# An Approach to ECG Delineation using Wavelet Analysis and Hidden Markov Models Maarten Vaessen (FdAW/Master Operations Research) Iwan de Jong (IDEE/MI)

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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 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

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

O1O1 O2O2 O3O3 b b1 (O 1 )b QRS (O 2 ) b QRS (O 3 ) O4O4 O5O5 b QRS (O 4 ) b T (O 5 ) Markov chain: Observation sequence: HMM Topology ECG/Wavelet/HMM/WTSign/T&R/Conc p QRS T b2 b1 TQRSPb2 Observation Probabilities: a b2-b2 a b2-P

HMM Parameters Train model supervised –State transitions probabilities  derive from annotated ECG. –Observations  O t = 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 O t 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 T 0.95 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 b1TQRSPb3 O 1,O 2,…,O d1 p(d1) ECG/Wavelet/HMM/WTSign/T&R/Conc p QRS T b2 b1

HSMM How do we calculate the observation probability –HMM  b i (O t ). –HSMM  b P (O 1,O 2,…,O d1 ) = b P (O 1 )*b P (O 2 )*…* b P (O d1 ). 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(N 2 T), –HSMM  O(N 2 T ½ D 2 ), ½ D 2 = 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 i1 S 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

Overview ECG/Wavelet/HMM/WTSign/T&R/Conc

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 T off 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?

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