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Medical Engineering & Physics 33 (2011) 980– 986

Contents lists available at ScienceDirect

Medical Engineering & Physics

j o ur nal homep age : www.elsev ier .com/ locate /medengphy

omparison between approximate entropy, correntropy and time reversibility:pplication to uterine electromyogram signals

ahmoud Hassana,b,∗, Jérémy Terrienb, Catherine Marquea, Brynjar Karlssonb

UMR CNRS 6600, Biomécanique et Bio-ingénierie, Université de Technologie de Compiègne, Compiègne, FranceSchool of Science and Engineering, Reykjavik University, Reykjavik, Iceland

r t i c l e i n f o

rticle history:eceived 22 October 2010eceived in revised form 17 March 2011

a b s t r a c t

Detection of nonlinearity should be the first step before any analysis of nonlinearity or nonlinear behaviorin biological signal. The question is which method should be used in each case and which one can best

ccepted 23 March 2011

eywords:onlinear signal processingurrogates dataterine EMG signalsetection of preterm labor

respect the different characteristics of the signals under investigation. In this paper we compare threemethods widely used in nonlinearity detection: approximate entropy, correntropy and time reversibility.The false alarm rates with the numbers of surrogates for the three methods were computed on linear,nonlinear stationary and nonlinear nonstationary signals. The results indicate the superiority of timereversibility over the other methods for detecting linearity and nonlinearity in different signal types. Theapplication of time reversibility on uterine electromyographic signal showed very good performance inclassifying pregnancy and labor signals.

. Introduction

For any data analysis, the application of nonlinear time seriesethods has to be justified by establishing the nonlinearity of the

ime series under investigation.Several measures have been proposed to detect nonlinear char-

cteristics in time series. The first category includes methodsnspired from chaos theory such as: maximal Lyapunov expo-ents, correlation dimension [1] and transfer entropy [2]. Theain disadvantage of these methods is that they depend on dif-

erent parameters, like embedding dimension, which complicatehe interpretations of the results. The second category of methodss based on the predictability of time series. These include delay-ector variance [3] and approximate entropy [4]; this category isore robust than the first one but its interpretation is still not easy

ue to its sensitivity to the choice of the different parameters [5].he last category of methods is based on a statistical approach. Thisategory includes methods such as: time reversibility [6] and higherimensional autocorrelation functions [7]. A new method called

orrentropy was recently proposed by Santamaria et al. It computes

similarity index that combines the signal time structure and thetatistical distribution of signal amplitudes in a single function [8].his method is then used as a measure for nonlinearity test [5].

∗ Corresponding author. Tel.: +33 3 44 23 44 23x4844.E-mail addresses: mahmoud.hassan@utc.fr (M. Hassan), jeremy@ru.is (J. Terrien),

atherine.marque@utc.fr (C. Marque), brynjar@ru.is (B. Karlsson).

350-4533/$ – see front matter © 2011 IPEM. Published by Elsevier Ltd. All rights reserveoi:10.1016/j.medengphy.2011.03.010

© 2011 IPEM. Published by Elsevier Ltd. All rights reserved.

A well-known way to test the performance of nonlinearitydetection methods is to use the surrogate technique. The method ofsurrogate data [6] provides a rigorous framework for nonlinearitytests, which main elements are the null hypothesis and a nonlin-earity measure. The most commonly used null hypothesis statesthat the examined time series is generated by a linear Gaussianstochastic process collected through a static nonlinear measure-ment function. Thus, properly designed surrogate data should havethe same linear properties (autocorrelation and amplitude distribu-tion) as the original signal, and be otherwise random. The generatedsurrogate data are compared to the original data under a discrim-inating nonlinear measure. We test if the value of the measure forthe original time series is likely to be drawn from the distributionof values of the surrogates within a confidence level. If the measuregives comparatively different values for the original series, the nullhypothesis is rejected and the original series is considered to benonlinear.

