Extraction of fetal electrocardiogram using adaptive neuro-fuzzy inference systems.
ABSTRACT In this paper, we investigate the use of adaptive neuro-fuzzy inference systems (ANFIS) for fetal electrocardiogram (FECG) extraction from two ECG signals recorded at the thoracic and abdominal areas of the mother's skin. The thoracic ECG is assumed to be almost completely maternal (MECG) while the abdominal ECG is considered to be composite as it contains both the mother's and the fetus' ECG signals. The maternal component in the abdominal ECG signal is a nonlinearly transformed version of the MECG. We use an ANFIS network to identify this nonlinear relationship, and to align the MECG signal with the maternal component in the abdominal ECG signal. Thus, we extract the FECG component by subtracting the aligned version of the MECG signal from the abdominal ECG signal. We validate our technique on both real and synthetic ECG signals. Our results demonstrate the effectiveness of the proposed technique in extracting the FECG component from abdominal signals of very low maternal to fetal signal-to-noise ratios. The results also show that the technique is capable of extracting the FECG even when it is totally embedded within the maternal QRS complex.
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ABSTRACT: Various areas of research need to be considered in order to establish a mathematical model of a vehicle crash. To enhance the modeling process, a novel ANFIS-based approach to reconstruct behavior of impacting vehicles is presented in this paper. Kinematics of center of gravity (COG) a vehicle involved in an oblique barrier collision is reproduced by application of a five-layered ANFIS structure. Then, the same ANFIS system is used to simulate a different collision type than the one which was used in the training stage. The points of interests are selected to be the locations of accelerometers mounting. The accuracy of the proposed method is evaluated by the comparative analysis with the reference measurements from full-scale vehicle collisions.Mechatronics (ICM), 2013 IEEE International Conference on; 01/2013 - SourceAvailable from: Ali Esmaeili[Show abstract] [Hide abstract]
ABSTRACT: In this re search, a numerical procedure is used to solve the Navier -Stokes equation on a submerge hydrofoil and the estimation of hydrofoil performance is don e by an Adaptive Neuro -Fuzzy Inference System (ANFIS) model. A pressure-based implicit technique and a non-orthogonal mesh with collocated ﬁnite volume formulation are used to simulate ﬂow around the hydrofoil. The procedure incorporates the k-�e eddy viscosity turbulence model and a Volume of Fluid (VOF) process has been utilized to simulate two-phase ﬂuid (water and air ). In the mentioned met hod, the analyses of thickness and camber effect of hydrofoil, submerge distance (h / c ), and the angle of at tack (AOA) make an impression on the hydrofoil performance. To verify the numerical simulation, a part of the presented results is compared with the published experimental data. This comparison conﬁrms the numerical process. Moreover, the hydrofoil conﬁguration and operating condition are assessed by ANFIS model . Consequently, the results prove that t he ANFIS model can predicate t he hydrofoil performance very well. - SourceAvailable from: Ali Esmaeili[Show abstract] [Hide abstract]
ABSTRACT: In this research, optimization of shape and operating conditions of a submerged hydrofoil is investigated by a heuristic optimization approach, been a combination of an adaptive network based fuzzy inference system model (ANFIS) and particle swarm optimization (PSO). The constrained discrete variables such as the thickness and camber of hydrofoil, angle of attack and submerge distance are clearly defined as design variables and the lift to drag ratio is selected as a nonlinear objective function, which is extracted from an accurate numerical procedure. The Navier–Stocks equation is numerically solved, and volume of fluid (VOF) method has been utilized to simulate two-phase fluid (water and air). The results demonstrate that the resulted body of the hydrofoil in the optimum operating conditions should reach a maximum value of lift to drag ratio.Ocean Engineering 10/2014; 92(1):55-63. · 1.16 Impact Factor
Page 1
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 1, JANUARY 200759
Extraction of Fetal Electrocardiogram Using
Adaptive Neuro-Fuzzy Inference Systems
Khaled Assaleh, Senior Member, IEEE
Abstract—In this paper, we investigate the use of adaptive
neuro-fuzzy inference systems (ANFIS) for fetal electrocardio-
gram (FECG) extraction from two ECG signals recorded at the
thoracic and abdominal areas of the mother’s skin. The thoracic
ECG is assumed to be almost completely maternal (MECG) while
the abdominal ECG is considered to be composite as it contains
both the mother’s and the fetus’ ECG signals. The maternal com-
ponent in the abdominal ECG signal is a nonlinearly transformed
version of the MECG. We use an ANFIS network to identify
this nonlinear relationship, and to align the MECG signal with
the maternal component in the abdominal ECG signal. Thus, we
extract the FECG component by subtracting the aligned version
of the MECG signal from the abdominal ECG signal. We validate
our technique on both real and synthetic ECG signals. Our re-
sults demonstrate the effectiveness of the proposed technique in
extracting the FECG component from abdominal signals of very
low maternal to fetal signal-to-noise ratios. The results also show
that the technique is capable of extracting the FECG even when it
is totally embedded within the maternal QRS complex.
