A Calderon Regularized Symmetric Formulation for the Electroencephalography Forward Problem

The symmetric formulation of the electroencephalography (EEG) forward problem is a well-known and widespread equation thanks to the high level of accuracy that it delivers. However, this equation is first kind in nature and gives rise to ill-conditioned problems when the discretization density or the brain conductivity contrast increases, resulting in numerical instabilities and increasingly slow solutions. This work addresses and solves this problem by proposing a new regularized symmetric formulation. The new scheme is obtained by leveraging on Calderon identities which allow to introduce a dual symmetric equation that, combined with the standard one, results in a second kind operator which is both stable and well-conditioned under all the above mentioned conditions. The new formulation presented here can be easily integrated into existing EEG imaging packages since it can be obtained with the same computational technology required by the standard symmetric formulation. The performance of the new scheme is substantiated by both theoretical developments and numerical results which corroborate the theory and show the practical impact of the new technique

Quantitative comparisons of forward problems in MEEG.

This document gives comparisons between several methods that solve the forward problem in MEEG by comparing their precision on a 3-layer spherical model. These methods are based on finite elements which either use surfacic meshes with triangles, volumic meshes with tetrahedra, or implicit elements deduced from levelsets

OpenMEEG: opensource software for quasistatic bioelectromagnetics

Background: Interpreting and controlling bioelectromagnetic phenomena require realistic physiological models and accurate numerical solvers. A semi-realistic model often used in practise is the piecewise constant conductivity model, for which only the interfaces have to be meshed. This simplified model makes it possible to use Boundary Element Methods. Unfortunately, most Boundary Element solutions are confronted with accuracy issues when the conductivity ratio between neighboring tissues is high, as for instance the scalp/skull conductivity ratio in electro-encephalography. To overcome this difficulty, we proposed a new method called the symmetric BEM, which is implemented in the OpenMEEG software. The aim of this paper is to presen

Fast and Efficient Formulations for Electroencephalography-Based Neuroimaging Strategies

L'abstract è presente nell'allegato / the abstract is in the attachmen