Biomedical Signal Processing Forum , August 30th 2005

1. Biomedical Signal Processing Forum,August 30th 2005

2. BioSens (2/2): wavelet based morphological ECG analysis Joel Karel, Ralf Peeters, Ronald L. Westra Maastricht University Department of Mathematics Biomedical Signal Processing Forum,August 30th 2005

3. Biosens: prehistory from 1994 onwards TU Delft micro electronics UM mathematics Richard Houben Medtronic Bakken Research Maastricht Other companies UM Fysiology Prof. M. Allessie

4. BIOSENS TU Delft micro electronics UM mathematics Medtronic Bakken Research Maastricht TU Delft DIMES UM Fysiology STW project Biosens 2004-2008 Organization & research consortium

5. Focus on: morphological analysis Research topics studied so far 1. Efficient analog implementation of wavelets • Analog implementation of wavelets allows low-power consuming wavelet transforms for e.g. implantable devices • Wavelets cannot be implemented in analog circuits directly but need to be approximated: A good approximation approach will allow reliable wavelet transforms 2. Epoch detection and segmentation • Application of the Wavelet Transform Modulus Maxima method to T-wave detection in cardiac signals. 3. Optimal discrete wavelet design for cardiac signal processing • What is the best wavelet relative to the data and pupose?

6. 1. Efficient implementation of analog wavelets Biosens team: J.M.H. Karel (PhD-student), dr. R.L.M. Peeters, dr. R.L. Westra Accepted papers: BMSC 2005 (Houffalize, Belgium), IFAC 2005 (Prague, Czech Republic), and CDC/EDC 2005 (Sevilla, Spain)

7. Implementation of wavelets • Analog implementation of wavelets allows low-power consuming wavelet transforms for e.g. implantable devices • Wavelets cannot be implemented in analog circuits directly but need to be approximated

8. Wavelet approximation considerations • A good approximation approach will allow reliable wavelet transforms • will allow low-order implementation (low-power consuming) of wavelet transforms • allows approximation of various types of wavelets • is relatively easy applicable

9. Wavelet approximation methodology

10. Initial high-order discrete time MA-system • Sampled wavelet function • Required i.r. • State-space realization in controllable companion form

11. Model reduction with balance and truncate • Balance Lyapunov-equations • Note that P is identity matrix • Reduce system based on Hankel singular values

12. L2-approach • Wavelet is approximated by impulse response of system • The model class is determined by the system who’s i.r. is used as a starting point

13. Morlet approximation

14. Daubechies 3 wavelet

15. Wavelet approximation methodology • Allows approximation of wavelet function that previously could not be approximated • Allows approximation of more generic functions • Publications accepted for: IFAC 2005 (Prague, Czech Republic), CDC/ECC 2005 (Sevilla, Spain), and BMSC 2005 (Houffalize, Belgium),

16. 2. ECG morphological analysis using designer wavelets Biosens team: J.M.H. Karel (PhD-student), dr. R.L.M. Peeters, dr. R.L. Westra Graduation students: Pieter Jouck, Kurt Moermans, Maarten Vaessen

17. Signal Data Analyzing wavelet Purpose of application Wavelet based signal analysis

18. Signal morphology and optimal wavelet design (1) • Design wavelet such that they detect morphology in signal • Wavelet transform can be seen as convolution • Maximum values if wavelet resembles signal in an L2 sense • Fit a wavelet to signal or create optimal wavelet in wavelet domain

19. Signal morphology and optimal wavelet design (2) • Can be used to detect epochs • Detecting morphologies related to pathologies • Computational efficient

20. Example of optimized wavelet for R-peak detection

21. Resulting transform

22. 2.1 Application of the wavelet Transform Modulus Maxima method to T-wave detection in cardiac signals J.M.H. Karel, P. Jouck, R.L. Westra

