Introduction to EEG and MEG - Max Planck Society · EEG WS 2012/2013, Thomas R. Knösche Max Planck...

EEG WS 2012/2013, Thomas R. Knösche Max Planck Institute for Human Cognitive and Brain Sciences

Introduction to EEG and MEG

Thomas R. Knösche

Max Planck Institute

for Human Cognitive and

Brain Sciences


History: Discovery of Biological Electricity

Luigi Galvani (1737-1798) "Ich secirte einen Frosch, präparierte ihn und legt ihn auf

einen Tisch, auf dem eine Electrisirmaschine stand, weit

von deren Conductor getrennt. Wie nun der eine von den

Leuten, die mir zur Hand gingen, mit der Spitze des

Skalpellmessers die inneren Schenkelnerven des Frosches

zufällig ganz leicht berührte, schienen sich alle Muskeln an

den Gelenken wiederholt derart zusammenzuziehen, als

wären sie anscheinend von heftigen tonischen Krämpfen

befallen. Der andere aber, welcher uns bei den

Electrizitätsversuchen behilflich war, glaubte bemerkt zu

haben, dass sich das ereignet hätte, während dem

Conductor der Maschine ein Funken entlockt wurde."

1789

Physician, anatomist, biophysicist


History: Theory of Bioelectricity

• Foundations of

electrophysiology

• Discovery of

electrical activity in

nerves and

muscles (1848)

Emil Heinrich du Bois-Reymond

(1818-1896)


History: Discovery of Human EEG

Hans Berger (1873-1941)

(published 1929)

1924


EEG: Recording

Electrodes

Amplifier

Display

1929 2012


EEG Electrodes

Shape

Material: gold (durable, no DC), silver/silver chloride (care

intensive, DC), tin (cheap)

Attachement

ring cup sponge

glue geodesic nets caps


EEG Amplifiers

• differential amplifiers

• sometimes separated into pre- and main amplifiers

• integrated high pass filters

• high input impedances, minimal distance from head

• AD converter: discretization in time and voltage

ANT - high-density amplifier

Number of channels 32, 64, 128 and 256

Sampling frequency 256, 512, 1024 and 2048 Hz

Resolution 22 bit, 71.5 nV per bit

Input impedance > 1012 Ohm

Noise < 1.5 Vpp (at 100 Hz)

CMRR > 110 dB

Connection to PC fiber optic to PCI card or USB2


Electrode placement

10-20 system (Jasper, 1958)

21 positions

10-10 system (Chatrian, 1985)

74 positions

10-5 system (Oostenveld 2001)

~300 positions

Geodesic nets (Tucker)

64, 128, 256, … positions


Reference and Montage

• Unipolar (against nasion, mastoid, Cz, …)

• Average reference (against mean of all channels)

• Bipolar (e.g., neighbouring electrodes in ant.-post. direction,

homologuous electrodes between hemispheres)


EEG Display and Analysis


Spontaneous EEG

Alpha waves: ca. 10 Hz

Delta waves: ca. 0.5 – 4 Hz

Subdelta: < 0.5 Hz

Slow waves/ spindles

Beta/gamma waves: >12 Hz


Spontaneous EEG - Interpretation

Normal EEG – adult, light sleep


Spontaneous EEG - Interpretation

Epileptiform discharges Creutzfeld-Jacob disease, different stages

left delta

epileptiform discharges


Artifacts

Biological artifacts

• Movement (esp. MEG)

• Eye movement

• Eye blink

• muscle

• cardiac

Technical artifacts

• Electrodes

• Drifts

• Picking up from environment


Treatment of Artifacts

Rejection

• Contaminated epochs are rejected

Advantages

• simple

• no signal distortion

Drawbacks

• Loss of data (especially if number of

epochs is limited)

• Selection bias

• Extra task „do not move your eyes“ can

influence experiment.

Correction

• Artifacts will be mathematically

eliminated

Advantages

• Avoidance of disadvantages of

rejection

Drawbacks

• Signal can and will be distorted. Extent

of distortion difficult to quantify.


Event-related Potentials

sampling

250-2000 Hz

10-1000,

typically

20-200

epochs

32-256

electrodes


Event-related Potentials - Example

Musical phrasing musical culture

CZ

Source: Nan, Knösche & Friederici, 2006

Stimulus material is presented in 4 variants, which differ in

two two-stage factors..

German, phrased

Chinese, phrased

German, unphrased

Chinese, unphrased

II: 100 - 300 ms

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Chinese music Western music

diffe

rence a

mplit

ude (

uV

)

Chinese musicians

German musicians


Magnetoencephalography


• DC-SQUIDs RF-SQUIDs two Josephson contacts one contact more difficult to make, more sensitive

Josephson contacts:

Weak links in superconduction

Sensitive to changes in magnetic field

Super conduction:

Material property at low temperatures and

magnetic field strengths

No Ohmic resistance

Super conducting Quantum Interference Devices


Detector Coils

a) Magnetometers

b) Planar gradiometers 1. ord.

c) Radial gradiometers 1. ord.

d) Radial gradiometers 2. ord.


