response-time corrected averaging of event-related potentialshecke/archiv/timewarp.pdf ·...

Response-Time Corrected Averaging of Event-Related Potentials

Response-Time Corrected Averaging ofEvent-Related Potentials

Hecke [email protected]

Bernstein Center for Computational Neuroscience GöttingenUniversity of Göttingen, Institute for Nonlinear Dynamics

CNS*2007Workshop

Synchronization of brain signals:What is real, what is not?

göttingen


Outline

1 Introduction

2 Event Related Potentials

3 Response Latency Correction

4 Discussion

göttingen


Introduction

Introduction

What are ERP components?

Our Background

BCCN Project C4: ”aging effects in selective attention”

joint project of modelers and experimentalists

main research tool: negative priming

EEG recordings to access internal mechanisms

A Modelers Interest in ERPs

clarification of temporal variance

localization of mechanisms in time and space

göttingen


Introduction

A Physicists Questions

If the components of event related potentials reflect differentprocessing stages during an experimental trial, ...

... how can they be found by pure grand averaging?

Problems to cope with

signal to noise ratio ≈ 10%

strong variation in a subjects reaction times

huge interindividual reaction time differences

different strategies amongst subjects

göttingen


Introduction

Eliminating Reaction Time Variance

Main Statement

Behavioral reaction times can be used to normalize the timeinterval between stimulus onset and response for averaging.

But where does the temporal variance come from?

A linear stretch is unlikely.

At least perceptual stages are highly automatic.

Which processing stages contribute how strong to thereaction time variance?

Is this question reasonable?

göttingen


Event Related Potentials

EEG Data Cleaning

downsampling to 500Hz

band pass filter: [0.2,20]Hz

conditional segmentation [-100,1500]ms

baseline correction for [-100,0]ms

ocular correction (Gratton & Coles), VEOG channel: FPz

reconstruction of FPz = (FP1+FP2)/2

individual low cutoff filter 0.5Hz

baseline correction for [-100,0]ms

artifact rejection, bounds [-100,100]µV)≤ 10% trials excluded

new reference: (TP10+TP9)/2, reconstruction of FCz

average

göttingen



ERP Analysisan old slide

NPPPCO

1s

10µ

V

Fp1 Fp2

F3 F4

C3 C4

P3 P4

O1 O2

F7 F8

T7 T8

P7 P8

Fz

Cz

Pz

Oz

FC1 FC2

CP1 CP2

FC5 FC6

CP5 CP6

TP9

F1 F2

C1 C2

P1 P2

AF3 AF4

FC3 FC4

CP3 CP4

PO3 PO4

F5 F6

C5 C6

P5 P6

AF7 AF8

FT7 FT8

TP7 TP8

PO7 PO8

Fpz

AFz

CPz

POz

J. Behrendt, H. Gibbons, HS, M. Ihrke, J. M. Herrmann, M. HasselhornEvent-Related Brain Potential Correlates of Identity Negative Priming,in preparation

göttingen



ERP Analysisan old slide

NPPPCO

1s

10µ

V

Fp1 Fp2

F3 F4

C3 C4

P3 P4

O1 O2

F7 F8

T7 T8

P7 P8

Fz

Cz

Pz

Oz

FC1 FC2

CP1 CP2

FC5 FC6

CP5 CP6

TP9

F1 F2

C1 C2

P1 P2

AF3 AF4

FC3 FC4

CP3 CP4

PO3 PO4

F5 F6

C5 C6

P5 P6

AF7 AF8

FT7 FT8

TP7 TP8

PO7 PO8

Fpz

AFz

CPz

POz

J. Behrendt, H. Gibbons, HS, M. Ihrke, J. M. Herrmann, M. HasselhornEvent-Related Brain Potential Correlates of Identity Negative Priming,in preparation

P5 NPPPCO

P6 NPPPCO

göttingen



Behavioral Data

Reaction Times for the ERPs

RT SD effect Cohen d[ms] [ms] [ms] effect

CO 779 196 — —PP 641 136 138 0.967NP 808 210 -29 0.149

Both effects are highly significant.

How can we trust EEG-component differences that ...

needed such a complex data cleaning,

and still include a temporal variance of >20%.

So why not normalize the reaction times?

göttingen


Response Latency Correction


What is the real ERP?

We want to maximize the quality of the ERP average.Therefore we have to minimize the impact of reaction timevariance on the ERP average.