23. T-wave detection in electrocardiograms • Pilot study based on state-of-the-art approach (e.g. Li 1995, Butelli 2002) • WTMM-based algorithm • Approximation of singular value (Lipschitz coefficient) did not show to be particularly discriminating • Approach successful on a variety of R&T-wave morphologies • Classification strategy rather ad hoc

24. Epoch detection and segmentation

25. Example: Application of the Wavelet Transform Modulus Maxima method to T-wave detection in cardiac signals

26. Objectives • ECG segmentation: epoch detection • Characterization of epoch

27. Testcase: T-wave detection • Complications with T-wave detection: • low amplitude • Wide variety of T-waves types • fuzzy positioning

28. Conventional Methodes • 1st step : Filter → filtering of fluctuations and artifacts • Different types of filters • Differential filters • Digital filters • 2d step : Signal comparsion using threshold

29. Conventional Methods • Advantages: • Simple and straightforward methodology • Ease of implementation • Disadvantages: • Sensitive for stochastic fluctuations • Bad detection of complexes with low amplitudes

30. Wavelet Transform • Wavelet transform of signal f using wavelet : • Frequency and time domain • Spectral analysis by scaling with a(dilation) • Temporal analysis by translation with b

31. Example WTMM

32. WTMM-based QRS detection (1) • Dyadic transform scales : 21 22 23 24

33. WTMM-based QRS detection (2) • Identification of Modulus Maxima • QRS-complex → 2 modulus maxima (MM) • Find all MM on all scales • Delete redundant MMs • 2 positive or 2 negative recurring MMs • Proximate MM multiples (too close for comfort)

34. WTMM-based QRS detection (3) • Positioning of R-peak • Zero-crossing between positive and negative MMs

35. Adjustments for T-wave detection • Transform to scale 10

36. Adjustments for T-wave detection • Search for Modulus Maxima • Only MMs above a given threshold • Position of T-wave peak • Normal T-wave → MM pare → zero-crossing • T-wave with single increase/decrease → one MM near peak

37. Results • Sensitivity of WTMM-based methode to: • Low T-wave amplitudes • Noise and stochastic variation • Baseline-drift • complex T-wave morphology

38. Results

39. Results • Testcases: Signals from: i) MIT-BIH database, and ii) Cardiology department of Maastricht University. • Performance: • Number of True Positive detections (TruePos) • Number of False Positive detections (FalsePos) • Number of True Negative detections (TrueNeg) • Number of False Negative detections (FalseNeg) • Total number of peaks (TotalPeak) • Percentage of detected T-waves (Sensitivity) • Percentage of correct detections (PercCorr)

40. Testcase 1

41. Testcase 2

42. Testcase 3

43. Testcase 4

44. Discussion • Problems • Low amplitude + high noise levels • Extremely short ST-intervals • Not all types of T-wave are detected • Improvements • Automatic scale adjuster • More decision rules • Learning algorithm

45. Conclusion • Reliable method • Robust and noise-resistent • Good performance in sense of sensitivity and percentage correct (typically > 85%)

46. 2.2 Optimal discrete wavelet design for cardiac signal processing J.M.H. Karel, R.L.M. Peeters and R.L. Westra EMBC 2005(= 27th Annual International Conference of the IEEE Engineering in Medicine and Biology Society), 1-4 September 2005, Shanghai, People’s Republic of China

47. Optimal Wavelet Design What is a good wavelet for a given signal and a given purpose? • Freedom in choice for analyzing wavelet (t) • Best output (= wavelet coefficients ck) are well positioned in frequency-temporal space, i.e. sparse representation • Essentials: perfect reconstruction, orthogonal wavelet-multi resolution structure, vanishing moments of wavelets, flatness of filter, smooth wavelets • Measure the performance of a given signal x(t) and a trial wavelet (t) with a criterion function V[]

48. Optimal Wavelet Design Orthogonal wavelets and filter banks

49. Wavelet analysis and synthesis • Low pass filter with transfer function C(z) • High pass filter with transfer function D(z) • Combination with down-sampling •  has compact support C, D are FIR

50. Wavelets: analysis and synthesis