Model-based detection of event- related signals in electrocorticogram Jeffrey A. Fessler, Se Young...
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Model-based detection of event-related signals in electrocorticogram
Jeffrey A. Fessler, Se Young ChunEECS Department
Jane E. Huggins, Simon. P. LevineDept. of Physical Medicine and Rehab., and Biomedical Engineering
The University of Michigan, Ann Arbor, MI
NIPS BCI Workshop, 2004-12-17
UM-DBI Project
The University of Michigan Direct Brain Interface (UM-DBI) project seeks to detect voluntarily produced electrocortical activity (ECoG) related to actual or imagined movements in humans as the basis for a DBI.
Signal Source
Subdural implantation Location selected for
epilepsy monitoring, not necessarily on motor cortex
Macro electrodes 4 mm diameter 1 cm center-to-center
Grids and/or strips 4 - 126 electrodes
ECoG Data
Subjects perform about 50 repetitions of
up to 6 different (real) voluntary actions. Events (unprompted) separated by 3 to 10 seconds Action marked by EMG signal (partial labeling). No feedback or training. 10,000+ ECoG traces (not all useful)
Initial Detection Method
Data: sampled ECoG signals from a single electrode Detection of event-related potentials (ERPs):
Cross-correlate ECoG signal with a signal template Template: triggered average of training data Compare output to an empirical threshold
Cross-Correlation based Template Matching (CCTM)
ERP Template Example
ECoG signals from 5 events
Average of 23 events
(ERP template)
Cross Correlation Method: Its Implicit Model
Two hypotheses for an ECoG signal block x: H0 : x ~ N(0, 2 I) “rest” H1 : x ~ N(, 2 I) “task/event”where denotes the template signal vector
Neyman-Pearson optimal detector, under the above model, formed from the likelihood ratio, is x’ which is cross correlation (CCTM).
But the “white noise” signal model ignores changes in the signal power spectrum!
Power Spectrum Changes The ECoG signal spectrum changes during tasks.
Event-related desynchronization (ERD) and event-related synchronization (ERS)
(ERD/ERS maps from B. Graimann et al, Graz)
Concurrence of ERP and Spectral Changes
Moving-window spectra
Time “0” is the event trigger times. The power spectrum changes significantly near event onset.
Power Spectrum Changes
Short-time power spectrum minus baseline power spectrum
Moving-window Spectra(Individual events)
Spectral changes are evident even in single events!
Spectrum-BasedDetection Strategies
Feature based: Extract spectral signal features
e.g., band power, adaptive AR methods (Graz) Apply feature-based detection (e.g., LDA)
Model based: Develop “optimal” detector based on signal models
that attempt to capture key signal characteristics.
Quadratic Detector based on Two-Covariance Signal Model
Two hypotheses for the ECoG signal (block) x: H0 : x ~ N(0, K0) “rest”
H1 : x ~ N(, K1) “task/event”
where Kn denotes the covariances in each state
Neyman-Pearson optimal detector, formed from the likelihood ratio, is:
x’ (K0-1 - K1
-1) x
which is a quadratic detector (cf Mahalanobis distance). (For now, ignore the ERP component
Challenges / Solutions Large covariance matrices => many model parameters? Solution: AR spectrum model (about 6th order)
AR models (non-adaptive) for K0 and K1
estimated from training data.
Unprompted events => incompletely labeled data. Solution: joint maximum-likelihood (ML) estimates
of labels and AR coefficients from training data.
Inversion of large covariance matrices? Solution: simple FIR filters due to AR model.
Quadratic DetectorBlock Diagram
Two FIR filters (AR inverse) Moving sum-of-squares (innovation power) Normalize by ML estimates of variances Compare “which model fits better” Neyman-Pearson => most powerful (per block)
Feature-based vs Model-based Spectra of simulated signals:
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0
1 0
2
1 0
3
1 0
4
P S D H 0
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0
1 0
2
1 0
3
1 0
4
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0
1 0
2
1 0
3
1 0
4
P S D H 0
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0
1 0
2
1 0
3
1 0
4
H0
H1
ROC from Simulation
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
1 0 0
P r o b . F a l s e A l a r m
P r o b . D e t e c t i o n
R O C - S a m p l e L e n g h 0 . 2 5 s . - B P 4 x
M o d e l
B a n d p o w e r
A A R
Quadrat
ic
Band-power
AAR / LDA
Test Data & Results
Representative subset of 20 data sets from 10 subjects 2184 ECoG channels Evaluate in terms of “HF difference”
% of “hits” (a detection within an acceptance window) minus % of false detections.
