Exploiting temporal delays in interpreting EEG/MEG data in terms of

brain connectivity

Fraunhofer FIRST, Berlin

G. Nolte

Problem of volume conduction

)(1 tx

)(2 tx )(3 tx)(4 tx

?

)(iz complex Fourier amplitude in the i.th channel

Cross-spectrum

)()()( jiij zzS Cross-spectrum

Coherency = normalized cross-spectrum

)()(

)()(

jjii

ijij

SS

SC

Coherence = absolute value of coherency

)()( ijij CCoh

Power: Task-Rest

Coherence: C3-others Coherence: C4-others

C3 C4

EEG-simulation of ERD (two sources)

Rest: Real background + simulated dipolesTask: Real background

Fake!! Sources were indepent!!

Rest Coherence

EEG-simulation of ERD (1 source)

Rest: Real background + simulated dipoleTask: Real background

Inverse using beamformer (DICS) on cortex

Simulated dipole Estimated power ratio: Rest/Task

Coh., signal+background Coh., background

Coh., difference

seed

Coh., signal+background Coh., background

Coh., difference

seed

seedoriginal dipole location

Observation:

Independent sources do not contribute to the imaginary part of the cross-spectrum

1 (non-interacting) source

Interaction with time delay

volume cond.

Many sources

)()(

)()(

2

1

ii

ii

sbz

saz

Assumption:

sources are non-interacting

imaginary part of coherency must arise from interacting sources

Explicit derivation

)()()( 2112 zzS

real for instantaneous volume conduction(Stinstra and Peters, 1998)

Real !

2)(iii

i

sba )()(,

jijiji

ssba

=0 for ij

Coherence

Imaginary coherency

Imaginary coherency

Coherence

movement

Power

Selfpaced movement, C3-C4 relationships

Observations:

• coherence follows power

• imaginary part has onset 5secs before movement

• imaginary part not related to power

Nolte, et.al., Clinic. Neurophys., 2004

Significance; False Discovery Rate (FDR)

Simulated non-interacting sources

Imaginary coherency

Interaction exists!

Task-related activity exists!

Is task-related actvity interacting?

differences should be based on cross-spectra

2/12/1 Bjj

Bii

Bij

Ajj

Aii

Aij

SS

S

SS

S

2/12/1 Bjj

Bii

Ajj

Aii

Bij

Aij

SSSS

SS

movement

2/12/1 Bjj

Bii

Bij

Ajj

Aii

Aij

SS

S

SS

S

2/12/1 Bjj

Bii

Ajj

Aii

Bij

Aij

SSSS

SS

Difference of normalized cross-spectra

Normalized difference of cross-spectra

Imag, Cross-Spectrum, Left-Right

MEG, Cross-Spectrum; imag, alpha

Imaginary part, 5 dipoles

S1

S2

“Philosophy”

“Philosophy”

Method A

interesting phenomena non-interesting phenomena

Data

Method B

“Philosophy”

Pairwise Interacting Source Analysis (PISA)

2211 )()()( atsatstx

independent

ICA

spectrum

ICAwith temporal decorrelation(Sobi, TDSEP)

TT aafpaafpfC 222111 )()()(

spatial pattern

ISA

))((ˆ))(Im( 11111TT abbafpfC

“interaction spectrum” 2 spatial patterns

Nolte, et.al., Phys. Rev. E., 2006

EEG, imagined foot movement

ISA1 ISA2

• finds systems blindly

• no 1/f spectrum

• clear higher harmonics

Observation:

2D-subspace of channel space

Model for each grid-point:

3D-subspace

MUSIC

Angle

A: measured field

B

MUSICchannel-subspaces for each voxel (here 2 dipole-directions)

field for dipole in x-direction

field for dipole in y-direction

AP BPProjector on A Projector on B

1cos1 show weplotsin -Φ-

ABA PPPΦ of eigenvaluelargest cos2

MUSIC RAP-MUSIC

Example 1

MUSIC RAP-MUSIC

Example 2

ISA-pattern;

left mu-rhythm

RAP-MUSIC

first scan

Conclusion

• Imaginary parts of cross-spectra is not affected by non-interacting sources valuable quantity to study interactions

• ICA-like decompositions finds and separates interacting systems blindly

• Localization with MUSIC and/or dipole fit