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Multi-scale heart rate dynamics detected by phase-rectified signal averaging predicts mortality after acute myocardial infarction

Masaya Kisohara, Phyllis K. Stein, Yutaka Yoshida, Mari Suzuki, Narushi Iizuka, Robert M. Carney, Lana L. Watkins, Kenneth E. Freedland, James A. Blumenthal, Junichiro Hayano
DOI: http://dx.doi.org/10.1093/europace/eus409 437-443 First published online: 17 December 2012


Aims Acceleration and deceleration capacity (AC and DC) for beat-to-beat short-term heart rate dynamics are powerful predictors of mortality after acute myocardial infarction (AMI). We examined if AC and DC for minute-order long-term heart rate dynamics also have independent predictive value.

Methods and results We studied 24-hr Holter electrcardiograms in 708 post-AMI patients who were followed up for up to 30 months thereafter. Acceleration capacity and DC was calculated with the time scales of T (window size defining heart rate) and s (wavelet scale) from 1 to 500 s and compared their prognostic values with conventional measures (ACconv and DCconv) that were calculated with (T,s) = [1,2 (beat)]. During the follow-up, 47 patients died. Both increased ACconv and decreased DCconv predicted mortality (C statistic, 0.792 and 0.797). Concordantly, sharp peaks of C statistics were observed at (T,s) = [2,7 (sec)] for both increased AC and decreased DC (0.762 and 0.768), but there were larger peaks of C statistics at around [30,60 (sec)] for both (0.783 and 0.796). The C statistic was greater for DC than AC at (30,60) (P = 0.0012). Deceleration capacity at (30,60) was a significant predictor even after adjusted for ACconv (P = 0.020) and DCconv (P = 0.028), but the predictive power of AC at (30,60) was no longer significant.

Conclusion A decrease in DC for minute-order long-term heart rate dynamics is a strong predictor for post-AMI mortality and the predictive power is independent of ACconv and DCconv for beat-to-beat short-term heart rate dynamics.

  • Heart rate variability
  • Non-linear dynamics
  • Deceleration capacity
  • Phase-rectified signal averaging
  • Myocardial infarction
  • Mortality

What's new?

• While acceleration and deceleration capacity (AC and DC) for beat-to-beat short-term heart rate dynamics have been reported as powerful predictors of mortality after acute myocardial infarction (AMI), this study demonstrates that DC for minute-order long-term heart rate dynamics also have strong predictive power for post-AMI mortality.

• For minute-order heart rate dynamics, DC has greater predictive power than AC, indicating asymmetric predictive value between the different directions of heart rate regulation.

• DC but not AC for minute-order heart rate dynamics predicts post-AMI mortality independent of conventional beat-to-beat AC and DC.


Phase-rectified signal averaging (PRSA) is a novel method for the analysis of heart rate variability. This method estimates individual capacity for increasing and decreasing heart rate from spontaneous heart rate fluctuations as acceleration and deceleration capacity (AC and DC).1,2 Phase-rectified signal averaging is gaining increasing attention since reduction in DC is a powerful predictor for adverse outcomes in various clinical settings, particularly in patients after acute myocardial infarction (AMI).35

In PRSA, increase and decrease in heart rate are detected over a given set of time scales; time scale T for determining the window size for comparing heart rates and scale s for wavelet scale. Phase-rectified signal averaging provides the averaged waveform of R-R intervals surrounding the anchor points from which heart rate accelerates or decelerates in a given time scale defined as T.2 Phase-rectified signal averaging waveform shows quasi-periodicity, decaying to both sides on the time axis. The waveforms are analysed with wavelet transforms and the magnitudes at the centre portion determined by wavelet scale s are measured as AC and DC (see Appendix and Figure 1).

Figure 1

Phase-rectified signal averaging waveforms for heart rate acceleration (A) and deceleration (B) with time scale T = 130 s in a patient. Acceleration and deceleration excursions (AE and DE) are measured as the excursion ranges of the waveform. Acceleration capacity (AC[T,s]) and deceleration capacity (DC[T,s)]) are calculated by Haar wavelet transformation with wavelet scale s from 1 to 500 s (C and D). L represents relative temporal position from anchor point (L = 0) of PRSA. 

