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An Approach to ECG Delineation using Wavelet Analysis and Hidden Markov Models. Maarten Vaessen (FdAW/Master Operations Research) Iwan de Jong (IDEE/MI) Ronald Westra (FdAW/Math) Jo ë l Karel (FdAW/Math). Presentation overview. ECG Wavelet Analysis Hidden Markov Models WTSign Method - PowerPoint PPT Presentation
Citation preview
An Approach to ECG Delineation using Wavelet
Analysis and Hidden Markov Models
Maarten Vaessen(FdAW/Master Operations Research)
Iwan de Jong (IDEE/MI)
Ronald Westra (FdAW/Math)
Joël Karel (FdAW/Math)
Presentation overview
• ECG
• Wavelet Analysis
• Hidden Markov Models
• WTSign Method
• Tests & Results
• Conclusions
• Questions
ElectroCardioGram
• Important components: QRS complex and T-wave.• QT-time clinically important.• Wide variety of morphologies possible.• Automatic analysis is difficult.
ECG/Wavelet/HMM/WTSign/T&R/Conc
• Wavelet Transformation (WT) decomposes signal in time-frequency space.– Different ECG waves have different temporal
features and different frequency content.– Visible at different locations and scales.– Filter noise.– Filter baseline-drift.
• Wavelet function (Mother wavelet) determines WT properties.
Wavelet Analysis
ECG/Wavelet/HMM/WTSign/T&R/Conc
Gaussian Wavelet
• Mother wavelet 1st derivative of Gaussian function (DOG)– WT of signal with Gaussian wavelet ψ(t) is the derivative of signal
smoothed by Gaussian window θ(t).
– Zero-crossings in WT maxima or minima signal.
– Maxima or minima in WT point of inflection in signal
ECG/Wavelet/HMM/WTSign/T&R/Conc
dt
ftWf )()(1
),(
ECG/Wavelet/HMM/WTSign/T&R/Conc
2
4
8
16
32
ECG
WT based methods
• Wavelet Transform Modulus Maxima Method – Use the local modulus maxima (MM) in WT to
detect ECG peaks– QRS = positive MM followed by negative MM– Features WT
• Amplitude MM
• Lipschitz exponent (measure for regularity signal).
ECG/Wavelet/HMM/WTSign/T&R/Conc
Properties WTMM
• WTMM uses decision rules and thresholds for detection.
• Disadvantages: – Thresholds are ‘hard’.– Difficult to extend method.– Not well suited for real-time analysis.
ECG/Wavelet/HMM/WTSign/T&R/Conc
Hidden Markov Model
• Probabilistic model – Markov-chain capture cyclic nature of ECG
components (P, QRS, T).– Can model statistical properties of the ECG.– Decisions are derived from maximum
likelihood.
ECG/Wavelet/HMM/WTSign/T&R/Conc
O1 O2 O3
bb1(O1) bQRS(O2) bQRS(O3)
O4 O5
bQRS(O4) bT(O5)
Markov chain:
Observation sequence:
HMM Topology
ECG/Wavelet/HMM/WTSign/T&R/Conc
p
QRS
Tb2
b1
b1 TQRSP b2
Observation Probabilities:
ab2-b2
ab2-P
HMM Parameters
• Train model supervised– State transitions probabilities derive from
annotated ECG.
– Observations Ot = Wf(t,{2,4,8}).
– Observation probabilities Gaussian mixture model, 2 mixtures.
ECG/Wavelet/HMM/WTSign/T&R/Conc
HMM Detection
• Viterbi algorithm– Given the observation sequence.– Calculate most probable state sequence.
– Relate observation Ot to a certain state.
ECG/Wavelet/HMM/WTSign/T&R/Conc
HMM State durations
• Modeling an ECG wave:– ECG wave (e.g. T-wave) has a certain duration
(number of samples in digitized signal).– For a correct detection, the HMM has to be in
the T-state for the duration of the T-wave.– Example: T-wave duration 0.1 sec. 40
samples.– The HMM has to make a self-transition from
state ‘T’ to state ‘T’ 40 times.
ECG/Wavelet/HMM/WTSign/T&R/Conc
HMM State duration
T0.95
0.05 ?
ECG/Wavelet/HMM/WTSign/T&R/Conc
HSMM
• Hidden Semi-Markov Model– State-durations are modeled explicitly by a
duration probability function– No more self-transitions.– HSMM can perform the same tasks as HMM
(Viterbi).
ECG/Wavelet/HMM/WTSign/T&R/Conc
HSMM
b1 TQRSP b3
O1,O2,…,Od1
p(d1)
ECG/Wavelet/HMM/WTSign/T&R/Conc
p
QRS
Tb2
b1
HSMM
• How do we calculate the observation probability– HMM bi(Ot).– HSMM
bP(O1,O2,…,Od1) = bP(O1)*bP(O2)*…* bP(Od1).
