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Dense electrical map reconstruction from ECG/MCG measurements with known fiber structure and standard activation sequence

Reconstruction of the current density in the myocardium from electrocardiography and magnetocardiography (ECG/MCG) measurements is an ill-posed inverse problem (the solution is not unique, or is unstable, or both). The equivalent current dipole model requires reconstruction of 6 parameters per dipole (position and moment). Considering the small number of measurements it is not realistic to perform a reconstruction of a dense dipole field without any a priori information. Our goal is to reconstruct a dense dipole field within a voxelized image of the myocardium at any given instant of the cardiac cycle. Each voxel is assigned a dipole (therefore the position is known) and the dipole moment orientation is given by the local myocardial fiber direction. Only the dipole moment magnitude must be determined. This simplified inverse problem is constrained using the knowledge of a standard activation sequence of the myocardium, thereby encouraging non-zero magnitudes in regions where the muscle should be activated and discouraging non-zero magnitudes in other regions. This constraint is implemented using half-quadratic regularization. The minimization of the regularized criterion is performed using a conjugate gradient algorithm. The method has been tested using the NCAT torso phantom.