Main

HR is an easily measured physiologic variable which largely mirrors intrinsic ANS activity, and much of our understanding of ANS functioning during fetal life has been inferred from spectral analysis of HR variability(1–7). The basis for the association between ANS activity, beat-to-beat variability, and spectral power is the assumption that there is a linear relationship between fluctuations in sympathetic-parasympathetic balance and instantaneous changes in HR. However, spectral analysis assesses HR fluctuations averaged over time, and thus provides only an overall measure of HR variability. As a result, although this method can be used to examine cyclic variations in HR, such as respiratory sinus arrhythmia, ANS mechanisms governing beat-to-beat changes may be masked by time averaging. This is important because sinus node depolarization, modulated by autonomic fluctuations, may produce nonlinearities in the temporal patterning of R-R intervals that cannot be detected with conventional autocorrelation and spectral analyses(8–11).

Beat-to-beat changes in HR are easily displayed using the Poincare return map, which is constructed by plotting each interbeat interval against the previous interbeat interval. Analysis of HR dynamics using the Poincare return map is based primarily on quantifying the extent of scatter in sequential R-R intervals at various positions along the line of identity(12). Schechtman et al.(13) calculated the range in the distribution of following interbeat intervals at slow (Ds) and fast (Df) index HRs and found significant differences in cardiac dynamics between normal infants and victims of SIDS. However, the dispersion coefficients, Ds and Df, are average measures of the relationship between two adjacent R-R intervals, which may limit the ability to identify nonlinearities in heart period data using these parameters.

There have been surprisingly few studies examining HR dynamics in human fetuses. Chaffin et al.(14) calculated the correlation dimension for 12 fetuses in labor and found that the HR pattern for 10 (83%) fetuses was suggestive of nonlinear dynamics. Shono et al.(15) and Karin et al.(3) found, in human fetuses, that slow HR fluctuations were inversely proportional to spectral frequency (i.e. a "1/f spectrum"), although this does not always indicate nonlinear HR control(16). In addition, approximate entropy has been used as a regularity measure for fetal HR analysis(17–19); but, as noted by Pincus(20), this parameter cannot distinguish between nonlinear deterministic and linear stochastic processes.

This study was undertaken to determine whether Ds and Df could be used as discriminatory statistics to identify nonlinearity in HR dynamics in human fetuses. This determination was made using the method of surrogate data to test the null hypothesis that fluctuations in heart period can be described by a linear stochastic process. The demonstration, in human fetuses, that Ds and Df for the original time series differ significantly from the linear models would help strengthen the argument that these coefficients can be used to identify nonlinear HR dynamics in subjects with an inherently immature ANS.

METHOD

Subjects. Eight pregnant mothers with no medical or obstetrical complications were recruited from the low risk obstetrics clinics at the University of South Alabama. Each mother was in the Medicaid program, five (62.5%) mothers were white, three (37.5%) mothers were black, and three(37.5%) fetuses were male. Gestational age was estimated based on either a known last menstrual period or a sonogram before 20 wk. This study was approved by the Institutional Review Board, and mothers gave written informed consent before participation.

The average gestational age of the eight fetuses at the time of testing was 38.7 ± 0.5 wk (range 38.0-39.4 wk), and the mean interval between fetal testing and delivery was 12.3 ± 4.8 d (range 2-16 d). Each infant was born between 38 and 42 wk, weighed >2800 g at birth, and had a 5-min Apgar score of ≥8. No infant was growth-restricted according to Alabama birth weight standards(21). Umbilical cord blood gas analyses were not routinely performed on study subjects. Each infant was admitted to the well baby nursery after vaginal delivery.

Instrumentation. The fetal cardiac electrical signal was sampled at a rate of 1024 Hz (per channel) over four channels using standard cardiac electrodes vectored across the mother's abdomen. The data acquisition system consisted of a personal computer (486-33 MHz) with a 16-Mb RAM drive interfaced with an analog-to-digital converter (Metrabyte DAS-20) and connected to four high performance, low noise preamplifiers (Grass P511). A double-queue RAM software routine allowed the data to be sampled continuously with no loss in fetal R wave structure. All data were written to the RAM drive and transferred at the end of each collection period to hard disk. The data were transferred to tape at the end of each study session for permanent storage (Colorado Memory Systems DJ-20).

Procedure. Mothers were instructed to fast after midnight before a scheduled study session and were given a standard meal (280 calories) on arrival at the fetal testing unit. After completing the meal, amniotic fluid volume was measured(22), and fetal HR was monitored for 60 min using a Doppler cardiotocograph (Hewlett-Packard model M1351 A, series 50). The mother was then asked to ambulate and use the restroom as needed. No study was begun after 1200 h.