Index Terms—Adaptive neuro-fuzzy inference systems, fetal
ECG, nonlinear transformation, signal alignment.
I. INTRODUCTION
T
tion on the health status of the fetus and, therefore, an early
diagnosis of any cardiac defects before delivery increases the
effectiveness of the appropriate treatment [1]. There are several
technical problems associated with the noninvasive extraction
of FECG from ECG signals recorded at the abdominal surface.
These problems are mainly due to the low power of the FECG
signal which is contaminated by various sources of interfer-
ence. These sources include the maternal ECG, the maternal
electromyogram EMG, 50 Hz power line interference, baseline
wander and random electronic noise [2], [3]. Assuming that
we are using state of the art low noise electronic amplifiers
with high common mode rejection ratio, the effect of the 50
Hz interference and electronic random noise can be eliminated.
The EMG noise can also be reduced but not necessarily elim-
inated with the use of classical low pass filtering techniques.
Therefore, it is safe to say that if one is able to eliminate the
maternal ECG component in the composite signal, a reason-
able estimate of the FECG signal can be obtained. To further
HE fetal electrocardiogram (FECG) signal reflects the
electrical activity of the fetal heart. It contains informa-
Manuscript received June 5, 2005; revised June 8, 2006.
The author is with the department of Electrical Engineering, American Uni-
versity of Sharjah, P. O. Box 26666, UAE (e-mail: kassaleh@aus.edu).
Color versions of Figs. 2, 5, 11, and 12 are available online at http://
ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TBME.2006.883728
enhance this FECG estimate, especially its P and T waves,
one needs to apply postfiltering techniques. These techniques
include nonlinear filtering via wavelet denoising [4].
Many signal-processing-based techniques for FECG extrac-
tion have been introduced with varying degrees of success.
These techniques include adaptive filters [3], correlation tech-
niques [5], singular-value decomposition (SVD) [6], wavelet
transform [7], [8], neural networks [9], [10], and blind source
separation (BSS) [11], [12]. BSS via independent component
analysis (ICA) is considered among the most recent and most
successful methods used for FECG extraction [13]. However,
in order for ICA to work properly, it requires multiple leads for
collecting several ECG signals. Two leads, as we are proposing
in this work, are certainly not enough for satisfactory FECG
extraction via ICA. This is so because of the nonlinear re-
lationship between the thoracic ECG and the maternal ECG
component in the abdominal ECG signals. ICA assumes that
compositesignals (abdominal)are obtainedvialinearmixing of
the thoracic and fetal components and other interfering signals.
Other techniques [3], [7], [9] that can use two leads have their
limitations especially when the fetal beats overlap with the
QRS wave of the maternal beats. In other words, one can see
remnants of the maternal component in the extracted FECG
especially when the R wave of maternal and fetal QRS overlap.
Recently, we have proposed a new FECG extraction technique
based on polynomial networks [14] which showed encouraging
results on extracting FECG from two ECG recordings.
In this paper, we aim to apply ANFIS for estimating the
FECG component from one abdominal ECG recording and one
reference thoracic MECG signal. We use ANFIS to nonlinearly
align the thoracic MECG with the abdominal ECG signal. This
nonlinear alignment between the two signals allows for can-
celing the maternal component from the abdominal signal and
hence offers an estimate of the FECG signal. We show results
on both synthetic and real ECG data. We specifically show
some analysis and comparative results of the proposed method
and two other FECG extraction techniques: Normalized least
means squares (NLMS), and polynomial networks.
The paper is organized as follows: In Section II, we present
the formulation of the FECG extraction and demonstrate the
need for nonlinear mapping. Section III will briefly review the
theory of ANFIS. In Section IV, we describe our proposed so-
lution for FECG extraction using ANFIS. Section V describes
the ECG data used for testing the proposed algorithm. It also
describes the methodology for modeling nonlinearity in synthe-
sizing the abdominal ECG data. In Section VI, we demonstrate
the performance of the algorithm on both real and synthetic
ECG signals. Finally, conclusions are presented in Section VII.
0018-9294/$25.00 © 2007 IEEE
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60 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 1, JANUARY 2007
Fig. 1. Depiction of the problem formulation—we need to estimate ???? when
only ???? and ???? are known.
