EEG/MEG Source Localization: Practical Applicationcone.hanyang.ac.kr/BioEST/Kor/pds/080502_KHBM_printver.pdf · Forward Problem 4 – 유한요소법(유한차분법) 백질(white

EEG/MEG Source Localization: Practical Application

Bioelectromagnetics and Neuroimaging Laboratory

Department of Biomedical Engineering, Yonsei University

Chang-Hwan Im, Ph.D.

http://bem.yonsei.ac.kr


Contents

1. Signal Processing

2. Pre-processing

3. Equivalent Current Dipole (ECD) Localization

4. EEG/MEG Source Imaging

5. Commercial/Open Software for EEG/MEG Source Imaging


Preparing Analysis

1. EEG/MEG Data (Raw data)

2. Structural MRI Data

3. Position of Electrodes or SQUID sensors

4. Anatomical Landmarks, Head Shape (optional)



EEG(MEG)Raw Data

Baselinecorrection

Filtering

SegmentationArtifactremoval

Averaging

EP/ERP

Spontaneouspotential


Baseline Correction

Baseline: 측정도중발생하는 shift 현상. (채널마다 zero level이달라지는현상)

Baseline correctionor Trend removing

Constant trend: 채널별로 baseline의 평균값을빼줌

Linear trend: 선형함수로근사하여선형함수값을빼줌


Filtering

Bandpass filtering(1 – 30 Hz)

일반적으로 band-pass filter 사용


Artifact Removal

왜발생하는가?

어떻게제거하는가?

ICA 등여러가지기술사용가능


Segmentation and Averaging

Segmentation – 자극또는반응에대해서일정구간으로나누는작업

Averaging – 특정한자극의 type에대해서평균을내는작업

Visual Evoked Potential의예

자극제시시점 (trigger)Pre-stimulus period


참고 – Average Reference (EEG)

1

1ˆ ( ) ( )MN

i i ref j refjM

V V V V VN =

= − − −∑

Why reference is needed??

Where to put reference??

Average reference??


Contents


2. Pre-processing





Forward Model의선정

Brain electrical sources Electromagnetic fields

Forward Problem(Forward Problem(정문제정문제)):

Head & source models

Inverse Problem(Inverse Problem(역문제역문제)):

ECD, distributed source models

뇌자도/뇌전도의 목적 – 머리 외부에서 측정한 전자기 신호를 이용하여뇌 내부의 전류원을 추정하는 것.


Forward Problem 1 – Homogeneous Sphere Model

MEG (J. Sarvas, 1987)

EEG (D. Yao, 2000)

03 2

0

cos1{ 2 [ ]}4 cosp p p

r RVr R r R r r

ϕπσ ϕ

− −= + +

+ −0 0R r R rP Ri

EEG의경우에비해 비교적 정확함.

축 방향성분은외부 자장을 생성하지않음

실제 문제에 적용하기에는 부적합함.

02

( ) ( , )( )

4 ( , )Q Q Q

Q

F FB r

Fμπ

× − × ⋅ ∇=

Q r Q r r r rr r

2( , ) ( )Q QF a ra r= + − ⋅r r r r


Forward Problem 2 – Concentric Sphere Model

brain

Inner skull

Outer skull

scalp

• EEG의 경우에는 정해(exact solution) 존재, MEG의경우에는근사해만존재.

• MEG의 경우에는 거의 사용 안 함 . MEG의 경우에는 두개골(skull) 밖으로나가는 전류가 대부분 차단되기 때문에단일 구형 도체 모델을 사용하는 경우와정확도차이가거의없음.

• EEG의 경우에는 정확도가 많이 향상됨. 하지만 실제 뇌의 구조를 고려하는경우와는 정확도 차이가 많이 남. 특수한영역에서만정확도보장

실제 문제에서는 보다 정확한 모델이필요하다.

Head fitting


Forward Problem 3 – 경계요소법

0 0( ) ( ) 2 ( )

1 '( ) ( ') ( ') ,2 ij

i j

i j Sij

V V

V d

σ σ σ

σ σπ

+ =

+ − Ω∑ ∫ r

r r

r r ∫⋅∇

=G

p

dvR

V ')'('4

1)(0

0rJr

πσ

∑ ∫ ×−+=ij

S ijjiij RV 'dSRrrBrB 3

00 )'()(

4)()( σσ

πμ

∫ ×= ')'(4

)( 30

0 dvR

pG

RrJrBπμ

In EEG

In MEG, after solving EEG problem

일반적으로 3~4층의다른전기전도도를지니는영역으로분류

하고각영역은균일하고isotropic conductivity를가진다

고가정함.

