Extraction of Fetal Cardiac Signals from an Array of Maternal Abdominal Recordings Reza Sameni Directed by: Christian Jutten Mohammad B. Shamsollahi GIPSA-lab, INPG, Grenoble, France Sharif University of Technology, Tehran, Iran July 7, 2008, Grenoble, France
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Extraction of Fetal Cardiac Signals from an Array ofMaternal Abdominal Recordings
Reza Sameni
Directed by:
Christian JuttenMohammad B. Shamsollahi
GIPSA-lab, INPG, Grenoble, France
Sharif University of Technology, Tehran, Iran
July 7, 2008, Grenoble, France
Overview
1 out of 125 babies are born with heart defects[Mar, 2005, Minino et al., 2007, AHA, 2008]
Early detection of cardiac abnormalities help medicationsand precautions during delivery
Most defects manifest in the heart-rate and morphologyof electrical and magnetic cardiac signals
But, we don’t have direct access to the fetus and the fetalsignals recorded from the mother’s abdomen are veryweak with high interferences
Noninvasive Fetal Cardiac Signal Extraction 2
Problem Definition
Objective: The noninvasive extraction of fetal cardiac signals from an array ofelectrodes recorded from the abdomen of a pregnant woman
x3
x4
xn
x1
x2
x(t) =
x1(t)x2(t)...xn(t)
y(t) =
y1(t)y2(t)...ym(t)
A set of electric or
magnetic recordings
Noisy observation signals Processed signals
Noninvasive Fetal Cardiac Signal Extraction 3
Outline
1 Background
2 State of the Art
3 MethodsAn ECG Modeling and Denoising FrameworkLinear Multichannel ECG ProcessingPeriodic Component AnalysisSubspace Decomposition by Deflation
4 Conclusion and Perspectives
Noninvasive Fetal Cardiac Signal Extraction 4
Background
Outline
1 Background
2 State of the Art
3 MethodsAn ECG Modeling and Denoising FrameworkLinear Multichannel ECG ProcessingPeriodic Component AnalysisSubspace Decomposition by Deflation
4 Conclusion and Perspectives
Noninvasive Fetal Cardiac Signal Extraction 5
Background
The Electrocardiogram
Electrocardiogram (ECG): Overall electrical activity of the heart recordedfrom the body surface
The R-peaks of the ECG are used to extract the heart-beat
R R R R
Noninvasive Fetal Cardiac Signal Extraction 6
Background
What is the Vectorcardiogram?
Vectorcardiogram (VCG): A 3D representation of the ECG,reconstructed from 3 ECG leads
VCG of orthogonal ECG leads give dipole approximations for bodysurface potentials: φ(t) ≈ a1s1(t) + a2s2(t) + a3s3(t)
Noninvasive Fetal Cardiac Signal Extraction 7
State of the Art
Outline
1 Background
2 State of the Art
3 MethodsAn ECG Modeling and Denoising FrameworkLinear Multichannel ECG ProcessingPeriodic Component AnalysisSubspace Decomposition by Deflation
4 Conclusion and Perspectives
Noninvasive Fetal Cardiac Signal Extraction 8
State of the Art
History of Fetal Electrocardiography
1906: M. Cremer observed the fetal ECG using string galvanometers[Cremer, 1906]
1950’s: Improvements in measurement and amplification techniques[Lindsley, 1942]
1970’s: Introduction of signal processing techniques in this domain[Farvet, 1968, Widrow et al., 1975]
1990’s: Application of multichannel signal processing in this domain[van Oosterom, 1986, Kanjilal et al., 1997, Zarzoso et al., 1997]
The problem has since been considered in biomedical and signalprocessing communities....
