Main idea - Cortech Solutions

Transcription

Real-time, noninvasive estimation
of neuroelectric activity
in brain regions of interest
Mark E. Pflieger
Source Signal Imaging, Inc.
San Diego USA
http://www.sourcesignal.com
g.tec & Cortech Solutions Neural Engineering Applications Seminar
Arlington, VA, March 16, 2005
Main idea
A 3D spatial filter that estimates
regional brain activity may be
designed offline, using structural MRI,
previously recorded EEG, and
(optionally) functional MRI.
Then it may be applied in real-time
via rapid matrix multiplication.
To handle multiple, simultaneous ROIs,
the matrices are simply concatenated.
NE Applications, 3/16/2005,
SSI/mep
EEG vector
 v1 (t ) 
 v (t ) 
v (t ) =  2 
 # 


 vm ( t ) 
ROI activity vector
 rk 1 (t ) 
 r (t ) 
rk (t ) =  k 2 
 # 


 rkd (t ) 
Estimator matrix
 E11
E
Ek =  21
 #

 Ed 1
E12
E22
#
Ed 2
" E1m 
" E2 m 

% # 

" Edm 
Multiple, simultaneous ROIs
Single ROI
rk (t ) = Ek v(t )
 r1 (t )   E1 
 r (t )   E 
 2  =  2  v (t )
 #   # 

  
rK (t )   E K 
Overview
Review of EEG source estimation
Global versus local estimators
Why real-time source estimation?
Noninvasive BCI
Regional activity estimation (REGAE)
3D spatial filter design using MRI
Illustration (offline)
fMRI-selected regions of interest (ROIs)
SSI/mep
I.
Brief review of EEG
source estimation
SSI/mep
Local vs. Global Source Analysis
Filter the data
Region by region
Independent design
Estimate activity
Then localize
Model the data
Whole brain
Coupled design
Localize sources
Then estimate
Examples
Examples
Resolution kernel
LCMV beamformer
REGAE
ST multiple dipoles
Linear distributed
Normalized MN
sLORETA
SSI/mep
Local estimators are particularly
suitable for real-time applications
Multiple dipole localization with unaveraged
data seems infeasible.
Source activity estimation using prescribed
dipole locations is an improvement; but the
fixed source model must explain the raw
data, and source activities are coupled.
Linear distributed global estimators can
provide ROI signals via restriction, but are
not generally optimal for this purpose.
Local estimators are “tuned” to specific
ROIs.
SSI/mep
II.
Why real-time
source estimation?
SSI/mep
Motivations
Adaptive control of experimental
sequences
Conditional stimulus presentations
ROI-centric studies
Epilepsy monitoring
Neurofeedback
BCI
Recovery of lost function
Augmented function
SSI/mep
Improved EEG-based BCI?
Leuthardt et al. (J. Neural Eng., vol.
1, pp. 63-71, 2004)

