1. Directed Component Analysis
DCA EEG Artifact Extraction Algorithm

2. Introduction Segments EEG data into a sequence of overlapping windows
Uniquely models artifactual and non-artifactual (cortical) activity in each window
Allows for non-stationary artifact and cortical topographies
DCA artifact extraction is applied separately to each window in turn

3. Types of Artifacts EKG Eye blinks Eye movements
Model artifactual activity as an outer product of its topography and corresponding time course of intensity
Artifacts can be described by single or multiple topographies and corresponding intensity time courses
Multiple topographies: EKG, Eye movements
Single topography: Eye blinks

4. Eye Anatomy

5. Eye Blink Artifact
Dipolar source across retina of each eye (metabolism)
Generates an omnipresent electric potential field ( mV)
During an eye blink => eye lids slide over cornea => current flow is established through the highly conductive cornea into the extra-ocular region via the eyelids
Current flow links the dipolar source to the scalp potential field

6. Eye Blink Artifact
Electrical activity resulting from eye blinks is a major source of contamination in scalp-recorded EEG data
Eye blinks can exceed 500uV, whereas typical EEG is approximately +/-25uV

7. Big Picture
DCA extracts eye blink activity by estimating the intensity of the blink topography at each time point
Intensity at each time point is a weighted sum of the scalp electrode voltages
Weights are the elements of the DCA spatial filter
Spatial filter must differentiate between eye blink and cortical intensity
Filter requires a model of eye blink activity: blink template
Filter also requires a model of non-artifactual activity to which it can assign, or share, the cortical intensity
Filter will not extract the intensity of any non-artifactual activity captured by the “cortical” model, even if the topography of that activity is correlated to the blink template, such as frontal activity
Filter will extract the intensity of any non-artifactual activity not described by the cortical model

8. The Models
DCA requires 2 models: a model of artifactual (eye blink) activity and a model of non-artifactual (cortical) activity
Eye Blink Activity
Blink activity is modeled by the blink template
At present, the blink template is the average of one or more EEG time slices acquired from about the peaks of one or more blink intervals
Cortical Activity
At present, cortical activity is modeled by a subset of the eigenvectors of the “blink-free” EEG data covariance matrix
Data covariance matrix is symmetric, positive-definite
Eigenvectors are orthogonal
Eigenvalues are non-negative
Eigenvectors capture directions of maximal data variance in channel space, subject to orthogonality constraint
Efficient, parsimonious representation of “blink-free” EEG data
Cortical model must not capture the blink template
If so, spatial filter cannot recognize the eye blinks

9. Eye Blink Topography Source model: Extracted from recorded EEG:
Spherical, FDM, FEM
Accuracy of geometry & tissue conductivity values
Extracted from recorded EEG:
Specific to each individual subject
Average of topographies at blink peaks over a chosen time interval
Blink topography changes slowly over time

10. Cortical Topographies
Eye Blink Topography
Deriving cortical topographies from blink-free EEG ensures that we:
Minimize misallocation of eye blink energy to the cortical topographies during filtering
Allow for accurate representation of cortical EEG from frontal sources, not eye blinks, by retaining cortical topographies with significant correlation to the blink topography (r > 0.75)
Eliminate the effect of “bad” channel activity on subsequent spatial filtering by zeroing out corresponding elements of the cortical topographies
Cortical Topography (Eigenvector)

11. Blink and Cortical Topography Extraction
Identify intervals of eye blink activity in real time by accounting for:
EEG amplitude, slope, and blink template correlation thresholds
AC-coupled amplifier recovery time
Compute average topographies of each eye blink interval to provide the forward model with a dynamic, localized representation of blink activity
Extract cortical EEG, free of eye blink activity, from consecutive EEG data windows to provide for the computation of a dynamic, localized representation of brain activity