Echocardiography: sonograghy of the heart using ultrasound[Wladimiroff & Pilu, 1996, Drose, 1998]
Phonocardiography: heart sounds using acoustic microphones[Zuckerwar et al., 1993, Varady et al., 2003]
Magnetocardiography: magnetic fields of cardiac signals[Kariniemi & Hukkinen, 1977, Stinstra, 2001]
Electrocardiography: electric fields of cardiac signals
Invasive: measurable during labor only [Outram et al., 1995, Lai & Shynk, 2002]
Noninvasive: measurable throughout pregnancy [Cremer, 1906, Lindsley, 1942]
Noninvasive Fetal Cardiac Signal Extraction 11
State of the Art
Previous Processing Techniques
Direct Fetal ECG Analysis: Used in early studies; only possible in highsignal-to-noise ratios[Larks, 1962]
Adaptive and Matched Filtering: Partially effective; require referenceelectrodes[Farvet, 1968, Widrow et al., 1975, Park et al., 1992, Outram et al., 1995, Shao et al., 2004, Martens et al., 2007]
Linear Decomposition: Rather effective; decompose the signals ontofixed or data-driven basis functions[Li et al., 1995, Khamene et al., 2000, Akay et al., 1996]
[van Oosterom, 1986, Zarzoso et al., 1997, Cardoso, 1998, De Lathauwer et al., 2000]
State-State Representation of the ECGProcess equation:
θk+1 = (θk + ωδ)mod(2π)
sk+1 = −N∑
i=1
δαiω
b2i
∆θiexp(−∆θ2
i
2b2i
) + sk + η
ω = 2π × HR, ∆θi = (θk − θi )mod(2π), δ = 1/fs and η is process noise
Observation equation:{φk = θk + uk coarse ECG phaseyk = sk + vk noisy ECG
(Linearized KF Equations 22)
Noninvasive Fetal Cardiac Signal Extraction 22
Methods An ECG Modeling and Denoising Framework
Single-Channel Denoising Scheme
The Kalman filter uses the a priori information from the ECG dynamicsand the noisy observations to estimate the true ECG
dynamic model noisy ECG estimated ECG
8>><>>:
θk+1 = (θk + ωδ)mod(2π)
sk+1 = −NX
i=1δ
αi ω
b2i
∆θi exp(−∆θ2
i2b2
i
) + sk + η
�φk = θk + ukyk = sk + vk
sk
Noninvasive Fetal Cardiac Signal Extraction 23
Methods An ECG Modeling and Denoising Framework
Application: Maternal ECG Cancellation
We can remove maternal ECG contaminants using the Kalman filter andKalman smoother 1
(1) Original noisy fetal ECG
1This data has been taken from the DaISy database [De Moor, 1997]
Noninvasive Fetal Cardiac Signal Extraction 24
Methods An ECG Modeling and Denoising Framework
Application: Maternal ECG Cancellation
We can remove maternal ECG contaminants using the Kalman filter andKalman smoother 1
(1) Original noisy fetal ECG
1This data has been taken from the DaISy database [De Moor, 1997]
Noninvasive Fetal Cardiac Signal Extraction 24
Methods An ECG Modeling and Denoising Framework
Application: Maternal ECG Cancellation
We can remove maternal ECG contaminants using the Kalman filter andKalman smoother 1
(1) Original noisy fetal ECG (2) EKS of the maternal ECG
1This data has been taken from the DaISy database [De Moor, 1997]
Noninvasive Fetal Cardiac Signal Extraction 24
Methods An ECG Modeling and Denoising Framework
Application: Maternal ECG Cancellation
We can remove maternal ECG contaminants using the Kalman filter andKalman smoother 1
(1) Original noisy fetal ECG (2) EKS of the maternal ECG
(1) - (2) Residual fetal signal
1This data has been taken from the DaISy database [De Moor, 1997]
Noninvasive Fetal Cardiac Signal Extraction 24
Methods An ECG Modeling and Denoising Framework
Application: Maternal ECG Cancellation
We can remove maternal ECG contaminants using the Kalman filter andKalman smoother 1
(1) Original noisy fetal ECG (2) EKS of the maternal ECG
(1) - (2) Residual fetal signal Fetal signal after post-processing
1This data has been taken from the DaISy database [De Moor, 1997]
Noninvasive Fetal Cardiac Signal Extraction 24
Methods An ECG Modeling and Denoising Framework
Confidence Intervals
Several fetal ECG beats before and after the post-processing EKS,together with the ±σ and ±3σ confidence envelopes
Noninvasive Fetal Cardiac Signal Extraction 25
Methods An ECG Modeling and Denoising Framework
Summary of Findings of Part I
We can generate realsitic multichannel maternal/fetal ECG signals
The Kalman filter based on this model outperforms classical filters
Applications:
ECG enhancement
ECG cancellation
Limitation: During maternal/fetal PQRST-complex overlap, multichannelprocessing is required
Noninvasive Fetal Cardiac Signal Extraction 26
Methods Linear Multichannel ECG Processing
Outline
1 Background
2 State of the Art
3 MethodsAn ECG Modeling and Denoising FrameworkLinear Multichannel ECG ProcessingPeriodic Component AnalysisSubspace Decomposition by Deflation
4 Conclusion and Perspectives
Noninvasive Fetal Cardiac Signal Extraction 27
Methods Linear Multichannel ECG Processing
Multichannel ECGObjective: To find linear transforms of the form y(t) = Bx(t) with propertiessuch as: uncorrelatedness, independence, periodicity, etc.
