ESTIMATION OF CORTICAL SOURCES OF EEG POTENTIALS BY USING SURFACE LAPLACIAN

F. Babiloni¹, C. Babiloni¹, F. Carducci¹, L. Carotenuto¹, P. M. Rossini^3,4, F. Cincotti^1,2
1Dip. Fisiologia Umana e Farmacologia, Univ. "La Sapienza", Rome, Italy. ²IRCCS Fondazione Santa Lucia, Rome, Italy. ³AFaR, Ospedale "S. Giovanni Calibita" FBF, Rome, Italy. ⁴IRCCS "S. Giovanni di Dio" FBF, Brescia, Italy.

Abstract: In the present study we evaluate the improvement in accuracy obtained by using surface Laplacian transformed EEG potentials for the estimation of the cortical current source density. With this procedure, EEG potentials are preliminarily Laplacian-transformed (LT) to remove brain electrical activity generated by subcortical sources (i.e. not represented into the usual source cortical models). The source estimates obtained with LT-EEG potentials were compared to those obtained with raw EEG in the framework of a simulation study. Furthermore, the simulation tested the dependence of the model on: i) the presence of a subcortically generated disturbance ii) the signal to noise ratio (SNR) of the scalp simulated data; iii) the criterion for cortical sources weighting in the inverse operator used for source estimation; and iv) the number of virtual scalp electrodes. Accuracy is assessed by using as the dependent variable the Relative Error between the imposed and the estimated source strength at the level of cortical regions of interests. Realistic head and cortical surface models were used. Analysis of Variance (ANOVA) unveiled that all the considered factors significantly affect the accuracy of source estimation. As a main result, it was observed that, for most combinations of the other variables, the use of LT-EEG potentials yields the best estimation of cortical source currents.

Keywords: Surface Laplacian, High resolution EEG, Linear inverse problem

INTRODUCTION

In a previous paper [1], we introduced the linear inverse source estimate performed using a Laplacian Transformation (LT) of EEG potentials used as data input. We showed that LT i) enhances the intrinsic spatial resolution of the estimation method and ii) minimizes the influence of subcortical sources on estimated cortical activity.

In this simulation study, we tested in a more realistic design the advantages in the use of LT as a data pre-processing in the framework of linear estimation of EEG potentials distributed sources.

METHODOLOGY

The experimental design was drawn as follows:
1)       for every configuration of cortical source activation, the corresponding scalp potential sampled by the electric sensor arrays with variable number of electrodes (128, 61, and 29) was computed by means of the electric lead field matrix A, to produce three separate HREEG data sets;
2)       the same procedure is repeated, after activation of the subcortical ROI.
3)       white noise was added to these three datasets, with seven levels of signal-to-noise ratios (SNRs; ¥, 30, 20, 10, 5, 3, and 1), recalling the typical range of SNR commonly encountered in evoked, cognitive and motor-related tasks. To increase reliability of the statistical results obtained, 32 realization of noise were generated for every level of SNR.
4)       estimated cortical activity was obtained from each noisy dataset by solving the regularized inverse problem with four types of weights: MN, WMN, LT-MN and LT-WMN.
5)       the estimated cortical ROIs activity configuration  was obtained.
6)       RE was computed between impressed and estimated cortical activation waveforms at ROI level.

Figure 1. Regions of Interest (ROIs) into which part of the about 3000 equivalent dipoles that constitute the source model have been segmented into. ROIs correspond to:1) Supplementary Motor Area (SMA), 2) bilateral hand representation of the Primary Motor Area (l-M1 and r-M1), 3) bilateral hand representation of the Primary Sensory Area (l-S1 and r-S1), and 4) two areas that roughly correspond to Brodmann Area 7b (l-A7 and r-A7).

TABLE 1. Factors and levels of the experimental design.

Statistical analysis

The results were subject to Analysis of Variance (ANOVA), in a full within design. Table 1 summarizes the independent variables used in the design along with the levels of each variable. The dependent variable was the relative error. For each combination of levels of the independent variables considered, the 32 values of RE obtained for different noise realizations constitute the cases of the ANOVA

RESULTS

ANOVA results showed a statistical significance of all the main factors, with exception of DIPWEIGHT, as well as of all interactions between significant factors in reducing the variance of the RE.

Scheffe’s post hoc tests, performed at the 0.05 level of significance demonstrated the statistical increase of RE values as estimated from LT based inverse method with respect to the others at 128 electrodes when the data presented SNR variable from 30 to 1.

Figure 2 shows the mean values of the RE in function of three of the main factors, namely SNR, DISTURB, and TRANSF. Number of sensors was fixed at 128 and the inverse problem was solved by MN estimation.

The dependence of accuracy on the noise level is evident. RE ranges from 0.45-0.60 in absence of noise, to 0.80-0.85 when SNR=1.

SL transformation of data improves the accuracy of estimation, at least until noise is at a reasonable level. Only at SNR=1, solution of the inverse problem with or without LT of scalp potentials yields comparable results.

Superimposition of potentials generated by unmodeled sources generally decreases accuracy. This effect is less marked in case of LT pre-processing, when noise is low, while source estimation from unprocessed raw potentials seems to be less sensitive to the disturbance in concomitance to higher noise levels.

Figure 2. Plot of mean RE in function of three of the main factors. Separate averages for each combination of SNR (one level per panel), TRANSF (raw, R; and LT, L), and DISTURB (see legend) are shown. The other variables were kept fixed (NELECT=128 and DIPWEIGHT=MN)

Discussion and conclusions

The results offered by the present simulation study stated the general efficacy of the linear inverse estimation methods employed in the recovery of the simulated cortical activity. This is particularly true when the proposed LT weighting of the residuals is introduced into the solution of the inverse problem. In fact, the recovery of each ROI’s activity is generally acceptable under the variety of situation of SNR and electrodes number employed.

The efficacy of LT based source estimation methods in removing the effect of unmodeled sources is assessed, but only in the hypothesis of a limited noise level on recorded data. This may be explained by the fact that SL transformation is an estimate itself. Errors in this first estimation propagate during the solution of the inverse problem, up to a value that voids the intrinsic good features of the method.

The effects of SNR is of course relevant on the estimation of the current density. The rate of improvement of the estimation quality with the SNR increase is constant for 29, 61 or 128 electrodes, even though at different (decreasing) absolute values.

On the other side, it seems that, in the limit of conditions imposed during the present study, a substantial equivalence of the estimation results exist between different dipole weighting strategies.

This study suggest that the use of LT as a pre-processing of raw data, prior to solution of the inverse problem is useful under a variety of EEG operative conditions characterized by different number of electrodes and variable SNR.

REFERENCES

[1] F. Babiloni, C. Babiloni, L. Locche, F. Cincotti, P.M. Rossini and F. Carducci, “High resolution EEG: source estimates of Laplacian-transformed somatosensory-evoked potentials using a realistic subject head model constructed from magnetic resonance images”, Medical & Biological Engineering & Computing, 38: 512-9, 2000.