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Chaotic and periodic heart rate dynamics in uncomplicated intrauterine growth restricted fetuses
Early Human Development 53 (1998) 121–128
Chaotic and periodic heart rate dynamics in uncomplicated intrauterine growth restricted fetuses Jong-Min Lee a , Kwang-Suk Park a , Jung-Hae Hwang b , Mun-Il Park b , c, Myung-Kul Yum * a
Dept. of Biomedical Engineering, Seoul National University School of Medicine, 28 Yongon-Dong, Chongno-Gu, Seoul 110 -799, Korea b Dept. of Obstetrics and Gynecology, Hanyang University School of Medicine, 17 Haengdang-dong, Sungdong-ku, Seoul 133 -792, Korea c Dept. of Pediatric Cardiology, Hanyang University School of Medicine, 17 Haengdang-dong, Sungdong-ku, Seoul 133 -792, Korea Received 10 December 1997; received in revised form 2 March 1998; accepted 15 May 1998
Abstract We studied how chaotic and periodic heart rate dynamics differ between normal fetuses (n 5 192) and uncomplicated intrauterine growth restricted fetuses (n 5 86), aged 31–42 weeks of gestation. We analyzed each fetal heart rate time series for 25 min. We quantified the chaotic dynamics of each fetal heart rate time series by correlation dimension. The periodic dynamics were analyzed by power spectral analysis. The correlation dimension and, therefore, the complexity, of the heart rate dynamics of the uncomplicated intrauterine growth restricted fetuses was significantly lower than that of the normal fetuses, which was marked at 38–42 weeks of gestation. The low-frequency (0.04–0.15 Hz) component and, therefore, the periodicity of the low-frequency range was significantly higher than that of the normal fetuses during all the gestational weeks. These results mean that, although the intrauterine growth restricted fetuses are not severely compromised, the overall integrity of their cardiovascular control is impaired, especially at term; and sympathetic modulation is increased, both of which may contribute to increased perinatal mortality. 1998 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Chaos; Power spectrum; Uncomplicated intrauterine growth restricted fetus *Corresponding author. Address for correspondence: Hanyang University Kuri Hospital, Department of Pediatric Cardiology, 249-1 Kyomundong, Kuri-shi, Kyunggi-do, 471-701, Korea. Tel.: 182-346-60-2252; Fax: 182-2-442-1331; E-mail: [email protected] 0378-3782 / 98 / $ – see front matter PII: S0378-3782( 98 )00046-2
1998 Elsevier Science Ireland Ltd. All rights reserved.
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J.-M. Lee et al. / Early Human Development 53 (1998) 121 – 128
1. Introduction Intrauterine growth restriction is associated with an increased risk of perinatal mortality and morbidity [1]. The incidence of fetal distress is high in these fetuses [2], and these fetuses commonly demonstrate heart rate abnormalities before or during labor [3]. The conventional indexes of fetal heart rate (FHR) variability such as long-term variability and the number of decelerations and accelerations have not succeeded in distinguishing abnormal fetuses from normal ones, until the former are significantly compromised [4–8]. This is probably because the indexes give no information about the underlying dynamic structure of beat-to-beat variability. Power spectral analysis and chaotic analysis such as correlation dimension have been fruitful in quantifying the periodic and complex dynamics in heart rate variability [9,10]. In addition, they give insight to the status of the underlying heart rate regulating system which produces the dynamics. Spectral analysis quantifies autonomic regulation. Correlation dimension gives information about the number of functional components that regulate the heart rate and about the degree of nonlinear coupling between these components. The correlation dimension, therefore, quantifies the overall complexity of the cardiovascular control system, which is an index of cardiovascular integrity and health [11–13]. Intrauterine growth restricted fetuses, although they are not severely compromised, may have functional immaturity of the cardiovascular control system which may be due to physical growth restriction and undetected low-grade hypoxia [3]. It can be hypothesized, therefore, that the overall cardiovascular integrity, including autonomic regulation, may be altered in uncomplicated intrauterine growth restricted (uIUGR) fetuses. Motivated by this, we chose to test whether the complex and periodic heart rate dynamics in the uIUGR fetuses is different from normal fetuses by comparing the correlation dimension and the power spectral component. This should give some understanding concerning the pathophysiology of heart rate control systems of the uIUGR fetuses.
