Realtime identification of cardiac substrate anomalies Author Philippe

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

Contents § Motivation § Forward modelling § Inverse methods § Results § Conclusions

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

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

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

Forward modelling (2) § Fitzhugh-Nagumo model – Partial differential equation – –

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

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

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

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

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

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

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

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

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

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

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