A Hybrid Integral Equation Approach to Solve the Anisotropic Forward Problem in Electroencephalography

摘要

The boundary element method provides a computationally efficient solution to the Electroencephalography (EEG) forward problem on piece-wise homogeneous head models by using surface integral equations. However, realistic modeling of the head medium requires a proper account of the anisotropic electric nature of the human skull, which cannot be handled by standard surface integral equations. This work addresses this issue by presenting a new formulation which perturbs the standard Lippmann-Schwinger approach with volume elements within the skull. The resulting surface/volume integral equation can handle computations of fully realistic modeling for both skull and white matter. Numerical results will confirm the validity of the approach as well as its applicability to real case scenarios.