2. Materials and methods
2.1. Patients Among the pregnant women who visited the outpatient obstetrics clinic at Hanyang University Hospital from January 1994 to December 1995, 192 normal pregnant women and 86 pregnant women suspected of intrauterine growth restriction, confirmed after delivery, were included in this study. Informed consent was obtained and the study was approved by the Committee on Human Experimentation of Hanyang University. All were single pregnancies, with gestational ages between the 31st and 42nd week, calculated using the date of the last menstrual period. All births were without any major malformations, chromosomal anomalies, or any other perinatal problem except low birth weight. Using Brenner’s growth standards, the infants’ birth weights were determined according to the gestational age [14]. Infants
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with birth weights below the 10th percentile were regarded as having intrauterine growth restriction. At the time of recording, pregnant women in labor or taking drugs that can affect FHR variability were excluded. Women who were smokers were excluded from this study.
2.2. Data collection and preprocessing All the subjects were in a semirecumbent position for a minimum of 10 min before data collection, all of which occurred from 2–6 pm. FHR time series were recorded for more than 40 min using a Corometrics 115 (Corometrics, Model 115, USA) external fetal monitor, during which fetal movements and fetal breathing were included. The recorded data was sampled into a personal computer with a digital serial interface. Whenever missing data was found, it was recorded as zero. When the off-line FHR data of zero (missing data) or below 60 bpm or above 200 bpm were encountered, they were removed. From the heart rate data, corresponding RR intervals were calculated. They were 1000-Hz linearly interpolated by their RR interval to construct a real time series of RR intervals, and 2 Hz subsampled. We extracted a 25-minute ( 3 60 3 2 Hz 5 3000 points) time series of RR intervals during which fetal movements actively occurred and analyzed them. After we calculated the mean and variance which is the square of the standard deviation, we removed a linear trend from each FHR data set.
2.3. Power spectral analysis [9] For each set of FHR data, we estimated power spectral density functions by classical methods (Fig. 1-left). We calculated low-frequency (LF) and high-frequency (HF) components by integrating the power spectral density curve between the 0.04–0.15 Hz and the 0.15–0.5 Hz range, respectively.
2.4. Correlation dimension To calculate the correlation dimension we implemented the Grassberger and Procaccia algorithm [13,15–17]. Their algorithms utilize the correlation integral C(r) in phase-space:
O
O
N 1 ref 1 ]] C(r) 5 ] u (r 2 iz(i) 2 z( j)i) Nref j 51 N 2 1 j ,i
where z is the strange attractor, Nref is the number of reference points and?is the heavyside function (u (x)50 if x,0, u (x)51 if x$0). If the embedding dimension and data points (N) are sufficiently large, the correlation dimension is the slope at the scaling region in C(r). Fig. 1-middle is the three dimensional phase-space plot (four or more dimensions can’t be visualized). Fig. 1-right is log 10 2log 10 plot of the correlation integral C(r) for the embedding dimension m52, 3, 4, . . . , 20. The correlation dimension is the
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Fig. 1. The spectral density functions (left), Three dimensional phase-space plots (middle) and correlation integral curves (right) of a normal and a uIUGR fetus. Left. The LF component (0.04–0.15 Hz) is significantly larger in the uIUGR fetus. Middle. Unlike the normal fetus, the dots (state) pertaining to the uIUGR fetus do not diffusely fill the three dimensional phase space and reveals a strange attractor, This represents the dynamic state of the uIUGR fetus is less complex than the normal one. Right. The decreased complexity is confirmed by the decreased correlation dimension of 1.896, when compared to that of the normal fetus with 4.581. The correlation dimension is the slope of the correlation integral curve of m520 at the scaling region.
slope of the correlation integral curve of m520 at the scaling region. The scaling region is in the range of 22,log 10 C(r), 21.
2.5. Statistical analysis Each group of normal and uIUGR fetuses were divided into three subgroups according to the gestational ranges of 31–35, 35–38 and 38–42 weeks. The SAS (SAS 6.2) univariate analysis verified that all data was normally distributed. To test the statistical difference of the mean, variance, LF component, HF component, and correlation dimension between the normal and uIUGR groups, we used SAS general linear models. When a significant statistical difference of a variable during the entire gestational periods was identified between the normal and the uIUGR fetuses, the
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difference of each variable within each gestational period was compared using standard t tests. All the analyses were performed using an alpha level of 0.05 as the criterion for statistical significance. All the data are presented as mean values 6standard error.