Although earlier clinical studies3,4 have reported that decreased DC obtained with T = 1 beat and s = 2 beats is a powerful predictor for post-AMI mortality, Kantelhardt et al.2 have shown that AC and DC for T from 1 to 45 s and s from 1 to 12 s are also relevant to post-AMI mortality risk. These suggest that the predictive power of PRSA may not localize to beat-to-beat short-term heart rate dynamics but may instead distribute over minute-order long-term heart rate dynamics. Indeed, the predictive power of post-AMI mortality has been reported for impaired heart rate regulations that appear at longer-time scales, such as chronotropic incompetence,6,7 delayed heart rate recovery in the first minute after exercise,8,9 and altered power law behaviour at very low frequency (VLF; 0.0033–0.04 Hz) or lower.10,11 However, predictive values of PRSA for a wide range of time scales have not been investigated systematically.

In the present study, we performed PRSA of 24-hr heart rate in post-AMI patients with known clinical outcomes. We computed PRSA waveforms for T from 1 to 500 s and analysed AC and DC for s from 1 to 500 s. The hypotheses we tested were (i) PRSA for minute-order long-term heart rate dynamics has prognostic value for post-AMI mortality independently of that for beat-to-beat short-term heart rate dynamics, (ii) the predictive value of PRSA for long-term dynamics, if any, is asymmetric between AC and DC, depending on the direction of heart rate regulations.



We used an archival database of the Enhancing Recovery in Coronary Heart Disease (ENRICHD) clinical trial.1214 The database consisted of 24-hr Holter electrcardiograms (ECG) and clinical data at baseline and follow-up outcomes in 716 post-AMI patients. The details of this database have been reported elsewhere.13,14 Briefly, out of 716 patients, 333 were depressed and 383 were non-depressed at baseline. The depressed patients participated in the ENRICHD clinical trial and were randomly allocated to receive usual care or usual care plus cognitive behaviour therapy. However, there was no significant difference in event-free or overall survival curves between the groups.12 The non-depressed patients were otherwise eligible for ENRICHD study but had no prior episodes of major depression or current depression symptoms (Beck Depression Inventory score ≥10).

The Holter ECG was recorded within 28 days after an index AMI. The data were excluded if patients: (i) had other life-threatening illnesses; (ii) had analysable Holter ECG data <22 h or sinus rhythm <80% of total recorded beats; (iii) had atrial fibrillation, atrial flutter, or an implanted pacemaker or defibrillator; or (iv) declined to provide informed written consent. The patients were subsequently followed up for up to 30 months (median, 25 months) with the composite endpoint of all-cause mortality or recurrent non-fatal AMI, although only the mortality endpoint was used in the present study. The use of the archival dataset of the ENRICHD clinical trial in the present study was approved by the Institutional Review Board of the Washington University School of Medicine (number, 96-0849).

Data analysis

Holter recordings were scanned at the Heart Rate Variability Core laboratory at Washington University School of Medicine on a Marquette SXP Laser scanner with software version 5.8 (Marquette Electronics) using standard procedures. QRS complexes were considered as sinus rhythm only when (i) they had a narrow morphology, (ii) R-R intervals were between 300 and 2000 ms and differed ≤20% from the average of 5 preceding sinus rhythm R-R intervals, and (iii) differences in consecutive R-R intervals were ≤20% and also ≤200 m. Holter analyses were reviewed and any errors in R-wave detection and in QRS labelling were edited manually. The labelled beat file was exported to a personal computer for PRSA and other heart rate variability analysis.

Multi-scale phase-rectified signal averaging

Phase-rectified signal averaging was performed according to a previously published method.2 The details of the analysis are reported in the Appendix. Briefly, R-R interval time series were interpolated using only normal-to-normal (NN) intervals and resampled at 2 Hz. We computed acceleration and deceleration PRSA waveforms for T = 1–500 s. Wavelet transform was performed for s = 1–500 s to calculate AC(T,s) and DC(T,s) using Haar wavelet. In addition to AC and DC measures, we also measured the range of excursion of PRSA waveforms for each T value as acceleration and deceleration excursions [AE(T) and DE(T)] (Figures 1A and 1B).

