A regularization technique for nonlinear ill-posed problems applied to Myocardial Activation Time Imaging

A regularization technique for nonlinear ill-posed problems is applied to noninvasive activation time imaging on the epi- and endocardium from simulated and measured electrocardiographic (ECG) and magnetocardiographic (MCG) mapping data. The regularization parameter applying second-order Tikhonov regularization is obtained by the L-curve method. The physical model is based on the bidomain theory. The transmembrane potential - the sources of the ECG and MCG - is modeled with an arctan template function. Because of the nonlinear relation between the transmembrane potential and the activation time, an iterative algorithm which extends the regularization method from the linear to the nonlinear case is developed. The initial activation time map is calculated by the critical point theorem. The method is checked for a normal cardiac propagation of the ventricle. The iterative approach converges after a few iterations resulting in a dramatic decrease in computation time and it shows a remarkable stability against variations in geometry and conductivity of the lungs and the torso. This noninvasive activation time imaging is also remarkable stable against variations in amplitude of the mapping data. High-quality inverse solutions are obtained from measured single beat ECG mapping data even using a smaller number of electrodes and (or) a standard model for the volume conductor.