Mixed discretization formulations for the direct EEG problem

This work presents a new discretization scheme for the integral equation based Electroencephalography direct problem. The scheme is based on mixed discretizations and presents level of accuracy that are higher than those obtained with currently available formulations. The discretization scheme is conforming with respect to the Sobolev space mappings of all operators involved. Numerical results show the effectiveness of the new approach.

[1]  Daniël De Zutter,et al.  Accurate and Conforming Mixed Discretization of the MFIE , 2011, IEEE Antennas and Wireless Propagation Letters.

[2]  Olivier D. Faugeras,et al.  A common formalism for the Integral formulations of the forward EEG problem , 2005, IEEE Transactions on Medical Imaging.

[3]  H. Spekreijse,et al.  Mathematical dipoles are adequate to describe realistic generators of human brain activity , 1988, IEEE Transactions on Biomedical Engineering.

[4]  Snorre H. Christiansen,et al.  A dual finite element complex on the barycentric refinement , 2005, Math. Comput..

[5]  D. E. Edmunds,et al.  Introduction to Potential Theory , 1972 .

[6]  Francesco P. Andriulli,et al.  Improving the MFIE's accuracy by using a mixed discretization , 2009, 2009 IEEE Antennas and Propagation Society International Symposium.

[7]  Jianming Jin,et al.  Improving the Accuracy of the Second-Kind Fredholm Integral Equations by Using the Buffa-Christiansen Functions , 2011, IEEE Transactions on Antennas and Propagation.

[8]  S. Jarvenpaa,et al.  Electromagnetic surface integral equation representations in terms of scalar functions , 2013, 2013 International Conference on Electromagnetics in Advanced Applications (ICEAA).

[9]  J. Nédélec.  Acoustic and Electromagnetic Equations : Integral Representations for Harmonic Problems , 2001 .

[10]  Z. Zhang,et al.  A fast method to compute surface potentials generated by dipoles within multilayer anisotropic spheres. , 1995, Physics in medicine and biology.