The DaISy dataset [De Moor, 1997]
[Kanjilal et al., 1997, Zarzoso et al., 1997, Cardoso, 1998, De Lathauwer et al., 2000, Barros & Cichocki, 2001, Zhang & Yi, 2006, Li & Yi, 2008]
Noninvasive Fetal Cardiac Signal Extraction 28
Methods Linear Multichannel ECG Processing
Issues of Interest
Why do linear transforms extract multiple ECG components?
What do these components correspond to?
Can we relate these components with multipole expansions?
A typical segment of independent componentsextracted from ECG signals
Noninvasive Fetal Cardiac Signal Extraction 29
Methods Linear Multichannel ECG Processing
Interpretation of the Extracted Components
3D VCG x − y plane
x − z plane y − z plane
Scatter plot of a VCG and column vectors of a mixing matrix estimated by JADE
Noninvasive Fetal Cardiac Signal Extraction 30
Methods Linear Multichannel ECG Processing
Summary of Findings of Part II
Dimensionality of the ECG; theoretical and practical
Multidimensional properties of cardiac signals vs. VCG loops
Impact and necessity of preprocessing for fetal ECG extraction
Limitation: ICA is not ideal for ECG decomposition; a transform thataccounts for periodicity is more appropriate
Noninvasive Fetal Cardiac Signal Extraction 31
Methods Periodic Component Analysis
Outline
1 Background
2 State of the Art
3 MethodsAn ECG Modeling and Denoising FrameworkLinear Multichannel ECG ProcessingPeriodic Component AnalysisSubspace Decomposition by Deflation
4 Conclusion and Perspectives
Noninvasive Fetal Cardiac Signal Extraction 32
Methods Periodic Component Analysis
Periodic Component Analysis (πCA)
Objective: To find a special linear transform y(t) = Bx(t) fordecomposing ECG signals into periodic components
The components should be ranked according to their relevance
Method: Gather measures of ECG pseudo-periodicity in C1 & C2, andfind a B to diagonalize them:
BC1BT = I , BC2BT = Λ
→ Generalized Eigenvalue Decomposition (GEVD) of (C1, C2)
The method is related to algebraic ICA methods, such asAMUSE and SOBI → how to choose the time-lags?
Noninvasive Fetal Cardiac Signal Extraction 33
Methods Periodic Component Analysis
Periodic Component Analysis Algorithm
Algorithm:1 Detect the R-peaks of the ECG of interest (a priori information)
2 Calculate the ECG phase signal θ(t)
3 Calculate the time-varying lag τt = min{τ |φ(t + τ) = φ(t), τ > 0}
3 Finding coarse estimates of fetal MCGs using ICA
4 Refind maternal MCG using maternal/fetal πCA
→ Cx = Cmx − (C f1
x + C f2x )
5 Refind fetal ECG through post-processing
Noninvasive Fetal Cardiac Signal Extraction 38
Methods Periodic Component Analysis
Example II: Twin Fetal MCG (continued)
A segment of extracted components
Noninvasive Fetal Cardiac Signal Extraction 39
Methods Periodic Component Analysis
Summary of Findings of Part III
πCA finds pseudo-periodic signals ranked in order of relevance
It uses GEVD that is a fast and accurate algorithm
Limitation: Requires the R-peaks as prior information
Noninvasive Fetal Cardiac Signal Extraction 40
Methods Subspace Decomposition by Deflation
Outline
1 Background
2 State of the Art
3 MethodsAn ECG Modeling and Denoising FrameworkLinear Multichannel ECG ProcessingPeriodic Component AnalysisSubspace Decomposition by Deflation
4 Conclusion and Perspectives
Noninvasive Fetal Cardiac Signal Extraction 41
Methods Subspace Decomposition by Deflation
Motivation
Objective: To decompose (degenerate) mixtures of signal andnoise/artifact, without prior knowledge of the subspace dimensions andwithout reducing the data dimensions
x(t) = xs(t) + xn(t)
y(t) = Bx(t) = B[xs(t) + xn(t)] = ys(t) + yn(t)
Full-rank noise is limiting for linear methods and can be amplified incomponents extracted by ICA
Solution: Break the linearity by combining single-channel denoising andmultichannel decomposition
Noninvasive Fetal Cardiac Signal Extraction 42
Methods Subspace Decomposition by Deflation
Assumptions
1 The desired signals in different channels are dependent→ Processing gain is achieved through multichannel analysis
2 We have some a priori information about the desired signals→ The desired and undesired parts can be roughly separated usinglinear/nonlinear filters
Noninvasive Fetal Cardiac Signal Extraction 43
Methods Subspace Decomposition by Deflation
Subspace Decomposition by Deflation
/
Iteration stopping criterion
/LinearDecomposition
LinearRecomposition
/Linear/Nonlinear DenoisingL L
N-LInput array Output array
B B-1
The iterative subspace decomposition procedure
Linear decomposition: based on non-stationarity, spectral contrast,periodicity, etc. → Generalized eigenvalue decomposition (GEVD)
Denoising: based on a priori information
Applications: EEG, EMG, MCG denoising, or etc.
