A mathematical procedure for solving the inverse potential problem of electrocardiography. Analysis of the time-space accuracy from in vitro experimental data

The inverse potential problem of electrocardiography leads to a Cauchy problem for an elliptic operator and is strongly ill posed. Its solution must be determined by some regularization technique in which a parameter controls the amount of regularization of the solution. Therefore the choice of this smoothing parameter is important for achieving the best accuracy attainable given the discrete approximation errors and the noise level on the data. A regularized inverse procedure is applied to data from an in vitro experiment, and a new criterion for the choice of a quasi-optimal value of the smoothing parameter is described. The performance of this criterion is investigated, and a detailed analysis of the accuracy of the results is carried out. This analysis concerns both the recovered epicardial maps (space analysis) and the ECGs (time analysis). The inverse potential problem of electrocardiography leads to a Cauchy problem for an elliptic operator and is strongly ill posed. Its solution must be determined by some regularization technique in which a parameter controls the amount of regularization of the solution. Therefore the choice of this smoothing parameter is important for achieving the best accuracy attainable given the discrete approximation errors and the noise level on the data. A regularized inverse procedure is applied to data from an in vitro experiment, and a new criterion for the choice of a quasi-optimal value of the smoothing parameter is described. The performance of this criterion is investigated, and a detailed analysis of the accuracy of the results is carried out. This analysis concerns both the recovered epicardial maps (space analysis) and the ECGs (time analysis).