Integral equation modelling of brain fibers for handling white matter anisotropies in the EEG forward problem

Boundary element methods are widely used in solving the Electroencephalography (EEG) forward problem, a key step in electric-based neuroimaging. Their high accuracy and computational efficiency have contributed to the popularity of EEG as an high resolution neuroimaging strategy. This notwithstanding, however, standard boundary element methods limit the scope of the models they can handle as they require the human head to be modeled as a piecewise isotropic and homogeneous medium. This can be a serious limitation given the anisotropic nature of the white matter. In this work, we present a new integral formulation that alleviates these shortcomings. Its accuracy and efficiency arise from the 1D modelization of the axon fibers, that can then be used to model white matter anisotropies. Numerical results validate and demonstrate the high accuracy of the presented technique.