ECoG signals
Brief training periods (minutes)
More precise closed-loop control
However: Highly invasive; high risk of
infection probably limits duration
Can individuals control source signals
more readily than scalp signals?
SSI/mep
III.
Regional activity
estimation (REGAE)
SSI/mep
Source domain, dipole elements,
source space
Source domain
Underlying volumes and/or surfaces in the brain
where possible generators of extracranial
measurements may reside
Macroscopic ionic currents; gray matter
Dipole element
ECD on a relatively small scale
n = ~10K elements; discretization of source domain
Volume: triples per location
Surface: normal orientation
Source space
n-dimensional vector space spanned by the dipole
elements in the source domain
SSI/mep
Measurement domain, etc.
Measurement domain
Sensors and channels
m
Measurement space (a.k.a. signal space)
m-dimensional vector space spanned by the
measurements
Derived channels
Derivation matrix, D, [l-by-m]
l-dimensional derived measurement space
SSI/mep
Forward solution
Volume conductor model (a.k.a. head
model)
Physical approximations + geometry +
settings of bulk parameters + solver
Analytic, BEM, FEM
Forward matrix, F, [m-by-n]
Net gain matrix, G=DF, [l-by-n]
SSI/mep
ROI and non-ROI
The ROI may taper from a central location of interest (like the
passband of a bandpass filter). R, diagonal, [n-by-n]. The non-ROI
is the complement of the ROI over the source domain, I-R. The
ROI center is specified in advance. Size (FWHM or radius) may be
fixed or automatically adjusted. ROIs may be customized.
SSI/mep
Spatial bandpass filtering
Signal of interest (SOI)
measurement effects generated from the region
of interest (ROI)
Signal of no interest (non-SOI)
measurement effects generated (at the same
time) from the rest of the brain
Noise
measurement effects not of brain origin
Spatial bandpass filtering
Pass the signal of interest while rejecting signal
of no interest and noise
Use models, but do not model the data
SSI/mep
Primary filter = L2-norm matrix
Norm matrix, H, [l-by-l]
We seek a norm that assigns, for each y
in the derived measurement space, a
magnitude h(y) = |y|H = (ytHy)1/2 that
reflects the signal of interest only
“Quasi-norm”: H may have singularities
h(y) is a nonnegative scalar that reflects
total signal of interest
~ total observed ROI activity
SSI/mep
Estimator performance is gauged
via signal detection performance
An estimator h may be converted to a
signal detector by setting a threshold
ROC analysis of signal detectability
Source covariance matrix, S, [n-by-n]
Maximum entropy subject to some constraints
Noise covariance matrix, N, [l-by-l]
Simulate: yhit = Gx + ε
Simulate: yfa = G(I-R)x + ε
Generate ROC curve
AUROC measures performance [0.5, 1.0]
SSI/mep
Tradeoff between spatial resolution
and signal detectability
1
0.9
0.8
hit rate
0.7
10
20
30
40
50
0.6
0.5
0.4
0.3
0.2
0.1
1.0
0.9
0.8
0.7
0.7
0.6
0.5
0.4
0.4
0.3
0.2
0.1
0.1
0.0
0
false alarm rate
SSI/mep
Regional variability
1
0.9
0.8
hit rate
0.7
10
20
30
40
50
0.6
0.5
0.4
0.3
0.2
0.1
false alarm rate
SSI/mep
0.9
0.9
0.8
0.7
0.6
0.6
0.5
0.4
0.4
0.3
0.2
0.1
0.1
0.0
0
KLD (quasi-)norm matrix
Kullback-Leibler divergence (KLD)
A quasi-distance between two densities
Measures information available for
discriminating the densities
Is the ½ the trace of a matrix that may
be used as a REGAE norm (Gaussians)
C = GSGt + N
CI-R = G(I-R)S(I-R)Gt + N
HR = (C-CI-R)((CI-R)-1-C-1)
SSI/mep
REGAE estimator matrix
A practical approximation
H = Et E
E is the [d-by-l] estimator matrix
d = estimator dimension
Typically, d<l
Vector spatial filter
May vary from region to region
~Current configurations
x(t) = Ey(t)
SSI/mep
Derived time series
SSI/mep
IV.
Illustration
SSI/mep
Dataset: Verbal working memory
EEG + sMRI + fMRI
Clark CR, Moores KA et al., 2001
Task
“High-load” (VT) versus “low-load” (FT)
visual verbal working memory task
128-channel event-related EEG
Whole-head structural MRI
Functional MRI
SPM VT vs. FT, thresholded
SSI/mep
Summary of Processing Steps
Step
Description
sMR
I
fMRI
3D
sensors
1
Parcellate brain and head tissues
√
2
Make cortical mesh (brain model)
√
3
Make head model meshes
(volume conductor geometry)
√
4
Register sensors to sMRI
√
√
5
Calculate forward matrix
√
√
6
Obtain measurement covariance matrix
7
Estimate source covariance matrix
(maximum entropy estimate)
√
8
Select regions of interest
√
√
9
Derive REGAE estimators
√
10
Characterize signal detection properties
of REGAE estimators (ROC curves)
11
Apply estimators to real-time EEG
EEG
presample
EEG
realtime
√
√
√
√
√
√
√
√
√
√
√
√
√
√
√
Step 1: Parcellate brain & head tissues
SSI/mep
Step 2: Make cortical mesh
SSI/mep
Steps 3-5: Make head model meshes, register
electrodes, & calculate forward matrix
SSI/mep
Steps 6 & 7: Measure sensor covariance matrix &
estimate maximum entropy source covariance matrix
SSI/mep
Step 8: Select ROIs
SSI/mep
SSI/mep
Steps 9 & 10: Derive REGAE estimators &
characterize signal detection
ROC curves for ROIs
AUROC ~ 0.75
1
0.9
0.8
0.7
p(Hit)
0.6
HRLFl
0.5
SubPSl
0.4
RCalcSr
AGr
0.3
MFGr-IFS
0.2
IFSl-IFG
IFGrf
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p(False Alarm)
SSI/mep
Step 11: Apply estimators to
real-time EEG
Yet to be done
Off-line “simulation”
SSI/mep
Single trial example A (high occipital alpha)
SSI/mep
Single trial example B (“Event” near Broca’s area, HRLFl)
SSI/mep
Conclusion
The whole procedure is feasible
Limitations:
Accuracy of volume conductor model
Source statistics model highly complex
Tradeoff between spatial resolution and
the ability to discriminate ROI signals
from remaining brain activity
Real-time or quasi-real-time derived
signals may help to improve BCIs
SSI/mep
SSI
SSI/mep
References
Leuthardt EC, Schalk G, Wolpaw JR, Ojemann JG, Moran
DW (2004): “A brain-computer interface using
electrocorticographic signals in humans,” J Neural Eng 1:
63-71.
Greenblatt RE, Ossadtchi A, Pflieger ME (in press): “Local
linear estimators for the bioelectromagnetic inverse
problem,” IEEE Trans Signal Proc.
Pflieger ME, Greenblatt RE, Kirkish J (in press):
“Regional resolving power of combined MEG/EEG,”
Neurol Clin Neurophysiol.
Pflieger ME (in press): “Maximum entropy estimation of
neuroelectric source covariance statistics,” IJBEM.
Clark CR, Moores KA, Lewis A, Weber DL, Fitzgibbon S,
Greenblatt RE, Brown R, Taylor J (2001): “Cortical
network dynamics during verbal working memory
function,” Int J Psychophysiol 42: 161-76.
SSI/mep