovascular regulation of negative and positive feedback mechanisms. In Lown, B,

Malliani A, and Prosdocimi M, eds. Neural mechanisms and cardiovascular disease.

Padova-Berlin, Liviana Press Springer Verlag. 1986, p. 1-9.

17

15. Montano N, Gnecchi Ruscone T, Porta A, Lombardi F, Pagani M, and Malliani A.

Power spectrum analysis of heart rate variability to assess the change in sympathovagal

balance during graded orthostatic tilt. Circulation 90: 1826-1831, 1994.

16. Nollo G, Del Greco M, Disertori M, Santoro E, Maggioni AP, and Sanna GP.

Absence of slowest oscillations in short term heart rate variability of post-myocardial

infarction patients. GISSI-3 arrhythmias substudy. GISSI-3 Arrhythmias Substudy

Investigators. Auton Neurosci 90: 127-131, 2001.

17. Nollo G, Faes L, Porta A, Pellegrini B, and Antolini R. Synchronization index for

quantifying nonlinear causal coupling between RR interval and systolic arterial pressure

after myocardial infarction. Comp in Cardiol 27: 143-146, 2000.

18. Nollo G, Porta A, Faes L, Del Greco M, Disertori M, and Ravelli F. Causal linear

parametric model for baroreflex gain assessment in patients with recent myocardial

infarction. Am J Physiol Heart Circ Physiol 280: H1830-H1839, 2001.

19. Palus M. Detecting phase synchronization in noisy systems. Phys Lett A 235: 341-351,

1997.

20. Parati G, Di Rienzo M, Bertinieri G, Pomidossi G, Casadei R, Groppelli A, Pedotti

A, Zanchetti A, and Mancia G. Evaluation of the baroreceptor-heart rate reflex by 24-

hour intra-arterial blood pressure monitoring in humans. Hypertension 12: 214-222,

1988.

21. Pitzalis MV, Massari F, Mastropasqua F, Fioretti A, Guida P, Colombo R,

Balducci C, and Rizzon P. Age effect on phase relations between respiratory

oscillations of the RR interval and systolic pressure. PACE 23: 847-853, 2000.

18

22. Porta A, Baselli G, Guzzetti S, Pagani M, Malliani A, and Cerutti S. Prediction of

short cardiovascular variability signals based on conditional distribution. IEEE Trans

Biomed Eng 47: 1555-1564, 2000.

23. Porta A, Baselli G, Lombardi F, Montano N, Malliani A, and Cerutti S. Conditional

entropy approach for the evaluation of the coupling strength. Biol Cybern 81: 119-129,

1999.

24. Scher AM. Carotid and aortic regulation of arterial blood pressure. Circulation 56: 521-

528, 1977.

25. Steptoe A and Vogele C. Cardiac baroreflex function during postural change assessed

using non-invasive spontaneous sequence analysis in young men. Cardiovasc Res 24:

627-632, 1990.

26. Task force of the European Society of Cardiology and the North American Society

of Pacing and Electrophysiology. Heart rate variability. Standards of measurement,

physiological interpretation, and clinical use. Eur Heart J 17: 354-381, 1996.

27. Taylor JA and Eckberg DL. Fundamental relations between short-term RR interval

and arterial pressure oscillations in humans. Circulation 93: 1527-1532, 1996.

28. Theiler J, Eubank S, Longtin A, Galdrikian B, and Farmer JD. Testing for

nonlinearity in time series: the method of surrogate data. Physica D 58: 77-94, 1992.

29. Zuanetti G, Mantini L, Hernandez-Bernal F, Barlera S, di Gregorio D, Latini R,

and Maggioni AP. Relevance of heart rate as a prognostic factor in patients with acute

myocardial infarction: insights from the GISSI-2 study. Eur Heart J 19 Suppl F: F19-

F26, 1998.

19

Figure Legends

Figure 1

Selection of the samples of the systogram (s) for the prediction of the tachogram (t). The

example shows the construction of the patterns of length three of s, s3(i)=(s(i),s(i-1),s(i-2)),

and of the mixed patterns, (t(i),s3(i)).

Figure 2

Corrected cross-conditional entropy (CCE) (a) and synchronization function (b) evaluating the

predictability of the tachogram from the systogram as functions of the length L of the patterns

obtained from the systogram. The maximum of CCE is obtained for L=0 and represent the

Shannon Entropy of the tachogram. At a given value of L, the amount of information of the

tachogram explained by the systogram is represented by the difference between the CCE

maximum (dashed line) and the CCE value (circle symbol) in (a), and is reported after

normalization in (b). The maximum of the synchronization function (filled circle in (b))

represents the causal synchronization χt/s.

Figure 3

Distributions and mean values ± SD of the synchronization global indexes evaluated in the

three populations during rest and tilt conditions. Filled circles represent the subjects in which

no significant coupling was detected by the surrogate data analysis. Moving from rest to tilt,

the synchronization increased in Young and decreased in AMI, while no significant changes

were revealed in Old. Paired t-test: * P=0.001 vs. Rest.

