Implementing a Consistency Criterion in Numerical Solution of the Bioelectric Forward Problem

The bioelectric forward problem is frequently formulated as an integral equation that relates unknown surface potentials with their known current generators, in a given volume conductor. The matrix of the discretized equations is singular, and this may cause difficulties in obtaining a numerical solution to the problem. A consistency criterion for the discretized equations is utilized in a new algorithm for the forward problem. Some examples of sources in a uniform spherical volume conductor were solved employing the new algorithm. It was found that the algorithm is reliable even when the number of discretized elements was relatively small. A comparison with the deflation method was done. In some examples the results were very close to each other. In other examples the results of the new algorithm were better.