INTRODUCTION

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FETAL HEART RATE (HR) variability is an important noninvasive index of cardiovascular function that appears to be regulated largely by the autonomic nervous system (23). In clinical settings, diminished beat-to-beat variability is an ominous sign that may indicate a seriously compromised fetus. Our previous study (16) on the spectral analysis of R-R variability in fetal sheep found that decreased HR variability, especially in the low-frequency (LF) area (0.025-0.15 cycles/beat), was associated with fetal hypoxemia and acidemia. Various modalities, including spectral analysis, have been developed to analyze fetal heartbeat variability and can be classified into three types: 1) time-domain analysis, which applies various methods in quantifying the variance of the biosignal; 2) frequency-domain analysis, which applies spectral analysis to determine the periodic components of the signal; and 3) fractal analysis, which applies the methods of nonlinear dynamics to quantify the structured order in aperiodic signals and thereby attempts to describe its complexity.

Decreased fetal HR variability, such as in short-term variability (STV) as observed by time-domain measures, is often associated with fetal acidemia (8) and is evidence of nutritional deprivation. Beat-to-beat variability is thought to result from a push-pull phenomenon between the sympathetic and parasympathetic nervous systems. Indeed, power spectral densities of R-R intervals, obtained as frequency-domain measures by spectral analytic methods, can be used as an index of autonomic nervous activity. However, these statistical measures provide only limited information on fetal HR behavior, because nonlinear mechanisms can also be involved in HR dynamics. Accumulated evidence in cardiac physiology indicates that the adult living body is controlled by mechanisms that are nonlinear in nature (11). Previous studies have also described the complexity of fetal heartbeat fluctuation with respect to the central nervous system (7), autonomic nervous systems (6), and changes in certain hormones and other maternal influences (18, 26).

We previously reported that the fractal structure imbedded in temporal changes in the LF domain during spectral analysis of fetal heartbeat fluctuation was maintained in fetal hypoxemia but collapsed in fetal acidemia (17). This result suggested that analysis of fractal dimensions (FDs) applied to fetal heartbeat variability could be useful in quantifying the complexity of these time series. Chaffin et al. (5) proposed a nonlinear analysis based on the FD of R-R intervals in utero instead of more conventional stochastic measurements. If such measurements are to become reliable clinical tools in the assessment of fetal health, it is important to define the range of normal variation and to understand the factors that might influence that range.

Conventional STV, long-term variability (LTV), and LF powers in the spectral component of fetal heartbeat intervals have been shown to have 24-h rhythms that correspond to the sleep-wake cycle. Changes in the FDs of HR time series have also been found to have diurnal rhythms in adults (22, 25, 27).

The purposes of this study were 1) to examine changes in fetal cardiac interbeat interval dynamics over 24 h in healthy subjects; and 2) to compare changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling.

	MATERIALS AND METHODS

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Surgical preparation and experimental protocol. This study was approved by the Animal Care Committee of the Tohoku University School of Medicine in accordance with the guidelines on Animal Care. Five mixed-breed pregnant ewes were surgically prepared at 116-125 days gestation (average term = 148 days). Sheep were kept in a room with lighting on at 8 AM and off at 8 PM. Surgery was carried out after the ewes were fasted for 24 h, with general anesthesia induced by inhalation of a mixture of oxygen and nitrogen oxide gasses supplemented with sevoflurane after tracheal intubation. The uterus was then exposed through a midline abdominal incision, and polyvinyl catheters were inserted aseptically into the fetal carotid artery and jugular vein through a small incision over the fetal neck. Tripolar cardioelectrodes were stitched subcutaneously to the chest of the fetus, with one positioned on each side of the heart and the third in the back of the fetus. The catheters and leads were brought out through the flank of the ewe and stored in a small bag sutured to her back. On the day of the operation and each day thereafter, the ewe received 1.5 g flomoxef sodium intramuscularly and another 0.5 g given to the fetus.

HR variability measures. Twenty-four-hour fetal ECG were recorded, and R-R interbeat interval data were downloaded to a computer (NEC PC9801 RA; Tokyo, Japan) for analysis. More than 24 h of ECG data, including >95% normal sinus beats, were recorded for all subjects. ECG data were digitally sampled at 1,000 Hz and transferred to a computer for analysis of HR variability. Premature beats and artifacts were carefully eliminated both automatically and manually. Measures of R-R interval dynamics were calculated from each hour to study possible diurnal differences.

FD analysis. The methodological details for computing FDs have been published elsewhere and will be described briefly (14). First, for a given time series X(m) (m = 1, 2, 3... k), a new time series _m(k) is constructed

where [ ] denotes Gauss' notation, m is the initial time, and k is an interval of the time series. Both k and m are integers. The length of the curve is given by
such that the curve length for the time interval k is the average value over the k set of L_m(k) and is specified by L(k).

