Brain symmetry and topographic analysis of lateralized event-related potentials

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Abstract

Objective: We investigated the influence of symmetry assumptions implicit in the derivation and the use of event-related lateralized potentials (ERLs), such as the lateralized readiness potential (LRP). We describe these assumptions and demonstrate several alternative computational methods.

Methods: Using analytical methods and forward simulations, we computed the error in the ERL topography that results from deviations in symmetry between homologous brain areas. Based on analytical considerations we show that, for source analysis, the ERL derivation provides no benefits compared to a single subtraction of the two (left-lateralized and right-lateralized) conditions underlying the ERL.

Results: Relative errors of 10% in the ERL topography are found if the location of an active region in one hemisphere differs by 10 mm from the symmetric location as compared to the other hemisphere A difference of 30° in orientation results in a relative error of the ERL of 40%. Differences in source strength between hemispheres result in an ERL error that is half the size of the relative strength difference.

Conclusions: We estimate that, due to violations of the symmetry assumption underlying the ERL, errors in the ERL topography of 10–40% can be expected. Source analysis does not benefit from the ERL. In topographic mapping and source analysis, the double subtraction of the ERL should be approached with caution and the single subtraction of the ERPs of two lateralized conditions should be first analyzed whenever possible. We suggest that analyses based on the topography of the ERL should only be performed after the assumption of symmetry has been validated.

Introduction

Much like the whole body, the brain has a large degree of symmetry in its anatomical structure. Research has shown that, in spite of important functional and anatomical asymmetries, the global body symmetry is to a large extent reflected in the brain. In electroencephalography (EEG) it is often assumed that part of this symmetry in the cortex will be reflected in the electric sources in the brain and the potential distributions they generate. This symmetry can potentially be helpful in the analysis of event-related potentials (ERPs).

Lateralization of brain potentials is quantified by comparing the potential on homologous electrodes over both hemispheres (e.g. locations C3 and C4 from the 10–20 system). In the computation of event-related lateralizations (ERL) on homologous electrodes, it is assumed that the potential at these symmetric electrodes predominantly reflects the activity in brain regions underneath each electrode. In the construction of the ERL, the lateralization towards the left hemisphere in a task that involves a behavioral orientation (e.g. attentional or motor) to the right, is averaged with the lateralization towards the right hemisphere in a task that is oriented to the left. The ERL on an homologous electrode pair thus obtained is a single measure of lateralization in both conditions. Its purpose is to enhance the detectability and facilitate the quantification of lateralized activity by removing all non-lateralized activity.

One of the best known examples of an ERL is the lateralized readiness potential (LRP), which is computed on central electrodes while the subject is preparing a movement (de Jong et al., 1988, Coles, 1989). The LRP can be used to study aspects of the ‘Bereitschafts’ or readiness potential, enabling the measurement of (lateralized) movement-related EEG activity in the presence of overlapping stimulus related activity. The basis of the LRP is an experimental design in which the non-motor related responses are assumed to be identical in left- and right-hand movement conditions. The LRP is used as an index of central activation of motor responses and many applications are interested mainly in its latency and direction of lateralization, for which recording with a single pair of electrodes placed at C3 and C4 above the motor cortex is sufficient (Eimer, 1998). The same is true for the N2pc, an ERL associated with visuospatial selection (Luck and Hillyard, 1994), which can, in principle, be measured with just one pair of electrodes at left and right occipito-temporal electrode sites. However, these and other ERL potentials have more recently been studied with higher resolution EEG, yielding topographic information relevant to both the functional characterization and the generation of these potentials (e.g. Leuthold and Jentzsch, 2001, Verleger et al., 2000, Praamstra and Plat, 2001). The topographic analysis of ERLs raises questions regarding the symmetry assumptions underlying the derivation of ERL potentials.

This study addresses the usefulness and limitations of symmetry assumptions in topographic analysis of ERL potentials. For this purpose, it is necessary to define exactly the terminology to be used. With ‘symmetry,’ we mean that two cortical areas in the left and right hemisphere display the same amount of electric activity when a task is performed. The symmetry relates to the position and orientation of the electric sources with respect to the brain's midplane. ‘Lateralization’ means that brain activity linked to the performance of a specific task is larger in one hemisphere than at the corresponding location in the other hemisphere. A third concept used throughout the text is ‘anti-symmetric.’ With this we mean that the position and strength of the sources in both hemispheres are the same (i.e. symmetric), but that the orientation of the sources is reversed. An anti-symmetric topographic representation of brain activity results from the subtraction of the potential distributions of activity lateralized to one hemisphere from that lateralized to the other hemisphere.

