Statistical analyses

Table 4-3 summarizes the results of the repeated measures analyses of variance. In all analyses, the interactions of MODEL x LOCATION and COORDI- NATES x LOCATION were significant. The main effects of MODEL and of CO- ORDINATES were significant for SCP1 and SCP5, while only the main effect of MODEL was significant for PS. The estimates of effect size (η2_{) indicated a strong}

effect for the head model and a small, but still significant effect for the COORDI- NATES factor. However, the interaction of these two factors with the factor LOCA- TION revealed similar effect sizes.

Fig. 4-2 shows the electrode-specific pattern of deviations. Interestingly, the highest differences between methods were observed for electrodes which were most active during task processing (see, e.g., electrodes Pz, CP1, CP2, C3, C4, OP1 and OP2 in Fig. 4-1; see also chapters 6 and 7 for a detailed description of the SCP topographies during task solving). This was not only the case for the SCP components, but also for the PS value (see Fig. 4-3). The highest difference be- tween the four methods was observed for electrode Pz. For PS, SCP1 and SCP5 this difference amounted to 0.66, 1.37 and 1.78 µV, respectively. In some elec- trodes (e.g., F3 or Oz), the deviations were almost identical. Also, there was no clear pattern as to whether a more medially placed electrode shows a higher dif-

Table 4-2: Root mean square ± standard deviation for the four different map- ping methods and the three different parameters. Note that RMS is lowest for all parameters when maps are calculated with individual coordinates and a realistic head model.

Parameter Realistic_Individual Realistic_Standard % difference

PS 1.30 ± .64 1.33 ± .66 2.26 SCP1 2.08 ± .98 2.21 ± 1.1 4.88 SCP5 2.73 ± 1.52 2.84 ± 1.57 3.87 Spherical_Individual Spherical_Standard PS 1.47 ± .75 1.49 ± .66 1.34 SCP1 2.30 ± 1.09 2.40 ± 1.25 4.17 SCP5 3.03 ± 1.66 3.12 ± 1.75 2.88 % difference % difference PS 11.56 10.74 SCP1 9.57 7.92 SCP5 9.90 8.97

ference between interpolation methods. For instance, Pz and Fpz showed a large difference between methods, while Oz or Cz did not.

Post-hoc linear contrasts were calculated for parameter SCP5 to assess whether electrodes placed over regions with less task-specific activity (Fp3, Fpz, Fp4, F7, F8) showed smaller differences between methods as electrodes placed over task-relevant areas (CP3, CP3, P3, Pz, P4, OP4, OP4). When maps calcu- lated with individual vs. standard coordinates were contrasted (irrespective of the head model), a significant result with F=6.04 and p=.022 was observed. This indi- cated a higher difference in deviations over the active (i.e., parietal) region. When the two head models were compared (irrespective of the coordinates used), the contrast was also significant with F=6.70 and p=.022. Again, a higher difference over the active (i.e., parietal) scalp region was indicated. Another set of post-hoc

Table 4-3: Results of the three repeated measures analyses of variance. Factor 1=MODEL, Factor 2=COORDINATES, Factor 3=LOCATION; p-values marked with a '*' have been cor- rected using epsilon-adjustment of degrees of freedom (with epsilon having been calculated according to Greenhouse & Geisser, 1959).

Effect df(effect) df(error) epsilon F-value p-value Eta2

PS 1 1 24 - 20.33 <.001 .46 2 1 24 - .719 .405 .03 3 39 936 .05 11.62 <.001* .33 1 x 2 1 24 - .140 .71 .01 1 x 3 39 936 .07 6.6 .001* .22 2 x 3 39 936 .08 2.83 .046* .11 1 x 2 x 3 39 936 .121 1.82 .119* .07 SCP1 1 1 24 - 14.42 .001 .39 2 1 24 - 4.8 .037 .17 3 39 936 .06 7.64 .001* .24 1 x 2 1 24 - .34 .562 .01 1 x 3 39 936 .09 4.23 .006* .15 2 x 3 39 936 .06 4.81 .009* .17 1 x 2 x 3 39 936 .08 2.41 .071* .09 SCP5 1 1 24 - 20.96 <.001 .47 2 1 24 - 4.06 .034 .17 3 39 936 .06 7.80 <.001* .25 1 x 2 1 24 - .10 .759 <.01 1 x 3 39 936 .06 4.19 .013* .15 2 x 3 39 936 .05 2.88 .065* .11 1 x 2 x 3 39 936 .06 2.00 .134* .08

Fig. 4-2: Grand mean squared deviation between interpolated and genuine amplitude values for parameter SCP5. Note that the highest deviations were observed for the parietal, occipital and central electrodes, and that - apart from a few exceptions, e.g. electrode Fpz - deviations were smaller when a realistic head model and individual electrodes were used.