Recently, much attention has been paid to the use of nonlin-ear analysis techniques for the characterization of biological signal(i.e. EEG data [9–11]). Few nonlinear analysis methods have beenapplied to uterine electromyogram, also called electrohysterogram(EHG). Most of them are only descriptive and aim at demonstratingthe presence of nonlinear characteristics in EHG signal, not at classi-

fying pregnancy/labor signals for labor prediction. We can cite herethe use of approximate entropy [12] to detect nonlinearity in uter-ine activity signals, the use of fractal dimension to analyze uterinecontractions [13] and the comparison between linear (peak andmedian frequency, etc.) and nonlinear methods (Lyapunov expo-

d.

eering & Physics 33 (2011) 980– 986 981

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M. Hassan et al. / Medical Engin

ent, sample entropy and correlation dimension) to separate EHGecords of term and pre-term delivery groups [14]. The questionhat arises here is what is the most appropriate method? Andhich one could best respect the different signals characteristics

or example nonstationarity.In this paper we present a comparison between three methods

argely used for nonlinearity detection: (i) time reversibility (Tr),ii) approximate entropy (ApEn) and (iii) correntropy (CorrEn). Weomputed the false alarm rate (FAR) with the number of surrogatesn different types of signals (linear, nonlinear stationary and non-inear nonstationary), in order to evaluate the efficiency of each

ethod in the detection of nonlinearity characteristics. Two of theethods, including the method with the lowest FAR, were then

pplied on real EHG signals during labor and pregnancy, in order tovaluate their possible use for labor prediction in women.

. Materials and methods

.1. Data

.1.1. Synthetic signalsTo compare approximate entropy, correntropy and time

eversibility, we used different types of synthetic signals: linearAR: autoregressive), nonlinear stationary (Rossler, Henon, logisticnd TAR: threshold autoregressive) and nonlinear nonstationaryARCH: autoregressive conditionally heteroscedastic). Table 1 sum-

arizes the signals equations and the parameters used for eachignal, while Fig. 1 shows an example for each signal. The numberf point is fixed at 1000 for all the signals.

.1.2. Real signalsThe real EHG signals used in this study are recorded on 7 women

uring pregnancy and 5 women during labor. The measurementsere performed by using a 16-channel multi-purpose physiolog-

cal signal recorder, most commonly used for investigating sleepisorders (Embla A10). We used reusable Ag/AgCl electrodes. Theeasurements were performed at the Landspitali University hos-

ital in Iceland, following a protocol approved by the relevantthical committee (VSN 02-0006-V2). As the methods used herere “monovariate” (i.e. processing only one signal) we used for thistudy only one bipolar channel, obtained by taking the difference ofignals from two successive electrodes located on the same verticalow of a 4 × 4 matrix located on the women’s abdomen. This chan-el is located on the median vertical axis of the uterus (see [15] for

ore details). The signal sampling rate was 200 Hz. The recording

evice has an anti-aliasing filter with a low pass cut-off frequency of00 Hz. The concurrent tocodynamometer (Toco) paper trace wasigitized in order to ease the identification of contractions. TheHG signals were segmented manually to extract segments con-

able 1inear Gaussian, linear non-Gaussian and nonlinear processes used to generate the synth

Label Model

AR(0.4,1) Xt = 0.4Xt−1 + εt

TAR(2;1,1) Xt = {Logistic xn+1 = 4xn − 0.8xn(1 −

Rossler

dx1

dt= −wxx2 − x3

dx2

dt= wxx1 + 0.15x

dx3

dt= 0.2 + x3(x1 −

Henon x(n + 1) = 1.4 − x2(n)

ARCHXt = εt

√ht with

ht = 0.000019 + 0.

R: autoregressive; TAR: threshold autoregressive; Rossler: Rossler dynamic systems; HenS: linear stationary; NLS: nonlinear stationary; NLNS: nonlinear nonstationary.

Fig. 1. Examples of the synthetics signals used. From top to bottom: autoregressive(AR), logistic map, threshold autoregressive (TAR), Rossler, Henon, and ARCH.

taining uterine activity bursts. After the segmentation we got 30pregnancy bursts and 30 labor bursts. Electrodes placement andtypical example of pregnancy and labor bursts are illustrated inFig. 2.