뇌자도는일반적으로두개골안쪽경계부분만사용


Forward Problem 4 – 유한요소법 (유한차분법)

백질(white matter)의 이방성: Diffuse tensor MRI 이용 - 아직 연구 중인 topic

두개골의 이방성

(축방향 전도도가 더 크다)

유한요소법 (FEM), 유한차분법 (FDM)

• 요소 분할이 어려움 (folded surface)

• 현재 기술로 정확한 이방성 추정 어려움

pV J⋅∇=∇⋅∇ )(σ


When anatomical information is not available

1. Use of standard head model/sensor configuration: MNI model is usually used.- CURRY, BESA, BrainStorm 등에서모두지원하며 LORETA는 standard만지원함

2. Scalp surface를이용한 BEM model의생성


Pre-processing for EEG/MEG Analysis

Boundary Element Method와 Distributed Source Model을 사용한다고 가정하였을 때의 Pre-processing 과정


Preprocessing for MEG Analysis

1.1. Transforming Sensor Coordinates into Transforming Sensor Coordinates into

Head Coordinates Head Coordinates

2. Generation of Boundary Element

Meshes

3. Segmentation and Tessellation of

Cortical Surface

4. Transforming MRI Coordinates into Head

Coordinates

5. Cortical Surface Decimation

Marking coil과 digitized head position을 이용하여 좌표 변환

148채널 magnetometer 시스템.




1. Transforming Sensor Coordinates into

Head Coordinates

2.2. Generation of Boundary Element Meshes Generation of Boundary Element Meshes


Cortical Surface


Coordinates

5. Cortical Surface Decimation Inner skull boundary만을 삼각형 요소를 이용하여 분할.





Head Coordinates


Meshes

3.3. Segmentation and Tessellation of Segmentation and Tessellation of

Cortical SurfaceCortical Surface


Coordinates

5. Cortical Surface Decimation BrainSuite (USC)를 이용하여 삼각형 요소로 tessellation수행





Head Coordinates


Meshes


Cortical Surface

4.4. Transforming MRI Coordinates into Head Transforming MRI Coordinates into Head

CoordinatesCoordinates

5. Cortical Surface Decimation Tessellated scalp surface 와digitized head position을 맞춤으로써 좌표 변환.





Head Coordinates


Meshes


Cortical Surface


Coordinates

5.5. Cortical Surface Decimation Cortical Surface Decimation

Initial cortical surface:

510,267 triangular elements

255,329 vertices

Decimation

Extracting about 10,000 vertices.

초기의 요소는 visualization을 위해서 사용된다.



Cortical Surface Decimation

dec·i·mate〔d s m it〕〔L 「10번째의사람을뽑다」의 뜻에서〕 vt.1 (특히고대 로마에서처벌로서) 열 명에 한명씩 제비뽑아 죽이다2 <질병·전쟁 등이> 많은사람을죽이다

a population decimated by disease 병으로격감한인구3 《폐어》 …의 10분의 1을 제거하다d c·i·m ·tion n. -m ·tor n.

It is too many!!!


Cortical Surface Decimation

Area of influence


Preprocessing for EEG Analysis

1.1. Cortical Surface Tessellation and Cortical Surface Tessellation and

DecimationDecimation


Meshes

3. Positioning Electrodes on the BEM

Meshes

Extract about 10,000 vertices from 641,195 elements and 321,698 vertices using decimation process.




1. Cortical Surface Tessellation and

Decimation

2.2. Generation of Boundary Element MeshesGeneration of Boundary Element Meshes

3. Positioning Electrodes on the BEM

Meshes

3260 elements and 1836 vertices




1. Cortical Surface Tessellation and

Decimation


Meshes

3.3. Positioning Electrodes on the BEM Positioning Electrodes on the BEM

MeshesMeshes

MRI 좌표계에서의 marker 위치와 digitizer로 측정한 위치좌표를 일치시킴.



Coordinate Transform


Constructing Leadfield Matrix

x = As + n

Orientation Constraint가있을경우: Size of A - #sensors by #variables

구하는방법

Orientation Constraint가없을경우: Size of A – #sensors by #variables*3

구하는방법


Contents


2. Pre-processing





Equivalent Current Dipole Localization

ECD MethodDistributed sources are concentrated at some discrete points

K. Uutela, M. Hämäläinen and R. Salmelin, “Global optimization in the localization of neuromagnetic sources,”

IEEE Trans. Biomed. Eng., vol. 45 pp.716-723, 1998.

