32nd Annual International Conference of the IEEE EMBS Buenos Aires, Argentina, August 31 - September 4, 2010
Nonlinearity of EHG signals used to distinguish active labor from normal pregnancy contractions. Hassan M., Terrien J., Alexandersson A., Marque C. and Karlsson B. Abstract—Labor prediction using the electrohysterogram has immediate clinical applications and has been the aim of several studies in recent years. Studies using various linear methods such as classic spectral analysis do not give clinically useful results. In this paper we present the use of two methods that investigate nonlinearity to predict normal labor. We show the comparison between a linear method that is known from the literature (mean power frequency) and two nonlinear methods (approximate entropy and time reversibility) using ROC analysis. The comparison indicates that the best method for pretreatment to classify pregnancy and labor signals is time reversibility. The results indicate that time reversibility is a very promising tool for distinguishing between labor and physiological contractions during pregnancy. This could be the first step in developing a clinical application method to predict preterm labor.
I. INTRODUCTION In research on uterine EMG, particularly in our project, the goal is to find the best method for differentiating between signals recorded from women during pregnancy and signal recorded from women in labor. When able to evidence this difference we expect to be able to find pertinent tools that will permit the prediction of preterm labor. It is well known that temporal and spectral characteristics of uterine EMG activity change from pregnancy to parturition [1] [2]. Traditional techniques such as spectral analysis have been used in the past in the attempt to detect this change, i.e. the use of Power Density Spectrum (PDS) [3]. These techniques implicitly assume that the process generating the contractions is linear and hence may be biased or in other ways unsuitable. This study was supported by the Icelandic center for research RANNIS and the French National Center for University and School (CNOUS). M. Hassan, J. Terrien and B. Karlsson are with the School of Science and Engineering, Reykjavik University, Reykjavik, 103 Iceland. (corresponding author: +354-599-6200; fax: +354-599-6301; e mail:
[email protected]). M. Hassan and C. Marque are with the Université de Technologie de Compiègne – CNRS UMR 6600 Biomécanique et Bio-ingénierie, F60205 Compiègne Cedex, France. B. Karlsson is with the department of physiology, University of Iceland, Reykjavik, Iceland. A Alexandersson is with the faculty of medicine, University of Iceland, Reykjavik, Iceland.
978-1-4244-4124-2/10/$25.00 ©2010 IEEE
Recently, much attention has been given to the use of nonlinear analysis techniques for the characterization of biological signal (i.e. EEG recordings). Few nonlinear analysis methods have been applied to EHG and most of those are only descriptive and aim to demonstrate the presence of nonlinear characteristics in uterine EMG, not at classifying pregnancy/labor signals for labor prediction. We can cite here the use of Approximate Entropy (ApEn) [4] to detect nonlinearity in uterine activity signals and the use of fractal dimension to analyze uterine contractions [5]. In this paper we compute the z score of the results of two nonlinear methods (approximate entropy and time reversibility). We then use the z score as a parameter to attempt to classify pregnancy and labor signals. To compute the z score we use surrogates data analysis [6] which provides a rigorous framework for nonlinearity statistical tests. The most commonly used null hypothesis states that the examined time series is generated by a linear Gaussian stochastic process collected through a static nonlinear measurement function. The original time series is then likely to be drawn from the distribution of values of the surrogates within a confidence level. In this paper we present a comparison between three methods: one linear method (mean power frequency) and two nonlinear methods (time reversibility and approximate entropy). In order to test the ability of the different methods to differentiate between signals recorded during pregnancy and signals recorded during labor, we applied ROC tests to the three methods. II.
MATERIALS AND METHODS
A. Data As the methods used here are ―monovariate‖ (i.e. processing only one signal) we used only one channel (bipolar vertical 7: Vb7) from the 4*4 matrix located on the women abdomen. This channel is located on the median vertical axis of the uterus (see [7] for more details). We studied 7 women: 4 recorded during pregnancy (33-39 week of gestation) and 3 during labor (39-42 week of gestation). The measurements were performed at the Landspitali University hospital in Iceland, following a protocol approved by the relevant ethical committee (VSN 02-0006-V2). The frequency sampling was 200 Hz. The EHG signals were segmented manually to extract segments
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containing uterine activity bursts. After segmentation we got 20 labor bursts and 20 pregnancy bursts. All the analysis below was applied to these segmented uterine bursts. B. Mean power frequency We compare the nonlinear methods with the mean power frequency (MPF) which is a well known frequency parameter that has already been used for the prediction of preterm labor [8]. As pretreatment, the signals are numerically filtered between 0-3 Hz. The MPF is computed from the power spectral density (PSD) of the signal obtained by Welsh's averaged periodogram method. C. Time reversibility A time series is said to be reversible only if its probabilistic properties are invariant with respect to time reversal. In reference [9] the authors proposed a test for the null hypothesis that a time series is reversible. Rejection of the null hypothesis implies that the time series cannot be described by a linear Gaussian random process. So time irreversibility can be taken as a strong signature of nonlinearity [6]. In this paper we used the simple way, described in [6] to compute time reversibility for signal S: N 1 3 Tr ( ) ( Sn Sn ) N n 1 where N is the signal length and in this paper we used =1. D. Approximate Entropy Approximate entropy first proposed by Pincus [10] is a measure that quantifies the regularity and predictability of the signals. The ApEn value is low for regular time series and high for complex, irregular ones. The first step in computing ApEn for
a given time series, yi, i = 1. . . N is to construct the state vectors in the embedding space, Rm, by using the method of delays,
xi yi , yi , yi 2 ,..., yi ( m1)
N -( m-1) 1 m ( r ) N -( m-1) log Cim ( r ) i 1 In this paper, we used the ―differential entropy based method‖ [11] to compute the optimal m and values. We define the filter parameter r as r=0.2*SD which is a common choice of r , where SD is the standard deviation of the signal.