For comparison with earlier observations,3,4 we also calculated AC and DC using the conventional method;2 i.e. (i) NN intervals that differed >5% of the previous NN interval were excluded from the anchors, (ii) T = 1 beat and s = 2 beats were used as time scales, and (iii) AC and DC were quantified by Haar wavelet as Embedded Image, where Embedded Image is the average of R-R intervals at anchors and Embedded Image is the average of R-R intervals i beats from the anchors. The AC[1,2 beat)] and DC[1,2 (beat)] thus obtained are represented here as ACconv and DCconv.

Statistical analyses

The endpoint of this study was all-cause death. Differences between survivors and non-survivors were evaluated by the Student's t-test for quantitative data and by the χ2 test for categorical data. Differences in PRSA measures at different T values were evaluated by repeated measures analysis of variance and, when significant interaction with T was detected, the range of T values causing a significant difference were detected by generating single-degree-of-freedom contrasts with Helmert transformation. Predictive power of PRSA and other indices for all-cause mortality was evaluated by logistic regression analysis with C statistic. The difference in C statistic was evaluated by the method of DeLong et al.15 We evaluated the independence of new predictors by logistic regression models adjusted for ACconv or DCconv. Receiver-operating characteristic curve analysis was used for determining cut-off values for PRSA measures, which were used for calculating sensitivities and specificities to predict mortality. We defined a P value <0.05 as statistically significant. We used SAS version 9.3 (SAS Institute) for statistical analyses.


Among 716 patients with ECG data, 8 were excluded due to <22 h of analysable ECG or <80% of sinus rhythm. Thus, the analysis was performed on ECG data in 708 patients. As reported previously,13,14 47 deaths occurred during a median follow-up period of 25 months; all of these patients had provided analysable data. Table 1 shows the characteristics of 661 survivors and 47 non-survivors.

View this table:
Table 1

Patients' characteristics

CharacteristicsSurvivor (n = 661)Non-survivor (n = 47)P
Age (years)58.9 ± 11.564.9 ± 10.70.0006
Women262 (40%)20 (43%)0.69
Non-white157 (24%)14 (30%)0.35
Body mass index (kg/m2)29.00 ± 5.9529.82 ± 6.360.39
Systolic blood pressure (mmHg)122.4 ± 18.6128.8 ± 25.00.11
Hypertension126 (19%)12 (26%)0.28
Diabetes mellitus162 (25%)33 (70%)<0.0001
Current smoker221 (33%)7 (15%)0.008
Depression296 (45%)33 (70%)0.0007
LVEF (%)47.2 ± 12.031.2 ± 13.5<0.0001
Killip class III–IV26 (3.9%)8 (17%)<0.0001
Anterior wall AMI201 (30%)14 (30%)0.95
Creatinine (mg/dL)1.08 ± 0.671.80 ± 1.510.002
Prior AMI127 (19%)17 (36%)0.005
Prior coronary bypass58 (8.8%)14 (30%)<0.0001
β-Blocker522 (84%)38 (81%)0.96
ACE inhibitor305 (46%)28 (60%)0.074
Coronary angioplasty <24 h420 (64%)15 (32%)<0.0001
  • ACE, angiotensin-converting enzyme; LVEF, left ventricular ejection fraction.

The predictive power of AC(T,s) and DC(T,s), expressed as the C statistic, is presented in Figure 2. A sharp peak was observed in short-time scale (second-order) AC and DC at (T,s) = (2,7) s (C statistic, 0.762 and 0.768). This was concordant with the strong predictive power that was observed for ACconv and DCconv calculated with (T,s) = (1,2) beat (C statistic, 0.792 and 0.797). As shown in Figure 2, a larger peak was also observed in long-time scale (minute-order) AC and DC at (T,s) = (30,60) s (C statistic, 0.784 and 0.797). Although ACconv, AC(2,7), and AC(30,60) were greater and DCconv, DC(2,7), and DC(30,60) were smaller in non-survivors than in survivors (Table 2), DC(30,60) showed a greater C statistic than AC(30,60) (P = 0.0012), indicating asymmetric predictive value between these PRSA measures for minute-order long-term heart rate dynamics. No significant difference in C statistic was observed between AC(2,7) and DC(2,7) (P = 0.072) or between ACconv and DCconv (P = 0.34).