II. PROBLEM FORMULATION
Theproblemisformulatedasfollows.TwoLeadsareattached
to the body of a pregnant woman at the thoracic and abdominal
areas. The two leads are routed through the proper equipment
to provide two sampled ECG signals. These signals are denoted
as
and to correspond to the thoracic and abdominal
ECG signals respectively. Embedded in the abdominal signal,
, are three signals: One is a deformed version of
travels from the chest to the abdomen, another is the fetal ECG
and a third is additive noise from other sources. The problem is
pictorially depicted in Fig. 1.
The abdominal signal,
of a deformed version of the maternal ECG,
version of the fetal ECG,
such that
as it
, can be expressed as the sum
, and a noisy
(1)
(2)
(3)
ThedeformationofthematernalECGcomponentin
to the fact that the signal is measured far away from its source
(the mother’s heart), and consequently it encounters some non-
linear transformation as it travels to the abdominal area. The
problem becomes trivial if the transformation
if all what
encounters by traveling from the heart to the
abdominal areas was time delay and attenuation). In that case,
can be aligned with
can be extracted by simply subtracting the aligned
from . Similarly, the problem would be easily solved in
the frequency domain by spectral subtraction if the spectra of
and were nonoverlapping. Unfortunately, the trans-
formation between
and the maternal component in
, is highly nonlinear as shown in Fig. 2 where there is
both time warping and time varying scaling. Fig. 2 shows a
360-sample record of normalized
respondingnormalizedrecordof
signals sampled at rate of 500 samples/s. The data points in the
two diagonal ellipses in Fig. 2 indicate association between the
two signals, and hence, correspond to the maternal component
which is existent in both signals. However, the data points in
the horizontal ellipse in the region around
and correspond to the QRS wave of the FECG signal
which exists only in the composite signal
see the nonlinear nature of the mapping between
maternal component in
by the irregularity in the deviation
isdue
was linear (i.e.,
via correlation and the signal
,
plotted against the cor-
bothtakenfromrealECG
. One can easily
and the
Fig. 2. Normalized ???? versus the corresponding normalized record of ????
of 360 samples record.
of the data points in the diagonal ellipses from the unity-slope
line.
The thoracic signal
is predominantly maternal, and
hence we assume that the fetal component in it is negligible.
It should be noted that a proper placement of the thoracic and
abdomen electrodes would result in a clean estimate of the
FECG such that
not placed low enough on the mother’s abdominal area then
the resulting noisy fetal ECG estimate can be cleaned by post
filtering using nonlinear filtering such as median filtering or
wavelet denoising.
Our goal is to approximate the nonlinear transformation
which will operate onand yield a signal,
perfectly aligned with the maternal component in
alignment will allow for suppressing the maternal component
in
and hence the extraction of an estimate of the FECG
signal
. In our proposed method, we do so by an ANFIS
network with multi-input and a single output. The input in this
case would be the MECG signal
its derivatives or delays along with the desired signal being the
composite signal
. The ANFIS network will find a non-
linear transformation that operates on
. The right ANFIS network should, therefore, output an
estimate of the maternal component in
by
in (1).
. If the abdomen electrode is
, which is
. This
and a finite number of
and aligns it with
which we denoted
III. ADAPTIVE NEURO-FUZZY INFERENCE SYSTEMS (ANFIS)
FuzzyLogichasbeen widelyused inthedesignand enhance-
ment of a vast number of applications [15]. It is conceptually
simple and straightforward. However, its proper use is heavily
dependentonexpertknowledge,whichmaynotalwaysbeavail-
able. The proper selection of the number, the type and the pa-
rameter of the fuzzy membership functions and rules is crucial
for achieving the desired performance and in most situations, it
is difficult. Yet, it has been done in many applications through
trial and error. This fact highlights the significance of tuning
fuzzysystem.ANFISarefuzzySugenomodelsputintheframe-
work of adaptive systems to facilitate learning and adaptation
[17]. Such framework makes fuzzy logic more systematic and
less relying on expert knowledge.
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ASSALEH: EXTRACTION OF FECG USING ANFIS61
Fig. 3. ANFIS Architecture.
There are many benefits to using ANFIS in pattern learning
and detection as compared to linear systems and neural net-
works. These benefits are centered on the fact that ANFIS com-
bines the capabilities of both neural networks and fuzzy sys-
tems in learning nonlinearities. Fuzzy techniques incorporate
information sources into a fuzzy rule base that represents the
knowledge of the network structure so that structure learning
techniques can easily be accomplished. Moreover, ANFIS ar-
chitecturerequirementsandinitializationsarefewerandsimpler
compared to neural networks, which require extensivetrails and
errors for optimization of their architecture and initializations
[16].
