Sensitivity Analysis of the Forward Electroencephalographic Problem Depending on Head Shape Variations

A crucial aspect in clinical practice is the knowledge of whether Electroencephalographic (EEG) measurements can be assigned to the functioning of the brain or to geometrical deviations of the human cranium. The present work is focused on continuing to advance understanding on how sensitive the solution of the forward EEG problem is in regard to the geometry of the head. This has been achieved by developing a novel analytic algorithm by performing a perturbation analysis in the linear regime using a homogenous spherical model. Notably, the suggested procedure provides a criterion which recognizes whether surface deformations will have an impact on EEG recordings. The presented deformations represent two major cases: (1) acquired alterations of the surface inflicted by external forces and (2) deformations of the upper part of the human head where EEG signals are recorded. Our results illustrate that neglecting geometric variations present on the heads surface leads to errors in the recorded EEG measurements less than 2%. However, for severe instances of deformations combined with cortical brain activity in the vicinity of the distortion site, the errors rise to almost 25%. Therefore, the accurate description of the head shape plays an important role in understanding the forward EEG problem only in these cases.