Sensitivity Analysis for the EEG Forward Problem - Troparevsky, Maria I.; Rubio, Diana; Saintier, Nicolas (Frontiers in Computational Neuroscience, 2010)
Sensitivity Analysis can provide useful information when one is interested in identifying the parameter $θ$ of a system since it measures the variations of the output $u$ when $θ$ changes. In the literature two different sensitivity functions are frequently used: the Traditional Sensitivity Functions (TSF) and the Generalized Sensitivity Functions (GSF). They can help to determine the time instants where the output of a dynamical system has more information about the value of its parameters in order to carry on an estimation process. Both functions were considered by some authors who compared their results for different dynamical systems (see Banks 2008, Banks 2001, Kappel 2006). In this work we apply the TSF and the GSF to analyze the sensitivity of the 3D Poisson-type equation with interfaces of the Forward Problem of Electroencephalography (EEG). In a simple model where we consider the head as a volume consisting of nested homogeneous sets, we establish the differential equations that correspond to TSF with respect to the value of the conductivity of the different tissues and deduce the corresponding Integral Equations. Afterwards we compute the GSF for the same model. We perform some numerical experiments for both types of sensitivity functions and compare the results.