Sensitivity Analysis On A Simplified Model Of The Eeg Inverse Problem

Abstract

The electroencephalography (EEG) inverse problem consists in finding the location of a source
inside the brain from measurements of the potential collected via electrodes placed on the scalp. This
method provides a noninvasive technique that would contribute in the treatment of neurological diseases
such as epilepsy. The electric activity in the head is usually modeled by an elliptic equation with interfaces
on a bounded domain with Cauchy data on the boundary. The source is often assumed to be a dipole where
its location is a parameter of the model.
Inspired in the EEG problem, we define a parametric second order ordinary differential equation defined
on a real bounded interval with an interface where Dirichlet and interface conditions are imposed. The 1D
inverse problem we are interested in consists in estimating the location of the source from measurements of
the solution near to the endpoint of the interval. In this work sensitivity analysis is conducted and the impact
of the results in the IP for different models for the source is discussed.