3. Results There were significant differences in birth weight, the mean and variance of FHR, LF and HF component, and correlation dimension between normal fetuses and uIUGR ones during entire gestational periods (Table 1). The correlation dimension of the normal fetuses is significantly higher than that of the uIUGR fetuses at 31–35 weeks and 38–42 weeks (Table 2). Although statistically insignificant, the correlation dimension of the normal fetuses at 35–38 weeks is higher than that of the uIUGR fetuses. It is interesting to note that the difference is the largest at 38–42 weeks. While the LF component of the normal fetuses is significantly lower than that of the uIUGR fetuses (Fig. 1-left) at all gestational ranges, the HF component of the normal fetuses is significantly lower only at 35–38 weeks. In the uIUGR fetuses, the three dimensional phase-space easily reveals some fractal structure (strange attractor) (Fig. 1-middle, lower). In contrast, the normal fetuses usually do not show any dynamic structure in the three dimensional phasespace (Fig. 1-middle, upper). Four or more dimensions, therefore, are needed to characterize their dynamic structure. This signifies that the status of heart rate dynamics in uIUGR fetuses is less complex than in normal ones. The correlation dimension quantifies the complexity. In contrast to the correlation dimension of 4.581 in a normal fetus, the lower dimension of 1.896 in an uIUGR fetus quantitatively confirms this decreased complexity (Fig. 1-right). Table 1 Descriptive characteristics, mean FHR, spectral indexes, and correlation dimension in normal fetuses and uIUGR fetuses for entire gestational periods
Maternal age (yr) Gestational age (wks) Birth weight (gm) Mean FHR (bpm) Variance of FHR (bpm 2 ) LF (msec 2 ) HF (msec 2 ) Correlation dimension
Normal fetuses (n5192)
uIUGR fetuses (n586)
Significance
29.160.2 39.960.1 3273.9620.1 144.660.1 46.362.5 116.265.5 24.961.1 3.9360.06
28.260.3 39.960.3 2384.5637.6 146.460.9 76.665.6 169.8615.81 33.163.0 3.4460.11
NS NS P50.001 P50.0001 P50.0001 P50.001 P,0.005 P50.001
Data are represented as mean6SE. bpm: beats per min; NS: not significant; uIUGR: uncomplicated intrauterine growth restricted; FHR: fetal heart rate; LF: low-frequency component (0.04–0.15 Hz); HF: high-frequency component (0.15–0.5 Hz).
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Table 2 Correlation dimension and power spectrum according to gestational period in normal fetuses and uIUGR fetuses Gestational Period
31–35 weeks
35–38 weeks
38–42 weeks
Parameter
Normal fetuses (n5192)
UIUGR fetuses (n586)
N
N
Correlation Dimension LF(msec 2 ) HF(msec 2 )
53
Correlation Dimension LF(msec 2 ) HF(msec 2 )
59
Correlation Dimension LF(msec 2 ) HF(msec 2 )
80
value 3.9660.11
21
116.969.7 26.562.1 3.9960.16 124.8611.2 25.462.4 3.8460.11 109.168.5 23.361.7
value 3.3960.22 182.4633.2 33.364.1
29
3.8560.1 177.8627.74 39.866.9
36
Significance
3.0260.17 155.9624.0 27.563.7
P,0.05 P,0.05 NS NS P,0.05 P,0.05 P50.0001 P,0.05 NS
Data are represented as mean6SE. NS: not significant; uIUGR: uncomplicated intrauterine growth retarded; LF: low-frequency component; HF: high-frequency component.