• 가장간단하면서오래된방법

• Dipole의위치 (x, y, z)및 dipole moment vector (Qx,Qy,Qz)의값을최적화알고리즘을이용하여찾음.

• 최근에는 spatio-temporal dipole fit을많이사용함.

• Deterministic algorithms: Levenberg-Marquardt method, Downhill simplex search, etc. – 국소최적점에수렴할가능성크다.

• Global optimization algorithms: Genetic Algorithm (GA), Simulated Annealing (SA), etc. – 많은수의dipole을 localize하기 힘들다.


Equivalent Current Dipole Localization (Cont’d)

Instantaneous Dipole Fit vs Spatio-temporal Dipole Fit

Spatio-temporal Dipole Fit이 Noise 성분에대해보다 robust하다 (대부분사용).

2|| ( ) ||FE = −x A p sError Function

where x is the measured electromagnetic signals, A lead field matrix that relates sensor positions and source locations, p location parameters of dipoles, and s corresponding dipole moment vectors.


Spatio-temporal Dipole Fit

Definition of Frobenius norm: 2|| ||F ija= ∑A

, where aij is i-th row and j-th column of the matrix A.

2|| ( ) ||FE = −x A p s

Spatio-temporal dipole fit utilizes series of multiple time samples.

Classification of ECDs:

(1) Moving dipole: 6 DOF – location vector (3 components) + moment vector (3 components)

(2) Rotating dipole: 3 DOF – location vector (3 components)

(3) Fixed dipole: do not need any nonlinear optimization


Procedures

1. Determination of initial number and locations of ECDs

2. Selection of forward models and optimization algorithms (deterministic vs. stochastic)

3. Visualization of localized ECDs on structural MRI (optional)


Scalp Potential Map (or Field Map)Spline interpolation of scalp EEG

- 임의의위치에서의 potential (또는 field)를추정

방법들

Spherical spline : 구형 scalp 가정

3D spline

Spherical spline의예


Scalp Potential Map

Potential Map의문제점

1. Reference electrode에 크게 영향을 받음. Average reference를 사용하더라도 유한한 sampling density와 전체를 cover하지 못하는 성질 때문에 정확도가 떨어짐

2. Scalp potential은 skull때문에 cortex의 potential에 비해서 blurring이됨.


감을익히자!!!

Tangential dipolar source in EEG

Tangential dipolar source in MEG

Radial dipolar source in EEG

Radial dipolar source in MEG

http://bem.yonsei.ac.kr Bioelectromagnetics and Neuroimaging Lab.Bioelectromagnetics and Neuroimaging Lab. Yonsei BME

Why Cortical Source Imaging is Required

1. EEG or MEG topographies cannot be directly attributed to the underlying cortical regions since sensors may contain information from multiple brain sources, some of which might overlap, and the topographic maps might be smeared out due to the inhomogeneous conductivity distributions in the human head.

How many sources are there???


2. A deep tangential source might generate two distinct peaks on the topographic map, which are hard to be distinguished from two radial sources around the peak locations.

one tangential source

or

two radial sources

???



3. A very small cortical activation in some cortical areas could yield widespread field distribution in the topographic maps, preventing one from identifying correct location of the actual cortical source and investigating coherence between different sensors.

Inner skull boundary Outer skull boundary Scalp



4. If a subject’s head is tilted, especially in a helmet-type MEG, so that one hemisphere is closer to the sensors than the other is, one could observe stronger activity at sensors closer to the subject’s head even when the strengths are equal at the cortical level.

Therefore, to overcome these limitations, source imaging of brain activity at the cortical level is necessary.



How to Estimate the Number of ECDs

1. Goodness of Fit (GOF)Goodness of Fit이 saturate되는 지점의 number of source 이용Goodness of Fit의정의: the squared sum of the signal explained by the model divided by the squared sum of the total signal

2. Independent Component Analysis (ICA)

3. MUSIC or FINE Algorithm

4. fMRI constraint


Use of ICA: Example 1


Use of ICA: Example 2

Submitted to Journal of Clinical Neurophysiology

Manual selection is necessary…


MUSIC (or FINE) Algorithm

}{)( min ii GTnoisenoiseGf UUiJ ΦΦ= λ

NAS +=Φ IAARR nT

s2σ+=Φ

spatial correlation matrix

eigen-decomposition

TSSS EEP = T

NNN EEP =

Projectors

( ) ( )xAPxf NN =Formulation of

cost functionResidual vectorEach local minimum is a source

[ ]nK eeEN ,,1+Spatio-temporal model

[ ]Ks eeE ,,1

A well-known subspace source localization method: MUSIC―Mosher JC, Lewis PS and Leahy RM IEEE Trans. Biomed. Eng. 1992