The mother's abdomen was thoroughly cleansed with ethyl alcohol and a commercially available preparation (Baxter electrode) was applied to the mother's skin. Four sets of Ag-AgCl electrodes were then attached with conducting gel patches across the maternal abdomen as determined by the position of the fetal heart. Final gain and filter settings and electrode placement were determined by optimizing fetal R wave recognition in at least two channels.

All examinations were performed in a quiet room with the mother resting comfortably in a semirecumbent position. To facilitate assignment of behavioral states, fetal HR was monitored continuously using the Doppler cardiotocograph; and fetal eye movements were assessed throughout the collection period by positioning a 5-MHz convex linear-array ultrasound transducer (Aloka 620, Corometrics) to obtain a parasagittal view of the fetal face. For each subject, the cardiac electrical signal was recorded for 15 min during fetal behavioral state 2F, which is analogous to active sleep in the neonate(23). State 2F was defined by the presence of continuous eye movement, a wide HR oscillation bandwidth with frequent accelerations, and frequent gross body movement(24); in cases where the fetal eyes could not be visualized, behavioral state was assigned based on HR pattern and body movement.

Data reduction. The raw signal recorded from the mother's abdomen contained both fetal R waves and the MCC. To remove the maternal signal, each 15-min block was scanned on the computer screen to identify maternal R waves. Each maternal R wave was located visually on the computer screen, and the exact location of the R wave was determined by a digital search routine that converged on either the maximum (upright R wave) or minimum (inverted R wave) electrical amplitude. A 350-ms segment on both sides of each maternal R wave was then used to model the MCC, and a maternal cardiac template was constructed by averaging the index MCC and the four MCCs immediately preceding and after the index MCC. This template was subtracted from the raw signal in a stepwise fashion, leaving a residual signal that contained only fetal R waves. The location of each fetal R wave was determined using the same interactive graphical interface and the same digital search routine.

Each 15-min block was visually screened to identify R-R intervals that were either approximately twice or less than one-half of the preceding R-R interval. Artifacts were replaced in the data stream by either averaging two aberrant R-R intervals, combining two or more small R-R intervals, or halving a single large R-R interval. There was a total of 15 733 R-R intervals (1967± 144 per subject); of these, 224 (1.4%) were identified as artifacts (28 ± 12 per subject), and no fetus had >3% of their total R-R intervals replaced. Because the surrogate data sets were generated by reordering the interbeat intervals in the original time series, editing R wave artifacts in the original time series resulted in identical changes in the surrogate data. All analyses were performed using the edited fetal R wave data.

Data analysis. Cardiac dynamics. In general, the dynamic behavior of a time series consisting of sequential R waves is determined by the relationship between two adjacent R waves, three adjacent R waves, and so on. To examine HR dynamics in simpler terms, pair and triplet correlations were analyzed separately. For two-body correlations,N(r) was defined as the proportion of pairs of adjacent interbeat intervals differing by ≤r ms. As defined, N(r)→ 1 as r → ∞, regardless of the nature of the underlying cardiac dynamics. In contrast, the behavior of N(r) as r → 0 is determined entirely by the relationship between pairs of adjacent interbeat intervals. For example, for a sequence of temporally uncorrelated R waves, N(r) → 0 as r→ 0; otherwise, this limit is >0 but ≤1, with the precise value determined by the relationship between pairs of interbeat intervals. Because R waves were detected with a resolution of ± 1 ms,r = 2 ms is the lowest practical limit for r. Therefore, N(r = 2) was used as a measure of two-body correlations in this study.

As a special case of two-body correlations, the parameters Ds and Df represent the range in scatter in following R-R intervals at long and short index interbeat intervals, respectively(12); or, equivalently, the maximum separation in time between R-R interval pairs at specific index interbeat intervals. To minimize the effect of outliers(12), all (x, y) pairs were sorted according to the length of x to identify the upper and lower 10th percentiles in x. For fast HRs, the upper and lower 10% of y values at upper 10th percentile were determined and Df was calculated by taking the difference between these values. The dispersion coefficient at slow HR was calculated by taking the difference between the upper and lower 10th percentile in y values at the lower 10th percentile.

Although a distribution function can be defined to quantify the relationship between three adjacent interbeat intervals, it is computationally simpler, in this case, to examine the pattern of change across sequential R-R intervals(12). Because N(r = 2) accounts for pairs of adjacent interbeat intervals separated by ≤2 ms, we considered three-body correlations in a more general sense, looking at the following conditions: 1) a decrease in the R-R interval followed by an increase, 2) two consecutive increases in the R-R intervals, 3) two consecutive decreases in the R-R intervals, and 4) an increase in the R-R interval followed by a decrease. The distribution in the number of R-R interval triplets provides a measure of the trend in HR across three consecutive interbeat intervals, independent of the magnitude of the HR changes.

