Multiple Component Event-Related Potential (mcERP) EstimationKH Knuth1, ST Clanton1, AS Shah2,3, WA Truccolo4, M Ding5, SL Bressler5, LJ Trejo1, CE Schroeder2,3

1. NASA Ames Research Center, Moffett Field, CA, USA 4. Dept of Neuroscience, Brown University, Providence, RI, USA2. Dept of Neuroscience, Albert Einstein College of Medicine, Bronx, NY, USA 5. Center for Complex Systems, Florida Atlantic University, Boca Raton, FL, USA3. Cog Neurosci & Schizophrenia Prog, Nathan Kline Institute, Orangeburg, NY, USA

Multiple Component Event-Related Potential (mcERP) EstimationKH Knuth1, ST Clanton1, AS Shah2,3, WA Truccolo4, M Ding5, SL Bressler5, LJ Trejo1, CE Schroeder2,3

1. NASA Ames Research Center, Moffett Field, CA, USA 4. Dept of Neuroscience, Brown University, Providence, RI, USA2. Dept of Neuroscience, Albert Einstein College of Medicine, Bronx, NY, USA 5. Center for Complex Systems, Florida Atlantic University, Boca Raton, FL, USA3. Cog Neurosci & Schizophrenia Prog, Nathan Kline Institute, Orangeburg, NY, USA 506.4

AbstractAbstract

Factor Analysis (FA)Factor Analysis (FA)

SimulationsSimulations

V1

Thalamic input

Spiny

Stellate Cell

Component 1

Pyramidal

Cell

Component 2

Component 3

Component 1 - thalamic input to lamina 4 spiny stellate cell

Component 2 - pyramidal cell activation in supragranular laminae

Component 3 - volume conducted far-field component

The mcERP ModelThe mcERP Model

Recorded Signalin the mth channelduring the rth trial

Stereotypic waveformof the nth component

Amplitude of the nth component during the rth trial

1=na

Latency of the nth componentduring the rth trial

0=nt

( )Â +-==

N

nmrnrnnrmnmr ttsCtx

1)()( hta

Coupling betweenthe nth source andthe mth channel

Unpredictable Signal Componentin the mth channel during the rth trial

(Ongoing Activity plus Noise)

Index Legend

m - channeln - componentr - trial

ReferencesReferences

For More Info andApplications Please Visit

506.5 Shah et al

For More Info andApplications Please Visit

506.5 Shah et al

ConclusionsConclusions

PerformancePerformance

mcERPmcERPComponent 1 Component 2 Component 3

SyntheticResponse

+ + =

The algorithm implementing this model has been tested usingartificial data sets designed to approximate componentryexpected in a visual experiment. Below is a diagram showingthe main responses in Macaque V1 during the presentation of ared flash. Artificial data were generated to simulate 15 channelsof recordings from a linear array microelectrode.

The amplitude-scaled and latency-shifted components areprojected onto the 15 channels and are summed to producethe synthetic response.

We have found that distinct generators of the ERP exhibitdifferential variability. Not only is this variability of interest toresearchers, but we demonstrate that it can also be used toseparate the signals produced by these generators.

We define an ERP component as being a stereotypicalwaveform that on any given trial may vary with respect toamplitude and/or onset latency. As we often have multiplechannel recordings, we introduce a matrix describing thecoupling between the components and the recording channels.In the field of source separation, this is known as a mixingmatrix. We call it a coupling matrix.

To estimate these model parameters from the data a MaximumA Posteriori (MAP) algorithm is derived, which allows asolution to the entire set of model parameters to be founditeratively using a fixed point algorithm.

For each synthetic experimental trial, each component isindependently amplitude-scaled by a, which is randomly drawnfrom a log normal distribution, and latency-shifted by t, whichis randomly drawn from a normal distribution. Such a scalingand shifting for component 1 is shown below for trial r.

)(1 ts )(11 tsra )( 111 rr ts ta -

hhr ¥1a

r1t

Independent Gaussian Noise is then added to each channel.

We consider two sets of 50 trials of synthetic data:

Set 1:No Trial-to-Trial VariabilitySNRs of 4.3 dB, -9.6 dB, 1.5 dBfor the three components

Set 2:Trial-to-Trial Variabilityanr from log-normal withsample andtnr from normal dist withsample andSNRs of 7.2 dB, -6.7 dB, 4.5 dBfor the three components

0.1=ampm

0=latm

0.1=amps

mslat 0.10=s

Set 2

Set 1

Trial 16

Trial 33

Trial 47

Channel 10

Trial 16

Channel 10

11

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Factor Analysis was used to examine both data sets. It was usedto examine both the trial-averaged response and the entire single-trial dataset. A Matlab implementation was used to performthese examinations (Ghahramani).

Set 1:No Trial-to-Trial Variability

Trial-Averaged Responses Single-Trial Responses

Set 2:Trial-to-Trial Variability

Trial-Averaged Responses Single-Trial Responses

Time (ms) Time (ms)

Time (ms)Time (ms)

FA is unable to separate the three components in any of the fourcases. Notice that the peaks in the variability case are broaderreflecting one of the effects of trial-to-trial variability.

Synthetic Source SignalsSynthetic Source SignalsFor visual comparison, we show the three original sourcesignal components below:

Independent Component Analysis (ICA) was used to examineboth data sets in the same manner that FA was employed. TheMATLAB Toolbox for ICA applied to psychophysiological datawas used to perform these examinations (Makeig).

Given 15 channels of data, ICA returns 15 sources. We reducedthe results by choosing the three sources that were maximallysimilar to the original sources as measured by their dot product.

