21 22 1 METHODS 24 1.1 Determining the site of stimulation 25In the following, the two approaches to determine the congruence factor are presented. The site of effective stimulation 26 is determined by combining the measured I/O-curves of the MEP amplitude with the simulation results of the induced 27 electric field. An operator is derived to transform the brain-wide MEP amplitude curves with 1, … , 28indicating the experimental condition, given as a function of stimulator intensities x, to an element-wise quantity , 29given in the electric field space, i.e. . The quantity is termed the congruence factor. The basic 30 principle to determine is shown in Fig. 5. For each experimental condition, the corresponding electric field 31 distribution is determined. Due to the linear relationship between the stimulator intensity and the magnitude of the 32 induced electric field, the MEP curves can be projected and accordingly scaled to each element in the cortex. As a result, 33the global stimulator intensity vs MEP curves are transformed from the stimulator intensity space to the 34 electric field space , containing spatial information. Therefore, a series of MEP curves is assigned to 35 each element. The definition of the congruence factor is based on the assumption that the causative electric field, which 36 stimulates the neuronal population of interest resulting in the observed behavioral effect is stable across the 37 experimental conditions. For this reason, we are seeking the cortical region, where all MEP curves are similar and 38 assume that this region corresponds to the site of stimulation. This principle is illustrated in Fig. 6, highlighting an 39 element with a low congruence factor, where the E-MEP curves are strongly diverging from each other and an element 40 with a high congruence factor, where the E-MEP curves are similar. The congruence factor is computed in the ROI 41considering the magnitude of electric field | | as well as its normal (| |) and tangential (| ∥ |) components. Two 42 different approaches can be applied to determine the congruence factor, which are described in the following. 43 1.2 Parametrizing the fractional anisotropy of the electrical conductivity tensors 44 Here, we present the methodology to vary the level of anisotropy of the electrical conductivity of the head model, which 45 affects the induced electric field profile. The anisotropic properties of GM and WM result from the alignment of the 46 pyramidal cells in the cortex and the fiber pathways in the white matter 1 . The level of anisotropy is quantified using the each iteration. In order to decrease the computational cost substantially, the electric fields are estimated based on a 112 separate gPC-approximation. The electric field gPCs are determined with the adaptive algorithm proposed by Saturnino 113 et al., (2018) 3 in a pre-processing step with a leave-one-out cross validation error of <0.05%. The electric field gPC 114 approximations act as sub-modules in the model of the congruence factor. Depending on the experimenta...
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