EP_den v2

© Rodrigo Quian Quiroga (2003)

Tutorial

Introduction

Event-related potentials (ERPs) are the changes in the ongoing electroencephalogram (EEG) due to stimulation (e.g. tone, light flash, etc.). By arranging sequences of stimuli in paradigms, it is possible to analyze the responses of the brain to different tasks, thus allowing the study of several sensitive and cognitive functions, states and pathologies.

Due to the low amplitude of ERPs, responses to several stimuli are averaged in order to distinguish them from the background EEG. Averaging accomplishes a reduction in the number of data as well as an increase in the signal-to-noise ratio. However, when averaging, information concerning the variability between single trials is lost. This tutorial describes a recently proposed denoising implementation that helps to visualize the ERPs at the single-trial level. In passing, I will briefly mention some of my own results using wavelets in ERPs, so that they can be (at least partially) reproduced using this software and the data examples.

1 – Average ERPs

Let us first load the program by typing EP_den_v2 in matlab and load the data ja_o1t.asc, which contains 16 trial ERPs. In the upper panel the average ERP will appear. There are 3 evoked responses: the P100 (a positive peak at about 100ms), the N200 (the negative deflection following it) and the P300 (the largest positive peak at about 400ms). For more details on the data and experimental setup see [1].

2 – Wavelet decomposition

The lower panel discloses the wavelet decomposition of the average ERP. The coefficients show the correlation of the average ERP with the wavelet function (biorthogonal B-spline) at different scales (D1- D5, A5) and times. See [2] for details on how this decomposition is done and [9] for a review of wavelet decomposition applied to ERP analysis. Clicking in “Bands” we see the reconstructed signal for each scale (which is calculated using the inverse wavelet transform).

Let us now see how the decomposition works by changing the number of scales. By setting “Scales” to 1, the average ERP is decomposed in only one detail level (D1) with the high frequencies (~ 64-128 Hz) and one approximation level (A1) with the low frequency activity (~ 0 – 64 Hz). If we set “Scales” to 2, we then subdivide A1 into D2 and A2. Analogously, by setting “Scales” to 3 we subdivide A2 into D3 and A3 and so on. See how the signal gets decomposed up to “Scale” 5 and check also how the coefficients look like.

3 – Low-pass filtering

Let us now filter the signal using wavelets. Due to its high time-frequency resolution, wavelets have advantages over conventional filtering methods, as described in [1, 2].

For low pass filtering the signal, lets click on “Apr” in the right side of the “Wavelet Filtering” menu and then click on “Filter”. You can see the result in the average ERP and also in the coefficients and band pass filter signal (using “Band”). Since the filter is applied to the single-trials, we can also plot the single trials results with the two lower buttons of the “Make Plots” submenu. For increasing the low-pass filter limits we can include more scales (e.g. try including D4 and D5 and see the result in the single-trials). Similarly, we can have a high-pass filter by setting only the high frequencies (e.g. try with D1, D2 and D3).

4 – Band-pass filtering

We can also band-pass filter the signal by activating the different scales and then clicking on “Filter”. Let us now see the responses using only D4, which correspond roughly to the alpha band (~ 8 – 16 Hz). Again, we can see the single-trial responses and also change the number of trials to be plotted with the lower left number in the “Make Plots” menu (e.g. set it to 10 and click “Single Trials” again). Such an analysis was used in [1], where increases in alpha event-related oscillations were reported. Further analysis [3] also showed that these were mostly due to phase locking (i.e. resetting of the alpha phases after stimulation) as one can visualize with the “Contour Plot”. A similar analysis in the gamma band (with another dataset) was presented in [4].

5 – Wavelet denoising

Let us now go back to the original wavelet decomposition (select all the frequency bands and click on “Filter”) and see the “Bands” plots. Clearly, the P300 has most of its activity at the lowest (A5) scale. The P100 and N200 have their activity distributed mostly between D4 and D5. If we pick up this 3 frequency bands and filter, we can more or less reproduce the 3 peaks, but we can’t eliminate the surrounding EEG activity. For doing this, we will make use of the time resolution of wavelets.

