Computational Aspects of Electrocardiological Inverse Solutions

The purpose of this work is to investigate the effect of certain numerical factors on the electrocardiographic inverse solution. Since usually the zero-order Tikhonov regularization is applied in order to solve the inverse problem, choosing the right regularization parameter is very important. The used linear equation system solver also plays an important role in the accuracy of the solution. Therefore these two factors were studied in a well defined model environment. Reference epicardial and body surface potential maps were generated in 1003 epicardial and 344 body surface points, respectively, by the Wei-Harumi model, for the QRS interval. The inverse problem has been solved with various regularization parameters and linear equation system solvers. The highest correlations (> 0.9) occurred in the first half of the QRS interval and the correlation fell below 0.6 at the end of the QRS. The result was highly dependent on the chosen regularization parameter and equation system solver, and it was significantly influenced also by the complexity of the epicardial potential distribution. The optimal solving configuration proved to be the application of the Cholesky factorization with the regularization parameter of 10 −14 .