1 / 38

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

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

hedy
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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. ECG/Wavelet/HMM/WTSign/T&R/Conc ElectroCardioGram • Important components: QRS complex and T-wave. • QT-time clinically important. • Wide variety of morphologies possible. • Automatic analysis is difficult.

  4. ECG/Wavelet/HMM/WTSign/T&R/Conc Wavelet Analysis • 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.

  5. 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

  6. ECG/Wavelet/HMM/WTSign/T&R/Conc

  7. 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).

  8. 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.

  9. 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.

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

  11. ECG/Wavelet/HMM/WTSign/T&R/Conc 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.

  12. 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.

  13. 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.

  14. ECG/Wavelet/HMM/WTSign/T&R/Conc HMM State duration ? T 0.05 0.95

  15. 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).

  16. ECG/Wavelet/HMM/WTSign/T&R/Conc HSMM QRS T p b2 b1 P b1 QRS T b3 p(d1) O1,O2,…,Od1

  17. ECG/Wavelet/HMM/WTSign/T&R/Conc 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.

  18. ECG/Wavelet/HMM/WTSign/T&R/Conc 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.

  19. ECG/Wavelet/HMM/WTSign/T&R/Conc WTSign Methode • ECG components consist of rising and falling edges • First localize edges in ECG by wavelet coefficients. • Then classify them by a HMM.

  20. 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.

  21. ECG/Wavelet/HMM/WTSign/T&R/Conc Localization

  22. 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.

  23. ECG/Wavelet/HMM/WTSign/T&R/Conc Edge features • Amplitude Modulus Maxima WT, at scales 4,8. • Length edge. • Lipschitz exponent.

  24. ECG/Wavelet/HMM/WTSign/T&R/Conc Edge features

  25. ECG/Wavelet/HMM/WTSign/T&R/Conc HMM for WTSign S i1 R T1 Q Q RST T2 i2

  26. ECG/Wavelet/HMM/WTSign/T&R/Conc S i1 R T1 Q RST T2 i2

  27. ECG/Wavelet/HMM/WTSign/T&R/Conc S i1 R T1 Q RST T2 i2

  28. ECG/Wavelet/HMM/WTSign/T&R/Conc S i1 R T1 Q RST T2 i2

  29. ECG/Wavelet/HMM/WTSign/T&R/Conc Tests & Results • Test set • MIT/BIH QT-database. • 105 record. • Cardiologist Annotations: (p)(N)t). • Golden standard.

  30. 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

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

  32. HMM Concatenated set

  33. HSMM Concatenated set

  34. WTSign

  35. ECG/Wavelet/HMM/WTSign/T&R/Conc 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.

  36. 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.

  37. 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.

  38. Questions?

More Related