Automatic Generation of Volume
Conductor Models of the Human
Head for EEG Source Analysis
Benjamin Lanfer
WWU Münster / BESA GmbH
BaCI 2015
EEG Source Analysis and Volume Conductor Models
Inverse Problem
Volume conductor
model
FEM (BEM, FDM, ...) solution of
quasi-static Maxwell equations
Forward Problem
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Generation of Individual, Realistic Head Models
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What Do We Know About the Segmentation?
A-priori Knowledge
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Exploiting a-priori knowledge about . . .
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. . . arrangment of head tissues
. . . occurence of tissues at locations relative to (anatomical) reference
surfaces
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Segmentation in a Bayesian Framework
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Bayesian a-posteriori probability as measure for good segmentation
P (x | y) ∝ l(y | x)
| {z }
P (x)
| {z }
Likelihood A-priori Probability
I
Likelihood: how well does the current segmentation explain the
observed image?
1
1
| −1
p
l(yi | xi , λc ) =
exp − (yi − µc ) Σc (yi − µc )
2
(2π)k |Σc |
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The Markov Random Field Model
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The Markov Random Field Model (cont.)
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Markov Random Field (MRF)
P xi | xS\{i} = P (xi | xNi )
Markovianity
Each MRF is equivalent to a Gibbs Random Field
1
2
Gibbs distribution
P (x) = exp − U (x)
Z
T
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The Markov Random Field Model (cont.)
I
Gibbs energy function as a sum of single-site and pairwise clique
potentials V1 , resp., V2
X X
X
V1 (i, xi ) +
U (x) =
V2 i, i0 , xi , xi0 + . . .
i∈S i0 ∈Ni
i∈S
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Definition of pairwise clique potentials using pseudo transition
probabilities Pxi ,xi0 (i, i0 )
V2 (i, i0 , xi , xi0 ) = − ln Pxi ,xi0 (i, i0 )
BG
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Skin /
Muscle
CoB
CSF
SCT
CaB
Dura
GM
WM
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The Atlas-Based A-priori Probability
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Atlas Generation and Projection
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20 labeled, template images from BrainWeb database1
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Averaging and normalization of local tissue histograms
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Atlas: local tissue probability mass functions depending on distances
to reference surfaces
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Projection to individual reference surfaces
Template image
1 Aubert-Broche
et al., NeuroImage, 2006
Local histogram
Atlas Generation and Projection
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20 labeled, template images from BrainWeb database1
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Averaging and normalization of local tissue histograms
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Atlas: local tissue probability mass functions depending on distances
to reference surfaces
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Projection to individual reference surfaces
Individual MRI and reference surfaces
1 Aubert-Broche
et al., NeuroImage, 2006
Local probability mass function
The Segmentation Algorithm
Validation vs. Manual Raters
Proposed
approach
...
aj
ity
or
M
te
vo
...
...
...
Averaging
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Results Validation vs. Manual Raters
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Summary and Outlook
Summary
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Accurate segmentation of the four most relevant tissues for EEG
source analysis
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Low effort enables wider application of individual, realistically shaped
FEM models in EEG source analysis, tDCS simulations, . . .
Outlook
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Improved segmentation of the skull base and the facial skull, e.g.,
using templates
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Important for high-density electrode caps, temporal lobe activity
Treatment of pathological anatomies (lesions, skull trepanation holes)
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Thank you!
WWU / IBB
I PD Dr. Carsten H. Wolters
I Prof. Dr. Martin Burger
I Prof. Dr. Christo Pantev
I Ümit Aydin
I Felix Lucka
I Johannes Vorwerk
I Sven Wagner
I Dr. Harald Kugel
BESA GmbH
I Dr. Michael Scherg
I Dr. Tobias Scherg
I Theo Scherg