2.2. Nonlinearity detection methods

2.2.1. Time reversibilityTime reversibility causes observed time series to look ‘differ-

ent’ when viewed in forward and reverse time (imagine playingan audio tape backwards). Reversible time series ‘look similar’ (e.g.have similar dynamic flows) when viewed both in forward (natural)time or reverse time. Linear Gaussian random processes (LGRP) arereversible. Verification of irreversibility for observed data excludesthese types of process as possible models. Irreversibility is a ‘symp-tom’ of nonlinearity [16].

A time series is said to be reversible if and only if its proba-bilistic properties are invariant with respect to time reversal. In[17], the authors proposed a test for the null hypothesis to indi-cate that a time series is reversible. Rejection of the null hypothesisimplies that the time series cannot be described by a linear Gaus-

sian random process, so time irreversibility can be taken as a strongsignature of nonlinearity [6]. One of the simplest ways to measuretime asymmetry is by taking the first differences of the series tosome power. In this paper we used this simple way to compute

etic signals.

Type

LSNLS

xn) NLS

2

10)

where wx = 0.95 NLS

+ bxx(n − 1) where bx = 0.3 NLS

846{

X2t−1 + 0.3X2

t−2 + 0.2X2t−3 + 0.1X2

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} NLNS

on: Henon dynamic systems; ARCH: autoregressive conditionally heteroscedastic;

982 M. Hassan et al. / Medical Engineering & Physics 33 (2011) 980– 986

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ig. 2. (A) Electrode’s placement on the woman’s abdomen, (B) monopolar configurnd labor bursts, respectively, both from BP7 located on the median axis of the uter

ime reversibility for signal S, described in [6] as:

r(�) = 1N − �

N∑n=�+1

(Sn − Sn−�)3 (1)

here N is the signal length. In this paper we used � = 1 which is aommon choice for �.

Time reversibility has been applied on different physiologicalignals such as the investigation of the nonlinear characteristics ofhe EEG signals during epilepsy [18] and during sleep in children19].

.2.2. CorrentropyCorrentropy is a similarity measure of signals, mapped nonlin-

arly into a feature space [8]. In essence, correntropy generalizeshe autocorrelation function to nonlinear spaces: if

{xt, t ∈ T

}is a

trict stationary stochastic process within an index set T, then theutocorrelation and correntropy functions are defined respectivelys:

R(s, t) = E {〈xs, xt〉}V(s, t) = E

{⟨�(xs), �(xt)

⟩} (2)

here � is a nonlinear mapping from the input space to the featurepace [8]. Correntropy makes use of the “kernel trick” which defineshe inner product of the nonlinear mappings as a positive-definite

ercer kernel [20]:

(xs, xt) =⟨

�(xs), �(xt)⟩

(3)

A widely used Mercer kernel is the Gaussian kernel given by

(xs, xt) = 1√2˘�2

exp

(−‖xs, xt‖2

2�2

)(4)

and the corresponding bipolar signals BPi (C) and (D) typical example of pregnancy

where � is the size of the kernel. Using a Taylor series expansionfor the Gaussian kernel, it can be shown that the information pro-vided by the autocorrelation is included within the correntropy bysubstituting n = 1 in the expansion [8]:

V(s, t) =∞∑

n=0

(−1)n

2n�2nn!E‖xs − xt‖2n (5)

The two functions have many properties in common: both aresymmetric with respect to the origin, and take on their maximumvalue at zero lag. Moreover, it can be observed that for n > 1, corren-tropy involves higher order even moments of the term ‖xs − xt‖ andexhibits other important properties that autocorrelation functiondoes not possess.

Fourier transforms of statistical measures yield major functionsemployed in spectral analysis. Examples of such prominent Fouriertransform pairs are the autocorrelation and power spectral den-sity functions and bicorrelation. In Principe and coworkers [8] theFourier transform of correntropy was introduced as the generalizedpower spectral density and named correntropy spectral density(CSD). Its expression is given as follows:

Pv[w] =∞∑

m=−∞V [m]e−jwm (6)

It retains many properties of the conventional power spec-tral density. In this study, the bandwidth of the kernel is selectedaccording to Silverman’s rule of thumb [21] defined as:

� = 0.9AN−1/5 (7)

where N is the data length and A stands for the minimum of theempirical standard deviation of data; the data interquartile rangeis scaled by 1.34 as defined in Silverman’s rule.

eering

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M. Hassan et al. / Medical Engin

The critical value computed by the Kolmogorov–Smirnoff testas set at 1.36 corresponding to a significance level of 95%.

