NON-LINEAR ANALYSIS OF FETAL HEART RATE

IN CARDIOTOCOGRAPHY USING SAMPLE ENTROPY

J. A. L. Marques,

P. C. Cortez,

J. P. V. Madeiro

and F. S. Schlindwein

Department of Informatics, University Lusiada of Angola, 1

of December St., Lobito, Angola

Department of Engineering of Teleinformatics, Federal University of Ceará, Fortaleza, Brazil

Department of Engineering, University of Leicester, Leicester, United Kingdom

Keywords: Fetal Heart Rate, Sample Entropy, Nonlinear Analysis.

Abstract: The complex system of mother and foetus interacting during pregnancy contains both dependent and

independent subsystems and it is unlikely that it can be studied using only linear techniques. Considering

this, the conventional medical analysis of Fetal Heart Rate (FHR) based on Cardiotocography (CTG) traces

can be expanded considering nonlinear approaches. This work presents the use of Sample Entropy

(SampEn) as a measure of system complexity, using a 5 minutes window of FHR signal (1200 samples),

using values for parameters m and r based on literature to analyse the signal complexity behaviour in time.

The database is comprised of 22 pre-classified intrapartum exams, expected to have a high degree of time

domain dynamics. The analysis shows that severe FHR decelerations result in small values of SampEn,

reflecting a low level of complexity. On the other hand, a set of high level transient FHR accelerations also

causes the same effect. The occurrences of repetitive patterns (similar to sinusoidal waves, which are

pathological) cause a drop of SampEn values. The results encourage us to consider SampEn as one viable

parameter for nonlinear FHR signal analysis.

1 INTRODUCTION

The CTG examination is the simultaneous and

continuous recording of the FHR, fetal movements

and uterine contractions. The analysis of these

signals can help diagnose a large set of fetal diseases

or health problems (Ingemarsson, Ingemarsson, &

Spencer, 1993).

A partial CTG trace with FHR and the uterine

tonus monitoring is shown in Figure 1. The

occurrence of uterine contractions usually indicates

the intrapartum period. The diagnostic based on

these two signals provides early detection of fetal

health problems.

The fetal heart rate and the interval between the

beats change periodically and non-periodically in

time and this variability is normally considered as a

health indicator.

The fetal cardiac rhythm is influenced by many

different subsystems, such as the heart, brain and

neural system development, fetal oxygen supply and

also the maternal conditions (such as fever or high

blood pressure). This complex scenario suggests the

presence of nonlinear behaviour and characteristics

in FHR.

Figure 1: FHR and uterine contractions signals in a CTG.

According to Savi, from the point of view of

mathematical modelling, the description of

biological phenomena could be more realistically

modelled with nonlinear analysis rather than with

linear analysis. Surrogate data obtained from the

244

A. L. Marques J., Cortez P., Madeiro J. and Schlindwein F..

NON-LINEAR ANALYSIS OF FETAL HEART RATE IN CARDIOTOCOGRAPHY USING SAMPLE ENTROPY.

DOI: 10.5220/0003776502440248

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2012), pages 244-248

ISBN: 978-989-8425-89-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

analyzed time series can be used to present

evidences of nonlinear components in the signal

(Kantz & Schreiber, 1997).

Nonlinear approaches to calculate biological

time series complexity can be obtained using

nonlinear entropy measures such as Approximate

Entropy (Pincus, 1991); Lempel-Ziv complexity

(Doganaksoy & Göloglu, 2009) and Sample Entropy

(Richman & Moorman, 2000).

The Sample Entropy is a metric based on

Approximate Entropy that has been already applied

to evaluate the complexity in cardiovascular time

series (Richman & Moorman, 2000).

This work presents a nonlinear analysis of FHR,

which is the most significant signal monitored in a

CTG, based on Sample Entropy (SampEn)

behaviour in time.

2 MATERIALS AND METHODS

2.1 Sample Entropy

The SampEn of a time series is the negative natural

logarithm of the probability that two similar

sequences of m points remain similar at the next

point. The polarization of self-matches is not

considered. Low values of SampEn indicate lower

complexity and more regularity in the time series.