Figure 4

Results of surrogate data analysis for testing the significance and the presence of nonlinearity

in the coupling between heart rate and systolic pressure. Bar graphs show the partition of the

three populations in subjects exhibiting nonlinear coupling (black area of bars) and pure linear

20

coupling (white area of bars) obtained by type II surrogate data analysis during rest and after

tilt manoeuvre. The height of the bars represent the total number of subjects for which RR and

SAP series resulted significantly coupled after type I surrogate data analysis. Chi-square test:

* P<0.01, ** P<0.001 vs. AMI.

Figure 5

Mean values ± SD of the causal synchronization indexes (χs\t and χt\s) in the three populations

during rest and tilt conditions. At rest, whereas in Young the coupling on the two causal

verses was balanced, in Old and AMI χs\t was prevalent on χt\s. After tilt, both χs\t and χt\s

increased in Young, preserving their balancing. While a slight increase of χt\s balanced the

regulation in Old, a decrease of both causal synchronization indexes and the maintenance of

the unbalance were observed in AMI. Paired t-test: * P<0.05, ** P<0.005 vs. Rest; # P<0.01,

## P<0.001 χs\t vs. χt\s.

21

Table 1. Population characteristics and time domain measures of the cardiovascular

parameters at rest and during tilt.

Young Old AMI

N. of subjects 20 12 35

Age, years 25.0 ± 2.6 63.1 ± 8.3 58.5 ± 10.2

Rest

Mean RR, ms 884 ± 124 797 ± 85 1019 ± 154

SD RR, ms 46 ± 25 27 ± 12 29 ± 23

Mean SAP, mmHg 122.1 ± 20.7 129.8 ± 12.3 120.7 ± 18.5

SD SAP, mmHg 3.8 ± 1.3 4.1 ± 1.2 2.7 ± 1.1

Tilt

Mean RR, ms 703 ± 66 ‡ 719 ± 121 † 861 ± 163 ‡

SD RR, ms 42 ± 16 18 ± 15 † 21 ± 15 †

Mean SAP, mmHg 117.7 ± 14.9 131.8 ± 12.8 112.3 ± 26.5 †

SD SAP, mmHg 6.0 ± 1.6 ‡ 4.4 ± 1.6 3.3 ± 1.3 †

† P<0.05, ‡ P<0.005 vs. Rest

Values are mean ± SD.

22

Table 2. Summary of surrogate data analysis

Young Old AMI

Rest Tilt Rest Tilt Rest Tilt

Non significant coupling

N. of subjects 3 1 5 4 9 18

χ 0.036 0.047 0.037 0.042 0.038 0.038

χ, type I surrogates 0.032 0.035 0.031 0.033 0.031 0.033

Significant linear coupling

N. of subjects 11 18 1 5 2 1

χ 0.078 0.141 0.058 0.089 0.138 0.066

χ, type II surrogates 0.068 0.134 0.059 0.087 0.132 0.064

Significant nonlinear coupling

N. of subjects 6 1 6 3 24 16

χ 0.101 0.188 0.099 0.111 0.108 0.089

χ, type II surrogates 0.053 0.078 0.050 0.066 0.043 0.042

χ: global synchronization index. Values of χ are mean over the specified number of subjects.

23

Table 3. Nonlinear causal synchronization between systolic pressure and cardiac cycle length

variability series.

Young Old AMI

Rest

χs/t 0.054 ± 0.028 0.069 ± 0.042 0.089 ± 0.053 ‡

χt/s 0.072 ± 0.037 0.041 ± 0.023 † 0.050 ± 0.030 †

Significance >0.05 0.006 0.00003

Tilt

χs/t 0.108 ± 0.053 0.069 ± 0.044 † 0.060 ± 0.040 ‡

χt/s 0.125 ± 0.071 0.065 ± 0.052 †* 0.040 ± 0.019 ‡

Significance >0.05 >0.05 0.0002

† P<0.05, ‡ P<0.005 vs. Young

* P<0.05 vs. AMI

Values are mean ± SD. χs/t: causal synchronization from tachogram to systogram; χt/s: causal

synchronization from systogram to tachogram.

t (i )

s (i )s (i -1)s (i -2)

132

138

860

940

s 3 (i )

(t (i ),s 3 (i ))ii -1i -2i -3i -4 i +1 i +2

ii -1i -2i -3i -4 i +1 i +2

s [m

mH

g]t

[mse

c]

Figure 1

0 1 2 3 4 5L

1.0

1.1

1.2

1.3

1.4

1.5

Cor

rect

edC

CE

(a)

0 1 2 3 4 5L

0.00

0.02

0.04

0.06

0.08

0.10Sy

nchr

oniz

atio

nfu

nctio

n

0 1 2 3 4 5L

0.00

0.02

0.04

0.06

0.08

0.10Sy

nchr

oniz

atio

nfu

nctio

n

(b)

χt/s

Figure 2

YOUNG

Rest Tilt

*

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Sync

hron

izat

ion

OLD

Rest Tilt0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

AMI

*

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

Figure 3

REST

Young Old AMI

**

0

10

20

30

N.o

fsub

ject

s

0

10

20

30N

.ofs

ubje

cts

TILT

Young Old AMI

**

*

Figure 4

χt\s

χs\tYOUNG

Rest Tilt

**

*

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion χt\s

χs\tOLD

Rest Tilt

#

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

izat

ion

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

zatio

n χt\s

χs\tAMI

Rest Tilt

##

**

*

##

0.00

0.05

0.10

0.15

0.20

0.25

Sync

hron

zatio

n

Figure 5