Two volume integral equations for the inhomogeneous and anisotropic forward problem in electroencephalography

• Published in: Journal of computational physics Vol. 348; pp. 732 - 743
• Main Authors: Rahmouni, Lyes, Mitharwal, Rajendra, Andriulli, Francesco P.
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.11.2017; Elsevier Science Ltd; Elsevier
• Subjects: Adjoint double layer; Anisotropy; Brain; Computational physics; Differential equations; Double layer; Electroencephalography; Electromagnetic scattering; Electronics; Engineering Sciences; Formulations; Forward problem; Integral equations; Mathematical analysis; Poisson's equation; Studies; Volume integral equations; Poisson's equation; Double layer; Electroencephalography; Volume integral equations; Adjoint double layer; Anisotropy
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2017.07.013

This work presents two new volume integral equations for the Electroencephalography (EEG) forward problem which, differently from the standard integral approaches in the domain, can handle heterogeneities and anisotropies of the head/brain conductivity profiles. The new formulations translate to the quasi-static regime some volume integral equation strategies that have been successfully applied to high frequency electromagnetic scattering problems. This has been obtained by extending, to the volume case, the two classical surface integral formulations used in EEG imaging and by introducing an extra surface equation, in addition to the volume ones, to properly handle boundary conditions. Numerical results corroborate theoretical treatments, showing the competitiveness of our new schemes over existing techniques and qualifying them as a valid alternative to differential equation based methods. •Two new volume integral equations for the Electroencephalography forward problem.•The equations can handle inhomogeneous and anisotropic conductivity profiles of the head/brain medium.•They are applicable to real case scenarios and represent a competitive alternative in EEG imaging to differential equation schemes.