Extraction of Fetal Electrocardiogram Using Adaptive Neuro-Fuzzy Inference Systems Khaled Assaleh, Senior Member,IEEE M97G0224 黃阡.

Extraction of Fetal Electrocardiogram Extraction of Fetal Electrocardiogram Using Adaptive Neuro-Fuzzy Inference Using Adaptive Neuro-Fuzzy Inference

SystemsSystems

Khaled Assaleh, Senior Khaled Assaleh, Senior Member,IEEEMember,IEEE

M97G0224 黃阡

OUTLINEOUTLINE

• INTRODUCTIONINTRODUCTION• PROBLEM FORMULATIONPROBLEM FORMULATION• ADAPTIVE NEURO-FUZZY INFERENCE ADAPTIVE NEURO-FUZZY INFERENCE

SYSTEMSSYSTEMS• PROPOSED SOLUTION FOR FECG PROPOSED SOLUTION FOR FECG

EXTRACTIONEXTRACTION• ECG DATA USED IN THIS STUDYECG DATA USED IN THIS STUDY• EXPERIMENTAL RESULTSEXPERIMENTAL RESULTS

INTRODUCTIONINTRODUCTION

• The fetal electrocardiogram (FECG) The fetal electrocardiogram (FECG) signal reflects the electrical activity signal reflects the electrical activity of the fetal heartof the fetal heart

• Technical problemsTechnical problems– Low power of the FECG signal which is Low power of the FECG signal which is

contaminated by various sources of contaminated by various sources of interferenceinterference

INTRODUCTION (cont.)INTRODUCTION (cont.)

• Contaminated sourcesContaminated sources– Maternal ECGMaternal ECG– Maternal EMG– 50 Hz power line interference– Baseline wander– Random electronic noise


• SolutionSolution– Using low noise electronic amplifiers Using low noise electronic amplifiers

with high common mode rejection ratiowith high common mode rejection ratio•50 Hz interference and electronic random

noise can be eliminated

•EMG noise can also be reduced but not necessarily eliminated


• These techniques includeThese techniques include– Adaptive filtersAdaptive filters– Correlation techniquesCorrelation techniques– Singular-value decomposition (SVD)Singular-value decomposition (SVD)– Wavelet transformWavelet transform– Neural networksNeural networks– Blind source separation (BSS)Blind source separation (BSS)


• BSS via independent component BSS via independent component analysis (ICA) is considered among analysis (ICA) is considered among the most recent and most successful the most recent and most successful methods used for FECG extractionmethods used for FECG extraction

• ICA requires multiple leads for ICA requires multiple leads for collecting several ECG signalscollecting several ECG signals– Not enough for satisfactory FECG Not enough for satisfactory FECG

extraction via ICAextraction via ICA


• We aim to apply adaptive neuro-We aim to apply adaptive neuro-fuzzy inference systems (ANFIS) for fuzzy inference systems (ANFIS) for estimating the FECG component from estimating the FECG component from one abdominal ECG recording and one abdominal ECG recording and one reference thoracic maternal one reference thoracic maternal ECG (MECG) signalECG (MECG) signal

PROBLEM FORMULATIONPROBLEM FORMULATION

• Two Leads are attached to the body Two Leads are attached to the body of a pregnant womanof a pregnant woman

• These signals are denoted as and These signals are denoted as and to correspond to the thoracic and to correspond to the thoracic and abdominal ECG signals respectivelyabdominal ECG signals respectively

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PROBLEM FORMULATION PROBLEM FORMULATION (cont.)(cont.)

• Abdominal signal are three Abdominal signal are three signals signals – Deformed version of Deformed version of – Fetal ECGFetal ECG– Additive noise from other sourcesAdditive noise from other sources

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)(nx



• The abdominal signal can be The abdominal signal can be expressed as the sum of a deformed expressed as the sum of a deformed version of the maternal ECG and a version of the maternal ECG and a noisy version of the fetal ECG noisy version of the fetal ECG such thatsuch that

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)()()(

))(()(

)()()(

nnsns

nxTnx

nsnxnw


• Maternal ECG is measured far away Maternal ECG is measured far away from its source and consequently it from its source and consequently it encounters some nonlinear encounters some nonlinear transformation as it travels to the transformation as it travels to the abdominal areaabdominal area