Surrogate data. The null hypothesis, that the time series is the result of a linear stochastic process, was tested by comparing the original time series with linear models for the discriminatory statistics N(r = 2), Ds, Df, and the distribution of R-R interval triplets. Three different models, uniform-randomized, phase-randomized, and Gaussian-scaled, were constructed by generating surrogate data using the original fetal R wave data.

The simplest model, the uniform-randomized surrogate, had the same mean and SD as the original time series but did not preserve either the autocorrelation function or the power spectrum. Here, the surrogate data set was created by ordering the original interbeat intervals according to a uniform random number distribution. In this case the null hypothesis is that the observed time series represents temporally uncorrelated noise.

To construct the phase-randomized surrogate data set, the original time series was transformed by Fourier analysis, and the phases were sorted according to a uniform random number distribution. The surrogate time series was created by performing an inverse Fourier transformation using the original amplitude and the randomized phase values. As a result, the phase-randomized surrogate data set had the same mean, SD, autocorrelation function, and power spectrum as the original data set(25,26). For the phase-randomized model, the null hypothesis is that the time series represents linearly correlated noise and can be described entirely by the Fourier power spectrum(25,26).

To construct the Gaussian-scaled surrogate data set, a Gaussian distribution having the same mean and SD as the original data set was generated and rank-ordered in the same rank order as the original time series. The newly created Gaussian distribution was then phase-randomized as described above. The surrogate time series was constructed by rank-ordering the original time series in the rank order of the phase-randomized Gaussian distribution(27). As with the phase-randomized model, the Gaussian-scaled surrogate had the same mean, SD, autocorrelation function, and power spectrum as the original data set(25,26). Strictly speaking, the Gaussian-scaled time series is nonlinear, but the nonlinearity is not in the dynamics; instead, nonlinearity arises as a result of static nonlinear filtering of linearly correlated noise(26). Here, the null hypothesis is that the observed time series is a nonlinear distortion of a linear stochastic time series(25,26).

Calculations were performed for each fetus separately. First, 25 realizations of each surrogate algorithm were generated; and N(r = 2), Ds,Df, and the distribution of R-R interval triplets were calculated as described above. Then, for each 25-member surrogate ensemble, the mean and SD were calculated for each discriminatory statistic and compared with its value for the original time series. The comparison of the original time series and a surrogate model was facilitated by calculating aσ value for each discriminatory statistic(26); σ is defined as the absolute difference between the mean of the discriminatory statistic for the surrogate data and its value for the original data divided by the SD of the discriminatory statistic for the surrogate data. As defined, σ is a measure of the likelihood that the difference between the discriminatory statistic for the original time series and the mean discriminatory statistic for the model time series is greater than the variability in the discriminatory statistic for the surrogate ensemble.

The analysis was performed in a stepwise fashion. First, we compared the original time series and the uniform-randomized model to establish the presence or absence of temporal correlations in the original time series. Next, we compared the original time series and the phase-randomized model to determine whether temporal correlations could be explained by a linear stochastic process. Finally, we compared the original time series and the Gaussian-scaled model to determine whether the nonlinearity, detected by comparisons with the phase-randomized surrogate, was simply the result of nonlinear filtering of a linear stochastic process. All comparisons were made by calculating σ values. σ is an approximate measure of the difference between the original time series and the surrogate time series, such that the greater σ values, the smaller the p value and the more powerful the discriminatory statistic(26).σ values <2.0 generally indicate that heart period fluctuations in the original time series, as quantified by a particular discriminatory statistic, can be explained by a linear stochastic process(25,26).

RESULTS

The Poincare return maps for the eight fetuses are displayed in Figure 1. As shown, the shape of the plots was very similar across fetuses, and there was a strong tendency for the data to lie symmetrically along the line of identity. The dispersion coefficients for the original time series and the three surrogate data sets are given in Table 1, and the corresponding σ values are given in Table 2. For the original data, there was no consistent trend in the relative magnitudes of Ds and Ds, and the group-average values of Ds and Df were not significantly different (Ds versus Df: 30.6 ± 5.8 ms versus 26.1 ± 5.6 ms, p > 0.05). For each fetus, and for both Ds and Df σ was >4.0 for the uniform-randomized surrogate data (mean slow σ: 6.1± 1.9; mean fast σ 9.1 ± 4.0) and was usually>2.0 for the Gaussian-scaled surrogate (mean slow σ 1.4 ± 1.2; mean fast σ: 3.3 ± 1.9). However, σ was almost always <2.0 for the phase-randomized model (mean slow σ 1.0 ± 1.0; mean fast σ: 1.2 ± 1.0). For each fetus, σ for the ratio Ds/Df was <2.0 for the phase-randomized and Gaussian-scaled models.