A. ANFIS Architecture
To present the ANFIS architecture, let us consider two-fuzzy
rules based on a first-order Sugeno model
One possible ANFIS architecture to implement these two rules
is shown in Fig. 3. Note that a circle indicates a fixed node
whereas a square indicates an adaptive node (the parameters are
changed during training). In the following presentation
notes the output of node
in a layer
de-
.
Layer 1: All the nodes in this layer are adaptive nodes; is
the degree of the membership of the input to the
fuzzy membership function (MF) represented by
the node
(4)
and can be any appropriate fuzzy sets in
parameter form. For example, if bell MF is used
then
(5)
where
, , andare the parameters for the MF.
Layer 2:The nodes in this layer are fixed (not adaptive).
These are labeled
to indicate that they play the
role of a simple multiplier. The outputs of these
nodes are given by
(6)
The output of each node is this layer represents the
firing strength of the rule.
Layer 3:Nodes in this layer are also fixed nodes. These
are labeled N to indicate that these perform a
normalization of the firing strength from previous
layer. The output of each node in this layer is given
by
(7)
Layer 4: All the nodes in this layer are adaptive nodes.
The output of each node is simply the product of
the normalized firing strength and a first-order
polynomial
(8)
where
(consequent parameter since they deal with the
then-part of the fuzzy rule).
, and are design parameters
Layer 5:This layer has only one node labeled
that is performs the function of a simple summer.
The output of this single node is given by
to indicate
(9)
The ANFIS architecture is not unique. Some
layers can be combined and still produce the
same output. In this ANFIS architecture, there are
two adaptive layers (1 and 4). Layer 1 has three
modifiable parameters ( ,
the input MFs. These parameters are called premise
parameters. Layer 4 has also three modifiable
parameters ( ,
, and
first-order polynomial. These parameters are called
consequent parameters.
, and ) pertaining to
) pertaining to the
B. Learning Method of ANFIS
The task of training algorithm for this architecture is tuning
all the modifiable parameters to make the ANFIS output match
thetrainingdata.Noteherethat
,,anddescribethesigma,
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62 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 1, JANUARY 2007
slope and the center of the bell MFs, respectively. If these pa-
rameters are fixed, the output of the network becomes
(10)
This is a linear combination of the modifiable parameters. For
this observation, we can divide the parameter set
such as
into two sets
(11)
For the forward path, we can apply least square method to iden-
tify the consequent parameters. Now for a given set of values of
, we can plug training data and obtain a matrix equation
(12)
where
square problem, and the solution for
, is the least square estimator
containstheunknownparametersin.Thisisalinear
, which is minimizes
(13)
One can also use recursive least square estimator in case of
on-line training. For the backward path, the error signals prop-
agate backward. The premise parameters are updated by de-
scent method [17], through minimizing the overall quadratic
cost function
(14)
in a recursive manner with respect to
parameters in the th node in layer
. The update of the
can be written as
(15)
where
is the learning rate, and the gradient vector
(16)
being the node’s output and
error signal.
is the backpropagated
IV. PROPOSED SOLUTION FOR FECG EXTRACTION
To account for the possibility that the nonlinear transforma-
tion
might be time-variant, we structure our algorithm to be
frame-based. Consequently, the signals
titioned into
-samples long overlapping frames with overlap
of
samples. The th frames of
andare par-
andare given by
where
(17)
As we discussed in Section II, the ANFIS is used here to align
with the maternal component in
puts of the ANFIS in this case are data points (vectors) whose
elements are derived from
, while the desired output of the
ANFIS is
. The ANFIS is then trained to learn the map-
ping between
andand hence that between
. In vector and matrix notation, and for the th frame, the
ANFIS network is presented with the vector sequence (matrix)
and the vectoras the training data. This training data is
constructed from the thoracic and abdominal data frames such
that
. Therefore, the in-
and
and
(18)
Therefore,frompatternrecognitionpointofview,the throw
is a -dimensional data point whose desired output is
. The rows of the matrix
quence
and itssample delays. The inclusion of the de-
lays helps in incorporating the dynamics of the signal
makes the mapping easier and more accurate since the transfor-
mationof
intocanincludeechoesof
from the mother’s heart to her abdominal area.
