Brain Topography

, Volume 32, Issue 2, pp 229–239 | Cite as

A Finite-Difference Solution for the EEG Forward Problem in Inhomogeneous Anisotropic Media

  • Ernesto Cuartas Morales
  • Carlos D. Acosta-Medina
  • German Castellanos-Dominguez
  • Dante MantiniEmail author
Original Paper


Accurate source localization of electroencephalographic (EEG) signals requires detailed information about the geometry and physical properties of head tissues. Indeed, these strongly influence the propagation of neural activity from the brain to the sensors. Finite difference methods (FDMs) are head modelling approaches relying on volumetric data information, which can be directly obtained using magnetic resonance (MR) imaging. The specific goal of this study is to develop a computationally efficient FDM solution that can flexibly integrate voxel-wise conductivity and anisotropy information. Given the high computational complexity of FDMs, we pay particular attention to attain a very low numerical error, as evaluated using exact analytical solutions for spherical volume conductor models. We then demonstrate the computational efficiency of our FDM numerical solver, by comparing it with alternative solutions. Finally, we apply the developed head modelling tool to high-resolution MR images from a real experimental subject, to demonstrate the potential added value of incorporating detailed voxel-wise conductivity and anisotropy information. Our results clearly show that the developed FDM can contribute to a more precise head modelling, and therefore to a more reliable use of EEG as a brain imaging tool.


EEG FDM Forward problem Volume conductor Conductivity Anisotropy 



The work was supported the Colombian Program for Researcher Training (Grant 2012-528), the KU Leuven Special Research Fund (Grant C16/15/070), the Research Foundation Flanders (FWO) (Grants G0F76.16N, G0936.16N, and EOS.30446199).

Compliance with Ethical Standards

Conflict of interest

The authors declare that there are no potential conflicts of interest.

Ethical Approval

All procedures performed in human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed Consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Signal Processing and Recognition Group, Faculty of EngineeringUniversidad Nacional de ColombiaManizalesColombia
  2. 2.Research Center for Motor Control and NeuroplasticityKU LeuvenLeuvenBelgium
  3. 3.Functional Neuroimaging LaboratoryIRCCS San Camillo Hospital FoundationVeniceItaly

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