An Approach to ECG Delineation using Wavelet Analysis and Hidden Markov Models

1
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)

2
Presentation overview

• ECG
• Wavelet Analysis
• Hidden Markov Models
• WTSign Method
• Tests Results
• Conclusions
• Questions

3
ElectroCardioGram
ECG/Wavelet/HMM/WTSign/TR/Conc

• Important components QRS complex and T-wave.
• QT-time clinically important.
• Wide variety of morphologies possible.
• Automatic analysis is difficult.

4
Wavelet Analysis
ECG/Wavelet/HMM/WTSign/TR/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.

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Gaussian Wavelet
ECG/Wavelet/HMM/WTSign/TR/Conc

• Mother wavelet 1st derivative of Gaussian
  function (DOG)
• WT of signal with Gaussian wavelet ?(t) is the
  derivative of signal smoothed by Gaussian window
  ?(t).
• Zero-crossings in WT ? maxima or minima signal.
• Maxima or minima in WT ? point of inflection in
  signal

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ECG/Wavelet/HMM/WTSign/TR/Conc
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WT based methods
ECG/Wavelet/HMM/WTSign/TR/Conc

• 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).

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Properties WTMM
ECG/Wavelet/HMM/WTSign/TR/Conc

• WTMM uses decision rules and thresholds for
  detection.
• Disadvantages
• Thresholds are hard.
• Difficult to extend method.
• Not well suited for real-time analysis.

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Hidden Markov Model
ECG/Wavelet/HMM/WTSign/TR/Conc

• 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.

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ECG/Wavelet/HMM/WTSign/TR/Conc
HMM Topology
QRS
p
T
b2
b1
ab2-P
b1
T
QRS
P
b2
Markov chain
ab2-b2
Observation Probabilities
bQRS(O3)
bb1(O1)
bQRS(O2)
bQRS(O4)
bT(O5)
O1
O2
O3
O4
O5
Observation sequence
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HMM Parameters
ECG/Wavelet/HMM/WTSign/TR/Conc

• Train model supervised
• State transitions probabilities ? derive from
  annotated ECG.
• Observations ? Ot Wf(t,2,4,8).
• Observation probabilities ? Gaussian mixture
  model, 2 mixtures.

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HMM Detection
ECG/Wavelet/HMM/WTSign/TR/Conc

• Viterbi algorithm
• Given the observation sequence.
• Calculate most probable state sequence.
• Relate observation Ot to a certain state.

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HMM State durations
ECG/Wavelet/HMM/WTSign/TR/Conc

• 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.

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HMM State duration
ECG/Wavelet/HMM/WTSign/TR/Conc
?
T
0.05
0.95
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HSMM
ECG/Wavelet/HMM/WTSign/TR/Conc

• 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).

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HSMM
ECG/Wavelet/HMM/WTSign/TR/Conc
QRS
T
p
b2
b1
b1
T
QRS
P
b3
p(d1)
O1,O2,,Od1
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HSMM
ECG/Wavelet/HMM/WTSign/TR/Conc

• 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.

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Conclusions so far
ECG/Wavelet/HMM/WTSign/TR/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.

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WTSign Methode
ECG/Wavelet/HMM/WTSign/TR/Conc

• ECG components consist of rising and falling
  edges
• First localize edges in ECG by wavelet
  coefficients.
• Then classify them by a HMM.

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Localization
ECG/Wavelet/HMM/WTSign/TR/Conc

• 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.

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Localization
ECG/Wavelet/HMM/WTSign/TR/Conc
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Edge observation
ECG/Wavelet/HMM/WTSign/TR/Conc

• Edge is observation HMM.
• What features of the wavelet coefficients from
  the edge can be used for probability calculation.

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Edge features
ECG/Wavelet/HMM/WTSign/TR/Conc

• Amplitude Modulus Maxima WT, at scales 4,8.
• Length edge.
• Lipschitz exponent.

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Edge features
ECG/Wavelet/HMM/WTSign/TR/Conc
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HMM for WTSign
ECG/Wavelet/HMM/WTSign/TR/Conc
i1
S
T1
R
Q
Q
RST
T2
i2
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ECG/Wavelet/HMM/WTSign/TR/Conc
i1
S
T1
R
Q
RST
T2
i2
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ECG/Wavelet/HMM/WTSign/TR/Conc
i1
S
T1
R
Q
RST
T2
i2
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ECG/Wavelet/HMM/WTSign/TR/Conc
i1
S
T1
R
Q
RST
T2
i2
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Tests Results
ECG/Wavelet/HMM/WTSign/TR/Conc

• Test set
• MIT/BIH QT-database.
• 105 record.
• Cardiologist Annotations (p)(N)t).
• Golden standard.

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Tests Results
ECG/Wavelet/HMM/WTSign/TR/Conc

• 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

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Overview
ECG/Wavelet/HMM/WTSign/TR/Conc
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HMM Concatenated set
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HSMM Concatenated set
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WTSign
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Conclusions
ECG/Wavelet/HMM/WTSign/TR/Conc

• 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.

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Conclusions
ECG/Wavelet/HMM/WTSign/TR/Conc

• 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.

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Recommendations
ECG/Wavelet/HMM/WTSign/TR/Conc

• 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.

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Questions?