View this table:
Table 2

Phase-rectified signal averaging measures in survivors and non-survivors

CharacteristicsSurvivor (n = 661)Non-survivor (n = 47)P
ACconv (ms)−5.7 ± 2.4−3.4 ± 1.6<0.0001
AC(2,7) (ms)−29 ± 13−18 ± 12<0.0001
AC(30,60) (ms)−37 ± 16−23 ± 11<0.0001
DCconv (ms)5.4 ± 2.13.3 ± 1.6<0.0001
DC(2,7) (ms)31 ± 1418 ± 12<0.0001
DC(30,60) (ms)37 ± 1622 ± 11<0.0001
  • AC, acceleration capacity; conv, conventional; DC, deceleration capacity.

Figure 2

Three-dimentional plots of mortality predictive power of AC(T,s) (A) and DC(T,s) (B) on Ts matrix plains. Colour scales from violet (lower) to red (higher) correspond to the levels of C statistic.

As shown in Figure 3, AE and DE were smaller in non-survivors than in survivors (P < 0.0001) and there was no significant interaction by T value. For both AE and DE, the C statistic showed a small peak at T = 6 s and a large peak at T = 50 s (Figure 4). While the C statistic did not differ between DE(6) and AE(6) (0.757 vs. 0.750), it was greater in DE(50) than in AE(50) (0.794 vs. 0.773) (P = 0.0001), also indicating asymmetric predictive value.

Figure 3

Acceleration excursion (A) and DE (B) in survivors (closed circles) and non-survivors (open circles) for T values from 1 to 500 s. Data are presented for every 10th of T for T > 10 s.

Figure 4

Mortality predictive powers of AE and DE at T values from 1 to 500 s. C statistics had the maximum value at 50 s for both AE and DE (vertical line) and the C statistics at this point are significantly different between AE and DE (P = 0.0001).

Table 3 shows the independence of new PRSA measures from ACconv or DCconv in predicting post-AMI mortality. As expected, AC(2,7) and DC(2,7) had no significant independent predictive power after being adjusted for ACconv or DCconv. After the adjustment, AC(30,60) and AE(50) also has no significant predictive power. In contrast, the predictive power of DC(30,60) and DE(50) remained significant even after being adjusted for ACconv and DCconv.

View this table:
Table 3

Unadjusted and adjusted odds ratios estimated by logistic regression analysis for new phase-rectified signal averaging measures

 UnadjustedAdjusted for ACconvAdjusted for DCconv
OR (95% Cl)POR (95% Cl)POR (95% Cl)P
AC(2,7)3.00 (2.02–4.48)<0.00011.13 (0.58–2.21)0.7171.12 (0.60–2.10)0.729
AC(30,60)3.76 (2.42–5.84)<0.00011.88 (0.96–3.67)0.0651.78 (0.94–3.36)0.076
AE(50)3.42 (2.23–5.22)<0.00011.52 (0.79–2.91)0.2101.47 (0.80–2.70)0.221
DC(2,7)3.14 (2.09–4.72)<0.00011.23 (0.61–2.46)0.5661.21 (0.63–2.31)0.563
DC(30,60)4.10 (2.61–6.45)<0.00012.29 (1.14–4.61)0.0202.13 (1.09–4.16)0.028
DE(50)3.97 (2.54–6.22)<0.00012.13 (1.05–4.31)0.0361.98 (1.01–3.88)0.047
  • AC, acceleration capacity; AE, acceleration excursion; DC, deceleration capacity; DE, deceleration excursion; OR, odds ratio; CI, confidence interval.

Table 4 shows the cut-off values determined by ROC curve analysis for PRSA measures and their sensitivity and specificity to predict post-AMI mortality. The classification performance of decreased PRSA measures for minute-order long-term heart rate dynamics was comparable to that of decreased ACconv and DCconv for beat-to-beat short-term heart rate dynamics.

View this table:
Table 4

Sensitivity and specificity of phase-rectified signal averaging measures to predict mortality

Cut-off (ms)aSensitivity (95% Cl)Specificity (95% Cl)
ACconv>−4.387 (74–95)68 (65–72)
AC(2,7)>−2281 (67–91)73 (70–77)
AC(30,60)>−3285 (72–94)63 (59–67)
AE(50)<2581 (67–91)67 (63–71)
DCconv<4.489 (77–97)63 (59–67)
DC(2,7)<2281 (67–91)74 (71–78)
DC(30,60)<2883 (69–92)70 (66–74)
DE(50)<2385 (72–94)70 (66–73)
  • AC, acceleration capacity; AE, acceleration excursion; DC, deceleration capacity; DE, deceleration excursion; OR, odds ratio; CI, confidence interval.

