An alternative to the biomagnetic forward problem in a realistically shaped head model, the "weighted vertices"

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Abstract
The "weighted vertices" (WV), an alternative in solving the biomagnetic forward problem (BFP) for a realistically shaped head (RSH) model are presented. This proposed approach differs from the others in the way some terms in the governing integral equations are defined. The effects that WV has on important issues such as the "auto solid angle" and "stability of equations" are discussed. Two variants of the WV approach, i.e., the "linear weight" and the "quadratic weight," have been developed, and comparison of results produced by these two approaches shows that the implementation of quadratic elements to evaluate the integral produces significant improvements. This study is done with a focus on magnetic rather than electric phenomena, so a homogeneous conductor has been used in the numerical example. However, the thoughts behind this proposed method can be easily extended for cases where inhomogeneous conductors are involved. Significant improvement in the accuracy of the forward problem has been observed by use of the WV approach.