### 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.

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.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**