Fig. 4-3: Grand mean squared deviation between interpolated and genuine amplitude values for parameter PS. Note that the pattern of deviations was almost identical to the one observed for parameter SCP5, although deviations were consistently smaller.

contrasts was used to investigate whether the most lateral electrodes (F7, F8, T3, T4, T5, T6, O7, O8) showed less between-method differences than medially placed ones (Fpz, FCz, Fz, Cz, Pz, Oz). No significant results - neither for the co- ordinates nor for the head model - were observed in this case.

4.4 Discussion

The aim of this study was to assess whether using individual electrode co- ordinates and a realistic head model affects the accuracy of scalp potential map- ping. Generally, the results were consistent with the hypothesis that usage of indi- vidual electrode coordinates yields more accurate maps. For all three parameters, maps calculated with individual coordinates showed a smaller RMS of deviations compared to maps calculated with standard coordinates. An even stronger effect was observed for the head model that was used for the interpolation. The realistic head model led to almost 10% decrease in RMS error for parameter SCP5, which is more than twice as high as the 3.7% decrease attributable to the effect of the electrode coordinates. Although the mean differences between methods were generally rather small, between-method differences up to 1.78 µV were also ob- served (at electrode Pz). Regarding the average SCP amplitude of about 15 µV at this electrode, this represents a sub- stantial effect of the interpolation method.

As for the interaction of coordi- nates and head model with the electrode location, the results are more difficult to interpret based on the current analysis alone. The higher density in the occipital and parietal scalp region did not result in lower overall interpolation errors, as might have been expected. Unfortu- nately for this analysis (but very fortu- nately for the analysis of the brain re- gions involved in task processing), the regions of higher sampling vastly over-

Fig. 4-4: Potential and CSD-topography for parameter PS. Although amplitudes were generally rather low, a similar pattern of amplitudes as during task processing could be observed (cf. chapters 6 & 7)

lapped with the regions with higher task-related activity. This presumably resulted in an increase in interpolation error, since higher inter-electrode differences in am- plitude were observed over such regions. Thus, when one electrode was excluded from interpolation, this led to a considerable loss of information concerning the scalp potential field. The opposite seemed to apply to regions of less or now activ- ity. Since amplitudes of neighboring electrodes were almost identical, the exclu- sion of one electrode did only have a small effect.

On the other hand, parameter PS showed a similar pattern of results as the parameters related to task-processing. This would speak against the interpretation that higher errors are associated with more active regions, since the amplitudes of the pre-stimulus baseline should be near to zero. Although this is certainly correct, a close inspection of the topographic pattern of PS shows higher amplitudes am- plitudes in those areas which were more active during task processing (see Fig. 4- 4). This might either be due to SCP activity which did not completely resolve dur- ing the inter-stimulus interval (which is very likely, since this interval was rather short compared to the median processing time of about 12 seconds; see chapters 6 and 7), or due to a mobilization of task-specific areas preceding task presenta- tion. An analysis of different task paradigms in which the regions of higher activity do not overlap with the regions of higher sampling, and in which activity during complete rest is recorded, might help to resolve the issue whether the method of interpolation has larger effects in regions with more task-specific activity. For the moment, however, one can tentatively conclude that the increase of accuracy re- lated to the usage of individual coordinates and a realistic head model is higher in electrodes placed over task-relevant brain regions.

Another rather unexpected result was that the highest errors were observed for parameter SCP5, although this parameter showed the highest signal ampli- tude. Initially, it was expected that errors should be lower for parameters with more signal and less "noise." Again, an argument similar as the one for the higher error in task-specific areas might explain this result: When higher amplitudes are ob- served, removing one electrode might have a larger effect on the interpolation er- ror, particularly in those regions that show higher task-specific amplitudes. On the other hand, there was no clear pattern as to which parameter shows the highest differences between interpolation methods. While the increase in accuracy attrib- utable to the usage of individual coordinates was highest for parameter SCP1, PS showed the highest increase in accuracy related to the usage of a realistic vs. a spherical head model.

Based on the present study, it can be concluded that a higher accuracy in topographic mapping is achieved when individual instead of standard electrode coordinates are used for interpolation. Thus, digitization of individual electrode co- ordinates is highly recommended in ERP mapping. In addition, usage of realistic head models will result in an even higher increase in the spatial accuracy of ERP maps. Making this a new standard in ERP research should not be to difficult, since 3D-digitizers are now made available by several commercial providers (at a price of about 13.000 €), and since the ever increasing gain in computing power will re- move the main obstacle for the usage of realistic head models.

5. Consistency of inter-trial activity using single-trial fMRI: assessment of