.2.3. Approximate entropyApproximate entropy (ApEn) first proposed by Pincus [22], is a

easure that quantifies the regularity and predictability of signals.pEn value is low for regular time series and high for complex,

rregular ones. The first step in computing ApEn for a given timeeries, yi, i = 1. N is to construct the state vectors in the embeddingpace, Rm, by using the method of delays,

i ={

yi, yi+�, yi+2�, . . . , yi+(m−1)�

}1 ≤ i ≤ N − (m − 1)� (8)

here m and � are the embedding dimension and time delay,espectively. Then we define the correlation sum Cm

i(r) by:

mi (r) = 1

N − (m − 1)�

∑j=1

�(r − d(x(i), x(j))) (9)

here �(x) = 1 for x > 0, �(x) = 0, otherwise, is the standard heavyide function; r is the vector comparison distance and d(x(i),x(j)) is

distance measure defined by:

(x(i), x(j)) = maxk=1,2,...,m

(∣∣y(i + (k − 1)�) − y(j + (k − 1)�)

∣∣) (10)

ApEn is given by the formula:

pEn(m, r, �, N) = ˚m(r) − ˚m+1(r) (11)

here

m(r) = 1N − (m − 1)�

N−(m−1)�∑i=1

log Cmi (r) (12)

In this paper, we used the “differential entropy based method”23] to compute the optimal m and � values. We define the fil-er parameter r as r = 0.2SD which is a common choice of r, whereD is the standard deviation of the signal. For the real signals, webtain m = 2 and � = 6 as optimal values computed on set of uterineursts.

.3. Comparison of the three methods

The statistical significance of the results of the three meth-ds: approximate entropy (ApEn) correntropy (CorrEn) and timeeversibility (Tr) was tested by using surrogates. Surrogate data areime series that are generated in order to keep particular statisticalharacteristics of an original time series while destroying all oth-rs. The method of surrogate data is a popular tool for testing a nullypothesis on a time series against its temporally random realiza-ions through a discriminating measure. In nonlinearity literature,ne widely used null hypothesis is that the examined time seriess generated by a Gaussian linear stochastic process [6]. The orig-nal time series and its surrogates obtained by this method sharehe same power spectrum, and therefore the same autocorrelationunction. However, any underlying nonlinear dynamic structureithin the original data is altered by phase randomization. In thisork, we used the iterative amplitude adjusted Fourier transform

IAAFT) method [6].In the case of CorrEn the original and surrogates values are com-

ared to a reference value to reject or accept the hypothesis. We usehe nonlinearity test for CorrEn with surrogates data described in5]. For ApEn and Tr the acceptance and the rejection of the hypoth-

sis is based on the difference between original and surrogatesalues. The nonlinearity test for time reversibility for example isefined as follows:

When a time series has significant nonlinearity, the value ofr for the surrogate data (Trsurr) will be different than the one of

& Physics 33 (2011) 980– 986 983

the original time series (Trorg). Thus, nonlinearity can be tested bycomparing the Trorg and Trsurr. The underlying null hypothesis isthat, like the surrogate data, the original data was also created bya Gaussian linear stochastic process. The null hypothesis is testedby comparing the Trsurr and Trorg by using a statistical test. If thenull hypothesis is rejected, it is concluded that the original data hasnonlinear properties; whereas if the null hypothesis is accepted, itis concluded that the original data comes from a Gaussian linearstochastic process.

The “Rank test” is used to reject or accept the null hypothe-sis. Basically [Trorg; Trsurr] is sorted in increasing order and therank index for Trorg is returned. With a number of surrogates(n surr = 100 for example), if this rank is >95 and <5 (significancelevel of 95%), this means that it lies in the tail of the distribution,and that the null hypothesis can be rejected (two-tailed test) witha significance of p = 2(1/(n surr + 1)) = 0.019.

The test used for ApEn is essentially the same.