  • aCut-off values determined by receiver-operating characteristic curve analysis as that maximized Youden index.16


This is the first study to report the prognostic value of PRSA of heart rate dynamics for a wide range of time scales from 1 to 500 s. In a cohort of 708 post-AMI patients, we found that PRSA not only of beat-to-beat short-term but also of minute-order long-term heart rate dynamics has strong predictive power. We also found that the predictive powers of long-term PRSA measures are independent of that of short-term measures. In addition, for long-term heart rate dynamics, decrease in DC has greater predictive power than increase in AC, indicating asymmetric predictive value with the directions of heart rate regulation.

In an earlier study of post-AMI patients, Kantelhardt et al.2 have reported the prognostic relevance of AC and DC calculated over T from 1 to 45 s and s from 1 to 12 s. We also observed significant predictive power for AC and DC in these ranges of T and s (Figure 2). In the present study, however, we found the presence of two distinct peaks of C statistics, a sharp peak at (T,s) = (2,7) and a large broad peak around (T,s) = (30,60); the latter exists in the area of longer time scales beyond the region evaluated by Kantelhardt et al. To confirm this finding, we introduced new measures (AE and DE) that simply reflect the excursion range of the PRSA waveform defined by a single time scale of T. Acceleration excursion and DE also showed two peaks in the C statistic at T = 6 and 50 s (Figure 4). These suggest the presence of two distinct temporal regions, short-term (several seconds) and long-term (around 1 min), of heart rate regulations that are associated with post-AMI mortality.

Although the exact mechanisms for the presence of two distinct peaks are not clear, the time scale of measures seems an important clue. The studies of transfer function analysis of the autonomic neural regulations have indicated that beat-to-beat rapid heart rate fluctuation >0.15 Hz (9 cpm) is not mediated by the sympathetic nerves and is mediated solely by the vagus.17,18 Thus, the sharp peak in the area of second-order short time scales may reflect mortality risk associated with cardiac vagal dysfunction. Whereas, for the large broad peak in minute-order long time scales, we need to consider numerous mechanisms, which include both neural and humoral heart rate regulations. A study in conscious unanaesthetized dogs, Akselrod et al.19 demonstrated that angiotensin-converting enzyme inhibitor causes 2- to 4.5-fold increase in the power of heart rate variability at around 0.04 Hz (corresponding period of 25 s), suggesting that the activated renin–angiotensin system may be a possible cause of decreased long-term heart rate fluctuation and the mediator of its adverse outcome. Because the present data were obtained by ambulatory ECG recordings, heart rate response characteristics to daily activities may be reflected in long-term PRSA measures. Delayed heart rate recovery in the first minute after exercise has been known to predict mortality in cardiac patients8,9 including those after AMI20 independently of myocardial ischaemia or exercise capacity.6,7 Decrease in long-term DC and DE may be another representation of this phenomenon. Finally, altered power-law behaviour (increased spectral exponent β) of heart rate fluctuation at VLF or lower frequencies has been known as increased risk for post-AMI mortality.10,11 Although the long-term PRSA measures showed only modest correlations with β (data not shown), they may provide a useful probe into the pathophysiological meanings of heart rate variability at VLF or lower frequencies.

The ability to analyse the capacities separately for accelerating and decelerating heart rate is a unique feature of PRSA. In the present study, we found asymmetric predictive value between deceleration and acceleration measures for long-time scales with greater value for deceleration. No such difference was found for short time scale measures, including ACconv or DCconv. Earlier studies have reported that the heart rate recovery is mediated by parasympathetic reactivation during post-exercise period21 and that its predictive power is independent of an inability to increase heart rate during exercise (chronotropic incompetence).7 Decreased acceleration and deceleration measures for long time scales may also reflect deleterious heart rate regulation with different mechanisms.

