Fact and Fallacy in EEG Source Connectivity Courses... · 2017. 7. 5. · Joint EEG(10/20 system) and ECoG (128 channels) Forward head model (Valdes-Hernandez is to be used to test

Pedro A. Valdés-Sosa

JOINT CHINA-CUBA LABORATORY FOR FRONTIER RESEARCH IN

TRANSLATIONAL NEUROTECHNOLOGY中国-古巴神经科技转化前沿研究联合实验室

Fact and Fallacy in EEG Source Connectivity

There has been very early work with functional Connectomics using EEG

Livanov, M. N., Gavrilova, N. a., & Aslanov, A. S. (1964).Intercorrelations between different cortical regions of human brain during mental activity.Neuropsychologia, 2(4), 281-289

Correlation between EEG recordings

A more modern example plotting Imaginary Coherence between 60 EEG electrodes during thr resting state seems to indicate complex dynamics?

Consider this resting state (alpha rythym coherence matrix with Scalp (60 electrodes). Does it represent an interesting complex neural network?

Actually NO

Outline

• What is the Effective Brain Connectome?

• Why formulate the EBC is a State Space Model?

• Are there magical measures that find EBC without solving the EEEG inverse problem?

• Does the situation change by previously finding components?

• What would be the ground truth?

• What are some of the remaining Challenges?

4

Outline







5

In Brain Connectivity there are related but different concepts that are confused

Anatomical (axonal) Connectivity

Effective (causal) Connectivity

Direct Causal (hormonal) effect

Functional Connectivity=CorrelationNon causal

Functional Connectivity is not connectivity!!!

The Effective Brain Connectome (EBC) is the set of all Effective Brain Networks

An Effective Brain Network is a (hyper) graph:

A Ε Ψ Ψ T

Ε

Ψ

T

A

Effective Brain Network graph

Activity at nodes

delays

Effective Connectivity measure : Wiener-Akaike-Granger Schweder (WAGS)

Points (neural masses)

Manifolds (neural fields)

One WAGS measure is Granger Causality based on the Bivariate Autoregressive Model

1, 11 1, 1 12 2, 1 1,

2, 21 1, 1 22 2, 1 1,

t t t t

t t t t

a a e

a a e

1

2

0 21 2 1: 0 0H a I 1

2

Granger Non Causality

t t-1

t t-1

t =1,…,N

This is the basis of all connectivity measures

Multivariate Granger Causality is a test of whether the autoregressive coeffients are zero

1 1 1

1,1 1,2 1,1, 1, 1

1 1 12, 2, 12,1 2,2 2,

1 1 1, , 1,1 ,1 ,

2 2 2

1,1 1,2 1,

2 2 2

2,1 2,2 2,

2 2 2

,1 ,1 ,

s

s

s ss s s s

s

s

s s s s

Nt t

t tN

N t N tN N N N

N

N

N N N N

a a a

a a a

a a a

a a a

a a a

a a a

1, 2 1,

2, 2 2,

, 2 ,s s

t t

t t

N t N t

e

e

e

t =1,…,N

1

2

…

Ns

…

t t-1

1 1 1

1,1 1,2 1,1, 1, 1 1,

1 1 12, 2, 1 2,2,1 2,2 2,

1 1 1, , 1 ,,1 ,1 ,

s

s

s s ss s s s

Nt t t

t t tN

N t N t N tN N N N

a a a e

ea a a

ea a a

Connectivity Matrix Cartesian product (BrainX Brain)

=X1,1 1,2 1,

2,1 2,2 2,

,1 ,2 ,

p

p

p p p p

a a a

a a a

a a a

For the autoregressive Matrices the columns correspond to emitters and the rows to receivers

The MAR model has a compact mathematical expression which we will use in the rest of the talk

1

1

kN

t k t t

k

ψ A ψ e

𝐀𝟏𝐀𝟐

𝐀𝒑

(1)

(2)

( )

x

x

x I

x

(1,1) (1, )

( ,1) ( , )

x x J

x I x I J

X(1,1,1) (1, ,1)

( ,1,1) ( , ,1)

x x J

x I x I J

𝐗𝐱

A Vector is a 1-D tensor A Matrix is a 2-D tensor An example of a 3-D tensor

The Effective Brain Connectome is a 3 dimensional Tensor


(1,1,1) (1, ,1)

( ,1,1) ( , ,1)

J

I I J

Emitters


ReceiversDelays

, , a

Ε Ψ Ψ T A

,

Ψ ΨThe support of the marginal graph

Is the anatomical connectome

Outline



• Are thre magical measures that find EBC without solving the EEEG inverse problem?