Using the training vector sequence
output sequence
, an ANFIS network is constructed (i.e., its
premise and consequent parameters are obtained as described
in Section III). Once the network is constructed, the training
vector sequence
is evaluated through it to yield a non-
linearly transformed version of
aligned with the maternal component in
and according to (1), an estimate of
be obtained by subtracting the estimate of
method is depicted in Fig. 4. It should be noted that the ANFIS
is not used in the typical pattern recognition scenario (i.e., par-
tition data into training and test parts). Instead, for each frame
we train an ANFIS with
as input feature vectors, and
a sequence of outputs. Then, we evaluate the trained ANFIS on
the same input data,
, and use the resulting sequence,
estimating the FECG for that frame as
Before we demonstrate the FECG extraction results of our
algorithm we examine its effectiveness in aligning the thoracic
MECG
with the maternal component in the composite ab-
dominal signal
. Referring to Fig. 2 we would like to have
of
are composed from the se-
and
asittravels
and the desired
denoted by that is
. Consequently,
denoted by
from
can
. The
as
in
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ASSALEH: EXTRACTION OF FECG USING ANFIS 63
Fig. 4. Use of ANFIS for FECG extraction for frame ?.
Fig. 5. Alignment between ???? and ? ???? of the same data used in Fig. 2.
the maternal component to be aligned along the unity-slope line
with little or no alteration to the FECG data (marked in the hor-
izontal ellipse). We have processed the same 360 data points
fromboth
andthroughourproposedalgorithmtoob-
tain
. The degree of alignment is demonstrated in Fig. 5 by
plotting
against. The plot shows that the algorithm
was capable of transforming
with
without any noticeable change in the FECG compo-
nent. We will demonstrate later in the Section VI that this align-
ment enables us to extract the FECG component from
subtracting
from it.
intowhich is aligned
by
V. ECG DATA USED IN THIS STUDY
Having illustrated that our algorithm is capable of aligning
the thoracic signal with the abdominal signal, we need to show
how well it can extract the FECG component. To do so we test
the algorithm using synthesized and real ECG data.
A. Synthetic ECG Data Generation
For generating the synthetic ECG signals we use the dynam-
ical model recently developed by McSharry et al. [18]. Both
fetal and maternal ECG signals (
using this model using different parameters to account for dif-
ferent shapes and beat rates of the two signals. A model for
generating the abdominal signal
and ) are synthesized
is proposed as shown in
Fig. 6. Block diagram for simulating the abdominal ECG signal, ????.
Fig. 7. Nonlinear transformation of the QRS portion of one beat of ???? into
????.
Fig. 6. The MECG signal
to simulate the delays and the nonlinear effects it undergoes as
it travels from the heart to the abdomen. The attenuation effects
are reflected on the FECG signal
nonlinearly transformed MECG. Additive noise effects on
can be modeled by adding white Gaussian noise
produce
. Since our focus in this paper is on suppressing
the maternal component in the abdominal ECG signal, we will
ignore the effect of
throughout this paper. This is so be-
cause, as we mentioned earlier, we are interested in extracting
which can be cleaned later via postfiltering if needed. The
nonlinearity and multipath effects that
reaches the abdomen as
are modeled as
is processed through a system
before it is added to the
to it to
undergoes until it
(19)
The use of
in [7]. We felt that the FECG extraction algorithm needs more
challenge so we used the expression in (19) to increase the ef-
fectofnonlinearity.Theeffectofthenonlinearitythatthemodel
imposes can be best shown if we plot a portion of one beat of
theMECG,
, and its transformation into
the QRS portion of one beat of
earity is clearly manifested by the attenuation of the main lobe
(the R wave), the amplification of the side lobes (the Q and S
waves), and the change in the shape and width of the lobes.
For illustration purposes we show an example of a synthe-
sizedabdominalsignalgeneratedbythemodeldescribedabove.
to simulate nonlinearity was mentioned
. Fig. 7shows
where thenonlin-and
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64IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 1, JANUARY 2007
Fig. 8. (a) Simulated thoracic MECG (5 s), ????, and (b) synthetic abdominal
ECG (5 s), ????, for ????? ? ??? ??.
The MECG signal,
60 beats/min and the FECG signal
heartbeat rate of 170 beats/min. We used slightly different pa-
rametersforthedynamicalmodelineachcasetomaketheshape
of the waveforms different for the MECG and the FECG. We
have chosen
,
and for fetal to maternal signal-to-noise ratio (fmSNR)
, where fmSNR is computed as
is assumed to have a heartbeat rate of
is assumed to have a
, Fig. 8 shows the
(20)
B. Real ECG Data
The real ECG data used in this paper was a subset of a dataset
contributed by Lieven De Lathauwer [19].
The ECG signals in this dataset were recorded from eight
different skin electrodes located on different points of a preg-
nant woman’s body with 500-Hz sampling frequency. Five of
these simultaneous signals were obtained from the mother’s
abdominal region while the other three were obtained from
the mother’s thoracic region. We have only used one thoracic
recording and one abdominal recording. We have selected the
first abdominal recording which appeared to have the highest
fmSNR, and we arbitrarily chose the last thoracic recording
since all three thoracicrecordings appear to be hugely maternal.