12. Eye Blink Removal Sequence
Eye blink topography
EEG
Source model
Data Model
Matrix of eye blink topography
(KEB)
and cortical eigenvectors
(K1 .. KCT)
Cortical topography
EEG
Source model
Spatial Filter Generation
Matrix pseudo inverse
Extract temporal evolution of eye blink intensity
Refine Extracted Eye Blink Intensity
Nullspace filtering Frequency filtering
Extract Eye Blinks

13. Spatial Filter Derivation
Spatial filter extracts intensity of activity correlated to the blink topography and not captured by the principal eigenvectors of the “blink-free” EEG data covariance matrix
KEB: Blink topography
KC1, KC2, …, KCT: Cortical eigenvectors
K*EB, K*C1, …, K*CT: Pseudo-inverse of blink and cortical eigenvectors (Spatial filter: K*EB)
Blink Topography + Cortical Eigenvectors
KEB …
KC2
KC1
KCT
Matrix Pseudo - Inverse
K*EB
K*C1
K*C2
K*CT

14. MATLAB Demo Demonstration of: Covariance Matrix Eigenvector Estimation
Blink Template Simulation
Matrix Pseudo Inverse
Spatial Filter Extraction
Spatial Filter Properties
Left Nullspace

15. Spatial Filter Details
Eigenvectors of cortical topography covariance matrix (current data window)
Plot 1 … K1
KLNS
KCT
Left Nullspace
Cortical Eigenvectors
Plot 2
Plot 3
Plot 4
Spatial filter is a weighted sum of left nullspace eigenvectors
Plot 5
Weights are corresponding correlation coefficients from Plot 5
Plot 1: Cumulative fraction of EEG variance captured by all eigenvectors of cortical topography covariance matrix
Plot 2: Correlation of blink template with eigenvectors retained for cortical model (Cortical Eigenvectors)
Plot 3: Correlation of blink template with eigenvectors not retained for cortical model (Left Nullspace)
Plot 4: Correlation of spatial filter with cortical eigenvectors - Essentially zero to minimize cortical activity extraction
Plot 5: Correlation of spatial filter with left nullspace eigenvectors - Nonzero correlation
to allow for extraction of blink activity

16. Eye Blink Removal Sequence
Eye blink topography
EEG
Source model
Data Model
Matrix of eye blink topography
(KEB)
and cortical eigenvectors
(K1 .. KCT)
Cortical topography
EEG
Source model
Spatial Filter Generation
Matrix pseudo inverse
Extract temporal evolution of eye blink intensity
Refine Extracted Eye Blink Intensity
Nullspace filtering Frequency filtering
Extract Eye Blinks

17. Time Course of Eye Blink Intensity
Inner product of spatial filter and EEG electrode recordings at each time point extracts temporal stream of eye blink intensity
EEG Data Window
EEG1 …
EEG2
EEG3
EEGn
Spatial Filter
K*EB
Blink Intensity …
Topographies
(time slices)
Channels
(time series) or … …

18. Eye Blink Removal Sequence
Eye blink topography
EEG
Source model
Data Model
Matrix of eye blink topography
(KEB)
and cortical eigenvectors
(K1 .. KCT)
Cortical topography
EEG
Source model
Spatial Filter Generation
Matrix pseudo inverse
Extract temporal evolution of eye blink intensity
Refine Extracted Eye Blink Intensity
Nullspace filtering Frequency filtering
Extract Eye Blinks

19. Extracted Blink Intensity Refinement
Nullspace filtering
Frequency filtering
Cortical model is comprised of Eigenvectors K1 - KCT, capturing ~ 95 % of cortical EEG topography variance per window
Pseudo-inverse generates spatial filter as a weighted sum of Eigenvectors K1 - KLNS
Nullspace filtering deletes from the left nullspace all eigenvectors with minimal correlation to the blink topography (r < specified threshold)
Spatial filter is regenerated as a weighted sum of remaining left nullspace eigenvectors, and blink intensity stream is re-extracted from EEG data
Eigenvectors of cortical topography covariance matrix … K1
KLNS
KCT
Left Nullspace
Cortical Topographies
Subsequent to nullspace filtering, low pass filtering of blink intensity stream reduces the power of its high frequency (~ > 12 Hz) components
Before
After

