1. Model-Based ECG Fiducial Points Extraction Using a Modified EKF Structure Presented by: Omid Sayadi Biomedical Signal and Image Processing Lab (BiSIPL), Sharif University of Technology, Tehran, Iran

2. 2 Contents:  Introduction and Problem Statement  Theoretical Background  Model-Based Approaches  Modified EKF Structure  Simulation and Results  Conclusion & Future Work

3. 3 Introduction  Heart: a hollow muscular organ which through a coordinated muscle contraction generates the force to circulate blood throughout the body.  Electrocardiogram: a graph representing the electrical activity of heart, also called ECG.  5 dominant characteristic waveforms and FPs,  Single/Multiple beat features, including:  Amplitude features,  Time intervals,  Wave durations.

4. 4 Problem Statement  Arrhythmia Investigation, detection, diagnosis and treatment:  Major Problems: Decision Dependency, Variability, Noise and Drifts, Ischemia Sinus Bradycardia Wolf Parkinson White Branch Bundle Block (BBB) Ventricular Tachycardia (VT) Ventricular Bigeminy/Trigeminy Atrial/Ventricular Flutter (AFL/VFL) Premature Atrial Contraction (APC) Atrial/Ventricular Fibrillation (AF/VF) Premature Ventricular Contraction (PVC) Lack of sufficient morphological information.

5. 5 Problem Statement  Goal: Adaptive usage of the underlying ECG dynamical mechanism. Accuracy achievement for Arrhythmia Investigation:  Beat Detection,  Beat Classification,  Fiducial Points Extraction,  Interval Timing Calculation,  Feature Generation.

6. 6 Contents:  Introduction and Problem Statement  Theoretical Background  Model-Based Approaches  Modified EKF Structure  Simulation and Results  Conclusion & Future Work

7. 7 Theoretical Background  ECG Dynamical Model (EDM):

8. 8 Theoretical Background  EDM fit to an arbitrary ECG cycle: A prior estimate of the 5 Gaussian functions Nonlinear fit with Least Squares Error (LSE)  For an ECG waveform: Cycle to Cycle fit.

9. 9 Contents:  Introduction and Problem Statement  Theoretical Background  Model-Based Approaches  Modified EKF Structure  Simulation and Results  Conclusion & Future Work

10. 10 Model-Based Approaches  Mathematical Nonlinear Modeling:  Least Square Error Fit: If we integrate the last equation of EDM, we conclude that: An Optimization Problem: where, s : Recorded ECG z : ECG generated by EDM

11. 11 Model-Based Approaches  Adaptive Tracking:  Considering the nonlinear underlying dynamics for estimation → Extended Kalman Filter (EKF=linearized KF) The discrete polar form of EDM: random white noise which represents the baseline wander effects and models other additive sources of process noise sampling period (discretization step) result of discrete derivation:

12. 12 Model-Based Approaches  EKF formulation:

13. 13 Contents:  Introduction and Problem Statement  Theoretical Background  Model-Based Approaches  Modified EKF Structure  Simulation and Results  Conclusion & Future Work

14. 14 Modified EKF Structure  Remember the ECG Dynamical Model (EDM):  EKF2 ( Sameni et al 2005 )  ECG and wrapped Phase of ECG → states,  Gaussian parameters, angular frequency and baseline → noises,

15. 15 Modified EKF Structure  EKF17 ( Sayadi and Shamsollahi, IEEE TBME, 2008 )  ECG, wrapped Phase and the Gaussian parameters → states,  Angular frequency, baseline and the associated noises to the Gaussian parameters model → noises,  Advantages:  GMM parameters are considered as the states,  Ability to reconstruct ECG (i.e. for compression tasks),  Ability to show the features related to the fiducial points. EKF2 EKF17

16. 16 Modified EKF Structure  AR(1) GMM parameters → Modified EKF (EKF17)  Process equations:  Observation equations:

17. 17 Modified EKF Structure  Linearized state-space model at each time instant around the most recent state estimation:

18. 18 Modified EKF Structure  Interpretation of GMM parameters of EDM:  FP extraction  Tachogram (RR-interval variability) extraction fluctuative parts of the estimations

19. 19 Contents:  Introduction and Problem Statement  Theoretical Background  Model-Based Approaches  Modified EKF Structure  Simulation and Results  Conclusion & Future Work

20. 20 Results  Estimated Gaussians’ parameters with EKF17 for record 231 (MIT-BIH database)

21. 21 Results  Fiducial points extraction results for records 106 and 117: (MIT-BIH database)

22. 22 Results  Numerical performance evaluation:

23. 23 Contents:  Introduction and Problem Statement  Theoretical Background  Model-Based Approaches  Modified EKF Structure  Simulation and Results  Conclusion & Future Work

24. 24 Conclusion  An EDM-based ECG fiducial points extraction scheme was proposed. In summary: It is very simple, very precise and has a low computational cost, It needs a non-accurate initial estimate for the KF, It uses the underlying dynamics for ECG signal, so it can be adapted to any ECG having five major PQRST waveforms, No thresholding is used in determination of FPs, There is an intrinsic denoising using the EDM, The method guarantees adaptive tracking of the morphological characteristics of the ECG signal. The AR(1) models provides a simple dynamics for the newly introduced state variables (i.e. GMM parameters), The modification is applied to the process, not the observations,

25. 25 Future Work  Fitting the model to highly abnormal ECGs such as bundle blocks,  Modifications of the model: Using more than 5 Gaussians,  Modifications of the model: Using a lag-normal function,  Improving the method using more precise dynamics for the GMM parameters, instead of the AR(1),  Incorporating the effects of baseline drifts.

26. 26 Thank You ☺