4. Discussion The principal new finding of this study is that the heart rate dynamics of uIUGR fetuses are less complex and more periodic than those of normal fetuses. At term gestation, the lesser complexity was more marked. The chaotic and spectral analysis of FHR, therefore, has a discriminating value in differentiating uIUGR fetuses from normal fetuses. The conventional indexes of abnormal FHR patterns such as decreased long-term variation and increased number of decelerations are reliable, but they are rather late signs of fetal compromise in IUGR fetuses [4,5]. Cardiotocography has failed to identify IUGR fetuses with a pO 2 in the lower normal range [6]. FHR monitoring, therefore, is not considered to be a reliable screening method for forthcoming impairments. The present study succeeded in showing that the chaotic and periodic heart rate dynamics of the uIUGR fetus are significantly different from that of normal fetuses. This result signifies that the chaotic and spectral indexes appear to be sensitive probes in detecting subtle and possibly important changes in FHR originating from uIUGR, even in the absence of fetal distress. Since we did not study the uIUGR fetuses that eventually became distressed, it is not certain whether the indexes have the predictive value for identifying fetuses with forthcoming distress. Further research should be done to test for this predictable value. Decreased correlation dimension in the uIUGR fetuses indicates that their heart rate regulating system is less complex than that of the normal ones [13]. This decreased system complexity limits the uIUGR fetuses’ ability to maintain cardiovascular integrity, and therefore, to adapt to the variety of internal and external cardiovascular stresses. Another important finding is that the lower value of correlation dimension in uIUGR
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fetuses was more marked after 38 weeks gestation. This result suggests that catastrophic cardiovascular events are more likely to occur near term gestation, which may contribute to increased mortality and morbidity during the perinatal period. The increased LF component in the uIUGR fetuses during all the gestational ages indicates that sympathetic tone was elevated [9]. The results are in accord with Diver’s finding that mean concentration of norepinephrine and epinephrine are significantly elevated in the amniotic fluid of IUGR fetuses [18]. The increased sympathetic activity was considered to occur as a response to chronic metabolic and hemodynamic stress due to uteroplacental insufficiency. Whether the increased sympathetic activity contributes to morbidity or mortality is not clear. The HF component, which is the quantitative measure of respiratory sinus arrhythmia [9,19,20] is also elevated in the uIUGR fetus. Because the respiratory rate and respiratory depth of uIUGR fetuses are fast and irregular, the elevated HF component (or respiratory sinus arrhythmia) cannot be interpreted with certainty as being due to the elevation of respiration-modulated vagal tone [21–23]. There was an unavoidable limitation in this study: the behavioral status of uIUGR fetuses during the period of heart rate acquisition was not the same as that of normal fetuses. Since the spectral and chaotic indexes of heart rate change with behavioral state, we cannot exclude with certainty the possibility that the difference of the spectral and chaotic heart rate dynamics between the normal and uIUGR group may originate from different behavioral states. It can be concluded that the FHR of uIUGR fetuses can be distinguished from normal ones by the decreased complexity and increased periodicity of the low frequency-range. Despite elevated sympathetic modulation, the cardiovascular integrity of the uIUGR fetus is impaired, which is more marked near term gestation. This may contribute to increased perinatal morbidity and mortality. Further research should test the predictive value of chaotic and spectral indexes in identifying the intrauterine growth restricted fetuses that may encounter fetal distress.
Acknowledgements This study was supported by a grant (HMP-96-M-1-1003) from the Good Health R and D Project, the Ministry of Health and Welfare, R.O.K and supported by a grant (HMP-96-G-1-24) from the ’96 Highly Advanced National Project on the Development of Biomedical Engineering and Technology, Ministry of Health and Welfare, R.O.K.
References [1] Galbraith RS, Karchmar EJ, Piercy WN, Low JA. The clinical prediction of intrauterine growth retardation. Am J Obstet Gynecol 1979;133:281–6. [2] Usher RH. Clinical and therapeutic aspects of fetal malnutrition. Pediatr Clin North Am 1970;17:169–88.
