Automatic Generation of VolumeConductor Models of the HumanHead for EEG Source Analysis

Benjamin LanferWWU Munster / BESA GmbH

BaCI 2015

EEG Source Analysis and Volume Conductor Models

FEM (BEM, FDM, ...) solution ofquasi-static Maxwell equations

Volume conductormodel

Inverse Problem

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

I Exploiting a-priori knowledge about . . .I . . . arrangment of head tissuesI . . . occurence of tissues at locations relative to (anatomical) reference

surfaces

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Segmentation in a Bayesian Framework

I Bayesian a-posteriori probability as measure for good segmentation

P (x |y) ∝ l(y |x)︸ ︷︷ ︸Likelihood

P (x)︸ ︷︷ ︸A-priori Probability

I Likelihood: how well does the current segmentation explain theobserved image?

l(yi |xi, λc) =1√

(2π)k|Σc|exp

{−1

2(yi − µc)

ᵀΣ−1c (yi − µc)

}

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The Markov Random Field Model

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The Markov Random Field Model (cont.)

I Markov Random Field (MRF)

P(xi |xS\{i}

)= P (xi |xNi) Markovianity

I Each MRF is equivalent to a Gibbs Random Field

P (x) =2

Zexp

(− 1

TU(x)

)Gibbs distribution

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The Markov Random Field Model (cont.)

I Gibbs energy function as a sum of single-site and pairwise cliquepotentials V1, resp., V2

U(x) =∑i∈S

V1(i, xi) +∑i∈S

∑i′∈Ni

V2(i, i′, xi, xi′

)+ . . .

I Definition of pairwise clique potentials using pseudo transitionprobabilities Pxi,xi′ (i, i

′)

V2(i, i′, xi, xi′) = − ln

(Pxi,xi′ (i, i

′))

BGSkin /Muscle

SCT

CoB

CaB

CSF

Dura

GM WM

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The Atlas-Based A-priori Probability

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Atlas Generation and Projection

I 20 labeled, template images from BrainWeb database1

I Averaging and normalization of local tissue histograms

I Atlas: local tissue probability mass functions depending on distancesto reference surfaces

I Projection to individual reference surfaces

Template image Local histogram

1Aubert-Broche et al., NeuroImage, 2006

Atlas Generation and Projection

I 20 labeled, template images from BrainWeb database1

I Averaging and normalization of local tissue histograms

I Atlas: local tissue probability mass functions depending on distancesto reference surfaces

I Projection to individual reference surfaces

Individual MRI and reference surfaces Local probability mass function

1Aubert-Broche et al., NeuroImage, 2006

The Segmentation Algorithm

Validation vs. Manual Raters

... ... ......

Proposedapproach

Majority

vote

Averaging

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Results Validation vs. Manual Raters

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Summary and Outlook

Summary

I Accurate segmentation of the four most relevant tissues for EEGsource analysis

I Low effort enables wider application of individual, realistically shapedFEM models in EEG source analysis, tDCS simulations, . . .

Outlook

I Improved segmentation of the skull base and the facial skull, e.g.,using templates

I Important for high-density electrode caps, temporal lobe activity

I Treatment of pathological anatomies (lesions, skull trepanation holes)

B. Lanfer (benjamin.lanfer@besa.de) 13 / 13

Thank you!

WWU / IBB

I PD Dr. Carsten H. Wolters

I Prof. Dr. Martin Burger

I Prof. Dr. Christo Pantev

I Umit 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