• The problem becomes trivial if the The problem becomes trivial if the transformation was lineartransformation was linear

• In that case, can be aligned with In that case, can be aligned with via correlation and the signal via correlation and the signal can be extracted by simply can be extracted by simply subtracting the aligned fromsubtracting the aligned from

T

)(nx )(nw)(ns

)(nx )(nw


• In fact, the transformation between In fact, the transformation between and the maternal component in , and the maternal component in ,

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)(nw )(nx



• The thoracic signal is The thoracic signal is predominantly maternal, and hence predominantly maternal, and hence we assume that the fetal component we assume that the fetal component in it is negligible in it is negligible

• A proper placement of the thoracic A proper placement of the thoracic and abdomen electrodes would result and abdomen electrodes would result in a clean estimate of the FECG such in a clean estimate of the FECG such thatthat

)(nx

)()( nsns


• Our goal is to approximate the Our goal is to approximate the nonlinear transformation which will nonlinear transformation which will operate on and yield a signaloperate on and yield a signal

• We do so by an ANFIS network with We do so by an ANFIS network with multi-input and a single outputmulti-input and a single output– Input is the MECGInput is the MECG

T )(nx

)(nx

)(nx


• The ANFIS network will find a The ANFIS network will find a nonlinear transformation that nonlinear transformation that operates on and aligns it withoperates on and aligns it with

• The right ANFIS network should, The right ANFIS network should, therefore, output an estimate of the therefore, output an estimate of the maternal component in which we maternal component in which we denoted bydenoted by

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)(nw

)(nw )(nx

ADAPTIVE NEURO-FUZZY ADAPTIVE NEURO-FUZZY INFERENCE SYSTEMSINFERENCE SYSTEMS

• Fuzzy Logic has been widely used in Fuzzy Logic has been widely used in the design and enhancement of a the design and enhancement of a vast number of applicationsvast number of applications

ADAPTIVE NEURO-FUZZY ADAPTIVE NEURO-FUZZY INFERENCE SYSTEMS (cont.)INFERENCE SYSTEMS (cont.)• A. ANFIS ArchitectureA. ANFIS Architecture

• Rule1:if (x is A1) and (y is B1), thenRule1:if (x is A1) and (y is B1), then

• Rule2:if (x is A2) and (y is B2), thenRule2:if (x is A2) and (y is B2), then

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)( 2222 ryqxpf

ADAPTIVE NEURO-FUZZY ADAPTIVE NEURO-FUZZY INFERENCE SYSTEMS (cont.)INFERENCE SYSTEMS (cont.)

• Layer1:Layer1:– i is the degree of the membership of the i is the degree of the membership of the

input to the fuzzy membership function input to the fuzzy membership function (MF) represented by the node(MF) represented by the node

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2,1),(

2,1 iyu

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Bi

Aii


• Ai and Bi can be any appropriate Ai and Bi can be any appropriate fuzzy sets in parameter form. For fuzzy sets in parameter form. For example, if bell MF is used thenexample, if bell MF is used then

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• Layer2Layer2– These are labeled to indicate that These are labeled to indicate that

they play the role of a simple multiplier.they play the role of a simple multiplier.

2,1),()(,2 iyuxuwO BiAiii


• Layer3:Layer3:– These are labeled N to indicate that These are labeled N to indicate that

these perform a normalization of the these perform a normalization of the firing strength from previous layer.firing strength from previous layer.

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• Layer4:Layer4:– The output of each node is simply the The output of each node is simply the

product of the normalized firing strength product of the normalized firing strength and a first-order polynomialand a first-order polynomial

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• Layer5:Layer5:– This layer has only one node labeled This layer has only one node labeled

to indicate that is performs the function to indicate that is performs the function of a simple summer.of a simple summer.