14

ANATOMICAL EFECTIVE

Correlation

ICA

COCOMAC

Tractography

DCM

Granger

FUNCTIONAL

Imperfect knowledge

There is much current research about different types of Brain Connectivity:

Effective Brain Connectome must be estimated via a State-Space Model

Observation Equation

1

1

kN

t k t t

k

ψ A ψ e

t t tv Kψ ε

State Evolution Equation



1

1

kN

t k t t

k

ψ A ψ ett tv ψK ε


1

2

…

Ns

…

t t-1

1

2

…

Ne

…

t

Outline






18

This must be done using Bayesian inversion of the state space model with the appropriate priors

ESTIMATE

,

tv

A ψ

From

1

1

kN

t k t t

k

ψ A ψ e

t t tv Kψ ε

A common mistake is to attempt to estimate effective connectivity from the observations ignoring the observation equation

,

tv

A ψ

Instead of estimating

From

…Estimate

From

,

tv

A ψBy means of a “magical

Measure”

A common mistake is to attempt to estimate effective connectivity from the observations ignoring the observation equation


1

1

kN

t k t t

k

ψ A ψ e

t t tv Kψ ε


Refutations of “magical Measures” has recently been published

Why this wont work can be easily seen examining the formulas


1

1

kN

t k t t

k

ψ A ψ e

t t tv Kψ ε


1

1

kN

t k t t

k

v

K A ψ ξ

Implies that

There is no way for voume conduction NOT to affect the MAR as supported by by simulations

Truth

Estimated

Defenders of the magical measures show simulations in which there is no correct conslusions are obtained in spite of volume conduction

Unfortunately examples don’t refute general theoretical arguments

However a SINGLE example does refute a general claim

Mistrust any measure which is no obtained by using the lead Field!!!!!

At the heart of many magical proposals is the “phase fallacy”

a12 sensor

a12 source

It argues that measures based on phase or lag are note affected by volume conduction

For example some argue that looking at the imaginary component of the signal in the frequency domain is unaffected by volume conduction

Quote: The lead field is a real matrix therefore does not affect phase

Such is the argument that misinterprets Imaginary Coherence, which is easily shown to be false

1

1

kN

t k t t

k

v

K A ψ ξ

Remember the model for observations:

2

1

kNi f k

k

k

f e

H A

Transforms in the frequency domain to

f f fv f K H ψ ξ

Fourier transform

There is no way that Volume conduction is eliminated by takng the imaginary part of the signal!!!!!!!!!

Im Im Imf f fv f K H ψ ξ

1

2

…

Ns

…

t t-1

1

2

…

Ne

…

t

Taking the Fourier transform does not change the physics of the problem

Outline







29

EEG sources may also be found in the frequency domain

Topographic Maps

128 channel EEG recording

Descriptive EEG Spectral parameters

Source Spectra found using VARETA

Anothr approach is to do Component Analysis

EEG vstime

(t)

voxel(s)

=k

qk

bk

Require these to be either:

• Orthogonal PCA • nearly independent ICA

Component Analysis is a powerful method for analyzingfunctional connectivity

ICA extracts components by assuming independence

k

qk

bk

Tomography

STONNICA is ICA tomography not tomography of ICA carried out in the source space by ussiming nonoverlapping sources

Mv K e

L M Must be minimum in the L1 norm

Must also be column orthogonal and NonnegativeM

M1

M2M1

M2

1v

g

A different type of Component results from recognizing that EEG time/frequency data is a tensor

( , )tS

EEG

2

1 21 2 G GM LM

0VF

0GM

KICx

RR

R

IEICx

5 10 15 20 25 300

0.5

1

Frequency (Hz)

Spectral Factor

0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

Time (s)

Temporal Factor

LV

RV

Spectral Signature

Temporal Signature

Spatial Signature

VT

T

IETI

FI

FI

TI

Spatio Temporal Non Negative ICA (STONNICA) can be extended to T/F with a TENSOR model

The real answer to the network question of resting alpha is actually a bit simpler than some would want. For components one must also solve the inverse problem

Sources (3 Components)

Scalp (60 electrodes)

Outline







38

In the EEG state space model estimation of sources and connectivity interwined


1

1

kN

t k t t

k



1

2

…

Ns

…

t t-1

1

2

…

Ne

…

t



1

1

kN

t k t t

k



1

2

…

Ns

…

t t-1

1

2

…

Ne

…

t

Inverse solution first and then estimating connectivity is not optimal

Joint EEG(10/20 system) and ECoG (128 channels)

Forward head model (Valdes-Hernandez is to be used to test surface EEG estimated effective connective against actual ECoG effective connectivity

Connectivity methods shold be tested in experimental situations. One such set of data is available for simultanoues EEG/ECoG in a Macaque prepration

ECoG Connectivity in this situation is directly measurable

And in fact shows condierable correspondence with the EEG recorded simulatneoulsly as shown by Canocial Correlation Analysis