• Is this a good classifier?– No, WT is not Gaussian.– Observations are not independent.
ECG/Wavelet/HMM/WTSign/T&R/Conc
Conclusions so far
ECG/Wavelet/HMM/WTSign/T&R/Conc
• Markov chain of HMM can model the cyclic nature of the ECG components.
• Normal HMM has problems modeling long state durations.
• HSMM deals with this, but at the cost of increased computational complexity
– HMM O(N2T),
– HSMM O(N2T ½ D2 ), ½ D2 = 20000!
• Observation probabilities are not a strong classifier.
WTSign Methode
• ECG components consist of rising and falling edges
• First localize edges in ECG by wavelet coefficients.
• Then classify them by a HMM.
ECG/Wavelet/HMM/WTSign/T&R/Conc
Localization
• Localization of edges in ECG.
• Gaussian wavelet WT is smoothed derivative of signal.
• Wavelet coefficients– Modulus maximum = point of inflection edge.– Positive coefficient = rising edge.– Negative coefficient = falling edge.
ECG/Wavelet/HMM/WTSign/T&R/Conc
Localization
ECG/Wavelet/HMM/WTSign/T&R/Conc
Edge observation
• Edge is observation HMM.
• What features of the wavelet coefficients from the edge can be used for probability calculation.
ECG/Wavelet/HMM/WTSign/T&R/Conc
Edge features
• Amplitude Modulus Maxima WT, at scales 4,8.
• Length edge.
• Lipschitz exponent.
ECG/Wavelet/HMM/WTSign/T&R/Conc
Edge features
ECG/Wavelet/HMM/WTSign/T&R/Conc
HMM for WTSign
RST
T1R
Q
i1S
T2
i2
Q
ECG/Wavelet/HMM/WTSign/T&R/Conc
RST
T1R
Q
i1S
T2
i2
ECG/Wavelet/HMM/WTSign/T&R/Conc
RST
T1R
Q
i1S
T2
i2
ECG/Wavelet/HMM/WTSign/T&R/Conc
RST
T1R
Q
i1S
T2
i2
ECG/Wavelet/HMM/WTSign/T&R/Conc
Tests & Results
• Test set– MIT/BIH QT-database.– 105 record.– Cardiologist Annotations: (p)(N)t).
• Golden standard.
ECG/Wavelet/HMM/WTSign/T&R/Conc
Tests & Results
• Evaluation parameters– Sensitivity
• QRS, QRS onset, T-wave, T-wave offset.
– Positive predictive value• QRS onset, T-wave offset.
– Deviation from manual annotation• QRS onset, T-wave offset.
– Deviation QT-time
ECG/Wavelet/HMM/WTSign/T&R/Conc
OverviewSe QRS Se Qon P+ Qon m Qon (ms)
HMM 99,11% 99,94% 67,74% 15,7HSMM 98,79% 99,94% 93,16% 12,9WTSign 99,40% 95,34% 90,75% -5,8
Se T Se Toff P+ Toff m Toff (ms)HMM 66,86% 75,85% 49,84% 10,5HSMM 83,49% 84,05% 79,24% 9,9WTSign 94,65% 86,16% 83,56% 45,0
ECG/Wavelet/HMM/WTSign/T&R/Conc
manQTtime (ms) εQTtime (ms)HMM 422,1 -193,6HSMM 422,1 -58,6WTSign 422,1 38,0
HMM Concatenated set
HSMM Concatenated set
WTSign
Conclusions• HMM-WT approaches have been successfully
used for ECG delineation.• The WT of the ECG gives a well-suited
representation of the ECG as input for the HMM.• HMM can perform accurate ECG delineation on
certain records.• The HMM state duration is not adequate for the
ECG.• HSMM solves this problem.
ECG/Wavelet/HMM/WTSign/T&R/Conc
Conclusions• WT as input for a HSMM can perform accurate ECG
delineation on a large number of records.• HSMM has a high computational complexity.• The probability measure for the HMM and HSMM
observation are a weak classifier.• A new method (WTSign) has been developed to
overcome the shortcomings of the HMM and HSMM.• The WTSign method has the highest sensitivity.• Delineation accuracy for Toff is less then HMM and
HSMM.
ECG/Wavelet/HMM/WTSign/T&R/Conc
Recommendations• Other wavelet functions might have better
properties.• The topologies of the HMM and HSMM can be
further developed.• WTSign delineation accuracy can be improved
(edge detection or post processing).• The WTSign observation features can be further
researched.• WTSign HMM topology can be re-evaluated.
ECG/Wavelet/HMM/WTSign/T&R/Conc
Questions?