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[3] Odendall H. Fetal heart rate patterns in patients with intrauterine growth retardation. Obstet Gynecol 1976;48:187–90. [4] Becker DJ, Visser GHA, Mulder EJH, Poelmann-Weesjes G. Heart rate variation and movement incidence in growth-retarded fetuses: the significance of antenatal late heart rate deceleration. Am J Obstet Gynecol 1987;157:126–33. [5] Snijders RJM, Ribbert LSM, Visser GHA, Mulder EJH. Numerical analysis of heart rate variation in intrauterine growth-retarded fetuses: a longitudinal study. Am J Obstet Gynecol 1992;166:22–7. [6] Visser GHA, Sadovsky G, Nicolaides KH. Antepartum heart rate patterns in small-for-gestational-age third-trimester fetuses: correlation with blood gas values obtained at cordocentesis. Am J Obstet Gynecol 1990;162:698–703. [7] Gagnon R, Bocking AD, Richardson BS, McLean P. A flat fetal heart rate tracing with normal fetal heart rate variability. Am J Obstet Gynecol 1994;171:1379–81. [8] Samueloff A, Langer O, Berkus M, Field N, Xenakis E, Ridgway L. Is fetal heart rate variability a good predictor of fetal outcome?. Acta Obstet Gynecol Scand 1994;73:39–44. [9] Akselrod S, Gordon D, Ubel FA, Shannon DC, Barger AC, Cohen RJ. Power spectrum analysis of heart rate fluctuation. A quantitative probe of beat-to-beat cardiovascular control. Science 1981;213:220–2. [10] Denton TA, Diamond GA, Helfant RH, Khan S, Karaguezian H. Fascinating rhythm: a primer on chaos theory and its application to cardiology. Am Heart J 1990;120:1419–40. [11] Lipsitz LA, Goldberger AL. Loss of ‘complexity’ and aging. Potential applications of fractals and chaos theory to senescence. JAMA 1992;267:1806–9. [12] Goldberger AL. Nonlinear dynamics for clinicians: chaos theory, fractal, and complexity in bedside. Lancet 1996;347:1312–4. [13] Elbert T, Ray WJ, Kowalik ZJ, Skinner JE, Graf KE, Nirbaumer N. Chaos and physiology: deterministic chaos in excitable cell assemblies. Physiol Rev 1994;74:1–47. [14] Brenner WE, Edelman DA, Hendricks CH. A standard of fetal growth for the United States of America. Am J Obstet Gynecol 1976;126:555–62. [15] Grassberger P, Procaccia I. Measuring strangeness of strange attractors. Physica 1983;9D:189–208. [16] Sammon MP, Bruce EN. Vagal afferent activity increases dynamical dimension of respiration in rats. J Appl Physiol 1992;70:1748–62. [17] Fell J, Roschke J, Schaffner C. Surrogate data analysis of sleep electroencephalograms reveals evidence of nonlinearity. Biol Cybern 1996;75:85–92. [18] Divers WA, Wilkes MM, Babaknia A, Hill LM, Quilligan EJ, Yen SS. Amniotic fluid catecholamines and metabolites in intrauterine growth retardation. Am J Obstet Gynecol 1981;141:608–10. [19] Akselrod S, Gordon D, Madwed JB, Snidman NC, Shannon DC, Cohen RJ. Hemodynamic regulation: investigation by spectral analysis. Am J Physiol 1985;249:H867–75. [20] Eckerberg DL. Human sinus arrhythmia as an index of vagal cardiac outflow. J Appl Physiol 1980;54:961–6. [21] Devoe LD, Ruedrich DA, Searle DA. Value of observation of fetal breathing activity in antenatal assessment of high risk pregnancy. Am J Obstet Gynecol 1989;160:166–71. [22] Karin J, Hirsch M, Akselrod S. An Estimate of fetal autonomic state by spectral analysis of fetal heart rate fluctuations. Pediatr Res 1993;34:134–8. [23] Davidson SR, Rankin JHG, Martin CB, Reid DL. Fetal heart rate variability and behavioral state: analysis by power spectrum. Am J Obstet Gynecol 1992;167:717–22.
Chaotic and periodic heart rate dynamics in uncomplicated intrauterine growth restricted fetuses Jong-Min Lee a , Kwang-Suk Park a , Jung-Hae Hwang b , Mun-Il Park b , c, Myung-Kul Yum * a
Dept. of Biomedical Engineering, Seoul National University School of Medicine, 28 Yongon-Dong, Chongno-Gu, Seoul 110 -799, Korea b Dept. of Obstetrics and Gynecology, Hanyang University School of Medicine, 17 Haengdang-dong, Sungdong-ku, Seoul 133 -792, Korea c Dept. of Pediatric Cardiology, Hanyang University School of Medicine, 17 Haengdang-dong, Sungdong-ku, Seoul 133 -792, Korea Received 10 December 1997; received in revised form 2 March 1998; accepted 15 May 1998
Abstract We studied how chaotic and periodic heart rate dynamics differ between normal fetuses (n 5 192) and uncomplicated intrauterine growth restricted fetuses (n 5 86), aged 31–42 weeks of gestation. We analyzed each fetal heart rate time series for 25 min. We quantified the chaotic dynamics of each fetal heart rate time series by correlation dimension. The periodic dynamics were analyzed by power spectral analysis. The correlation dimension and, therefore, the complexity, of the heart rate dynamics of the uncomplicated intrauterine growth restricted fetuses was significantly lower than that of the normal fetuses, which was marked at 38–42 weeks of gestation. The low-frequency (0.04–0.15 Hz) component and, therefore, the periodicity of the low-frequency range was significantly higher than that of the normal fetuses during all the gestational weeks. These results mean that, although the intrauterine growth restricted fetuses are not severely compromised, the overall integrity of their cardiovascular control is impaired, especially at term; and sympathetic modulation is increased, both of which may contribute to increased perinatal mortality. 1998 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Chaos; Power spectrum; Uncomplicated intrauterine growth restricted fetus *Corresponding author. Address for correspondence: Hanyang University Kuri Hospital, Department of Pediatric Cardiology, 249-1 Kyomundong, Kuri-shi, Kyunggi-do, 471-701, Korea. Tel.: 182-346-60-2252; Fax: 182-2-442-1331; E-mail: [email protected] 0378-3782 / 98 / $ – see front matter PII: S0378-3782( 98 )00046-2