Lets again low-pass filter the signal using only the band “Apr”. Now, on the left panel of the “Wavelet Filtering” menu, lets select 9 and 14 at the scale Apr. and change to 0 the “all” values in the other scales. Click on “Denoise” and now the low-pass filter is limited to the time range of the P300. Lets now include the P100-N200 by adding the coefficients 8 – 13 in D5 and 17 – 21 in D4. Click again on “Denoise”. The P100 is still badly defined. For improving this, lets include 34 – 38 in D3. Alternatively we can also include 70 – 75 in D2 for improving further the P100. The coefficients selected can be visualized by clicking in “Coefficients” (the number of coefficients for each active scale appear in blue under (# Coeff.”). More details on how to select coefficients can be found in [5, 6, 7], but we remark that the selected coefficients should cover an appropriate time range that takes into consideration latency variations in the single-trials.

We can see the results on the single trials by clicking on “Single Trials” or on “Contour Plot”. Compared with the original traces, the ERPs are now easier to be visualized in the single-trials. For comparing the contour plot with the one of the original signal, select all the active bands (D1 – D5, A5) and click on “Filter” and then on “Contour Plot” (if it wasn’t selected). Now load the other dataset (cg25_o1t) and see the single-trial responses using the same coefficients (just click on “Denoise” and then on “Contour Plot”).

6 – Results storing and further steps

The save button will save the denoised data as a matrix that can be later restored for further analysis. Separate figures can be generated calling the function “Graphs.m” after re-loading the saved data. The possibility of getting the single-trial ERPs allows the study of variability between the single-trials [5] and how this influences the conventional ERP averages [6]. It also allows the study of systematic amplitude/latency changes due to habituation or sensitization [7], learning [8], etc. Better results with wavelet denoising in comparison with other approaches were shown in [6].

References:

[1] Functions and sources of evoked EEG alpha oscillations studied with the Wavelet Transform
R. Quian Quiroga and M Schürmann
Clin. Neurophysiol., 1999; 110: 643-654.

[2] Wavelet Transform in the analysis of the frequency composition of evoked potentials.
R. Quian Quiroga, O. Sakowicz, E. Basar and M. Schürmann.
Brain Research Protocols, 8: 16-24; 2001. Erratum: in fig.1, upsampling should precede convolution with G' and H'.

[3] Phase locking of event-related alpha oscillations.
Quian Quiroga R, Basar E and Schürmann M
In: Chaos in Brain? K. Lehnertz, CE Elger, J. Arnhold and P. Grassberger (eds.). World Scientific, 2000.

[4] Bisensory stimulation increases gamma-range responses over multiple cortical regions.
O. Sakowicz, R. Quian Quiroga, M. Schürmann and E. Basar.
Cognitive Brain Research; 2001, 11: 267-279.

[5] Obtaining single stimulus evoked potentials with Wavelet Denoising.
Quian Quiroga R.
Physica D, 2000; 145: 278-292.

[6] Single-trial evoked potentials with Wavelet Denoising.
R. Quian Quiroga and H. Garcia.
Clin. Neurophysiol. 114: 376-390, 2003.

[7] Habituation and sensitization in rat auditory evoked potentials: a single-trial analysis with wavelet denoising.
Quian Quiroga R and van Luijtelaar ELJM.
Int. J. Psychophysiol, 2002; 43: 141-153.

[8] Enthorinal inputs to dentate gyrus are activated mainly by conditioned events with long time intervals.
Talnov A, Quian Quiroga R, Meier M, Matsumoto G and Brankack J.
Hippocampus, in press.

[9] Quantitative analysis of EEG signals: Time-frequency methods and Chaos theory.
R. Quian Quiroga
Ph.D. Thesis; Lübeck, 1998.

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