Numerical solution of the potential due to dipole sources in volume conductors with arbitrary geometry and conductivity

The integral conservation equation for biological volume conductors with general geometry and arbitrary distribution of electrical conductivity is solved using a finite volume method. An effective conductivity was defined for the boundaries between regions with abrupt change of the conductivity to allow the simultaneous solution of the entire domain although the derivatives are not continuous. The geometrical singularities arising from the spherical topology of the coordinate system are removed using the conservation law. The resulting finite volume solution method is efficient both in central processing unit (CPU) time and memory requirements, allowing the solution of the volume conductor equation using a large number of mesh points (of the order of 10 ⁵) even on small workstations (like SGI Indigo). It results in very accurate solutions, as several comparisons with analytical solutions of head models reveal. The proposed finite volume method is an attractive alternative to the finite element and boundary element methods that are more common in bioelectric applications.