# Electric Field Distribution Induced by TMS: Differences Due to Anatomical Variation
## 5 Conclusions  
Electric field distributions induced by TMS applications show small, but indisputtable, variations across individual brains. FEM simulations on nineteen anatomical head models and their homogeneous duplicated ones, suggest a negative correlation among the distributions' quartiles and the sizes of the brain and head, as well as between the stimulated volume and age. In addition, the comparison of EF distributions for the homogeneous and anatomical versions of the head models reveals that the maximum distributions of the latter were higher than for the former, indicating that anatomy may affect the prediction of stimulation volumes.  
Conceptualization, M.T., T.S., and V.K.K.; methodology, M.T., T.S., and V.K.K.; software, M.T.; validation, M.T. and T.S.; formal analysis, M.T. and T.S.; investigation, M.T.; resources, E.C., K.K., N.F., V.K.K.; data curation, M.T. and T.S.; writing--original draft preparation, M.T.; writing--review and editing, T.S. and V.K.K.; visualization, M.T.; supervision, T.S. and V.K.K.; project administration, T.S. and V.K.K.; funding acquisition, V.K.K. All authors have read and agreed to the published version of the manuscript.  
This research was co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme 'Human Resources Development, Education and Lifelong Learning 2014-2020' in the context of the project 'Mapping of the human primary motor cortex (MI) with navigated Transcranial Magnetic Stimulation (navigated TMS, n TMS): method optimization with advanced neurophysiological and computational techniques' (MIS 5047847).  
The study was conducted in accordance with the Declaration of Helsinki, and approved by the National Ethics Committee of the Ministry of Health, Hellenic Republic (protocol code: CIV-19-10-029964 and date of approval: 14 October 2019 (118371)).  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.  
The authors declare no conflict of interest.  
Figure 16: Interindividual variability of the induced EF distributions visualized on subjects’ homogeneous brains, containing both grey and white matter, when the coil is placed at frontal position.  
Figure 16: Interindividual variability of the induced EF distributions visualized on subjects’ homogeneous brains, containing both grey and white matter, when the coil is placed at central position.  
Figure A4: EF lower quartile showed strong, and statistically significant negative, correlation to brain volume for every coil position/model version scenario; (**a**) frontal coil position on anatomical models; (**b**) frontal coil position on homogeneous models; (**c**) central coil position on anatomical models; (**d**) central coil position on homogeneous models.  
Figure 17: EF lower quartile showed strong, and statistically significant negative, correlation to head volume for every coil position/model version scenario; (**a**) frontal coil position on anatomical models; (**b**) frontal coil position on homogeneous models; (**c**) central coil position on anatomical models; (**d**) central coil position on homogeneous models.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Emax (V/m)** & **Emedian (V/m)** & **Vst (cm\({}^{3}\))** & **Vfrontal (cm\({}^{3}\))** & **Age (years)** & **Mass (kg)** \\ \hline _Vol01_ & 132.5 & 46.3 & 21.1 & 287.7 & 43 & 80 \\ _Vol04_ & 125.6 & 41.9 & 16.2 & 345.9 & 44 & 85 \\ _Vol06_ & 126.0 & 42.9 & 15.1 & 294.6 & 35 & 78 \\ _Vol08_ & 143.6 & 46.0 & 33.4 & 423.1 & 20 & 88 \\ _Vol14_ & 128.7 & 42.9 & 20.4 & 333.6 & 31 & 100 \\ _Vol17_ & 134.9 & 45.7 & 22.7 & 293.2 & 30 & 70 \\ _Vol18_ & 140.8 & 50.8 & 40.7 & 350.7 & 30 & 65 \\ \hline _Duke_ & 122.6 & 49.8 & 22.5 & 319.6 & 35 & 70.2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Stimulation metrics (Emax, Emedian, and Vst) on the frontal lobe and model parameters (frontal lobe volume, age, mass) of the homogeneous male models and the homogeneous version of the Duke ViP model.