1. Real-time identification of cardiac substrate anomalies Author : Philippe Haldermans Promoters : dr. Ronald Westra dr. ir. Ralf Peeters dr. ir. Ralf Peeters 13th September 2004

2. Contents  Motivation  Forward modelling  Inverse methods  Results  Conclusions

3. Motivation  Atrium fibrillation (AF) – cell triggers – wave maintenance by substrate anomalies  New spatial-temporal data  better image of wave propagation (movie) movie

4. Objective Can we develop a method that is able to identify substrate anomalies, using the new spatial-temporal data?

5. Forward modelling (1)  Biophysically detailed models + Luo-Rudy, Beeler-Reuter, … – Complicated for inverse method  Cellular automata + Simple and fast, especially for normal propagation – Absence of parameters for inverse estimation

6. Forward modelling (2)  Fitzhugh-Nagumo model – Partial differential equation – –

7. Forward modelling (3) –Discretized in time and space  Space : symmetric estimation  Time : normal estimation

8. Experiments (1)  Types of waves: – Planar – Spherical – Spiral  Different sorts of tissue: –Isotropic Anisotropic –Homogeneous Inhomogeneous

9. Experiments (2)  Refractory period  Re-entering waves –Spiral waves (spiral.avi) spiral.avi –Figure-8 reentry (figure8.avi) (figure8.avi)  Laws of physics –Rotations –Snellius’ law

10. Inverse methods  Rewriting equations  linear in the parameters  Iterative linear least squares estimation  Proof of usefulness – Robustness for rounding errors – Effect of noisy data

11. Results (1)  Simulated data: – Good estimation of the parameters – Method holds even with noisy data – Able to find anomalies (tissue) (demo) tissuedemotissuedemo  Data movies – Proved in theory  estimation works – Practical problems with matlab

12. Results (2)  Real data : – First dataset (movie) (movie)  shows normal propagation  method finds smooth surface (tissue) (tissue) –Second dataset (movie) (movie)  fibrillatory propagation  no anomalies in the conductivity (tissue) (tissue)  example of other problem : cell triggering?

13. Other inverse methods (1)  Bayesian approach – estimation of the uncertainty – groups of solutions – prior distribution & likelihood function  posterior distribution – can be used as first estimation for other methods

14. Other inverse methods (2)  Regularization – Moore-Penrose pseudo-inverse  Problems with : –Small singular values + noisy data  Possible solutions : – Truncated singular value decomposition – Tikhonov regularization

15. Conclusions  Identify spatial anomalies in the conductivity  Fitzhugh-Nagumo  Realistic properties  Estimation method works + is robust  Real data – able to give conductivity – these examples show no problems in the conductivity

16. Recommendations (1)  Other forward model – Biologically more detailled – Other properties  Different inverse method – Bayesian, regularization, … – Combination: least squares with Bayesian

17. Recommendations (2)  Real data – More datasets – More information about the data  Combination with the spatial-temporal data measurement  real-time identification