As we mentioned earlier, in a controlled setting, one would
want to place the two electrodes properly to obtain good SNRs.
The two (thoracic and abdominal) ECG signals that we selected
from the dataset are shown in Fig. 9.
VI. EXPERIMENTAL RESULTS
To illustrate the effectiveness of our proposed algorithm in
extracting FECG signals we test it on both synthetic and real
signals. The goodness of the algorithm is measured both objec-
tivelyandvisuallyinthecaseofthesyntheticdatasincewehave
the original FECG signal. However, in the case of the real ECG
data we provide the results and comment on their visual quality.
Fig. 9. (a) Real thoracic MECG (5 s) and (b) real abdominal ECG recordings
(5 s) of from a pregnant woman.
As for the ANFIS that we used throughout our experiments,
we have used 400 pairs of input data (
(0.8 s). The algorithm is not sensitive to the frame size. As a
matter of fact we can use a larger frame size as the signals
we dealt with are found to be stationary over several frames.
We have also used 4 membership rules which correspond to
16 fuzzy rules, 53 nodes, 48 consequent (linear) parameters,
24 (nonlinear) parameters. The choice of 4 membership rules
was simply done by trial and error as we tried 2, 4, and 6 mem-
bership rules and found the choice of 4 rules to be optimal in
terms of the FECG signal quality and the computational com-
plexity of the ANFIS. With 400 two-dimensional feature vec-
tors and four membership rules, the computational complexity
of training an ANFIS is a secondary issue if this algorithm is
to be implemented on a standard digital signal processing. The
delay caused due to computations will certainly be a fraction of
the frame time (i.e., 0.8 s), something that is totally acceptable
for such an application.
and)/frame
A. Results On Synthetic ECG Data
Both the maternal thoracic ECG and the fetal ECG signals
and) are generated as described in Section V. These
twosignalsareprocessedthroughthemodeldepictedinFig.6to
generate the abdominal signal
of the output of our proposed algorithm for
where the extracted FECG signal
original FECG signal
. Visually, thematch betweenthe two
signalsisclearlyimpressive.Toquantifythismatchwecalculate
a quality signal to noise ratio qSNR defined as
(
. Fig. 10 shows an example
is superimposed on the
(21)
For this particular example we found that the qSNR is equal to
22.7 dB.
To study the effect of the strength of the FECG component
in the abdominal signal on the quality of the extracted signal,
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ASSALEH: EXTRACTION OF FECG USING ANFIS65
Fig. 10. FECG extraction from synthetic ECG. (a) Synthetic abdominal
signal with ????? ? ??? ??, (b) original FECG, and (c) extracted FECG
?????? ? ???? ??.
we varied the fmSNR between
of 5 dB, and we computed the qSNR of the extracted FECG
signal. To further assess and validate our proposed technique,
we compare our ANFIS-based qSNR results on synthetic data
with two other FECG extraction techniques: The first technique
is based on classic adaptive filtering, and the second is our own
recent polynomial-networks-based method [18].
The adaptivefilteringmethodthatwe select isthe normalized
least means squares (NLMS) following Camps-Valls et al. [10]
in their recent work in which they compared dynamic neural
networks with classical adaptive methods based on LMS.
The qSNR results are shown in Fig. 11 which illustrates the
robustness of the proposed ANFIS-based technique as com-
pared to the two other techniques. The figure also shows that
the NLMS-based method yields the poorest FECG extraction
quality, and degrades quite rapidly as the fmSNR decreases.
Moreover, Fig. 11 shows that the qSNR values of the extracted
FECG signal for both the proposed ANFIS-based method and
the polynomial-networks-based method are comparable for
relatively high fmSNR values up to
fmSNR values below
clearly superior to the polynomial-networks-based method.
Another commonly used assessment measure for quantifying
the quality of the extracted FECG signal is the correlation co-
efficient, . To complement our results using qSNR, we report
additional comparison results with NLMS and polynomial net-
work using the correlation coefficient as a quality measure of
the extracted FECG signal. We continue to follow the work of
Camps-Valls et al. [10] in which they studied and reported re-
sults on numerous cases including the case which focuses on
maternal ECG as the main source of interference. For this case,
they evaluated the FECG recovery using LMS, NLMS and dy-
namic neural networks for varying fmSNRs between
and. Their results on synthetic data for this particular
case showedthatbothNLMSanddynamicneuralnetworks per-
form reasonably well
and in steps
. However, for
, the ANFIS-based method is
for. How-
Fig. 11. Effect of the fetal to maternal signal to noise ratio (fmSNR) on the
qualityofFECGextractionrepresentedbytheqSNRusingthreedifferentFECG
extraction techniques.