2.4. Statistical parameters

In order to evaluate the possible use of the more relevantmethod for the prediction of labor in women, we used the clas-sical receiver operating characteristic (ROC) curves. A ROC curveis a graphical tool permitting to evaluate a binary, i.e. two classes,classifier. A ROC curve is the curve corresponding to TPR (true posi-tive rate or sensitivity) vs. FPR (false positive rate or 1 − specificity)obtained for different parameter thresholds. ROC curves are classi-cally compared by mean of the area under the curve (AUC) and theaccuracy (ACC).

The AUC was estimated by the trapezoidal integration method.While the ACC is defined as:

ACC = (TP + FN)(TP + TN)(FP + TN)TP(FP + TN) + FP(TP + FN)

(13)

where TP, TN, FP and FN stand respectively for true positive, truenegative, false positive and false negative values. We additionallyused the Matthew’s correlation coefficient (MCC) defined as:

MCC = TP × TN − FP × FN√(TN + FN)(TN + FP)(TP + FN)(TP + FP)

(14)

In order to measure quantitatively the difference between theoriginal data and the surrogates, we compute the z score valuedefined as:

z =∣∣Sorg −

⟨Ssurr

⟩∣∣�surr

(15)

where Sorg denotes the value of the discriminating statistics for theoriginal data set. If Ssurr denotes the values of S for the realizationsof the surrogate time series, Ssurr is the Ssurr mean and �surr is theSsurr standard deviation.

It is important to notice here that the z score is used here fortwo aims: the first one is to test the significance of the nonlinearityof the signals, and the second aim is to use z score as a parameterto differentiate between pregnancy and labor contractions whencomputing the ROC curves. For statistical comparison, we used thetwo tailed sign test.

3. Results

3.1. On synthetic signals

We computed the false alarm rate (FAR) of approximate entropy,correntropy and time reversibility with different surrogate num-bers on different signals types: linear, nonlinear stationary andnonlinear nonstationary signals. Our first objective was to choosethe optimal number of surrogates. Our second objective was

984 M. Hassan et al. / Medical Engineering & Physics 33 (2011) 980– 986

100 200 300 400 500 600 700 800 900 10000

10

20

30

40

50

60

70

80

90

100

Number of surrogates

Fa

lse

Ala

rme

Ra

te (

%)

Approximate Entropy

AR

Rossler

Hen on

TAR

Logistic

ARCH

100 200 300 400 500 600 700 800 900 10000

10

20

30

40

50

60

70

80

90

100

Number of surrogates

Fa

lse

Ala

rme

Ra

te (

%)

CorrEntropy

AR

Rossler

Hen on

TAR

Logistic

ARCH

B

A

100 200 300 400 500 600 700 800 900 1000

0

10

20

30

40

50

60

70

80

90

100

Number of surrogates

Fa

lse

Ala

rme

Ra

te (

%)

Time Reversibility

AR

Ross ler

Heno n

TAR

Logistic

ARCH

C

FT

tEegssitnFmnalT

0 20 40 60 80 100 120-0.5

0

0.5Labo r burst

-0.5

0

0.5Correspo nding surrog ate

Am

plit

ud

e

with a probability of 95%. The null hypothesis cannot be rejectedwhen z score <1.96.

ig. 3. Evolution of FAR with the number of surrogates for ApEn (A), CorrEn (B) andr (C).

o choose the method with the lowest FAR to apply it on realHG signals for labor prediction purposes. In Fig. 3 we show thevolution of FAR with the number of surrogates on AR (autore-ressive), TAR (threshold autoregressive), Rossler, Henon dynamicystems and ARCH (autoregressive conditionally heteroscedastic)ignals. Fig. 3A indicates that ApEn correctly detects nonlinearityn Rossler, Henon, logistic and ARCH signals. ApEn totally failed inhe nonlinearity detection of TAR signal (FAR = 70% with surrogatesumber = 100) and gives high FAR with the linear signal AR (25%).ig. 3B indicates that the correntropy method provides good perfor-ance with the linear signal (AR), whereas it is less efficient with

onlinear signals as it totally failed with the TAR signal (100% FAR)

nd gave 30% FAR with Rossler signals. Fig. 3C shows that all theinear and nonlinear signals are almost perfectly classified by usingr with all our synthetic signals.