Statistical analysis. Results are expressed as means ± SE. Linear regressions were performed on the measures of HR variability, spectral powers, and FD. We used two-tailed tests and a probability level of 0.05 for significance.

	RESULTS

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The mean gestational age at data collection was 121.4 ± 1.69 days (mean ± SE; average term = 148 days). Arterial blood samples were obtained from five pregnancies during the study interval. All fetuses had pH values consistently >7.30 (mean pH 7.325 ± 0.016), PCO₂ <40.0 mmHg (mean PCO₂ 30.5 ± 2.444 mmHg), and PO₂ >20.0 mmHg (mean PO₂ 23.62 ± 0.962 mmHg). These values were within the normal ranges according to established standards for fetal sheep.

Analysis of time series of fetal R-R intervals in an hour showed a fractal structure (r = 0.9989 ± 0.0005, n = 5; Fig. 1). The daily changes in hourly mean values for individual fetuses are depicted in Fig. 2. STV, LTV, and LF and HF values increased during the night (from 8 PM to 8 AM), whereas the FD and LF-to-HF ratio values did not. While the FD values of the five fetuses ranged from 1.6763 to 1.8655, the values were almost constant over 24 h for each fetus. The mean value of FD in the daytime, 1.8033 ± 0.0154, was not significantly different from that at nighttime, 1.7934 ± 0.0147. The characteristics of the circadian periodicity in HR variability parameters for the five fetal sheep are summarized in Table 1. A circadian rhythm was evident for STV, LTV, and LF and HF values but not for FD and LF-to-HF ratio values. Figures 3 and 4 show the correlation between HR parameters. STV, LTV, and LF and HF values were all significantly and positively correlated (P < 0.0001), whereas LF, HF, and LF-to-HF values were significantly and negatively correlated (P < 0.01). In contrast, no significant correlations were found between the LF-to-HF ratio and STV or LTV values and between FD and STV, LTV, and LF or HF values.

View larger version (14K): [in this window] [in a new window]   Fig. 1.   Time series of fetal R-R intervals over 1 h showing a fractal structure. L(k) is the length of the time series, which is coarse grained by measure index k. The logarithm of curve length [log L(k)] for the time series is expressed as a function of log k. The straight line is fitted to points of log k vs. log L(k) by the least-squares method. When the correlation coefficient (R) of log k vs. log L(k) was ~1, we determined that the time series demonstrated fractality. The fractal dimension (FD) is measured as the absolute value of the slope of the line.

View larger version (21K): [in this window] [in a new window]   Fig. 2.   Application of cosinor analysis to mean heart rate parameters from 5 fetuses. The light-dark cycle in the colony is indicated by the bar on the x-axis. STV, short-term variability; LTV, long-term variability; LF, low frequency; HF, high frequency.

View larger version (32K): [in this window] [in a new window]   Fig. 3.   Linear regression between time (LTV and STV) and frequency components (LF and HF).

View larger version (20K): [in this window] [in a new window]   Fig. 4.   Linear regression between the FD and heart rate variability parameters such as STV, LTV, LF, and HF. In all graphs, the abscissa express the values of FD.

	DISCUSSION

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Our study confirmed the diurnal periodicity for STV, LTV, and spectral LF and HF powers, with peak variability at night. We also confirmed that fetal HR dynamics have a fractal-like temporal structure, with self-similar fluctuations over a wide time scale range. While these are similar to previous findings on fetal HR variability, we also found that the spectral LF-to-HF ratio and FD values of fetal R-R intervals were similar between day and night. These results suggested that the circadian rhythms in STV and LTV were mainly contributed to by changes in frequency components rather than by fractal components of fetal HR fluctuation.

Analysis of FDs is one method for studying the nonlinear nature of HR time series. It attempts to examine exactly how the fetal HR is determined under various circumstances, based on the assumption that HR variation is more chaotic than random. The FD reflects the complexity in HR time series and may give useful information on fetal conditions hidden from conventional visual evaluations (5, 9, 13). Chaffin and colleagues (5) demonstrated that fetal HR variability was nonlinear in nature and exhibited chaotic behavior. They analyzed the dimension of chaos using a box counting method in a time series of fetal HR variability consisting of 5,000 R-R intervals (~30 min) from fetal ECGs derived from scalp electrodes attached to 12 human fetuses. However, this box counting method can take a long time to calculate FDs. Although Albert et al. (1) questioned the validity of using established chaos in the analysis of adult HR, Gough (12) justified the application of the fractal measurement technique to fetal HR variability and examined the FD in a time series of 2,500 fetal heartbeats sampled by ultrasound. Analysis was performed according to Mandelbrot's method (19), which allowed the FD to be determined without the assumption of chaos. Higuchi's equation, which we introduced in this study, was used to raise the accuracy and precision of Mandelbrot's technique such that the fetal HR tracing was treated as a one-dimensional Brownian line. Higuchi's method greatly reduced the time required to calculate the exact fractal property of the time series compared with the box counting method.

