## Abstract

The physiological significance of spectral and fractal components of spontaneous heart rate (HR) variability in the fetus remains unclear. To examine the relationship between circadian rhythms in different measures of HR variability, R-R interval time series obtained by fetal ECGs were recorded continuously over 24 h in five pregnant sheep at 116–125 days gestation. Conventional measures of short-term (STV) and long-term variability (LTV), low-frequency (LF; 0.025–0.15 cycles/beat) and high-frequency (HF; 0.2–0.5 cycles/beat) spectral powers, the LF-to-HF ratio, and fractal dimension values were calculated from 24-h ECG recordings and quantified every 60 min. STV, LTV, and LF and HF spectral powers were minimal during the day but increased significantly to their highest values at night. We found a significant positive correlation between these measures, whereas the cosinor method showed significant similarity between their circadian rhythm patterns. Fetal R-R intervals also exhibited fractal structures. Fetal HR variability had a fractal structure, which was similar between day and night. These results suggested that the circadian rhythms exhibited by STV and LTV during the day were mainly due to changes in frequency components rather than to fractal components of fetal HR fluctuation.

- circadian rhythm
- fetal heart rate variability

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

#### 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.

Experiments took place after a minimum recovery period of 48–72 h. The fetal HR was monitored with a cardiotocogram (model 116, Corometrics) triggered by the cardioelectric signal. Fetal ECGs were recorded continuously (24–48 h) starting from 8 AM in the morning on a digital audio tape recorder (RD-130TE, TEAC; Osaka, Japan). Fetal arterial blood samples were taken before the start of the recording and every 12 h thereafter for blood gas analysis, which was performed on a Corning 178 system with a temperature correction of 39.0°C.

#### 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.

For time-domain analysis, we used a similar method to that used by Dawes et al. (28). Briefly, STV was obtained by averaging fetal R-R intervals over periods of 1/16 min (3.75 s). LTV was calculated as the maximum − minimum of fetal R-R intervals over periods of 1/16 min (3.75 s) during 1 min. Hourly mean values of STV and LTV were calculated for each time series over 24 h. An autoregressive model was used to estimate power spectral densities of HR variability for frequency-domain analysis. Spectral estimates were made using an assumption of maximum entropy. This estimates the spectrum of a maximally random series with the constraint that the spectrum must be consistent with the recorded data. We used the model of Brown et al. (2) to estimate the power spectral densities for R-R interval variability. In preparatory calculations, the nonstationary structure of fetal beat-to-beat fluctuations showed only 24-cycle stationary. Autoregressive coefficients, necessary to estimate power spectral densities, were calculated using Burg's algorithm based on 24-cycle stationary (3). Power spectra were quantified by measuring the area in two frequency bands: 0.025–0.15 cycles/beat (LF) and 0.20–0.50 cycles/beat [high frequency (HF)]. The ratio of these frequency components was also calculated.

#### 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*X̃*
_{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*)〉.

The logarithm of the curve length [log*L*(*k*)] calculated by the least-square method provides the FD that is the absolute value of the slope of the line. FD values were measured every 60 min, and the time series was measured during 24 h. A straight line was fitted to the points of log*k* vs. log *L*(*k*). When the correlation coefficient (*r*) of log *k* vs. log*L*(*k*) was ∼1 (*r* = 0.999), the time series was considered to have a fractal structure.

#### 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.

An off-line computer was used to calculate the three parameters from the 24-h mean values for each subject. Daily periodicities were evaluated by cosinor analysis. The three parameters were calculated from the least-square fit of the data set to a cosinor function during a period of 24 h and was evaluated with the following model equation
where *Y _{i}
* is the

*i*th (hourly) value of the parameter of interest, M is the mesor or mean of a rhythm-determined average around circadian oscillation, A is the amplitude of the cosine from mesor to peak value,

*T*is the

_{i}*i*th hour, and φ is the acrophase of the cosine function (in radians). The results of the application of the model to the data are summarized as the mean (±95% confidence interval). Correlations between actual time series data and estimates derived from the best-fit cosine model were computed to test the significance of the fit of the data to the model, with the zero-amplitude hypothesis used to test for the significance of the measurement's rhythm.

## RESULTS

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), Pco
_{2} <40.0 mmHg (mean Pco
_{2} 30.5 ± 2.444 mmHg), and Po
_{2} >20.0 mmHg (mean Po
_{2} 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 4show 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.

## DISCUSSION

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.

## Footnotes

Address for reprint requests and other correspondence: K. Okamura, Dept. of Obstetrics and Gynecology, Tohoku Univ. Graduate School of Medicine, 1-1 Seiryomachi, Aoba-ku, Sendai 980-8574, Japan (E-mail: okamura{at}mail.cc.tohoku.ac.jp).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “

*advertisement*” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.First published January 9, 2003;10.1152/ajpheart.00268.2002

- Copyright © 2003 the American Physiological Society