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Solving the inverse problem of electrocardiography (ECG) and magnetocardiography (MCG) is often referred to as cardiac source imaging. Spatial properties of ECG and MCG as imaging systems are, however, not well known. In this modelling study, we investigate the sensitivity and point-spread function (PSF) of ECG, MCG, and combined ECG+MCG as a function of source position and orientation, globally around the ventricles: signal topographies are modelled using a realistically-shaped volume conductor model, and the inverse problem is solved using a distributed source model and linear source estimation with minimal use of prior information. The results show that the sensitivity depends not only on the modality but also on the location and orientation of the source and that the sensitivity distribution is clearly reflected in the PSF. MCG can better characterize tangential anterior sources (with respect to the heart surface), while ECG excels with normally-oriented and posterior sources. Compared to either modality used alone, the sensitivity of combined ECG+MCG is less dependent on source orientation per source location, leading to better source estimates. Thus, for maximal sensitivity and optimal source estimation, the electric and magnetic measurements should be combined.

Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from the standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.

In epicardial potential imaging, the epicardial potential is reconstructed computationally from the measured body surface potential. The transfer function that relates the heart and body surface potentials is commonly constructed with some point-collocation-weighted boundary element technique, assuming an electrically homogeneous volume conductor. This assumption causes modeling errors. In this study, the system of surface integral equations that describes the relationship between the heart and body surface potentials is thoroughly derived in a piece-wise homogeneous volume conductor. The equations are discretized with the method of weighted residuals, enabling the use of Galerkin weighting in the numerical solution of the equations. The construction of the transfer matrix is described in detail for constant and linear collocation and Galerkin methods, and the resulting forward transfer matrices are validated via simple numerical simulations. The linear Galerkin method is found to generate the smallest errors. The presented method increases the accuracy of the forward-computed body surface potential and thus prepares the way for more accurate inverse reconstructions of epicardial potential.