Noninvasive Fetal Cardiac Signal Extraction 44
Methods Subspace Decomposition by Deflation
Application in Maternal ECG Cancellation
πCA
mECG cancellationusing Kalman filter
inverseπCA
first L components
recursion stopping criterion
array recordings contaminated with
maternal ECGarray recordings without maternal ECGlast N-L
components
periodicity measurematernal ECG phase
The iterative procedure for maternal ECG cancellation
Noninvasive Fetal Cardiac Signal Extraction 45
Methods Subspace Decomposition by Deflation
Example I: Maternal ECG Cancellation fromDegenerate Mixture 1
Original1 This dataset has been recorded by Dr. Evelyn Huhn and provided by Dr. Raphael Schneider
Noninvasive Fetal Cardiac Signal Extraction 46
Methods Subspace Decomposition by Deflation
Example I: Maternal ECG Cancellation fromDegenerate Mixture (continued)
Iteration 1
Noninvasive Fetal Cardiac Signal Extraction 47
Methods Subspace Decomposition by Deflation
Example I: Maternal ECG Cancellation fromDegenerate Mixture (continued)
Iteration 2
Noninvasive Fetal Cardiac Signal Extraction 48
Methods Subspace Decomposition by Deflation
Example I: Maternal ECG Cancellation fromDegenerate Mixture (continued)
Iteration 3
Noninvasive Fetal Cardiac Signal Extraction 49
Methods Subspace Decomposition by Deflation
Example I: Maternal ECG Cancellation fromDegenerate Mixture (continued)
Original (blue) and denoised (red)
Noninvasive Fetal Cardiac Signal Extraction 50
Methods Subspace Decomposition by Deflation
Example II: Invasive vs. Non-Invasive Fetal ECGExtraction
1 Invasive fetal scalp ECG recorded during labor 1
1This data has been recorded by Dr. A. Wolfberg and provided (confidentially) by Dr. G.D Clifford
Noninvasive Fetal Cardiac Signal Extraction 51
Methods Subspace Decomposition by Deflation
Example II: Typical Results
Fetal ECG recorded invasively from a scalp lead ECG
Fetal ECG extracted non-invasively from 22 abdominal leads
Noninvasive Fetal Cardiac Signal Extraction 52
Methods Subspace Decomposition by Deflation
Example II: Typical Results
Fetal ECG recorded invasively from a scalp lead ECG
Fetal ECG extracted non-invasively from 22 abdominal leads(with post-processing)
[Ensemble Averages 24]
Noninvasive Fetal Cardiac Signal Extraction 53
Methods Subspace Decomposition by Deflation
Summary of Findings of Part IV
Decomposition of (degenerate) mixtures of signal/interference subspaceswithout dimension reduction
Limitation: Requires prior information; not applicable to totally blindscenarios
Noninvasive Fetal Cardiac Signal Extraction 54
Conclusion and Perspectives
Outline
1 Background
2 State of the Art
3 MethodsAn ECG Modeling and Denoising FrameworkLinear Multichannel ECG ProcessingPeriodic Component AnalysisSubspace Decomposition by Deflation
4 Conclusion and Perspectives
Noninvasive Fetal Cardiac Signal Extraction 55
Conclusion and Perspectives
Summary
The main developments of this study include:
Realistic multichannel ECG modeling
Bayesian framework for ECG denoising
Study of multidimensional aspects of ECG
Periodic Component Analysis
Subspace decomposition by deflation
Much improvement was achieved using pseudo-periodicity priors
The performance is limited when the priors do not hold→ highly pathologic cases
Noninvasive Fetal Cardiac Signal Extraction 56
Conclusion and Perspectives
Perspectives
Clinical:Clinical verification of the proposed methods
Study of pathologic cases
Theoretical:Calculation of theoretical performance bounds for ECG processing
Theoretical aspects of the deflation method: convergence and stability
Experimental:Fetal ECG tracking for continuous monitoring
Development of fetal monitoring systems
Noninvasive Fetal Cardiac Signal Extraction 57
Conclusion and Perspectives
Byproducts of the Developed Methods
General functions for preprocessing and power-line cancellation
An open-source ECG toolbox (OSET), available at: http://ecg.sharif.ir/
Removing ECG artifacts from other biosignals: EEG, EMG, etc.
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Conclusion and Perspectives
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Conclusion and Perspectives
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