Canonical Correlations between EEG and ECog

Outline







• Improving Source connectivity estimates

• Dealing with wave phenomena44

The EEEG spectrum can be separated out into two component founds in the late 80’s

Pascual-Marqui, Valdes-Sosa, Alvarez Amador (1988) Int J Nsc 40 (1-2) 89-99

Alpha

Xi

A number of authors in the 80’s had found consistent Principal components for EEG topographies

Valdéa-Sosa , et al. Brain topography 4.4 (1992): 309-319

We speculated they might be Spherical Harmonics thus reflecting a cortical random isotropic random process on the cortical surface

lmY Y

Valdéa-Sosa , et al. Brain topography 4.4 (1992): 309-319

Neural field theory has revived Spherical Harmonic expansions

There is a deep connection between neural field theory and “Microstates”

“inverse solution” of microstates in terms of space/ time frequency

Dietrich Lehmann

50

Modeling the cortex as a spherical sheet allows the expansion of sources in terms of spherical harmonics

t t

t t

g Yg

p Yp lmY Y

50

The inverse Laplacian can be expressed also in this expansion :

1 ; ;t filter Y D Y D D

t t t

t t

v K Mp e

K Mp e

Leading to the following reformulation of the EEG measurement model:

51

The Local Nunez model exhibits highly damped activity spreading out from an occipital source: duality between wave and localized activity.

Occipital source time series

Source wave propagation

One second of activity

The estimation procedure evolves from global wave solution to local dynamics

Detecting EBC must follow a process

General theory of Brain Connectivity Image Fusion

The many levels of causal brain network discovery. Bressler& Mannino Physics of Life Review

Causal Time Series Analysis of functional Magnetic Resonance Imaging Data. Roebroeck, Seth. JMLR

Effective connectivity: Influence, causality and biophysical modelling. Friston & DanizeauNeuroimage

Introduction: multimodal neuroimaging of brain connectivity. Friston & Kotter PTRS

Extension to Brain Body network

Tensor Analysis and Fusion of Multimodal Brain Images. Karahan, Valdes, Bringas IEEEIncorporating priors for EEG source imaging and connectivity

analysis. Xu Lei FrontiersModel driven EEG/fMRI fusion of brain oscillations. Ozaki, Bosch, Riera, Iturria, Sotero, Aleman, Carbonell Hum Brain Map Concurrent EEG / fMRI analysis by multiway Partial Least Squares . Martinez, Miwakeichi, Goldman, Cohen NeuroimageA symmetrical Bayesian model for fMRI and EEG/MEG neuroimage fusion. Trujillo, Martinez, Melie. Int J Bioelect

EEG Source ConnectivityCritical comments on EEG sensor space dynamical connectivity analysis. Van De Steen, Faes, Karahan, Songsiri, Marinazzo BTOPCortical current source connectivity by means of partial coherence fields. Pascual, Riera. ArXivWhite matter architecture rather than cortical surface area correlates with the EEG alpha rhythm. Valdes Hdez, Ojeda, Martinez, Lage, Virues. NeuroimageMinimum Overlap Component Analysis (MOCA) of EEG/MEG data for more than two sources. Nolte, Marzetti. J Neurosc MethDecomposing EEG data into space-time-frequency components using Parallel Factor Analysis. Miwakeichi, Martinez Yamaguchi. Neuroimage

Gait Influence Diagrams in Parkinson’s Disease. Ren, Karahan … Bosch, Bringas IEEE

Collaborators Yasser Aleman

Eduardo Aubert

Mireille Besson

Maria A. Bobes

Miguel A. Bornot

Jorge Bosch

Maria L. Bringas

Jose L. Caceres

Felix Carbonell

Mark Cohen

Jean Danizeu

Karl Friston

Robin Goldman

Thalia Harmony

Yasser Iturria

Esin Karahan

Thomas Köening

54

Agustin LageXu LeiDaniel MarinazzoEduardo Martinez MontesFumikazu MiwakeichiLaura MarzettiLester MelieGuido NolteAlejandro Ojeda Torhu OzakiRoberto Pascual-MarquiJorge RieraPen RengPedro A. Rojas Roberto C. SoteroNelson Trujillo Pedro A. Valdes Hernandez Trinidad ViruesDezhong Yao

China-Canada-Cuba (CCC) AxisCCC China Cuba Canada alliance for Neuroinformation

http://sciencepolicy.ca/maryse-lassonde

Dezhong Yao, Bharat Biswal and Pedro Valdes are recruiting:

Professors

Postdocs

PhD students

[email protected]

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Fact and Fallacy in EEG Source Connectivity Courses... · 2017. 7. 5. · Joint EEG(10/20 system) and ECoG (128 channels) Forward head model (Valdes-Hernandez is to be used to test