Dense electrical map reconstruction from ECG/MCG measurements using a priori myocardial fiber structure and activation sequence information

Reconstruction of the current density in the myocardium from electrocardiography and magnetocardiography (ECG/MCG) measurements is an ill-posed inverse problem. If the current dipole model is used, 6 parameters must be determined per dipole: 3 for the dipole position, 3 for the dipole moment. Considering the small number of measurements it is not realistic to properly reconstruct a dense dipole field. A priori information is required. Our goal is to reconstruct a dense dipole field within a voxelized image of the heart at a particular instant of the cardiac cycle. A dipole is assigned to each voxel (therefore the position is known) and its orientation is given by the local muscle fiber direction eventually observed on an MR diffusion image of the heart. Only the dipole moment magnitude has to be determined. We constrain this simplified inverse problem using the knowledge of a standard activation sequence of the myocardium, thereby encouraging significant magnitudes in regions where the muscle is supposed to be activated at that time and discouraging non-zero magnitudes in other regions. This constraint is implemented using semi-quadratic regularization. The minimization of the regularized criterion is performed using a conjugate gradient algorithm. Preliminary results are provided using a homogeneous sphere.