A mixed discretized surface-volume integral equation for solving EEG forward problems with inhomogeneous and anisotropic head models

This work presents a new integral formulation to solve the EEG forward problem for potentially inhomogeneous and anisotropic head conductivity profiles. The formulation has been obtained from a surface/volume variational expression derived from Green's third identity and then solved in terms of both surface and volume unknowns. These unknowns are expanded with suitably chosen basis functions which systematically enforce transmission conditions. Finally, by leveraging on a mixed discretization, the equation is tested within the framework of a Petrov-Galerkin's scheme. Numerical results show the high level of accuracy of the proposed method, which compares very favourably with those obtained with existing, finite element, schemes.