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fwfwfO 2,1,,5


• B. Learning Method of ANFISB. Learning Method of ANFIS

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ADAPTIVE NEURO-FUZZY ADAPTIVE NEURO-FUZZY INFERENCE SYSTEMS (cont.)INFERENCE SYSTEMS (cont.)• For this observation, we can divide the For this observation, we can divide the

parameter set into two sets such asparameter set into two sets such as

set of total parametersset of total parameters

set of premise (nonlinear) parameters set of premise (nonlinear) parameters

set of consequent (linear) parametersset of consequent (linear) parameters

direct sumdirect sum

2

1

21

S

S

S

SSS


• Now for a given set of values of , Now for a given set of values of , we can plug training data and obtain we can plug training data and obtain a matrix equationa matrix equation

Where contains the unknown Where contains the unknown parameters inparameters in

1S

yA

2S


• Solution for , which is minimizes Solution for , which is minimizes , is the least square estimator , is the least square estimator

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• For the backward path, the error For the backward path, the error signals propagate backward. The signals propagate backward. The premise parameters are updated by premise parameters are updated by descent methoddescent method

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),()(2

1)(

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kykyJ


• The update of the parameters in the The update of the parameters in the th node in layer L can be written asth node in layer L can be written as

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PROPOSED SOLUTION FOR PROPOSED SOLUTION FOR FECG EXTRACTIONFECG EXTRACTION

• To account for the possibility that the To account for the possibility that the nonlinear transformation T might be nonlinear transformation T might be time-variant, we structure our time-variant, we structure our algorithm to be frame-based.algorithm to be frame-based.

0,10

))(()(

))(()(

iNm

mPNiwmw

mPNixmx

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PROPOSED SOLUTION FOR PROPOSED SOLUTION FOR FECG EXTRACTION (cont.)FECG EXTRACTION (cont.)

• Training data is constructed from the Training data is constructed from the thoracic and abdominal data frames thoracic and abdominal data frames such thatsuch that

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iiii

Tiiii

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jmxmxmxmx

NxxxX

)1(),...,1(),0()(

)(),...,1(),()(

)1(),...,1(),0(

PROPOSED SOLUTION FOR PROPOSED SOLUTION FOR FECG EXTRACTION (cont.)FECG EXTRACTION (cont.)

Use of ANFIS for FECG extraction for frame i.

ECG DATA USED IN THIS ECG DATA USED IN THIS STUDYSTUDY

• A. Synthetic ECG Data GenerationA. Synthetic ECG Data Generation– A model for generating the abdominal A model for generating the abdominal

signalsignal)(nw

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nx

))((tan))(sgn()(

)2()1()()(

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ECG DATA USED IN THIS ECG DATA USED IN THIS STUDY (cont.)STUDY (cont.)

• The effect of the nonlinearity that the The effect of the nonlinearity that the model imposes can be best shown if model imposes can be best shown if we plot a portion of one beat of the we plot a portion of one beat of the MECG , and its transformation into MECG , and its transformation into

)(nx

)(^

nx


• The MECG signal, is assumed to have The MECG signal, is assumed to have a heartbeat rate of 60 beats/min and a heartbeat rate of 60 beats/min and the FECG signal is assumed to have a the FECG signal is assumed to have a heartbeat rate of 170 beats/min.heartbeat rate of 170 beats/min.


• B. Real ECG DataB. Real ECG Data

EXPERIMENTAL RESULTSEXPERIMENTAL RESULTS

• A. Results On Synthetic ECG DataA. Results On Synthetic ECG Data

FECG extraction from synthetic ECG

EXPERIMENTAL RESULTS EXPERIMENTAL RESULTS (cont.)(cont.)

• Effect of the fetal to maternal signal Effect of the fetal to maternal signal to noise ratio (fmSNR) on the quality to noise ratio (fmSNR) on the quality of FECG extraction represented by of FECG extraction represented by the qSNR using three different FECG the qSNR using three different FECG extraction techniques.extraction techniques.


• B. Results on Real ECG DataB. Results on Real ECG Data

FECG extraction from real ECG data


• One frame (400 samples) of the One frame (400 samples) of the abdominal signal and the extracted abdominal signal and the extracted fetal component.fetal component.


(a) One frame of abdominal ECG with temporally overlapping maternal

and fetal components, and (b) extracted FECG signal


Extracted FECG signals from the same data of Fig. 14 using the proposed ANFIS technique, the polynomial networks technique, and the NLMS technique as labeled on the figure.

Thanks for your attentionThanks for your attention

Extraction of Fetal Electrocardiogram Using Adaptive Neuro-Fuzzy Inference Systems Khaled Assaleh, Senior Member,IEEE M97G0224 黃阡.

Documents

thatproblem formulation

mecgproblem formulation

eliminatedintroduction

icaintroduction cont

fecg component

abdominal signal

fetal component

maternal component