Figure 1
figure 1

Poincare return map, constructed by plotting each interbeat interval (R-Rn + 1) against the previous interbeat interval (R-Rn), for eight human fetuses in active sleep between 38 and 40 wk of gestation. Interbeat intervals are given in milliseconds.

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Table 1 Dispersion coefficients for individual fetuses
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Table 2 σ* for Ds and Df
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The normalized distribution function, N(r), is shown in Figure 2 for a representative fetus. To illustrate the typical behavior of N(r), calculations were performed for values of r between 2 and 80 ms. As shown,N(r) = 1.0 by a separation of approximately 25 ms for the original time series and the phase-randomized and Gaussian-scaled surrogates, but this limit was not achieved for the uniform-randomized surrogate until a separation of approximately 80 ms. A graph of σversus r is shown in Figure 3 for the same fetus. Although Figures 2 and 3 provide a more general description of N(r) and σ, respectively, than can be achieved using a single r value, the largest difference between the original and surrogate time series (i.e. the largest value of σ) occurred at r = 2 ms; andσ was <2.0 for the phase-randomized and Gaussian-scaled surrogate ensembles by a separation of approximately 20 ms. Therefore, original versus comparisons for N(r) were performed at the smallest measurable separation (i.e. r = 2 ms) and are given in Table 3 for the original time series and the three surrogate data sets; the corresponding σ values are given in Table 4. For each fetus, and for each surrogate ensemble, σ was >10.0 for the discriminatory statistic N(r = 2).

Figure 2
figure 2

Normalized distribution function for a single fetus, N(r), defined as the number of pairs of adjacent interbeat intervals separated in time by ≤r ms. Notation:◯-----◯, original time series; ·-·, phase-randomized;□-□ Gaussian-scaled; δ-δ uniformed-randomized.

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Figure 3
figure 3

σ as a function of separation r for the fetus shown in Figure 2. Notation: ·, phase-randomized; ▪, Gaussian-scaled;▴, uniformed-randomized.

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Table 3 Normalized distribution at small separation, N(r = 2), for individual fetuses
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Table 4 σ for N(r = 2)
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The pattern of distribution for three sequential interbeat intervals is summarized in Table 5 for the original time series and the three surrogate data sets; in constructing Table 5, triplets showing two consecutive increases were combined with those showing two consecutive decrease (same pattern), and triplets showing an increase followed by a decrease were combined with those showing a decrease followed by an increase (opposite pattern). Opposite patterns were seen in the original time series significantly more often than same patterns (opposite versus same: 0.380 ± 0.042versus 0.187 ± 0.024, t = -9.895, p< 0.001), indicating that HR changes over three consecutive R-R intervals were dominated by high frequency fluctuations. The corresponding σ values are given in Table 6. Except for subject 61-3(σ = 5.7), σ was >8.0 for opposite patterns for each surrogate ensemble; σ was generally smaller (i.e. > 3.0) for same patterns.

Table 5 Distribution of three sequential interbeat intervals according to pattern
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Table 6 σ for three sequential interbeat intervals
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DISCUSSION

The effectiveness of a particular discriminatory statistic, for identifying nonlinear cardiac dynamics, can be determined by comparing the magnitude of the discriminatory statistic for the original time series with the values calculated for dynamic models of the original time series. In this study, three stochastic models were constructed to preserve the major statistical properties of the original time series, including the mean and SD in R-R intervals (uniform-randomized, phase-randomized, Gaussian-scaled) and the autocorrelation function between adjacent R-R intervals (phase-randomized, Gaussian-scaled). In general, many realizations of the original time series would be needed to judge the validity of a particular discriminatory statistic for identifying nonlinearity in the original data set(25,26). However, because these data are usually not available, the original time series was compared with the dynamic models using Theiler's method of calculating σ values(25,26). For all discriminatory statistics, comparisons between the original time series and the uniform-randomized surrogate resulted in the largest σ values, indicating that temporal correlations were an important feature of the original time series. In the case of Ds and Ds σ was <2.0 for comparisons between the original time series and the phase-randomized surrogate; which, at first glance, suggested that the original time series represented linearly correlated noise. However, a different picture emerged when the analysis was performed for other discriminatory statistics;σ was large for N(r = 2) and R-R interval triplets for comparisons with the phase-randomized and Gaussian-scaled surrogates, indicating that interactions between R waves were not fully accounted for by linear correlations. This finding suggests that the fetal HR times series is nonlinear and that the magnitude of N(r = 2) and R-R interval triplets is determined primarily by nonlinear processes.