An Example

Potential problems

1. Solutions are dependent on the number of signal subspaces.

2. Cannot separate temporally correlated sources


fMRI constraint

fMRI SPM resultPlacing small number of regional

dipoles –Seeding initialsDipole source localization using

optimization algorithms

(Toma et al., 2002, NeuroImage)


fMRI constraint (Cont’d)

(Vanni et al., 2004, NeuroImage)

(Fujimaki et al., 2002, NeuroImage)


Optimization Algorithms Used for ECD Localization

Deterministic Algorithms Stochastic Algorithms

Levenberg-Marquadt algorithm

Nelder-Meade downhill simplex

Conjugate gradient method

Genetic Algorithm

Simulated Annealing

Evolution Strategy

분류기준?

차이점은?


Contents


2. Pre-processing





(Cortically) Distributed Source ModelDirectly reconstruct the distribution of current sources

C. H. Im, K. O. An, H. K. Jung, H. Kwon and Y. H. Lee, “Assessment criteria for MEG/EEG cortical patch tests,”

Phys. Med. Biol., Vol. 48, pp. 2561-2573, 2003.

• 많은 수의 ECD를 cortical surface에수직하게 배치한다 . 선형(L2) 또는 비선형(L1) 역산 과정 각ECD의 moment vector를 복원한다.

• ECD의 위치나 개수에 대한 사전정보가 필요 없다.

• 해부학적 정보를 사용하기 때문에ECD법에 비해서 생리학적으로 더실제적이다.

• 최근 많이 사용되고 있는 방법임.

Distributed Source Model (or Cortical Source Imaging)

Localization Imaging

Methods – already discussed in the previous talk


Volume Source Model

• 초기에사용한모델

• 뇌영역전체를일정한 grid로분할 (육면체 voxel(volume pixel) )

• 각 grid에 dipole source 1개씩할당 (rotating dipole)

• 뇌내부까지모델링가능 Deep source detection 및 regularization operator 사용에용이함.

• 지나치게많은 source가필요함. 따라서 resolution이떨어짐

• Spurious source (phantom source)의 발생

A는진짜B는가짜

(S. Bailet – Ph.D. Thesis)


Cortical Source Imaging

Based on those two physiological factsDale and Fischl, 2000, PNAS


Orientation Constraint

1. Cortical surface가잘생성되었을경우 orientation constraint를 부여하는것이좋음

2. Cortical surface가잘생성되지않았을경우 orientation constraint를부여하면정확한결과를얻을수없음


Orientation Constraint

sMRI의 field inhomogeneity에 의한incomplete segmentation

Orientation constraint 사용하면부정확한결과

(c.f) Loose orientation constraint (Lin et al., 2006, Hum. Brain Mapp.)

Cortical Surface Extracted from Chang-Hwan Im’s MRI


Leadfield (Depth) Normalization

1. 왜필요한가?

Without normalization With normalization


Leadfield (Depth) Normalization

2. Implementation

k-th dipole 성분에다음 term을곱해줌.

일반적인 p값은 ½를사용해왔음.

p = 0.75 가적합함을최근에밝힘 (Lin et al., 2006, Neuroimage)


Source Imaging에서 Pre-processing과 processing은분리가능!!

Forward model

Coordinate transform

Pre-processing

Generation of

Leadfield

Matrix A

Using Only

Geometry

Information

W = RAT (ARAT + λ2 C)-1

Linear inverse operator

sx = Ws

You can obtain A usingBrainStorm!


Source Imaging에서 Pre-processing과 processing은분리가능!!

Forward model

Coordinate transform

Pre-processing

Leadfield

Matrix A

A만저장하고있으면여러방법에적용가능

MNE

L1, Lp

sLORETA

SCEA

LORETA

FOCUSS/EPI-FOCUSS

dSPM

LORETA-FOCUSS

Multi-resolution

LAURA

Leadfield는동일하며

결국 operator의 차이가방법을결정!!