E. The surrogate data technique Surrogate data are time series that are generated in order to keep particular statistical characteristics of an original time series while destroying all others. The method of surrogate data is a popular tool for testing a null hypothesis on a time series against its temporally random realizations through a discriminating measure. In the literature, one widely used null hypothesis is ‗‗the examined time series is generated by a Gaussian linear stochastic process‘‘ [6]. The original time series and its surrogates obtained by this method share the same power spectrum, and therefore the same autocorrelation function. However, any underlying nonlinear dynamic structure within the original data is altered by phase randomization. The null hypothesis is tested by comparing the surrogates and the original data using a statistical test. If the null hypothesis is rejected, means that the original data has nonlinear properties, whereas if the null hypothesis is accepted it is concluded that the original data comes from a Gaussian linear stochastic process. In order to measure quantitatively the difference between the original data and the surrogates, we compute the z score value. In the case of time reversibility for example, z score is defined as:
where m and are the embedding dimension and time delay, respectively. Then we define the correlation sum m i
C (r ) by:
Trorg Trsurr
surr
where Trorg denotes the value of the discriminating statistics for the original data set. If Trsurr denotes the values of Tr for the realizations of the surrogates time series, Trsurr is the Trsurr mean and surr is the
m Ci ( r )
Trsurr standard deviation.
1
( r d ( x(i ), x ( j ))) N ( m 1) j 1
( x) 1 for x>0, ( x) 0 ,
otherwise is the
standard Heavy side function, r is the vector comparison distance and d(x(i),x(j)) is a distance measure defined by:
d ( x(i ), x( j ))
where
z
1 i N ( m 1)
where
m m1 ApEn(m, r , , N )= ( r ) - (r )
max ( y (i (k 1) ) y ( j ( k 1) ) ) k 1,2,...,m
ApEn is given by the formula:
F. Labor prediction To evaluate the performances of the proposed parameters for the prediction of labor in women, we used classical Receiver Operating Characteristic (ROC) curves. A ROC curve is a graphical tool that permit the evaluation of a binary, i.e. two classes, classifier. A ROC curve is the curve corresponding to TPR (True Positive Rate or sensitivity) vs. FPR (False Positive Rate or 1-Specificity) obtained for different
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parameter thresholds. ROC curves are classically compared by the mean of the Area Under the Curve (AUC) and accuracy (ACC) defined as:
(TP FN )(TP TN )( FP TN ) ACC TP( FP TN ) FP(TP FN ) The AUC was estimated by the trapezoidal integration method. We additionally used Matthew‘s Correlation Coefficient (MCC) defined as:
MPF 1 0.9
TP * TN FP * FN
0.8
(TN FN )(TN FP)(TP FN )(TP FP)
TPR or Sensitivity
MCC
low z score values during pregnancy and high values during labor. This means that the labor contractions present a much stronger nonlinear character than the pregnancy ones. A z score value above 1.96 indicates that the signal has a low probability of being generated by a Gaussian linear stochastic process (p=0.05).
where TP, TN, FP and FN stand respectively for True Positive, True Negative, False Positive and False Negative values. III. RESULTS ROC curve computed on the MPF values is calculated for each contraction, while the z score values computed with the surrogates method are used in ROC curves for Tr and ApEn. In table 1 we notice that MPF has a high sensitivity (0.8) and low specificity (0.5) while it is the opposite for ApEn with low sensitivity (0.52) and high specificity (0.8). Time reversibility indicates high sensitivity (0.93) and high specificity (0.90). The chance of correctly classifying labor increases markedly when applying the nonlinear methods (from 0.63 AUC with Mean power frequency to 0.98 with time reversibility).
MCC
AUC
0.5 0.4 0.3
0.1 0
0
0.1
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1
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FPR or (1- Specificity) ApEn 1 0.9
TPR or Sensitivity
0.8
COMPARISON OF ROC PARAMETERS FOR THE THREE METHODS FOR LABOR PREDICTION.
Sensitivity
0.6
0.2
TABLE I
Specificity
0.7
0.7 0.6 0.5 0.4 0.3 0.2 0.1
ACC (%)
MPF
0.5
0.8
0.32
0.63
65.66
ApEn
0.8
0.52
0.33
0.64
65.8
0
0
0.1
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0.3
0.4
0.5
0.6
FPR or (1- Specificity) Tr 1 0.9 0.8
0.90
0.93
0.85
0.98
92
Figure 1 shows the ROC curves from the three methods: Mean Power Frequency (MPF), Approximate Entropy (ApEn) and Time reversibility (Tr). The curves indicate how MPF does not detect clearly the difference between pregnancy and labor with AUC=0.63. The results of ApEn are slightly better with AUC=0.64, while the ROC curve for Tr shows a much better performance than the two other methods with AUC=0.98. As we can see from the ROC curves, Tr is the best of the three methods, and it allows us to distinguish clearly between signals from pregnancy and labor. In addition, the values of time reversibility indicated
TPR or Sensitivity
Tr
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
0.1
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0.6
FPR or (1- Specificity)
Fig.1.
Three ROC curves obtained from the three methods (MPF, ApEn and Tr) for labor vs. pregnancy classification.
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The results of Fig. 2 show that the median value of z scores for labor signals is > 1.69 and the median value of z scores for pregnancy signals is