Although σ was >4.0 for both dispersion coefficients for comparisons with the uniform-randomized model, the demonstration that σ was <2.0 for both Ds and DF for comparisons between the original time series and the phase-randomized surrogate indicated that neither Ds or Df is capable of discriminating between nonlinear and linear cardiac dynamics. However, it could be argued that the reason Ds and Df did not identify nonlinearity in the original HR time series was because either there was an insufficient number of data points or HR dynamics in the term fetus can be described by a linear model. The latter explanation can be excluded based on our analyses for two other discriminatory statistics [i.e. N(r = 2) and triplet correlations]: for each fetus, we found that the temporal patterning of interbeat intervals could not be described by dynamic models which preserved the mean, SD, and autocorrelation function of the original time series. However, it is known that calculations using other discriminatory statistics, e.g. the correlation dimension and the Lyapunov exponent, are especially sensitive to the number of data points(28). Although we cannot absolutely exclude this as a possible explanation for the poor discriminatory capabilities of Ds and DfD, we not that each time series contained >1500 R-R intervals, which is usually sufficient to ensure convergence in calculating the correlation dimension and Lyapunov exponent(29). Excluding the upper and lower 10% of the data points minimized the effect of outliers on the calculation of Ds and Df(12); each surrogate data set, which minimized effects due to number of data points(30); and Ds and Df were calculated the same way for the original time series and the dynamic models.

The normalized distribution function, N(r), describes the distribution of pairs of adjacent interbeat intervals separated in time by ≤r ms and has the property that N(r)→ 1 as r → ∞, regardless of the nature of the underlying cardiac dynamics. As a result, N(r) had poor discriminatory capability (i.e. small σ) at large r; but at small separations, N(r) was particularly sensitive to the relationship between adjacent R-R interval pairs in the original time series, as evidenced by large σ values in comparison with the dynamic models. For each fetus, N(r = 2) for the original time series was always greater than N(r = 2) for each surrogate model, indicating the presence of control processes, which maintained adjacent interbeat intervals closer to one another in the original time series compared with either of the three models. This was confirmed by calculating σ values; for each fetus and for each surrogate ensemble, σ was >10.0 for the discriminatory statistic N(r = 2), indicating the presence of nonlinear dynamics in the original time series. Furthermore, because Ds and Df are related to N(r) at large r (i.e. the maximum separation between adjacent R waves after correcting for outliers), it is no surprise that these parameters were not particularly effective at distinguishing between linear and nonlinear cardiac dynamics.

When we examined the trend in HR across three consecutive interbeat intervals, we found that opposite (high frequency) patterns occurred significantly more often the same (sustained) patterns. These data demonstrate that a change in HR is more likely to be followed by a change in the opposite direction, and hence a return toward baseline HR, than it is to be followed by a further change in HR in the same direction. Schecht et al.(13) found a similar relationship in healthy infants and SIDS victims, suggesting that this aspect of HR control does not change from fetal life to the neonatal period to infancy. As discussed by Schectman et al.(13), the preponderance of high frequency HR changes, indicating a tendency toward tight control of the mean HR, argues against random HR control and in favor of the existence of deterministic control mechanisms. In fact, our analyses indicated that the high frequency component was a stronger discriminatory statistic than sustained HR changes(i.e. σ > 8.0 versus σ > 3.0, respectively). The high frequency variations occur at a rate that is considerably faster than is typical of respiratory sinus arrhythmia(13), and the results of our calculations suggest that these high frequency HR changes may be a major factor contributing to the nonlinearities in cardiac dynamics in human fetuses.

In summary, the dispersion coefficients Ds and Df cannot be used to identify nonlinearity in HR dynamics, at least in this sample of low risk human fetuses. However, this does not mean that Ds and Df cannot be used to examine other aspects of HR control. Furthermore, these parameters may be useful in identifying certain at risk populations; Schechtman et al.(13) found that Ds was significantly smaller in SIDS victims compared with normal infants, suggesting the presence of altered autonomic control of HR in infants who succumb to SIDS. However, the results of our analyses also demonstrated the existence of nonlinear regulatory processes that maintain tight control of the mean HR and that cannot be described by spectral analysis. Therefore, if the difference between normal and abnormal infants is the result of aberrant control of nonlinear processes, then parameters which describe the nonlinearity, e.g. N(r = 2), may be more useful than Ds and Df in assigning a risk status.