## 4 Discussion  
The present study aims to elucidate, from a temporal and spatial point of view, the relation of the E-field induced by TMS stimulation and the ensuing electroencephalographic cortical response. We observed that post-TMS, there is an oscillating pattern in the correlation/covariance between the CSD/EEG and the E-field intensity as a function of latency, with alternating high correlation/anticorrelation periods. This implies the existence of an excitation-inhibition mechanism, which is triggered by the TMS administration and is correlated to the E-field distribution in the brain. With respect to the brain regions that were activated under our specific setup (stimulation with an H7 coil over the mid-central area and an SI of 120%LT), we show that cortical activation is essentially restricted near the stimulation locus and extends to a smaller area than the E-field. In essence, from the cortical neurons where a high E-field is induced, only a percentage is actually activated. This is in agreement with the theoretical considerations and results regarding the generation of cortical responses by TMS in [23]. To explore in detail the relation of TEPs and E-field for a wide range of sub- and suprathreshold stimulus intensities, we used exponential model fits and we observed moderate to substantially high adjusted \(R^{2}\) values. This is clear evidence of the causal relation between TMS-induced E-fields and TEP generation. Furthermore, the fact that the \(R^{2}\) values of linear model fits were smaller than those of the exponential model fits is evidence of the nonlinear nature of the relations in line with the theoretical considerations and experimental results in the pioneering study by [PERSON] et al. [23]. From a practical point of view, it is important to note that the model fits of TEP characteristics vs. E-field provided higher \(R^{2}\) than vs. the stimulation intensity. The superior fitting performance of E-fields should be ascribed to the fact that the E-field is a subject-specific parameter, whereas the stimulation intensity is not. The observation that the same intensity stimuli produce varying E-field distributions and varying cortical activation patterns in different subjects justifies the need for personalized analysis of TMS data. In clinical practice, the stimulation intensity is determined in a subject-specific manner (for instance, based on the motor threshold (MT) or on the basis of electroencephalographic criteria, such as the LT, when stimulating areas beyond the motor strip). However, it would be highly beneficial if the analysis was moved from the relatively arbitrary domain of stimulator intensity or even of a multiple of the MT/LT to a domain of physical meaning, such as the intensity of the induced E-field [53]. The results of the present study provide further physiological validation of the E-field modeling approach that is being increasingly employed for research and clinical purposes in the field of non-invasive brain stimulation. Previous studies, reviewed in [PERSON] et al. in [31], explored the relation between E-field properties and motor cortex excitability, as reflected in the motor evoked potential (MEP) amplitude and active or resting motor threshold. For instance, [PERSON] et al. [22] reported a strong correlation (\(0.70<r<0.91\)) for the regression between the mean E-field in area M1 and MEP amplitude, whereas [PERSON] et al. [54] reported a significant correlation (\(R^{2}=0.44\) ) between the E-field and resting MT. Our results extend these findings by correlating the E-field with individual TEP components as well as with the overall CEA in different time windows post-TMS. The advantage of employing TEPs for validating E-field models is that they constitute a more direct measure of cortical activation, compared to MEPs, and are applicable in every area of the cortical mantle, rather than being restricted to the motor strip.