Neuromag system

Three channels per chip

• Magnetometer

• Planar gradiometer

• Planar gradiometer


Magnetometers and/or Gradiometers?


MEG-Lab Gantry Sensor 3D-Digitizer

Shielded room

Stretcher


The Forward Problem

Thomas R. Knösche



Brain Sciences


The Forward Problem

R2

R1

R3

I U

Law of Ohm

I=U/R2

???

We know the source current,

and want to compute the

EEG/MEG.


Description of Electromagnetic Fields

0 E

JH

D

0 B

EJ

ED

HB

Quasistatic Maxwell equations

0

03

0

00

||

)()(

4

1)(

xx

xdxx

xxxJx

03

0

00

||

)()(

4)( xd

xx

xxxJxB

Sensor location Source location


Primary and Volume Currents

EJJ p

+

cell body

sink

source

synapse

+

Secondary/volume

currents Primary/ source currents


Volume Conductor: What needs to be modelled?

EEG

MEG

Modelling MEG Modelling EEG

MEG: Only volume

currents within the skull

need to be considered.

EEG: Also volume

currents outside the skull

interior must be modelled.


How to Describe the Head Geometry?

Spherical model

Simplest solution


Spherical Head Model

MEG EEG

Skull interior

Skull

Scalp

Described by: sphere center (M), radii (R) , conductivities ()

R3

R1

M 1

R2 R1

M 1

2

3



Advantage: Potential and magnetic field can be computed by

analytical (closed) formulas.

No numerics!

),,( 0 tgnQrrB

Solutions for single dipole:

),,,,,,,,,,,( 3322113210

tgnradtgnradtgnradRRRQrr

sensor loc. dipole loc. dipole moment

Sphere radii Anisotropic conductivities

(Sarvas 1987)

(de Munck 1989)

Magnetic field does not depend on radii!

No field for radial sources!



fromTanzer, PhD thesis 2006

Electrical potential and magnetic field have orthogonal

topographies.

MEG

EEG


Local Spherical Model

Dor each sensor a separate spher

is fitted to the local curvature of

the skull.


Ellipsoidal Head Model

• Ellipsoids have more degrees of

freedom compared to spheres.

• Also ellipsoidal volume

conductors can be described

analytically .


Boundary Elements Method (BEM)

• Realistic description of tissue

compartments with different

conductivities.

• Mostly: inner and outer skull

surface, outer head surface, but

also others, e.g. vetricles, CSF.

• Each compartment is described

by a homogeneous and isotropic

conductivity.


Segmentation Grid generation



Different tissues have different grey value in MRI.

T1 weighted MRI → suitable for , e.g., ventricles,

Outer skull boundary, boundary

between grey and white matter

Proton Density (PD)

MRI → suitable for inner and outer skull

boundaries



Boundary Elements Methods (Conductivities)

1

2

3

• 1 - 3 are equivalent values

• true conductivities are

inhomogeneous and anisotropic

in each compartment.

• How to get these values?

• Usual choices: 1 = 0.33 S/m, 2

= 0.004 S/m, 3 = 0.33 S/m


Finite Elements Method (FEM) Influence of anisotropic conductivity


Finite Elements Method (FEM)

from Tanzer, PhD thesis2006

• Volume is divided into small

tetraedras or cubes.

• In every element one

conductivity tensor!

• Simultaneous solution of

Poisson‘s equation in all

elements, with boundary

conditions.


Finite Elements Method (FEM) (Conductivities)

from Ramon et al (2006)

Values from Literature

However, no anisotropy DWI (see Tuch 2001)


Finite Elements Method (FEM)

In principle, FEM is the ideal method, since all relevant volume

conductor properties can be accounted for, at any desired

resolution.

However …

• … it is still an unsolved problem to obtain these values in

real situations.

• … the computations demands are very high (however, recent

advances in fast solver technology seem to ameliorate this

problem, see Wolters et al. 2004)

• … the correct modeling of the source injection is still a

problem (Schimpf et al. 2002)


Comparison of Methods

Analytical models (sphere, ellipsoid)

Advantages

• easy to implement, fast to compute

• no problems with model generation (no segmentation, grid

generation)

• analytical solution, no typically numerical problems, such as

accuracy, convergence, etc.

Drawbacks

• Heads are no balls! → Modelling error


BEM models

Advantages

• Individual head geometry can be accounted for

• Relatively fast and economic solution

• No problems with source injection

Drawbacks

• Constant and isotropic conductivity in each compartment

• Inhomogeneities, such as skull holes or fontanelles/surtures

cannot be modelled and cause large errors.



FEM models

Advantages

• All relevant volume conductor properties can be accounted

for, at any desired resolution.

Drawbacks

• Material parameters difficult to obtain

• Possible numerical problems with source singularity.

• Model generation can be challenge.