ROC evaluation seems infeasible due to unprompted actions / incompletely labeled data.
Quadratic vs CCTM: 1 sec Delay
Quadratic vs. CCTM at 1 second Delay Constraint
0
20
40
60
80
100
120
# = 100# >= 90# >= 80# >= 70# >= 60# >= 50
HF-difference Level
# Channels Above HF Level
Quadratic
CCTM
Quadratic vs CCTM: 0.5 sec Delay
ECoG channels above each HF-difference threshold
Quadtric vs. CCTM for 0.5 second Delay Constraint
0
10
20
30
40
50
60
# = 100# >= 90# >= 80# >= 70# >= 60# >= 50
HF-difference Level
# Channels Above HF
Quadratic
CCTM
Detection Delay
Important for feedback!
Quadratic Detector vs. Allowed Maximum Delay
0
20
40
60
80
100
120
# = 100# >= 90# >= 80# >= 70# >= 60# >= 50
HF-difference Levels
# Channels Above HF Level
1 second delay
0.5 second delay
0.25 second delay
Summary
Quadratic detector Based on two-covariance model. Captures spectral changes. Simple real-time implementation. Improved detection accuracy over CCTM. Reduced detection delay.
Recently implemented in our real-time system. Feedback studies with imagined movements forthcoming.
Future work
Combine two-covariance model with ERP component? Three-covariance model? (ERD / ERS / rest) Time-varying / adaptive models
state space / hidden Markov in collaboration with Victor Solo
Extend to multi-channel detection methods Integrate into real-time use for feedback studies Imagined movements (in progress)
Extra slides
Average ECoG from 32 electrode locations during pinch
Triggered ECoG Averages
CCTM Detection
Cross-correlate ERP template and ECoG
Detection: Correlation value exceeds an empirical threshold
Hit: Detection between 1.0 sec before and 0.25 sec after a trigger
Results quantified by Hit% - False Positive% (HF-difference)
Template
Continuous ECoG
Cross-Correlogram
Single Channel DetectionHit % and False % for best channel in each data set
(Average method, top 50 data sets for 18 subjects)
0
20
40
60
80
100
120
140
160
180
>=90>=80>=70>=60>=50
HF-Difference
# Channels >= HF-Difference
ECoG channels above each HF-differencesthreshold for the single-channel CCTM method.
211 datasets from 34 subjects
ML Estimates of Labels
Estimate center and width of “task” intervals
using log-likelihood under two-covariance model. (Requires search over center / width.)
ML labels vs MSE labels
Joint ML approach to labeling data yielded comparable performance to previous heuristic MSE approach.
Detection Delay
(not sure about this data from JV)
0
2 0
4 0
6 0
8 0
1 0 0
1 2 0
1 4 0
H F > 5 0 H F > 6 0 H F > 7 0 H F > 8 0 H F > 9 0 H F = 1 0 0
H i t - F a l s e P o s i t i v e D i f f e r e n c e
No. of Channels>=HF
1 s
0 . 5 s
0 . 2 5 s
0 s
C C T M C l a s s i f i e r
0
5
1 0
1 5
2 0
H F > 5 0 H F > 6 0 H F > 7 0 H F > 8 0 H F > 9 0 H F = 1 0 0
H i t - F a l s e P o s i t i v e D i f f e r e n c e
Number of channels
>=HF
2 s
1 . 5 s
1 . 2 5 s
1 s
Moving-window spectra
Time “0” is the event trigger times. Clearly the power spectrum changes near event onset. (Visible even in single event moving-window spectra.)