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

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P S D H 0

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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

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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

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# = 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

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# = 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

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# = 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)

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>=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

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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

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C C T M C l a s s i f i e r

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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.)