1998 Elsevier Science Ireland Ltd. All rights reserved.
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1. Introduction Intrauterine growth restriction is associated with an increased risk of perinatal mortality and morbidity [1]. The incidence of fetal distress is high in these fetuses [2], and these fetuses commonly demonstrate heart rate abnormalities before or during labor [3]. The conventional indexes of fetal heart rate (FHR) variability such as long-term variability and the number of decelerations and accelerations have not succeeded in distinguishing abnormal fetuses from normal ones, until the former are significantly compromised [4–8]. This is probably because the indexes give no information about the underlying dynamic structure of beat-to-beat variability. Power spectral analysis and chaotic analysis such as correlation dimension have been fruitful in quantifying the periodic and complex dynamics in heart rate variability [9,10]. In addition, they give insight to the status of the underlying heart rate regulating system which produces the dynamics. Spectral analysis quantifies autonomic regulation. Correlation dimension gives information about the number of functional components that regulate the heart rate and about the degree of nonlinear coupling between these components. The correlation dimension, therefore, quantifies the overall complexity of the cardiovascular control system, which is an index of cardiovascular integrity and health [11–13]. Intrauterine growth restricted fetuses, although they are not severely compromised, may have functional immaturity of the cardiovascular control system which may be due to physical growth restriction and undetected low-grade hypoxia [3]. It can be hypothesized, therefore, that the overall cardiovascular integrity, including autonomic regulation, may be altered in uncomplicated intrauterine growth restricted (uIUGR) fetuses. Motivated by this, we chose to test whether the complex and periodic heart rate dynamics in the uIUGR fetuses is different from normal fetuses by comparing the correlation dimension and the power spectral component. This should give some understanding concerning the pathophysiology of heart rate control systems of the uIUGR fetuses.
2. Materials and methods
2.1. Patients Among the pregnant women who visited the outpatient obstetrics clinic at Hanyang University Hospital from January 1994 to December 1995, 192 normal pregnant women and 86 pregnant women suspected of intrauterine growth restriction, confirmed after delivery, were included in this study. Informed consent was obtained and the study was approved by the Committee on Human Experimentation of Hanyang University. All were single pregnancies, with gestational ages between the 31st and 42nd week, calculated using the date of the last menstrual period. All births were without any major malformations, chromosomal anomalies, or any other perinatal problem except low birth weight. Using Brenner’s growth standards, the infants’ birth weights were determined according to the gestational age [14]. Infants
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with birth weights below the 10th percentile were regarded as having intrauterine growth restriction. At the time of recording, pregnant women in labor or taking drugs that can affect FHR variability were excluded. Women who were smokers were excluded from this study.
2.2. Data collection and preprocessing All the subjects were in a semirecumbent position for a minimum of 10 min before data collection, all of which occurred from 2–6 pm. FHR time series were recorded for more than 40 min using a Corometrics 115 (Corometrics, Model 115, USA) external fetal monitor, during which fetal movements and fetal breathing were included. The recorded data was sampled into a personal computer with a digital serial interface. Whenever missing data was found, it was recorded as zero. When the off-line FHR data of zero (missing data) or below 60 bpm or above 200 bpm were encountered, they were removed. From the heart rate data, corresponding RR intervals were calculated. They were 1000-Hz linearly interpolated by their RR interval to construct a real time series of RR intervals, and 2 Hz subsampled. We extracted a 25-minute ( 3 60 3 2 Hz 5 3000 points) time series of RR intervals during which fetal movements actively occurred and analyzed them. After we calculated the mean and variance which is the square of the standard deviation, we removed a linear trend from each FHR data set.
2.3. Power spectral analysis [9] For each set of FHR data, we estimated power spectral density functions by classical methods (Fig. 1-left). We calculated low-frequency (LF) and high-frequency (HF) components by integrating the power spectral density curve between the 0.04–0.15 Hz and the 0.15–0.5 Hz range, respectively.