Set 1:No Trial-to-Trial Variability

Single-Trial Responses

Set 2:Trial-to-Trial Variability

Trial-Averaged Responses Single-Trial Responses

Time (ms) Time (ms)

Time (ms)

ICA does much better separating the signals than FA (quantifiedon the Performance panel). The results with the single-trial dataare better than those with averaged data. In addition, trial-to-trialvariability apparently aids the algorithm even though ICA doesnot account for it.

ICAICA

Last we used the mcERP algorithm to examine the single-trialdata from both data sets. The analysis with the averageresponses was not performed as mcERP is a single-trialtechnique.

Set 1:No Trial-to-Trial Variability

Set 2:Trial-to-Trial Variability

With no trial-to-trial variability, mcERP does about as well asthe best results from FA and ICA. However, mcERP takesadvantage of trial-to-trial variability to accurately identify andseparate the sources as demonstrated with its impressive successin the variability case (data set 2).

In addition, notice the reduction in the noise in the estimates inset 2 as compared with FA and ICA under identicalcircumstances.

Time (ms)A

mpl

itude

(ar

b un

its)

Blue – Component 1 (SNRset 1 = 4.3 dB, SNRset 2 = 7.2 dB)

Green – Component 2 (SNRset 1 = -9.6 dB, SNRset 2 = -6.7 dB)

Red – Component 3 (SNRset 1 = 1.5 dB, SNRset 2 = 4.5 dB)

Time (ms)

Single-Trial Responses Single-Trial Responses

Time (ms)

Trial-Averaged Responses

Time (ms)

Knuth K.H., Shah A.S., Truccolo W.A., Ding M., Bressler S.L., Schroeder C.E. (In Preparation)Multiple Component Event-Related Potential (mcERP) Estimation using DifferentialAmplitude and Latency Variability

Shah A.S., Knuth K.H., Truccolo W.A., Ding M., Bressler S.L., Schroeder C.E. 2002. ABayesian approach to estimating coupling between neural components: evaluation of themultiple component event related potential (mcERP) algorithm. To be published in: C.Williams (ed.), Bayesian Inference and Maximum Entropy Methods in Science andEngineering, Moscow ID 2002, American Institute of Physics, Melville NY.

Knuth KH, Truccolo WA, Bressler SL, Ding M 2001. Separation of multiple evoked responsesusing differential amplitude and latency variability. Third International Workshop onIndependent Component Analysis and Blind Signal Separation (ICA 2001), San Diego CA.Available at: http://www.huginn.com/knuth/publications

Truccolo WA, Ding M, Knuth KH, Nakamura R, Bressler SL 2001a. Variability of corticalevoked responses: implications for the analysis of functional connectivity. ClinicalNeurophysiol. 113(2):206-26.

Truccolo WA, Knuth KH, Ding M, Bressler SL 2001b. Bayesian estimation of amplitude,latency and waveform of single trial cortical evoked components. In press: RL Fry and MBierbaum (eds), Bayesian Inference and Maximum Entropy Methods in Science andEngineering, Baltimore 2001, American Institute of Physics, Melville NY, pp. 64-73.

Ghahramani Z. EM for conditional factor analysis Matlab package:http://www.gatsby.ucl.ac.uk/~zoubin/software.html

Makeig, Scott et al., MATLAB Toolbox for ICA applied to psychophysiological data (Version3.52). WWW Site, Computational Neurobiology Laboratory, The Salk Institute for BiologicalStudies , 1997- [World Wide Web Publication], 2000.

The mcERP estimation algorithm represents a significant steptoward obtaining physiologically-relevant component estimatesusing single-trial data. Key to this endeavor is the variability ofthe ERP components, which in itself is of great interest as itreveals more about the dynamical interactions among brainregions than does averaged data. McERP not only estimatescomponent waveshapes, but also reveals their single-trialcharacteristics, such as amplitude scaling and latency shifts.When trial-to-trial variability is present, as we have shown is thecase in experimental data (Truccolo 2001a), mcERP outperformsboth FA and ICA.

Please see poster 506.5 for application to real data!

The Amari error, which characterizes the quality of separation, issummarized below. Without trial-to-trial variability mcERPperforms at the same level as ICA and better than FA. In thepresence of variability mcERP dramatically outperforms bothpopular methods.

Jumps in the mcERPAmari error indicatewhere each componentbecomes difficult toresolve (see coloredarrows).

McERP is robust to noise. It performs well to SNRs of –20 dBfor additive independent white Gaussian noise and –7 dB forcorrelated far-field noise.

We show how model-based estimation of the neural sourcesresponsible for transient neuroelectric signals can be improvedby the analysis of single trial data. Previously, we showed thata multiple component event-related potential (mcERP)algorithm can extract the responses of individual sources fromrecordings of a mixture of multiple, possibly interacting, neuralensembles. McERP also estimated single-trial amplitudes andonset latencies, thus allowing more accurate estimation ofongoing neural activity during an experimental trial. ThemcERP algorithm is related to infomax independent componentanalysis (ICA); however, the underlying signal model is morephysiologically realistic in that a component is modeled as astereotypic waveshape varying both in amplitude and onsetlatency from trial to trial. The result is a model that reflectsquantities of interest to the neuroscientist.

Here we demonstrate that the mcERP algorithm provides moreaccurate results than more traditional methods such as factoranalysis and the more recent ICA. Whereas factor analysisassumes the sources are orthogonal and ICA assumes thesources are statistically independent, the mcERP algorithmmakes no such assumptions thus allowing investigators toexamine interactions among components by estimating theproperties of single-trial responses.

Supported by:NASA Aerospace Operations Systems ProgramNASA Intelligent Systems ProgramNIH MH60358