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

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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)

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

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

ftWf )()(1

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).

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.

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.

O1 O2 O3

bb1(O1) bQRS(O2) bQRS(O3)

bQRS(O4) bT(O5)

Markov chain:

Observation sequence:

HMM Topology

b1 TQRSP b2

Observation Probabilities:

ab2-b2

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.

HMM Detection

• Viterbi algorithm– Given the observation sequence.– Calculate most probable state sequence.

– Relate observation Ot to a certain state.

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.

HMM State duration

0.05 ?

• 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).

b1 TQRSP b3

O1,O2,…,Od1

• 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.

Conclusions so far

• 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.

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.

Localization

Edge observation

• Edge is observation HMM.

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

Edge features

• Amplitude Modulus Maxima WT, at scales 4,8.

• Length edge.

• Lipschitz exponent.

Edge features

HMM for WTSign

Tests & Results

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

• Golden standard.

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

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

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.

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

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.

Questions?

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

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