EEG and MEG forward modeling, Part I:
Validation and evaluation of FEM based
source modeling techniques
Carsten Wolters
Institut für Biomagnetismus und Biosignalanalyse, Westfälische Wilhelms-Universität Münster
Münster, Dez. 13, 2016
Outline
•
Convergence analysis for FEM subtraction
approach (sections 6.5.1-6.5.3 of lecture
scriptum)
•
Other source models (section 6.5.4 of lecture
scriptum)
•
Multi-layer sphere model (section 6.2 of lecture
scriptum)
•
Forward modeling for EU-project ChildBrain
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Overview: Subtraction approach
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Subtraction finite element approach
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Subtraction finite element approach
Carsten Wolters, IBB, WWU Münster
Subtraction FEM approach
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Subtraction FEM approach
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Subtraction FEM approach
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Subtraction FEM approach
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Full subtraction approach
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Full subtraction approach
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Projected subtraction FEM
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Projected subtraction FEM
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Convergence analysis
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Convergence analysis
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Convergence analysis
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Convergence analysis
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Convergence analysis
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Convergence analysis
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Convergence analysis
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Convergence analysis
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Convergence analysis
Carsten Wolters, IBB, WWU Münster
[Wolters et al., SIAM J Sci Comp, 2007]
[Drechsler et al., NeuroImage, 2009]
[Wolters, Lecture scriptum, 2016]
Outline
•
Convergence analysis for FEM subtraction
approach (sections 6.5.1-6.5.3 of lecture
scriptum)
•
Other source models (section 6.5.4 of lecture
scriptum)
•
Multi-layer sphere model (section 6.2 of lecture
scriptum)
•
Forward modeling for EU-project ChildBrain
Carsten Wolters, IBB, WWU Münster
Source models
Carsten Wolters, IBB, WWU Münster
[Wolters, Lecture scriptum, 2016]
Partial integration (PI)
Carsten Wolters, IBB, WWU Münster
[Wolters, Lecture scriptum, 2016]
Partial integration (PI)
Carsten Wolters, IBB, WWU Münster
[Wolters, Lecture scriptum, 2016]
[Wolters, Lecture scriptum, 2016]
The partial integration source model
Right-hand side vector f has only 4 (for tetrahedra models)
non-zero entries and can be computed very fast
Carsten Wolters, IBB, WWU Münster
[Wolters, Lecture scriptum, 2016]
The Venant source model
Carsten Wolters, IBB, WWU Münster
[Wolters, Lecture scriptum, 2016]
The Venant source model
Carsten Wolters, IBB, WWU Münster
[Wolters, Lecture scriptum, 2016]
The Venant source model
Carsten Wolters, IBB, WWU Münster
[Wolters, Lecture scriptum, 2016]
The Venant source model
Carsten Wolters, IBB, WWU Münster
[Wolters, Lecture scriptum, 2016]
The Venant source model
Carsten Wolters, IBB, WWU Münster
The Venant source model
Right-hand side vector f has only about 27 (for
tetrahedra models) non-zero entries and can be computed
similarly fast as PI.
Carsten Wolters, IBB, WWU Münster
[Bauer, Pursiainen, Vorwerk, Köstler & Wolters, IEEE TBME, 2015]
[Pursiainen, Vorwerk & Wolters, Phys Med Biol, 2016]
Whitney source model
One of the three edge based face functions of a Whitney source model
Carsten Wolters, IBB, WWU Münster
[Bauer, Pursiainen, Vorwerk, Köstler & Wolters, IEEE TBME, 2015]
[Pursiainen, Vorwerk & Wolters, Phys Med Biol, 2016]
Whitney source model
Click on
blue face!
One of the three edge based face functions of a Whitney source model
Carsten Wolters, IBB, WWU Münster
[Bauer, Pursiainen, Vorwerk, Köstler & Wolters, IEEE TBME, 2015]
[Pursiainen, Vorwerk & Wolters, Phys Med Biol, 2016]
Whitney source model
On the right: Whitney source built up of all three edge-based face functions (each weighted with 1/3)
Carsten Wolters, IBB, WWU Münster
Thank you for your attention!
Carsten Wolters, IBB, WWU Münster