## 3 Results
### Relation of E-Field and Cortical Activity  
The investigation of the relation between the intensity of the induced E-field and the cortical activity strength is performed by means of exponential model fits of TEP characteristics vs. the average field intensity over the whole brain. The TEP characteristics that are employed are the two CEA measures and the components described in Section 3.3. Figure 6 shows the model fits for the CEA measures for individual subjects, along with the adjusted \(R^{2}\) value of the fit. We use a rule of thumb to assess the obtained values. We consider \(R^{2}>0.7\) to correspond to very good fit, \(0.3<R^{2}<0.7\) to moderate fit and \(R^{2}<0.3\) to weak or no fit. Performing statistical tests for the significance of the adjusted \(R^{2}\) is not appropriate in our case, due to the nonlinear fits, small sample size and non-normality of the data. Nonetheless, we tried statistical testing, and although the results are not very reliable, they were comparable to the ones from the rule of thumb (see Table S1). In 3 out of the 5 subjects (S2, S4, S5), there is a very good fit (adjusted \(R^{2}\sim 0.7\) to 0.9), in 1 (S3), the fit is moderate (\(R^{2}\sim 0.4\) and 0.5) and in 1 (S1) it is weak (\(R^{2}\sim 0.0\) and 0.3). This last subject was the one with the highest LT and, as such, the bad fit could be explained by the fact that most of the points correspond to subthreshold intensities that do not produce TEPs. Linear fits produced much smaller \(R^{2}\), with maximum value across all 10 cases being equal to 0.77 (see Figure S2). Although the number of points for each fit is rather small, the obtained adjusted \(R^{2}\) values are evidence of the relation between the E-field intensity and cortical response strength and suggests that the relation is nonlinear and most probably of the exponential type. In Figure 7, we present the model fit results for the pooled data of all subjects. Figure 7a,c show CEA(25,80) and CEA(25,275) vs. average E-field and produce \(R^{2}\) of 0.54 and 0.58, respectively. As a comparison, we show in Figure 7b,d the exponential model fit for CEAs vs. the stimulation intensity (percentage of MSO). For both CEA cases, these fits produce markedly smaller \(R^{2}\) at 0.41. Linear fits here produced even smaller \(R^{2}\) (more than 10% reduction in all cases). It is conceivable that the relation form would probably be of a sigmoid type with midpoint the LT value, but our data would mostly correspond to the left part of the sigmoid curve, and thus, such a model fit would be problematic. Nonetheless, we attempted sigmoid fits, and the results did not change significantly compared to the exponential fit (see Table S2 for \(R^{2}\) for the different fit types tested). Figure 6: Exponential model fits for the CEA measure vs. the average E-field for each subject separately. (**a–e**) correspond to subjects S1-S5, as indicated by the inset text. Top panels are for CEA(25,80) and bottom panels for CEA(25,275). The adjusted \(R^{2}\) for each model fit is shown inside each panel. Finally, in Figure 8, we present the results of the model fits for the TEP components, as well as the amplitude difference of successively time ordered components. With the exception of the cases of P90-N75 and P110-N75 (Figure 8g,h), all other components show some degree of substantial model fit. With a rule of thumb for the threshold of acceptable \(R^{2}\) equal to 0.5, the cases of N75, N75-P60 and P150-N110 exhibit the best fits with \(R^{2}=0.58,\ 0.63\) and 0.65, respectively (we also note P150 which marginally does not cross the threshold of 0.5, with \(R^{2}=0.49\)). It is interesting that the first two cases (N75 and N75-P60) correspond to early components, while the third (P150-N110) to late ones. Figure 8: (**a–e**) Exponential model fits of the TEP components vs. the average E-field value, and the difference of successive components values (**f–i**). The adjusted \(R^{2}\) for each model fit is shown inside each panel.