Review on mathematical modelling of electroencephalography (EEG)

DOI10.1365/s13291-018-0183-zzbMath1412.35339OpenAlexW2848910136MaRDI QIDQ666933

Marion Darbas, Stéphanie Lohrengel

Publication date: 12 March 2019

Published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1365/s13291-018-0183-z

zbMATH Keywords

modellingnumerical methodsinverse problemsEEGsource localizationforward problem

Mathematics Subject Classification ID

Neural biology (92C20) Biomedical imaging and signal processing (92C55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Inverse problems for PDEs (35R30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical analysis (educational aspects) (97N40)

Related Items

Numerical resolution of the inverse source problem for EEG using the quasi-reversibility method ⋮ Singularity extraction for elliptic equations with coefficients with jumps and Dirac sources ⋮ On a Calderón preconditioner for the symmetric formulation of the electroencephalography forward problem without barycentric refinements ⋮ An inverse dipole source problem in inhomogeneous media: application to the EEG source localization in neonates ⋮ On the geometrical perturbation of a three‐shell spherical model in electroencephalography ⋮ Music signal recognition based on the mathematical and physical equation inversion method ⋮ Electro-magnetoencephalography for a spherical multiple-shell model: novel integral operators with singular-value decompositions

Uses Software

• FreeFem++
• OpenMEEG

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An iterative method for solving the Cauchy problem for elliptic equations
• Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices
• Accuracy and run-time comparison for different potential approaches and iterative solvers in finite element method based EEG source analysis
• The construction of some efficient preconditioners in the boundary element method
• Linear integral equations.
• EEG in neonates: forward modeling and sensitivity analysis with respect to variations of the conductivity
• A finite difference method to solve the forward problem in electroencephalography (EEG)
• Hölder stability estimates for some inverse pointwise source problems
• A Calderon regularized symmetric formulation for the electroencephalography forward problem
• An inverse dipole source problem in inhomogeneous media: application to the EEG source localization in neonates
• Source localization using rational approximation on plane sections
• A Discontinuous Galerkin Method to Solve the EEG Forward Problem Using the Subtraction Approach
• A stable recovering of dipole sources from partial boundary measurements
• Identification of dipole sources in an elliptic equation from boundary measurements: application to the inverse EEG problem
• Numerical Mathematics of the Subtraction Method for the Modeling of a Current Dipole in EEG Source Reconstruction Using Finite Element Head Models
• Relaxation of a variational method for impedance computed tomography
• How can the meromorphic approximation help to solve some 2D inverse problems for the Laplacian?
• An inverse source problem in potential analysis
• Recovery of pointwise sources or small inclusions in 2D domains and rational approximation
• A Preconditioner for the Electric Field Integral Equation Based on Calderon Formulas
• Cortical mapping by Laplace–Cauchy transmission using a boundary element method
• Acoustic and electromagnetic equations. Integral representations for harmonic problems