0 20 40 60 80 100 120

Time(s)

Fig. 4. The original labor EMG burst (top) and corresponding surrogate (bottom).

3.2. On real EHG signals

The results presented above allowed us to choose the timereversibility method to use on the EHG signals, due to its powerto detect linearity and nonlinearity characteristics for differentsignals type. For a significance requirement of 95%, we needat least 39 surrogate time series for two-sided tests [6]. Asthe results of Fig. 3 did not show high FAR with all the sur-rogate‘s number, we decide to use 100 surrogates time seriesto boost the confidence with average uterine bursts lengthused about 24,000 samples (120 s). The aim then is to testthe ability of time reversibility to differentiate between sig-nals recorded during pregnancy and signals recorded duringlabor.

Fig. 4 presents an example of surrogate signal generated fromlabor burst by using the IAAFT method.

3.2.1. Burst segmentation effectAs the signals are segmented manually to extract the uterine

bursts, it may be possible that the bursts contain baseline (noise). Inorder to investigate the influence of the baseline on the results, wecomputed the distribution of Trsurr and Trorg on labor signals withbaseline (Fig. 5 left) and on the same bursts but without baseline(Fig. 6 left). The results indicated that the labor burst plus base-line signal provide significant difference (null hypothesis rejected)between original and surrogates data. The same labor burst with nobaseline signal also presents a significant difference. Furthermorethe results of the same test performed on pregnancy contrac-tions (Fig. 5 right) indicates that the difference between originaland surrogates data is not significant (null hypothesis accepted).The same conclusion was obtained on the signal without baseline(Fig. 6 right). These results clearly demonstrate that the linearityobserved for pregnancy bursts and the nonlinearity for labor onesare related to the uterine activity bursts and not to the presence orthe influence of baseline (noise). It permitted us to conclude thata very precise segmentation is not necessary when applying timereversibility to these signals.

3.2.2. Classification pregnancy/laborThe associated null hypothesis will be rejected with 95% level

for z score ≥1.96. That is to say, the original time series is nonlinear

The results presented in Fig. 7 show that the median value of zscore for labor signals is >1.96 and the median value of z score forpregnancy signals is <1.96. This indicates that generally the signals

M. Hassan et al. / Medical Engineering & Physics 33 (2011) 980– 986 985

0 20 40 60 80 100 120-0.5

0

0.5

Time(s)A

mp

litu

de

0 10 20 30 40 50 60 70 80 90 100-5

0

5

10

15x 10

-9

Surrogate number

Tr

Trsurr

Trorg

0 20 40 60 80 100 120-0.2

-0.1

0

0.1

0.2

Time(s)

Am

plit

ud

e

0 10 20 30 40 50 60 70 80 90 100-1

0

1

2x 10

-10

Surrogate number

Tr

Trsurr

Trorg

Fig. 5. (Top) uterine burst + baseline. (Bottom): the distribution of Trsurr and Trorg during pregnancy (right) and labor (left). The vertical lines present the start and the end ofthe uterine segmented bursts without baseline as presented in this figure. The * are the Trsurr values and the dashed lines represent the Trorg.

0 5 10 15 20 25 30-0.5

0

0.5

Time(s)

Am

plit

ud

e

0 10 20 30 40 50 60 70 80 90 100-5

0

5

10x 10

-8

Tr

Trsurr

Trorg

0 5 10 15 20 25 30 35 40 45-0.2

-0.1

0

0.1

0.2

Time(s)

Am

plit

ud

e

0 10 20 30 40 50 60 70 80 90 100-4

-2

0

2

4x 10

-10

Tr

Trsurr

Trorg

F t conta Trorg.

rdf(

Fni

3.2.3. Labor prediction

Surrogate number

ig. 6. (Top): same bursts as used in Fig. 4 but segmented in a way that they do nond labor (left). The * represent the Trsurr values and the dashed lines represent the

ecorded during pregnancy are reversible and the signals recorded

uring labor are irreversible. There is a significant (p = 0.0001) dif-erence between median values of z scores for the pregnancy burstsmedian = 0.702) and for the labor bursts (median = 3.97).

