# Electric Field Distribution Induced by TMS: Differences Due to Anatomical Variation
## 3 Results
### Visualization  
A simple visualization of the computed EF on the brain suffices to show the interindividual differences of the induced distributions, resulting from anatomical variations (Figure 2). Natural space coordinates were selected to highlight the morphology diversity that clinicians encounter during a TMS session. The distinctive characteristics of participants, such as the shape and size of their head, or even the head pose during the TMS session, have the potential to change the coil fitting and alter the stimulation's outcome, influencing both the stimulated area and the magnitude of stimulation. This study focuses on parameters that can be measured and attempts to associate the stimulation characteristics with four of them, including age and total volumes of head, CSF (excluding the ventricles) and brain. Furthermore, homogeneous models are not affected by the electrical conductivity distribution, which is present only in anatomical models, carrying the information of tissue distribution. Therefore, the variation of the EF in homogeneous models reflects mainly the effects of head shape and size, whereas the variation of the EF in anatomical models incorporates the effect of individual tissue anatomy.  
Figure 2 provides an indicative visual description of the variations in TMS-induced EFs for anatomical models and central coil positioning. Corresponding figures for homogeneous models and frontal coil positioning can be found in Appendix A. Complementary to EF visualization, Figures 3 and 4 show the EF distributions in individual brains as violin  
Figure 2: Interindividual variability of the induced EF distributions visualized in subject brains, containing both grey and white matter, when the H-coil is placed at the central position. Head and brain anatomy affect the area and magnitude of stimulation. Brain coordinates are plotted on their natural space.  
plots and IQRs, providing a comparison across models and between their anatomical and homogeneous versions, for the two coil positions.  
Figure 3: Violin plots and IQRs of the EF distributions for frontal coil positioning on anatomical (**a**) and homogeneous (**b**) models, and central positioning on anatomical (**c**) and homogeneous (**d**) models.  
As graphically expressed in Figure 3, the inter-subject distributions vary distinctly for both coil positions, regardless of the model's composition. Even for the homogeneous versions, the individual morphology is enough to create differences in the induced EFs among subjects, a fact that verifies the necessity of implementing personalized head models in TMS applications.  
Figure 4 depicts the differences of EF between anatomical and homogeneous models, focusing on the interquartile ranges of the corresponding EF distributions. Although IQRs seem to follow the same pattern for both versions, suggesting the contribution of unique physical characteristics, the quartiles are consistently higher for the anatomical models than for the homogeneous ones, indicating that anatomy, in terms of distinctive electrical conductivity tissues, may affect the prediction of stimulation volume. Comparison of  
Figure 4: Interquartile ranges of the EF distributions for the frontal (**a**) and central (**b**) coil positions.  
the EF distributions between anatomical and homogeneous models, using the Wilcoxon matched-pairs test (selected after failure of the Kolmogorov-Smirnov normality test) for IQRs and quartiles, found statistically significant differences (\(p\)-value \(<\) 0.05) between the two groups for both coil positions.