Source Reconstruction

Thomas R. Knösche



Brain Sciences



Measurement (EEG/MEG) Neuronal currents



Highly underdetermined

Measurement (EEG/MEG) Average currents in elements

of suitable size


M L J = +

measurements

max. 430 values

lead field matrix (forward solution)

each column for 1 dipole

dipoles (3 per voxel)

several thousand values

noise


Underdeterminedness Noise in data

Probability instead of certainty

Law of Bayes


2

22

1exp)|( jLmjm

Extremely simple example:

one electrode, 2 dipoles

Likelihood

-2

-1.5

-1

-0.5

0 0

0.5

1

1.5

2

0

0.5

1

Likelihood


object measurement

It is impossible to reconstruct the object just from the

shadow image

However: If we know that vases are in general rotationally symmetric and if we skip the

colouring, we can reconstruct an image that is similar to the original in important aspects.

Give up? Wait a minute ...


2

2

1exp)( jjprior

Extremely simple example:

one electrode, 2 dipoles

A priori information

-2

-1.5

-1

-0.5

0 0

0.5

1

1.5

2

0

0.5

1

Prior


A posteriori distribution – Bayes‘ law

)|()()|( jmjmj prior

-2

-1.5

-1

-0.5

0 0

0.5

1

1.5

2

0

0.5

1

Prior

-2

-1.5

-1

-0.5

0 0

0.5

1

1.5

2

0

0.5

1

Likelihood -2

-1.5

-1

-0.5

0 0

0.5

1

1.5

2

0

0.2

0.4

0.6

0.8

1Posterior


A posteriori distribution – Bayes‘ law

)|()()|( jmjmj prior

Mostly, only the expectation of the posterior distribution is

computed:

)))|(log())(min(log(arg jmjj prior

Maximum a posteriori (MAP) estimator


Where does a priori information come from

No information available – use mathematical constraints that select a

representative out of the class of possible solutions bearing maximum

likelihood

Specific qualitative function-anatomical knowledge

e.g. minimum norm, minimum support

e.g. sources are known to be focal for early evoked responses

Anatomical information

e.g. restriction to cortex by MRI

Quantitative functional information

e.g. weighting of positions by fMRI or PET


Different types of priors different methods

Restriction priors Certain solutions are impossible

Exclude certain brain areas (e.g. white matter) or certain current

directions (e.g. tangetial to cortex)

Often needs additional prior (e.g. minimum norm)

Limit the number of non-zero elements to a small number

Leads to overdetermined problem (e.g. dipole fit)

Examples:



„Qualitative“ priors Solutions with certain general

properties are preferred

Select the solution with a minimum

weighted lp norm

e.g. minimum l1 or l2 norm, LORETA

Select the sparsest solution

minimum support estimate

Examples:

p

prior jDj2

1exp)(

i i

iprior

j

jj

2

2

2exp)(



„Quantitative“ priors

Give a higher probability to regions that are active in an equivalent

imaging experiment

Mostly needs additional prior (e.g. minimum norm)

Source regions that appear connected by dwMRI based tractography

have a higher probability to be active together

Examples:

Source parameters have explicit

a priori distribution

Multimodal approaches


Inverse Methods

„True“ Inverse Methods

compute current density

that accounts for the

signals

Scanning Methods

compute a sources

strength at every point

independently

Low Parametric Models

sources are described by

fewer than signal values

Distributed Source

Models

sources are described by

many parameters


Low parametric models – spatio-temporal dipole fit C1

-8

-4

0

4

8

0 50 100

C2

-8

-4

0

4

8

0 50 100

C3

-8

-4

0

4

8

0 50 100

=

+

+

• spatio-temporal model

• restriction and qualitative priors:

• fixed number of non-zero elements

• positions/directions constant over time • overdetermined, estimate most probable solution


Distributed sources – cortical current density imaging

=

• spatial model

• restriction and qualitative priors:

• activity only in cortex with perpendicular direction

• minimum norm (e.g. L2, L1, LORETA) • estimate most probable solution

Dale et al. (Neuron 2000); Liu et al. (Proc. Nat. Acad. Sci. USA 1998)


Scanning methods

each voxel is evaluated separately – no true inverse

need to estimate of covariance matrix

assumption: sources are focal and uncorrelated

apaptive spatial filters / beamformers

multiple signal classification (MUSIC)

metric can be plotted


Take home messages

The inverse problem is non-unique. There is a multi-dimensional

manifold of solutions with equal maximum probability conditional

upon the measurements.

Every solution is equally valid conditional upon the data and the

priors.

Scanning methods are no true inverse solutions. Yet, they yield

much useful information on the sources.

Due to noise and errors, we cannot determine solutions with certaintly.

This is expressed by posterior distributions. However, mostly we

estimate the most probable solution.

We need priors. Priors can encode source space restrictions,

general qualitative properties or explicit quantitative knowledge.


Take home messages


Thank you

Thank you

Introduction to EEG and MEG - Max Planck Society · EEG WS 2012/2013, Thomas R. Knösche Max Planck...

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