20. Extraction of Blink Artifacts From EEG
Blink removal sequence is re-implemented for each consecutive EEG data window
Blink - Free EEG
“Blinky” EEG = - BT *
Blink Intensity

21. Eye Blink Removal Sequence
Eye blink topography
EEG
Source model
Data Model
Matrix of eye blink topography
(KEB)
and cortical eigenvectors
(K1 .. KCT)
Cortical topography
EEG
Source model
Spatial Filter Generation
Matrix pseudo inverse
Extract temporal evolution of eye blink intensity
Refine Extracted Eye Blink Intensity
Nullspace filtering Frequency filtering
Extract Eye Blinks

22. Blink Topography and Spatial Filter
Cortical and left nullspace eigenvectors span channel space
Blink topography can be expressed as a weighted sum of eigenvectors derived from cortical topography covariance matrix
Orthogonal eigenvectors permit representation of blink topography variance as sum of eigenvector weights squared
Consequence: As number of cortical eigenvectors increases => fraction of topography variance captured by cortical eigenvectors increases => fraction captured by left nullspace decreases (fewer
left nullspace eigenvectors) => ii2} decreases
BT = 1KC1mKCm1KL1nKLn
Cortical eigenvectors
Left nullspace
BT2 = 1m12n2

23. Blink Topography and Spatial Filter
Corresponding spatial filter is a weighted sum of left nullspace eigenvectors
Orthogonal eigenvectors permit concise expression for inner-product of blink topography and spatial filter
< BT , SF > = 1 by definition of pseudo inverse
Consequence: As ii2} decreases => jj2} increases to maintain constant unity inner product => supremum of the spatial filter weights,
max{|| … |n|}, increases
Consequence: Increased sensitivity of spatial filter to all activity not captured by cortical eigenvectors
Consequence: Optimal value for user-specified fraction of cortical EEG variance captured by cortical eigenvectors (~ 0.95)
SF = 1KL1nKLn
< BT , SF > = 11nn

24. Bad Channel Detection
Artifact removal method rests on several assumptions:
Eye blink intervals are detected and excluded during cortical topography extraction
Spatial distribution of eye blinks are described by a single, relatively stable topography in each data window
Variance of EEG activity not captured by cortical eigenvectors is minimal
Imperative to detect and exclude bad channels
Bad channel variance is not accurately captured by cortical eigenvectors, distorts eye blink topographies and can interfere with eye blink detection
Artifact removal framework provides for detection and exclusion of bad channels
Detect bad channels based upon:
Frequency band power
Voltage and variance thresholds
Correlation to own spherical spline interpolant (low if channel is bad)
Correlation to nearby channels (normally high due to volume conduction)
Spatial filter components corresponding to bad channels are
zeroed out

25. When It Works…

26. DCA Demo Blinksmrkd.1ms.40.seg.oar.raw GNG2_002.1v.cmb.raw
128 channels x 39,375 samples
Process time: ~13 seconds
GNG2_002.1v.cmb.raw
128 channels x 931,640 samples
Process time: ~346 seconds
EEG acquisition time: ~3, Hz

27. Next Steps
Short term:
Variable window overlap, down to one sample increments
More frequent model updating
Zero-lag IIR low-pass filter
Reduce filter transients
Monitor blink template stability
Local / Global blink template
Increase “Blink to Noise” ratio

28. Even More Next Steps Long(er) Term Improve the “cortical” model
Iterative refinement
Varimax / Promax rotation of EEG covariance matrix eigenvectors
Covariance matrix would be based on ALL data within time window
May allow for modeling of cortical activity currently excluded