The concepts of symmetry and lateralization are strongly, but not exclusively linked, as the following examples demonstrate: brain functions related to language are lateralized to the left hemisphere in the majority of the population. In contrast, movement control, at least at primary motor cortex level, is more or less symmetrically distributed in both hemispheres. In a task which requires either left or right limb motor activity, the cortical motor activity is lateralized to the contralateral hemisphere. A bimanual task activates motor areas in both hemispheres and thereby results in non-lateralized but symmetric brain activity. This comparison of a unimanual with a bimanual motor task clarifies that lateralization does not imply symmetry, but that lateralization can result from behavioral or experimental conditions with a task activating one of bilaterally present brain areas.

The main goal of using the ERL derivation is to enhance the detectability of lateralized activity. It does so by the following two means: (1) it suppresses symmetric activity within any single condition and (2) it suppresses all activity which is identical within the two conditions.

The ERL is defined on each homologous electrode pair (here for C3 and C4) asERL=12C4−C3L+C3−C4Rwhere L represents the activity in the condition lateralized to the left and R represents the lateralized condition to the right (Wascher and Wauschkuhn, 1996, Oostenveld et al., 2001). This particular notation of the ERL mainly stresses the averaging of left and right oriented behavioral tasks. By reordering the terms on the right-hand side in the above equation, it can be made more clear how the ERL achieves its two goals. For this purpose, we introduce a notation which represents the complete scalp potential distribution by Ψ. The symbol Ψ̄ denotes the potential distribution on all electrodes, mirrored with respect to the midplane. To obtain the potential distribution Ψ̄, the values for the potential are exchanged between all homologous electrode locations, e.g., the potential ΨC3 becomes Ψ̄C4 and ΨC4 becomes Ψ̄C3. Using this notation, the ERL can be rewritten for all electrode pairs simultaneously as follows.ERL=12Ψ−Ψ̄L+Ψ̄−ΨR=12ΨLΨ̄L+ΨRΨ̄R=12ΨL−ΨR+Ψ̄LΨ̄R=12ΨL−ΨR+ΨL−ΨRThe subscripts L and R denote the measurements from the left and right oriented behavioral tasks. Equation (2a) is a generalization towards all electrodes of the original definition of the ERL, i.e. the topographic distribution of the average over the lateralization towards the left and right side. Equation (2b) shows that, apart from the factor 1/2, the ERL is similar to the difference between the lateralization of both conditions without regarding the direction of the lateralization. Writing the ERL as , demonstrates that, except for the factor 1/2, the ERL can be computed by subtracting left and right conditions followed by the subtraction of the mirrored potential distribution from the non-mirrored potential.

By re-ordering the two subtractions from which it is composed, eq. (2d) best clarifies the achievement of the two goals by the ERL. The first subtraction of the potential distributions obtained in left and right conditions suppresses identical activity in both conditions. The fact that all identical activity and not only the symmetric activity in both conditions is removed, is not directly apparent from the original notation. The second step, computing the difference between this difference potential and its mirrored potential distribution, shows that activity is removed which is identical at homologous electrodes on both scalp sides, i.e. symmetric activity. This was already apparent from the subtraction of homologous electrodes in , . We prefer the representation of the ERL according to eq. (2d) over the original notation, since it reveals both the removal of all identical activity in left and right conditions, as well as the removal of the symmetric activity.

Fig. 1 demonstrates the construction of the ERL using a schematic representation of the potential along a line from left to right ear (bold dots). The potentials in the conditions lateralized to the left (ΨL) and to the right (ΨR) are given in the first two rows (Fig. 1A and B). Besides the lateralized component of interest, these potentials also contain a non-lateralized component which is symmetric (broad bell-shaped bump), as well as a lateralized component which is not symmetric (small triangular bump). In the third row (Fig. 1C) the subtraction of left- and right-lateralized potential distributions is given, which is the first step in the ERL construction when one would follow eq. (2d). In the bottom row of the figure (Fig. 1D), the actual ERL is shown, which results from subsequent subtraction over homologous electrodes, followed by a division by 2.