For a better understanding of these definitions as

a measure of system complexity, the mathematical

foundations of its calculation is provided.

Given S

as a time series with N samples S

= {S

2, ….,

} the first step to calculate SampEn(S

,m,r),

is the determination of two input parameters m and

r, where m is the length of a subset of S

and r is the

similarity criteria. Consider also that p

(i) is the

subsequence or pattern of S

beginning in sample i

and with m samples of length.

Consider two patterns p

(i) and p

(j), beginning,

at index i and j respectively. These patterns can be

considered similar if the scalar distance between

them, i.e., the module of the difference between

sample pairs is less than r. (1).

rSS

kjki

<−

(1)

for 0 < k < m.

Consider P

as the set of all patterns from S

with length m. The relation C

i,m

(r)

can now be

defined (2).

)(

+−

(2)

where n

i,m

(r) is the number of patterns similar to

(i) in P

. The parameter C

(r) must be calculated

as the average of all C

i,m

(r) for the entire P

set.

Finally, SampEn(S

,m,r) can be found (3).

)(

ln),,(

rmSSampEn

(3)

2.2 Development Environment

and CTG Database

The development environment was based on the

Matlab software, version 7.6.0.324 R2008a

(Mathworks, 2009).

The results were obtained using a database from

Trium GmBH, a project partner from Munich,

Germany. This database was labelled as the CTG-I

and contains 22 intrapartum exams (during labour

and delivery), all classified by medical staff.

This database was chosen because of the high

level of dynamics found during labour, especially

when the influence of uterine contractions can be

found in FHR signals.

2.3 Entropy Calculation Parameters

Sample entropy can be calculated for the whole FHR

signal, providing a long term index or, alternatively,

windows of samples can be used for short term

nonlinear characteristics evaluation.

Data were submitted to many tests with different

Δt

window sizes and also changing m and r

parameters.

In this paper, the FHR signal entropy

calculations consider a subset of 1200

samples,

which represents a 5 minute-long window. The aim

is the monitoring of the signal entropy based on its

time evolution. For example, the entropy behaviour

during pathological FHR events, such as prolonged

decelerations, could be a predictive tool for

electronic fetal monitoring.

The SampEn input parameters used were m=5

and r=0.2σ[FHR(t)], where FHR(t) is the FHR

signal and σ[FHR(t)] is the standard deviation of the

time series (Kaplan & Staffin, 2008).

3 RESULTS AND DISCUSSION

In this section, the general results obtained with the

CTG-I database are presented with some illustrative

examples of high and low values of SampEn and the

correspondent visualization of FHR trace in time.

NON-LINEAR ANALYSIS OF FETAL HEART RATE IN CARDIOTOCOGRAPHY USING SAMPLE ENTROPY

245

Several physiological changes occur in the

perinatal period and fetal signals are expected to

have high dynamics, hence, high values of entropy

are usually expected in these time series. The

presence of low values should be investigated.

The FHR and SampEn(FHR,m,r) plots for the

ctg20040215-0803261 examination are presented on

Figure 2. Notice that the SampEn is calculated only

for the specified windows of 1200 samples.

Figure 2: Exam ctg20040215-0803261 (a) FHR plot and

(b) SampEn calculation using the specified window.

As mentioned before, for a more clear

interpretation of the entropy behaviour, some

specific time intervals are analysed.

The first analysis is a zoom at the 18<Δt

<24

interval, where we can find high values of sample

entropy. In a closer look of the FHR signal in Figure

3, one can see that there are many oscillations.

Figure 3: Extracted trace from ctg20040215-0803261

exam with high values of SampEn.

During the same exam, right after the trace

shown in Figure 3, during the interval 25<Δt

<29,

we can find low values of SampEn, even when the

trace apparently shows that the signal is oscillating

and high values of sample entropy could be

expected. The reason for that can be seen in Figure

4. Actually, the signal complexity decreases because

the trace shows a periodic repetitive pattern

identified by the region S1. A sinusoidal behaviour

of FHR is considered as pathological in visual CTG

classification (Ingemarsson, Ingemarsson, &

Spencer, 1993). This encouraged us to consider low

values of SampEn as a possible index to predict fetal

health problems.

