On the geometrical perturbation of a three‐shell spherical model in electroencephalography

Abstract

The forward electroencephalography (EEG) problem is studied in the framework of a multilayered structure, which models the scalp, skull, cerebrospinal fluid, and brain. Both the exterior and all inner boundaries are perturbed spheres so that special localized defects in head-brain imaging are considered in analytic fashion. Linear perturbation analysis is implemented, providing exact expression for the first significant term of the forward EEG solution of the perturbed problem. Comparison with the solution of the corresponding unperturbed spherical problem is included, together with numerical demonstration of the produced errors in special deformation cases. The results suggest that significant errors are caused when large inaccuracies in the headbrain structure in the vicinity of EEG source are not taken into account. Moreover, the suggested procedure provides a mathematical tool for evaluating quantitatively the impact of special deformations in the head representation on the EEG forward analytic solution.

Mathematical Modeling of Brain Swelling in Electroencephalography and Magnetoencephalography

“…Toward this direction, the magnetic induction field in the exterior of an ellipsoidally inhomogeneous, four-conducting-layer model of the human head is obtained analytically up to its quadrupole approximation [12], while in [13], the octapolic contribution of the dipolar current to the expansion of the magnetic induction field is provided. Additionally, other models have considered the head as a non-homogenous conductor, in the sense that it is comprised of multiple layers with different electric conductivity [16], representing the cerebrum, the fluid layer, the scull, and the scalp [17][18][19], while others have considered perturbations in specific layers representing tumors or injuries [20,21], in the aim of continuing to advance the understanding of how sensitive the solution of the forward EEG problem is in regard to the geometry of the head.…”