In the clinical point of view, the most important finding of the present study is that long-term PRSA measures have predictive power not only comparable with but also independent of the predictive power of conventional short-term PRSA measures. We observed that the sensitivity and specificity of long-term PRSA measures to predict mortality were comparable to those of ACconv and DCconv and that their predictive power was significant even after being adjusted for ACconv and DCconv. These indicate that combined use of short-term and long-term PRSA measures may improve risk stratification for post-AMI mortality.


This study has several limitations. First, in the ENRICHD archival database, 329 (46.5%) out of 709 patients were at least mildly depressed and about half (n = 146) of the depressed patients had cognitive behavioural therapy in addition to usual AMI care. However, the frequency of patients with depression is comparable to the reported prevalence of depression in general post-AMI populations (45–47%).22,23 Moreover, we observed that DC(30, 60) and DE(50) were independent predictors of mortality even when analyzed after excluding depressed patients (data not shown). Also, because the cognitive behavioral therapy had no significant effect on mortality in the ENRICHD clinical trial,12 we did not include the effect of treatment in the present study. Second, the data of ENRICHD database were collected between October 1997 and January 2000.12 The frequency of primary percutaneous coronary intervention has been increasing. Consequently, the frequency of post-AMI patients with preserved LVEF has increased and most of post-AMI deaths arise in those patients recently.24 Thus, the present observations may not be applicable directly to the current post-AMI populations. Third, we did not consider sudden cardiac death as a separate endpoint, because the causes of cardiac death were not identified in the ENRICHD study database. Furthermore, the number of deaths, particularly of non-cardiac deaths, was small (n = 13), so we could not detect a possible association between PRSA measures and causes of death.


We conclude that decreases in DC and DE for minute-order long-term heart rate dynamics are strong predictors for post-AMI mortality and the predictive power is independent of AC and DC for beat-to-beat short-term heart rate dynamics.


This work was supported by the grant of the Knowledge Hub of Aichi, Japan [the Priority Research Project, P3-G1-S1-2b (J. H.)]; the Japan Society for the Promotion of Science, Japan [Grant-in-Aid for Scientific Research (C) 20590832, 23591055 (J.H.)]; the Ministry of Health, Labor and Welfare, Japan [Research Grant for Nervous and Mental Disorders 20B-7, 23-2 (J.H.)]; and the National Heart, Lung, and Blood Institute, National Institutes of Health [Grant no. 2 RO1 HL058946].

Conflict of interest: none declared.


Multi-scale phase-rectified signal averaging

The analysis was performed in 24 h R-R interval time series after labelling all QRS complexes for normal (sinus rhythm), ectopic beat, and noise/artefact. To obtain functions of true time, we used sec for the unit of time scales. R-R interval time series were interpolated using only normal-to-normal (NN) intervals with a step function and resampled at 2 Hz.

The anchors for computing acceleration capacity (AC) at time scale of T were defined as all Embedded Image satisfyingEmbedded Image

where Embedded Image is the interpolated R-R interval at time t. Similarly, the anchors for decelerating capacity (DC) were defined as all Embedded Image satisfying:Embedded Image

Then, segments of interpolated NN intervals from L s before to L− 1 s after the all anchor points were extracted with allowing overlapping between segments. Anchor points close to the beginning or end of the time series, where no full surrounding of length 2L were available, were excluded from the analysis. All segments thus obtained were aligned at the anchors and averaged over them to obtain the PRSA waveform asEmbedded Image

where M is the number of obtained segments, km is the position of anchor point in the mth segment (m = 1, … , M), and L is the half length of segment (in this study L = 512 s). The wavelet transform of Embedded Image isEmbedded Image

where s is the wavelet scale, p is time position in PRSA waveform, and w(t) is the mother wavelet. According to the earlier study by Kantelhardt et al.2 we employed Haar wavelet:Embedded Image

as w(t), and AC(T,s) and DC(T,s) were calculated as Embedded Image that reflects the wave magnitude of Embedded Image at the centre portion (l = –s, … , 0, … , s).

We performed these phase-rectified signal averaging analyses on a Microsoft Windows-based personal computer (Intel Core™ i7 870 processor, 2.93 GHz) with a FORTRAN program developed for this purpose. The computation took 0.78 s per one time scale T per one 24 h electrocardiogram recording.


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