fact and fallacy in eeg source connectivity courses... · 2017. 7. 5. · joint eeg(10/20 system)...
TRANSCRIPT
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
• 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?
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
The Effective Brain Connectome is a 3 dimensional Tensor
(1,1,1) (1, ,1)
( ,1,1) ( , ,1)
J
I I J
Emitters
The Effective Brain Connectome is a 3 dimensional Tensor
ReceiversDelays
, , a
Ε Ψ Ψ T A
,
Ψ ΨThe support of the marginal graph
Is the anatomical connectome
Outline
• What is the Effective Brain Connectome?
• Why formulate the EBC is a State Space Model?
• Are thre magical measures that find EBC without solving the EEEG inverse problem?
• What would be the ground truth?
• What are some of the remaining Challenges?
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
Effective Brain Connectome must be estimated via a State-Space Model
Observation Equation
1
1
kN
t k t t
k
ψ A ψ ett tv ψK ε
State Evolution Equation
1
2
…
Ns
…
t t-1
1
2
…
Ne
…
t
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?
• What would be the ground truth?
• What are some of the remaining Challenges?
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
Observation Equation
1
1
kN
t k t t
k
ψ A ψ e
t t tv Kψ ε
State Evolution Equation
Refutations of “magical Measures” has recently been published
Why this wont work can be easily seen examining the formulas
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
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
• What is the Effective Brain Connectome?
• Why formulate the EBC is a State Space Model?
• Are thre 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?
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
• What is the Effective Brain Connectome?
• Why formulate the EBC is a State Space Model?
• Are thre 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?
38
In the EEG state space model estimation of sources and connectivity interwined
Observation Equation
1
1
kN
t k t t
k
ψ A ψ ett tv ψK ε
State Evolution Equation
1
2
…
Ns
…
t t-1
1
2
…
Ne
…
t
Effective Brain Connectome must be estimated via a State-Space Model
Observation Equation
1
1
kN
t k t t
k
ψ A ψ ett tv ψK ε
State Evolution Equation
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
• What is the Effective Brain Connectome?
• Why formulate the EBC is a State Space Model?
• Are thre 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?
• 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
Dezhong Yao, Bharat Biswal and Pedro Valdes are recruiting:
Professors
Postdocs
PhD students
56