In Fig. 2 the construction of the ERL is stepwise demonstrated, based on a complete scalp potential distribution of only the lateralized components. Three different source configurations are depicted, each with a single dipole source in a central brain area lateralized in one hemisphere. The first two rows show only the lateralized potential distributions ΨL and ΨR that usually would be overlapped with non-lateralized components (hence the need for subtraction or ERL analysis, cf. Fig. 1). The first column shows a medial-lateral oriented dipole, which is approximately radial. The second column shows a tangential, anterior-posterior oriented dipole. The third column contains a representation of a diagonal dipole, which is oriented to have a frontal maximum on one hemisphere, combined with an parietal minimum on the opposite hemisphere. The third row contains the single subtraction ΨLΨR. Comparing the single subtraction with ΨL and ΨR shows that for the first two source configurations the distribution after the subtraction remains similar. Note, however, that after the subtraction the diagonal source configuration in the 3rd column results in a potential distribution without a clear dipolar pattern but with two foci of similar polarity on each hemisphere. The 4th row shows that, for ideal circumstances, the ERL potential distribution on a single hemisphere replicates the loci of activity in the two hemispheres.

Besides the original goal of the ERL, which is the enhancement of lateralized activity, it has other advantages compared to analyzing ERPs with a single subtraction of the two lateralized conditions. One advantage is that the ERL combines the potential at two electrode locations of interest into a single potential, reducing the amount of data by 50%. This can be advantageous in a simplified representation of the data and in statistical analysis. Another advantage, that will be demonstrated in this study, is that the noise level of the ERL is better than that of a single subtraction. For each of the source configurations in Fig. 2 it is shown that, in case of exact symmetry of ΨL and ΨR, the topography of the ERL is not different from that of the single subtraction. However, if the symmetry is not exact, the single subtraction will result in a non-symmetric distribution and, consequently, the ERL distribution will be different from the distribution on either hemisphere.

Whereas the ERL quantifies the assumed symmetry and lateralization in the scalp potential on a single hemisphere, symmetry can also be used in inverse source analysis using dipole models. A symmetric dipole model can be used to model the potential distribution of a single condition with bilateral activity. The potential distribution of the subtraction of left and right lateralized conditions can be fitted using an anti-symmetric dipole model. Alternatively, the ERL topography can be subjected to inverse source analysis, in which case the fitted source configuration in one hemisphere has an anti-symmetric counterpart in the other hemisphere (Praamstra et al., 1996b).

The use of symmetry constraints in dipole analysis especially can be helpful in source models containing multiple sources. Starting with an initial estimate for the source parameters that is far away from the optimal source parameters, a nonlinear fit of the parameters often prematurely ends in a local minimum in which multiple dipoles are located close to each other and partially cancel each other. A constraint on the source parameters based on physiological knowledge, such as bilateral activity, can help in getting from the initial estimate towards a more optimal estimate, still reflecting the bilateral activity. The constraints on the source parameters can subsequently be lifted, and the fitted symmetric parameters can be used as a new initial guess for the unconstrained source model.

We have compared the ERL to a single subtraction of two lateralized potential distributions. Specifically, we have studied the effect that incorrectly assumed symmetry in the sources has on the ERL. Using simulations, we have quantified the error in the ERL topography resulting from violations of this assumption. The influence of the topographical symmetry assumptions on source analysis were studied using analytic methods.

Section snippets

Methods

For the forward computations of the potential, a symmetric volume conductor model was used, consisting of a 3-sphere model with radii of 82, 92 and 100 mm and conductivities of 1, 1/80 and 1 (normalized to the brain conductivity). Over the upper surface of the sphere 69 electrodes were evenly distributed according to the extended 10–20 electrode system (American Electroencephalographic Society, 1994). A dipole pair with a single dipole in each hemisphere was used to model the source. The

Asymmetry in source location and orientation

Fig. 3 shows the absolute error in the ERL over all electrodes, plotted against the ERL magnitude itself. Each point in the graphs represents a single source configuration, i.e. source location and orientation, for which the perturbation was applied. The effect of each of the 5 perturbations on the ERL is between 0 and 0.05 μV, and is relatively constant for every ERL magnitude. The mean value and standard deviation (SD) of the ERL difference due to the perturbation in medial-lateral direction

Discussion

The goal of this study was to present an overview of the use of symmetry assumptions in the topographic analysis of lateralized ERPs, and to evaluate the effect of deviations in source symmetry. As symmetry is implicitly implied in the computation of ERLs, we targeted the forward computations specifically at the ERL.

The ERL is a useful technique for the representation of lateralized ERPs generated in symmetric brain areas. If the conditions of the ERL are met, it suppresses both symmetric

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