Visualization of Results

On MRI voxels

On cortical surface

On inflated cortical surface

Cortical surface segmentation, tessellation, and inflation FreeSurfer, BrainSuite, etc. (freeware)


Use of fMRI prior Information

1

0.1 • Liu et al. [1998] revealed that the distortion by the fMRI invisible sources could be reduced considerably by just giving a constant weighting factor to the diagonal terms of source covariance matrix in linear Wiener estimate operator.

Liu AK, Belliveau JW, Dale AM (1998): Spatiotemporal imaging of human brain activity using functional MRI constrained magnetoencephalography data: Monte Carlo simulations. Proc NatlAcad Sci 95:8945-8950.

W = RAt(ARAt + C)-1

The first paper that addressed the possibility of fMRI or PET prior constraint

Dale AM, Sereno M (1993): Improved localization of cortical activity by combining EEG and MEG with MRI surface reconstruction: a linear approach. J Cognit Neurosci 5:162-176.


Use of fMRI prior Information

More focalized source distribution

Reduced spurious sources

Temporal changes in fMRI activations

Advantages

If there exist significant mismatches between fMRI and EEG/MEG…

Some mismatched sources are missing in the source imaging.

The eliminated sources affect the inverse solution (cause distortion or

misidentification)


Consideration of Mismatches between fMRI and EEG/MEG

(Ahlfors and Simpson, 2004, NeuroImage)

75

2

4

13

8

6

(Im et al., 2005, Hum. Brain Mapp.)

(Liu et al., 2006, Clin. Neurophysiol.) (Im and Lee, 2006, Phys. Med. Biol.)

http://bem.yonsei.ac.kr 6464/15/15

Frequency-Domain Source Imaging

where A is a lead field matrix constructed by solving forward problems, R is a source covariance matrix, and C is a noise covariance matrix.

Fourier transformed signals B(fi)Re and B(fi)Im, i = 1, 2, …, n, where Re and Imrepresent real and imaginary parts, respectively

The real part qj(fi)Re and imaginary part qj(fi)Im of the current source vector at j-thcortical vertex with respect to the frequency of interest fi can then be evaluated by multiplying the corresponding rows (3j-2, 3j-1, and 3jth rows) in W with the Fourier transformed signals B(fi)Re and B(fi)Im.

2 2

1

1 ( || ( ) || || ( ) || )2

n

j j i Re j i Imi

f fn =

= +∑Q q qAbsolute current source power at j-th cortical vertex with respect to the frequency band of interest

(Linear Inverse Operator)

Frequency Domain Minimum Norm Estimation (FD-MNE)


Real-time Cortical Rhythmic Activity Monitoring System

(Im et al., 2007, Physiol. Meas.)


Experimental Study (Example 1)

Real-time cortical alpha (8-13 Hz) activity imaging

Subject: YJ (26 years old)

4 frames per second, 16 channels


Subject: JJ (23 years old)

4 frames per second, 16 channels

Real-time cortical mu (8-12 Hz) activity imaging

Experimental Study (Example 2)


Contents


2. Pre-processing





1. CURRY (Commercial)

Commercial software developed by Neuroscan

Integration of EEG, MEG, ECoG, ECG, MCG, with MRI, fMRI, CT, PET, SPECT.

Dipole scans, extended source (patch) scans, and MUSIC scans

Beamforming based on dipolar or extended sources.

Current density analysis, extended sources, Lp norms, sLORETA, SWARM.

User-friendly, but expensive


2. BESA (Commercial)

Commercial software (http://www.besa.de, Germany)

Integration of EEG, MEG with MRI, fMRIEquivalent current dipole (ECD) fitMinimum norm estimation (MNE) on rough cortical surface

User-friendly, but expensive


3. BrainStorm (Free, Matlab toolbox)

A free GUI software developed by USC group

Operated under Matlab (Mathwork, co.) environment (You have no need to learn it).

EEG, MEG, Combined Analysis

RAP-MUSIC, Minimum Norm Estimation, LCMV

Not that user-friendly

http://neuroimage.usc.edu/brainstrom


4. LORETA-Key (Free)

Free software developed by Dr. R. Pascual-Marqui (http://www.unizh.ch/keyinst, Switzerland)

Application of LORETA (low resolution electromagnetic tomography) to a standard Talairach brain

LORETA, sLORETA(standardized LORETA), frequency-domain source imaging

User-friendly, blurred source images (low resolution)


For More Information

Visit our web-page at


Thank you!

Documents

EEG/MEG Source Localization: Practical Applicationcone.hanyang.ac.kr/BioEST/Kor/pds/080502_KHBM_printver.pdf · Forward Problem 4 – 유한요소법(유한차분법) 백질(white