Figure 4: Trace extracted from ctg20040215-0803261

exam with low values of SampEn (repetitive pattern).

Figure 5: Exam ctg20011218-2348371 (a) FHR with low

variability and a drop of the baseline and (b) decreasing

SampEn values .

The ctg20011218-2348371 exam presented in

Figure 5 was previously classified as pathological,

with low values of short-term variability and also

because of the FHR baseline behaviour (Marques,

Cortez, & Madeiro, 2010). At the beginning there

can be seen a tachycardia, followed by the decrease

of the signal baseline. The SampEn trace shows high

BIOSIGNALS 2012 - International Conference on Bio-inspired Systems and Signal Processing

246

values at the beginning also followed by low values,

remaining at this level until the end of the

examination.

In the next analysis, the FHR sample entropy can

be used to indicate transient changes in the time

series. The ctg20040214-0722052 exam contains

severe FHR decelerations, correspondingly to very

low values of SampEn. For example, for the interval

36<Δt

<40, the entropy remains in the same level

until the original signal returns to its baseline, as can

be seen in Figure 6.

Figure 6: Exam ctg20040214-0722052 (a) FHR with

severe decelerations and (b) low values of SampEn.

On the other hand, during the ctg20020124-

1015523 examination, a set of transient accelerations

of FHR can be found. These changes and the

repetitive pattern presnt also result in low values of

entropy. For example, during the interval 5<Δt

<12,

the calculated sample entropy is very low, as shown

in Figure 7.

The results presented here as a set of examples of

FHR complexity in time were found on the entire set

of the CTG-I database.

As can be seen, the sample entropy does not

require a slow converging process, acting as a fast

technique for detecting changes in FHR, for the

considered set of windows.

For this kind of analysis, some complementary

information, such as fetal HRV low and high

frequency parameters, short-term and long-term

variability and other nonlinear measures could be

very useful for automatic or even visual analysis of

CTG traces.

Figure 7: Exam ctg20020124-1015523 (a) FHR with

severe decelerations and (b) low values of SampEn.

Some physiological interpretations can be done

from the SampEn calculation. First of all, it can be

used as a normality indice of the FHR long term

variability which is an important neural development

estimator. Besides, low entropy values found in

severe FHR accelerations and decelerations can

provide a first level monitoring parameter for the

detection of fetal distress.

Finally, as mentioned before, low entropy values

may also indicate repetitive patterns around the FHR

baseline which are not classified as accelerations or

decelerations. These are usually suspicious or

pathological and are difficult to detect with the

visual inspection only.

NON-LINEAR ANALYSIS OF FETAL HEART RATE IN CARDIOTOCOGRAPHY USING SAMPLE ENTROPY

247

4 CONCLUSIONS

Nonlinear measures of biological time series such as

FHR are important tools to improve the conventional

medical analysis. This work suggests the use of the

Sample Entropy for 5 minutes windows datasets to

visualize this nonlinear metric evolving in time.

One of the main conclusions is that repetitive

patterns of FHR result on small values of SampEn.

This agrees with usual medical interpretation and

could detect pathological cases related to this

condition, since high values of SampEn are usually

expected for healthy fetuses.

In the same way, low short-term FHR variability

also results in low levels of entropy. Another

important result is that the presence of significant

transient changes in FHR, such as decelerations and

accelerations also caused SampEn to decrease.

We suggest that medical staff should consider

the use of FHR SampEn as a measure of system

complexity and a viable complementary tool to help

measure fetal health.

Nonlinear surrogate FHR analysis is going to be

presented in future works. Besides, other approaches

can be considered, such as Approximate Entropy

and Lempel-Ziv Complexity to compare the results.

ACKNOWLEDGEMENTS

Dr. Marques wishes to acknowledge Trium Analysis

Online GmBH, Munich, Germany and LESC

(Laboratório de Engenharia e Sistemas de

Computação) at UFC, Fortaleza, Brazil for their

support.

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Ingemarsson, I., Ingemarsson, E., & Spencer, J. A. (1993).

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Fetal Heart Rate Variability Analysis in

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