0

2

4

6

8

10

12

LaborPregnancy

z s

co

re

ig. 7. Difference between median of z scores computed for Tr for the 30 preg-ancy bursts and the 30 labor bursts. The difference between the two distributions

s significant (p = 0.0001).

Surrogate number

ain any baseline. (Bottom): distribution of Trsurr and Trorg during pregnancy (right)

Fig. 8 shows the ROC curve from the time reversibility meth-ods using the z score as the discriminant parameter. As we cansee also from the ROC curve, time reversibility permits us to distin-

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

FPR or (1- Specificity)

TP

R o

r S

en

sitiv

ity

Time reversibili ty

Fig. 8. ROC curves obtained with the z score values for differentiating betweenpregnancy and labor bursts.

986 M. Hassan et al. / Medical Engineering

Table 2Parameter of the ROC curves obtained with different parameters.

Specificity Sensitivity MCC AUC ACC (%)

MPF 0.5 0.8 0.32 0.63 65.66

M

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4

odsnnwdo

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ApEn 0.8 0.52 0.33 0.64 65.8Tr 0.96 0.93 0.9 0.99 95

PF: mean power frequency; ApEn: approximate entropy; Tr: time reversibility.

uish clearly between signals recorded during pregnancy and labor.able 2 presents the ROC curve parameter comparison betweenpEn, Tr and a well-known linear method used in the literature

mean power frequency (MPF)). We observed that MPF has a highensitivity (0.8) and low specificity (0.5) while it is the oppositeor ApEn with low sensitivity (0.52) and high specificity (0.8). Timeeversibility has a high sensitivity (0.93) and high specificity (0.96).he probability of correctly classifying labor increases markedlyrom 0.63 AUC with mean power frequency to 0.99 with timeeversibility.

. Discussion and conclusion

In this paper a comparison between three nonlinear meth-ds (approximate entropy, correntropy and time reversibility) wasone on linear, nonlinear stationary and nonlinear nonstationaryignals in order to choose the best method to apply on real EHG sig-als. Indeed these signals are thought to exhibit nonlinear as well asonstationary characteristics. The evolution of FAR of each methodas computed with different surrogate numbers. The comparisonemonstrated the superiority of time reversibility in the detectionf linearity and nonlinearity of the different signals.

We tested EHG signals for their time reversibility property. Theesults indicate that uterine contractions during pregnancy areeversible, whereas labor contractions are temporally irreversible.

e showed how the time reversibility could be a powerful tool toifferentiate between pregnancy and labor contractions.

It should be pointed out that this nonlinearity measure, just likether statistical nonlinearity measures, is based on the comparisonith surrogate data. It is not a standalone measure needing the

eneration of surrogates. Therefore, the measure would fail if theeneration of proper surrogates fails.

We notice here that in our paper we did not take into accounthe Gaussianity/non-Gaussianity of the tested data set. Since non-aussianity is a characteristic common to both pregnancy and laborignals, we assume that it has no influence on the comparisonesults.

Furthermore, the choice of the time reversibility parameter isade empirically, in order to obtain the best results on the syn-

hetic signals and for the classification of pregnancy and laborignals. We think that it will be important to investigate morelosely the influence of this parameter on the detection of linearitynd nonlinearity for the different synthetic signals.

The results on the real data suggest that the property of timerreversibility is a strong characteristic for contraction measured on

omen in labor. This suggests that, for a more complete characteri-ation of such recordings, additional nonlinear analysis techniques

hould be applied.

Finally, the results provide a very powerful method for differen-iating between pregnancy and labor contractions. Although evenf we need to confirm this on more data, we think that the timeeversibility characteristic may help in detecting contractions lead-

[[

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& Physics 33 (2011) 980– 986

ing to term or preterm labor. Ultimately, these findings may havea considerable relevance in helping to prevent preterm labor.

Acknowledgments

This project is financed by the Icelandic centre for researchRANNÍS and the French National Center for University and School(CNOUS). The authors would like to especially thank Mr. ÁsgeirAlexandersson for his help in the acquisition of EHG signals.

Conflict of interest

There is no conflict of interest.

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