Noninvasive myocardial activation time imaging: a novel inverse algorithm applied to clinical ECG mapping data

Linear approaches like the minimum-norm least-square algorithm show insufficient performance when it comes to estimating the activation time map on the surface of the heart from electrocardiographic (ECG) mapping data. Additional regularization has to be considered leading to a nonlinear problem formulation. The Gauss-Newton approach is one of the standard mathematical tools capable of solving this kind of problem. To our experience, this algorithm has specific drawbacks which are caused by the applied regularization procedure. In particular, under clinical conditions the amount of regularization cannot be determined clearly. For this reason, we have developed an iterative algorithm solving this nonlinear problem by a sequence of regularized linear problems. At each step of iteration, an individual L-curve is computed. Subsequent iteration steps are performed with the individual optimal regularization parameter. This novel approach is compared with the standard Gauss-Newton approach. Both methods are applied to simulated ECG mapping data as well as to single beat sinus rhythm data from two patients recorded in the catheter laboratory. The proposed approach shows excellent numerical and computational performance, even under clinical conditions at which the Gauss-Newton approach begins to break down.