2.4. Correlation dimension To calculate the correlation dimension we implemented the Grassberger and Procaccia algorithm [13,15–17]. Their algorithms utilize the correlation integral C(r) in phase-space:
O
O
N 1 ref 1 ]] C(r) 5 ] u (r 2 iz(i) 2 z( j)i) Nref j 51 N 2 1 j ,i
where z is the strange attractor, Nref is the number of reference points and?is the heavyside function (u (x)50 if x,0, u (x)51 if x$0). If the embedding dimension and data points (N) are sufficiently large, the correlation dimension is the slope at the scaling region in C(r). Fig. 1-middle is the three dimensional phase-space plot (four or more dimensions can’t be visualized). Fig. 1-right is log 10 2log 10 plot of the correlation integral C(r) for the embedding dimension m52, 3, 4, . . . , 20. The correlation dimension is the
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Fig. 1. The spectral density functions (left), Three dimensional phase-space plots (middle) and correlation integral curves (right) of a normal and a uIUGR fetus. Left. The LF component (0.04–0.15 Hz) is significantly larger in the uIUGR fetus. Middle. Unlike the normal fetus, the dots (state) pertaining to the uIUGR fetus do not diffusely fill the three dimensional phase space and reveals a strange attractor, This represents the dynamic state of the uIUGR fetus is less complex than the normal one. Right. The decreased complexity is confirmed by the decreased correlation dimension of 1.896, when compared to that of the normal fetus with 4.581. The correlation dimension is the slope of the correlation integral curve of m520 at the scaling region.
slope of the correlation integral curve of m520 at the scaling region. The scaling region is in the range of 22,log 10 C(r), 21.
2.5. Statistical analysis Each group of normal and uIUGR fetuses were divided into three subgroups according to the gestational ranges of 31–35, 35–38 and 38–42 weeks. The SAS (SAS 6.2) univariate analysis verified that all data was normally distributed. To test the statistical difference of the mean, variance, LF component, HF component, and correlation dimension between the normal and uIUGR groups, we used SAS general linear models. When a significant statistical difference of a variable during the entire gestational periods was identified between the normal and the uIUGR fetuses, the
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difference of each variable within each gestational period was compared using standard t tests. All the analyses were performed using an alpha level of 0.05 as the criterion for statistical significance. All the data are presented as mean values 6standard error.
3. Results There were significant differences in birth weight, the mean and variance of FHR, LF and HF component, and correlation dimension between normal fetuses and uIUGR ones during entire gestational periods (Table 1). The correlation dimension of the normal fetuses is significantly higher than that of the uIUGR fetuses at 31–35 weeks and 38–42 weeks (Table 2). Although statistically insignificant, the correlation dimension of the normal fetuses at 35–38 weeks is higher than that of the uIUGR fetuses. It is interesting to note that the difference is the largest at 38–42 weeks. While the LF component of the normal fetuses is significantly lower than that of the uIUGR fetuses (Fig. 1-left) at all gestational ranges, the HF component of the normal fetuses is significantly lower only at 35–38 weeks. In the uIUGR fetuses, the three dimensional phase-space easily reveals some fractal structure (strange attractor) (Fig. 1-middle, lower). In contrast, the normal fetuses usually do not show any dynamic structure in the three dimensional phasespace (Fig. 1-middle, upper). Four or more dimensions, therefore, are needed to characterize their dynamic structure. This signifies that the status of heart rate dynamics in uIUGR fetuses is less complex than in normal ones. The correlation dimension quantifies the complexity. In contrast to the correlation dimension of 4.581 in a normal fetus, the lower dimension of 1.896 in an uIUGR fetus quantitatively confirms this decreased complexity (Fig. 1-right). Table 1 Descriptive characteristics, mean FHR, spectral indexes, and correlation dimension in normal fetuses and uIUGR fetuses for entire gestational periods
Maternal age (yr) Gestational age (wks) Birth weight (gm) Mean FHR (bpm) Variance of FHR (bpm 2 ) LF (msec 2 ) HF (msec 2 ) Correlation dimension
Normal fetuses (n5192)
uIUGR fetuses (n586)
Significance
29.160.2 39.960.1 3273.9620.1 144.660.1 46.362.5 116.265.5 24.961.1 3.9360.06
28.260.3 39.960.3 2384.5637.6 146.460.9 76.665.6 169.8615.81 33.163.0 3.4460.11
NS NS P50.001 P50.0001 P50.0001 P50.001 P,0.005 P50.001
Data are represented as mean6SE. bpm: beats per min; NS: not significant; uIUGR: uncomplicated intrauterine growth restricted; FHR: fetal heart rate; LF: low-frequency component (0.04–0.15 Hz); HF: high-frequency component (0.15–0.5 Hz).