Fig. 12. The mean values with the error bars of the correlation coefficients be-
tween the extracted and the actual FECG frames over a range of fmSNR values
using three different FECG extraction techniques.
ever, for fmSNR values below
rate with a slight advantage to dynamic neural networks. They
also show that NLMS results deteriorate more rapidly than dy-
namic neural networks for fmSNR values below
following, we show our comparative results for our proposed
ANFIS-based method, NLMS-based method, and the polyno-
mial-network-based method. We generated maternal and fetal
signals, as prescribed in Section V, equivalent to 1000 400-
sample frames. We then used the two signals as described in
Fig. 6 to generate thoracic and abdominal frame sets of fmSNR
values varying between
For each SNR value we extracted the FECG using our proposed
ANFIS-based technique, the NLMS technique, and the poly-
nomial networks technique. The FECG extraction is done in
a frame synchronous fashion whereby we obtain one correla-
tion coefficient/frame/SNR value for each of the three extrac-
tion techniques. The results over the 1000 frames are shown by
taking the mean, , and standard deviation,
correlation factors for each fmSNR value for each of the three
FECG extraction techniques. Fig. 12 shows the mean values
with the error bars of the 1000 correlation coefficients between
the extracted FECG frames and the actual FECG frames over
both methods deterio-
. In the
andin steps of 5 dB.
, of the resulting
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66 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 1, JANUARY 2007
Fig. 13. FECG extraction from real ECG data. (a) abdominal ECG signal and
(b) extracted FECG component.
a range of fmSNAr values using three different FECG extrac-
tion techniques. The figure clearly shows the inferiority of the
NLMS method and its very severe deterioration as the fmSNR
is decreased. This is not surprising, given that NLMS is a linear
technique. The polynomial networks technique shows a major
improvement over the NLMS, and it performs very well for fm-
SNRs as low as
. However, for
the performance of polynomial networks method degrades at a
similar rate like that of the NLMS method. The ANFIS-based
extraction method, however, exhibits the best performance as it
shows excellent robustness over a wide range of fmSNR values
as shown in Fig. 12. We believe that this is due to the fact that
ANFIS has a better capability to capture the nonlinearities of
the model than that of the polynomial networks.
Also, important is the spread of the correlation coefficients
for the different methods which is represented by the error bars
superimposed on the curves as shown in Fig. 12. The error bars
show one standard deviation,
fmSNR value. The ANFIS-based extraction shows a relatively
small spread with a gradual increase as the fmSNR decreases.
This shows a reasonably consistent FECG extraction over the
large number of frames that have a wide variety of overlapping
scenariosbetweenthematernalandfetalECGsignals.Thepoly-
nomial networks method also shows small spread that can be
slightly better that that of the ANFIS method for
. However, the spread in the polynomial case grows at a
faster rate, as the fmSNR value decreases, than that of ANFIS.
As for the NLMS technique, the spread is very large compared
totheothertwotechniques.ThedropinthespreadintheNLMS
case at low fmSNR values is meaningless since the mean values
of the correlation coefficient at these fmSNR values are very
low.
It should be noted that the NLMS parameters are selected
experimentally to yield the best possible correlation coefficient
in a way similar to what was done in [10].
, on either side ofat each
Fig. 14. (a) One frame of abdominal ECG with no temporal overlap between
the QRS wave of the maternal component and the fetal component, and
(b) extracted FECG signal.
B. Results on Real ECG Data
The data of the two channels described in Section V and il-
lustrated in Fig. 9 was used. The result of processing this data
through the proposed algorithm is shown in Fig. 13 where a
complete suppression of the maternal component from the ab-
dominal signal is accomplished. However, it is not easy to see
how well the FECG extraction is achieved by looking at a large
number of samples. Therefore, we zoom in Fig. 13 to illustrate
the power of the algorithm in extracting the FECG component.
Fig. 14 shows one frame (400 samples) of the abdominal
signal and the extracted fetal component. As it apparent in the
figure, no temporal overlap between the maternal and the fetal
components intheabdominal signal is present.This case is con-
sidered relatively easy since the two components are tempo-
rally separated. A more significant challenge is when the ma-
ternal and fetal components are fully overlapping as is the case
in Fig. 15. Fig. 15 shows another frame where full overlap is
present in the first beat showing that the fetal beat is totally em-
bedded in the much stronger maternal beat. The figure shows
thatthealgorithmwasstillabletosuccessfullyextracttheFECG
signal.