Most phenomena of nature, including the living body, appear to be nonlinear, which satisfactorily explains the failure of statistical descriptions of the world. Recent work in normal human adult systems suggested that HR control was best described using nonlinear dynamics with temporal fractal or chaotic structures (15, 29). The FD quantifies the irregularity in the time series by measuring randomness, such that a decrease in the FD reflects decreased complexity in the HR-regulating system. Chaos theory suggests that simple systems cannot respond with sufficient flexibility to efficiently cope with various hemodynamic stresses. Indeed, a decreased FD in HR has been noted in aging (21) and cardiac failure (24), and its marked decrease may precede sudden cardiac death (10). On the basis of these reports, it is likely that deterministic chaos or fractal structures underlying functions in the living body play a crucial role in the maintenance of the inherent biosystem in the absence of external perturbation.

There have been several reports concerning the circadian rhythmic fractal scaling of HR variability in adults. Otsuka et al. (22) reported that the normal adult FD had a clear circadian rhythm that peaked at night. Van Leeuwen et al. (27) suggested that the lower daytime FD compared with nighttime was a result of the synchronization of physiological functions of the cardiovascular control system during the day. However, there have been no reports on the circadian rhythms of FD values or comparisons with conventional (time and frequency domain) analyses in the fetus. Thus it remains unclear why the FD in the fetus had no circadian rhythm. Before resolving this issue, there was also the matter as to why STV, LTV, and LF and HF values did exhibit a circadian rhythm, and whether this rhythm was the same rhythm as in adults. In the fetus, both LF and HF properties increased during the night, which is thought to be related to parasympathetic and sympathetic nervous activity. The activity of both nervous systems has been shown to increase in the fetus at night. Indeed, it is well known that general activity, including fetal breathing movement, increases at night, which provides an explanation for the increased nocturnal LF and HF values (26). Nevertheless, questions remain as to why both nervous system activities increased at the same time and why the FD values remained unchanged. Our findings suggested that changes in STV and LTV participated in both the LF and HF components. Because STV, LTV, and LF and HF values were all significantly and positively correlated, all the measures showed significantly similar circadian rhythm. However, the LF-to-HF ratio did not correlate with the other parameters and did not exhibit circadian rhythm. In contrast, adult STV (or HF) increases during the night and LTV (or LF) increases during the day. The LF-to-HF ratio does exhibit a circadian rhythm in adults, with a peak during the day. Also, it is indicated that parasympathetic nervous system activity is mostly influenced by the circadian system, whereas sympathetic nervous system activity is mostly influenced by the sleep system in human adults (4). These findings indicated that the circadian rhythms in adults and fetuses were due to different mechanisms. It appears that fetal circadian rhythms do not result from internal fetal cardiac dynamics but from external influences, such as maternal hormone levels or uterine contractions.

Fetal cardiac internal dynamics were thought not to show a circadian rhythm, whereas FDs were an index of the state of the internal dynamics. Following the finding that the FD of the fetus did not show a circadian rhythm, it was then thought to result from the internal dynamics of the fetus, such as a lack of synchronization between physiological functions, or the lack of flexibility of the cardiovascular control system due to its immaturity. However, there have been no reports on circadian rhythms of FDs or comparisons with conventional (time and frequency domain) analyses in the fetus. Our results showed that despite the relationship between STV, LTV, and LF and HF values, LF-to-HF ratios showed no correlation with the other parameters, nor conformed to a circadian rhythm. This suggested that the balance between sympathetic and parasympathetic nervous activities in the fetal cardiac interbeat is dynamically fixed. This is supported by our previous work (16) in fetal sheep, and the finding that fetal cardiac internal dynamics showed no circadian rhythm with respect to the fractal component of HR variability, which remained stable throughout the daytime and nighttime.

Fetal HR monitoring allows for noninvasive measurements by taking advantage of the fact that beat-to-beat intervals can be recorded continuously with no restraint for many hours (23). It is usually carried out for clinical use for the evaluation of fetal HR variability. Our study showed that there was periodical similarity between STV, LTV, and the frequency components in fetal beat-to-beat fluctuation. Frequency analysis, useful in the fetal autonomic nervous system, is underdeveloped for midterm, when it is not in a normal state, and for fields of fixed quantity (20). Also, fractal analysis of R-R interval time series in the fetus, taking into account influences from the mother, should be useful in fetal diagnosis and therapy.

In conclusion, our study suggested that STV, LTV, and LF and HF values were controlled by the same regulating system and could be expressed as a rhythm of the HR, which appears to be maternally influenced. However, the FD showed intrinsic cardiac dynamics and was consistent, without a 24-h rhythm. The dynamic measures of R-R interval variability provided complementary information about HR behavior when used in concert with traditional measures of time- and frequency-domain HR variability.