Assumptions

There is a real ERP signal u(t) in every trial.

In the measured signal ui(t), the real ERP u(t) is distortedby possible time shifts of components

and very strong noise.

Components still have the same order.

Component latency differences correlate with reaction timedifferences.

göttingen




We are looking for a map

TW : R+ → C0, TW (RTi) = {φi : [0, RTi ] → [0, mean(RT )]}

argument: the current trial i ’s reaction time RTi

maps to: a time-warp function φi

which maps the interval of the current trial to the durationof the average of all trials

Properties of φi

monotonically increasing (no doubling of components)

continuous (no jumps in time)

it minimizes ||u(t) − ui(φi(t))|| in some norm

göttingen



The first attempt towards RLC

Use a static nonlinear time-warping function

Calculate the new latency of samplepoint t in trial iaccording to:

φi(t) = t + (RT − RTi)

(

tRTi

)k

k = 1, 2, 3, 4

early components are hardlyshifted

late samplepoints carry most shift

applied to optimizing only P300

k = 3 performed best.

RT

RT

i

j

RT

RT

H. Gibbons, J. Stahl. Response-time correceted averaging of event-related potentials,Clinical Neurophysiology, (118):197–208, 2007.

göttingen



A More Flexible Approach

We need a cleaner signal

Single trial ERPs

with wavelets 0 200 400 600 800 1000 1200 1400−20

−10

0

10

20

30RMSE=1.63SNR=9.83

Finding φi

Dissimilarity measured(s(x), u(y)) := |s(x) − u(y)| + |s′(x) − u′(y)|s(x) := s(x)−〈s〉x√

〈s2〉x

determining min(||s − u||d ) by finding the minimal paththrough the matrix djk = d(sj , uk )

T. Picton, M. Hunt, R. Mowrey, R. Rodriguez and J. MaruEvaluation of brain stem auditory evoked potentials using dynamic time warping,

Electroencephalography and Clinical Neurophysiology, 71(3):212–25,1988

göttingen



The Time-Warping Algorithm

Input

EEG data with time markers for trial onset and reaction time.

1 Calculate the ERP average (classically).2 Determine the φi .3 Time warp the data of every trial.4 Calculate a cleaner average based on the warped trials.

5 Iterate with the new average until convergence

Output

ERP average without variance due to reaction time differences.

göttingen



Alternative Approach

Model the φi as one chain of springs

Assumes a common source of the temporal variance.

Directly shows the processing steps that vary most.

Needs harder calculations.

göttingen



Performance Measures

How good is our method ?

Consider the pointwisevariance of the warpedtrials.

Generate artificial Dataand compare the outputwith the known underlyingERP.

...

−500 0 500 1000 1500−20

−10

0

10

20

−500 0 500 1000 1500−20

−10

0

10

20Single trials, generated with gaussian rts with sd=80

−500 0 500 1000 1500−500

0

500

1000

1500

2000

−500 0 500 1000 1500−20

−10

0

10

20Mean of single trials (black curve is error)

−500 0 500 1000 1500−20

−10

0

10

20

30Sample Trial with white gaussian noise added

−500 0 500 1000 1500−20

−10

0

10

20Mean of trials with white gaussian noise added

göttingen


Discussion

Self-Critical Questions

Do ERPs exist?

Is it possible to extract meaningful single-trial ERPs?Do we destroy the meaning of components by the method?

All psychological interpretations were done with theclassical averaging.

Do we generate artificial components by shifting the trialsuntil there are correlations?

What do you think?

göttingen


Discussion

Conclusion

Take Home Message

A response-time correction before averaging is necessary.

We know how to do it. At least roughly.

The φi can tell us, where the response-time variancecomes from.

Outlook

Implementation of the algorithm with your comments.

Optimization of the algorithm.

Plugin for the free matlab package EEGLAB.

göttingen


Discussion

Thanks ...

... to the Experts

Henning Gibbons

Torsten Wüstenberg

Ralph Meier

Miguel Valencia Ustárroz

... to the BCCN People

Theo Geisel

Michael Herrmann

Marcus Hasselhorn

Tobias Niemann

Jörg Behrendt

Matthias Ihrke

... and to You!

göttingen

response-time corrected averaging of event-related potentialshecke/archiv/timewarp.pdf ·...

Documents