It is useful to note that the visual quality of the extracted
FECG for this data using the proposed technique is compa-
rabletowhatweobtainedinourpolynomialnetworkstechnique
[14]. This is expected since the fmSNR of this data is around
. However, the NLMS method yields a relatively poor
FECG extraction with visible remnants of the maternal compo-
nent. Fig. 16 shows the results of the FECG extraction for the
same data frame used in Fig. 14. By visual inspection of the
figure, both the proposed ANFIS method and the polynomial
networks method cancel the maternal component to a very good
extent with a slight advantage to the ANFIS method. However,
in the case of NLMS method, the maternal component is still
visible in the extracted FECG signal as indicated by the two el-
lipses in Fig. 16.
Page 9
ASSALEH: EXTRACTION OF FECG USING ANFIS67
Fig. 15. (a) One frame of abdominal ECG with temporally overlapping ma-
ternal and fetal components, and (b) extracted FECG signal.
Fig. 16. Extracted FECG signals from the same data of Fig. 14 using the pro-
posed ANFIS technique, the polynomial networks technique, and the NLMS
technique as labeled on the figure.
VII. CONCLUSIONS
In this paper, we have applied ANFIS to extract the FECG
signal from two ECG signals recorded at the thoracic and
abdominal areas of the mother’s skin. This is done by em-
ploying ANFIS to identify the nonlinear relationship between
the maternal component in the abdominal ECG and the thoracic
MECG which is assumed to include no fetal component in it.
Once the MECG is nonlinearly transformed to be aligned with
the maternal component in the abdominal ECG, the FECG can
be extracted by subtracting the aligned version of the MECG
signal from the abdominal ECG signal.
We have validated our technique on both real and synthetic
ECG signals. In generating the synthetic abdominal ECG sig-
nals we have applied multipath and nonlinear effects to the tho-
racic signal to simulate the transformation it undergoes as it
travels from the heart to the abdomen. Then we added the fetal
component to it according to the fmSNR that we desire. We
have demonstrated the effectiveness of the proposed technique
inextractingtheFECGcomponentforverylowmaternaltofetal
SNRs. We have also compared the performance of the proposed
technique with those of two other FECG extraction techniques:
The NLMS technique and the polynomial networks technique.
Comparisons were done in terms of the quality of the extracted
FECG.ResultsonsyntheticdatashowedthattheNLMSmethod
is inferior to both the proposed technique and the polynomial
networks techniquefor anyfmSNR value.We havealso demon-
stratedthattheproposedtechniqueperformssimilartothepoly-
nomial networks technique for fmSNR values below
However, the proposed method showed a clear advantage in
performance over the polynomial networks method for fmSNR
valuesbelow
.Wehavealsoshowedsomeresultsonreal
data which illustrated that the proposed technique can success-
fully extract the FECG component whether it is overlapping or
nonoverlapping with the QRS wave of the maternal component.
In comparing the proposed technique with the NLMS and poly-
nomial networks on real data, the visual quality of the extracted
FECG signal confirmed our findings on synthetic data.
Since the focus of this paper has been on suppressing the
maternal component from the abdominal ECG signal, the ex-
tracted FECG signal may include other additive noise signals.
Webelievethatsuchnoisecanbesuppressedbypostprocessing
methods such as wavelet denoising that has proven useful with
other FECG extraction methods. We believe that attempting to
remove noise before FECG extraction may result in loosing the
fetal component from the composite signal especially when the
fmSNR is very low and the QRS regions of the fetal and ma-
ternal components are overlapping.
.
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Upper
Khaled
B.Sc.E.E. degree from Jordan University, Amman,
Jordan,in 1988,theM.S.E.Edegreefrom Monmouth
University, W. Long Branch, NJ, in 1990, and the
Ph.D. degree in electrical engineering from Rutgers,
The State University of New Jersey, Piscataway, in
1993.
After a 9-year career in industry, he joined the
Department of Electrical Engineering at the Amer-
ican University of Sharjah (AUS) in September
2002, where he is now an Associate Professor. Prior
Assaleh
(M’90–SM’02) receivedthe
to joining AUS, from March 1997 until July 2002 he was with Conexant
Systems, Newport Beach, CA, where he was a Senior Staff Engineer and later
a Group Leader. Before joining Conexant, he was a Senior Staff Engineer with
Motorola Inc., Phoenix, AZ, from November 1994–March 1997. From October
1993–November 1994, he was a Research Professor at the Center for Computer
Aid and Industrial Productivity (CAIP), Rutgers University. He holds 10 US
patents, and has published over 40 papers in fields related to signal processing
and its applications. His research interests include biometrics, speech and
image processing, and biosignal processing.