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Table 2 Correlation dimension and power spectrum according to gestational period in normal fetuses and uIUGR fetuses Gestational Period
31–35 weeks
35–38 weeks
38–42 weeks
Parameter
Normal fetuses (n5192)
UIUGR fetuses (n586)
N
N
Correlation Dimension LF(msec 2 ) HF(msec 2 )
53
Correlation Dimension LF(msec 2 ) HF(msec 2 )
59
Correlation Dimension LF(msec 2 ) HF(msec 2 )
80
value 3.9660.11
21
116.969.7 26.562.1 3.9960.16 124.8611.2 25.462.4 3.8460.11 109.168.5 23.361.7
value 3.3960.22 182.4633.2 33.364.1
29
3.8560.1 177.8627.74 39.866.9
36
Significance
3.0260.17 155.9624.0 27.563.7
P,0.05 P,0.05 NS NS P,0.05 P,0.05 P50.0001 P,0.05 NS
Data are represented as mean6SE. NS: not significant; uIUGR: uncomplicated intrauterine growth retarded; LF: low-frequency component; HF: high-frequency component.
4. Discussion The principal new finding of this study is that the heart rate dynamics of uIUGR fetuses are less complex and more periodic than those of normal fetuses. At term gestation, the lesser complexity was more marked. The chaotic and spectral analysis of FHR, therefore, has a discriminating value in differentiating uIUGR fetuses from normal fetuses. The conventional indexes of abnormal FHR patterns such as decreased long-term variation and increased number of decelerations are reliable, but they are rather late signs of fetal compromise in IUGR fetuses [4,5]. Cardiotocography has failed to identify IUGR fetuses with a pO 2 in the lower normal range [6]. FHR monitoring, therefore, is not considered to be a reliable screening method for forthcoming impairments. The present study succeeded in showing that the chaotic and periodic heart rate dynamics of the uIUGR fetus are significantly different from that of normal fetuses. This result signifies that the chaotic and spectral indexes appear to be sensitive probes in detecting subtle and possibly important changes in FHR originating from uIUGR, even in the absence of fetal distress. Since we did not study the uIUGR fetuses that eventually became distressed, it is not certain whether the indexes have the predictive value for identifying fetuses with forthcoming distress. Further research should be done to test for this predictable value. Decreased correlation dimension in the uIUGR fetuses indicates that their heart rate regulating system is less complex than that of the normal ones [13]. This decreased system complexity limits the uIUGR fetuses’ ability to maintain cardiovascular integrity, and therefore, to adapt to the variety of internal and external cardiovascular stresses. Another important finding is that the lower value of correlation dimension in uIUGR
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fetuses was more marked after 38 weeks gestation. This result suggests that catastrophic cardiovascular events are more likely to occur near term gestation, which may contribute to increased mortality and morbidity during the perinatal period. The increased LF component in the uIUGR fetuses during all the gestational ages indicates that sympathetic tone was elevated [9]. The results are in accord with Diver’s finding that mean concentration of norepinephrine and epinephrine are significantly elevated in the amniotic fluid of IUGR fetuses [18]. The increased sympathetic activity was considered to occur as a response to chronic metabolic and hemodynamic stress due to uteroplacental insufficiency. Whether the increased sympathetic activity contributes to morbidity or mortality is not clear. The HF component, which is the quantitative measure of respiratory sinus arrhythmia [9,19,20] is also elevated in the uIUGR fetus. Because the respiratory rate and respiratory depth of uIUGR fetuses are fast and irregular, the elevated HF component (or respiratory sinus arrhythmia) cannot be interpreted with certainty as being due to the elevation of respiration-modulated vagal tone [21–23]. There was an unavoidable limitation in this study: the behavioral status of uIUGR fetuses during the period of heart rate acquisition was not the same as that of normal fetuses. Since the spectral and chaotic indexes of heart rate change with behavioral state, we cannot exclude with certainty the possibility that the difference of the spectral and chaotic heart rate dynamics between the normal and uIUGR group may originate from different behavioral states. It can be concluded that the FHR of uIUGR fetuses can be distinguished from normal ones by the decreased complexity and increased periodicity of the low frequency-range. Despite elevated sympathetic modulation, the cardiovascular integrity of the uIUGR fetus is impaired, which is more marked near term gestation. This may contribute to increased perinatal morbidity and mortality. Further research should test the predictive value of chaotic and spectral indexes in identifying the intrauterine growth restricted fetuses that may encounter fetal distress.
Acknowledgements This study was supported by a grant (HMP-96-M-1-1003) from the Good Health R and D Project, the Ministry of Health and Welfare, R.O.K and supported by a grant (HMP-96-G-1-24) from the ’96 Highly Advanced National Project on the Development of Biomedical Engineering and Technology, Ministry of Health and Welfare, R.O.K.
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