# Skull Thickness Calculation Using Thermal Analysis and Finite Elements
## 5 Conclusions  
The goal of this study was to characterize how skull thickness changes with age and sex. Regardless of gender, the general trend of skull thickness increased with age. This increase was greatest in the frontal and parietal bones of the skull. To our knowledge, this is the first study to have calculated 3D skull thickness on the basis of thermal analysis for all age groups. In this study, thermal analysis was performed on the skull CT images of 150 patients (female: 80, 53.3%; male: 70, 46.7%; mean age: 14.3) of different sexes, aged 0-72 years. There was no significant difference in age between men and women patients (female: 14; male: 14.7 mean age). Since the procedure is non-surgical, it can be easily performed in a standard laboratory. Thus, skull thickness measurements were performed on the basis of thermal color maps, and the bone thicknesses were calculated at the desired points. The anatomical complexity of the skull bones was eliminated. Thanks to the developed method, human skull bone thicknesses were calculated on the basis of the thermal analysis and finite element methods, instead of by using invasive techniques. Experiments on CT skull data illustrated that the proposed thermal analysis-based model is discriminative and powerful for tasks involving the determination of skull bone thickness. The average thicknesses of skull bones for men (frontal: 7.8 mm, parietal: 9.6 mm, occipital: 10.1 mm, temporal: 6 mm) and women (frontal: 8.6 mm, parietal: 10.1 mm, occipital: 10 mm, temporal: 6 mm) was given. The difference (10%) between men and women appears to be statistically significant only for frontal bone thickness. Experimental studies proved that the results obtained using the proposed method were compatible with the related literature. However, the proposed method determined, in accordance with the literature, that the occipital bone was the thickest skull bone and the frontal bone was the second-thickest skull bone. It was also obtained using the proposed method that the temporal bones were the thinnest bones of the skull. The results obtained in this study offer convenience and speed to doctors when deciding on the material thickness required to join/repair broken bone in the skull. In addition, information will be available to experts when determining distinguishing diagnostic features of bones in skull injuries. Since some color irregularity may occur in skull images,  
Figure 17: The proposed method based on thermal analysis, the Ray-Triangle method, and the manual measurement results: (**a**) skull thickness values obtained from left temporal bone to right temporal bone; (**b**) skull thickness values obtained from the frontal bone to the parietal bone. there may be minimal change in the heat transfer of some parts of the skull. Future work will also focus on the color mapping robustness of our approach. The following are available online at [[https://www.mdpi.com/article/10.3390/app112110483/s1](https://www.mdpi.com/article/10.3390/app112110483/s1)]([https://www.mdpi.com/article/10.3390/app112110483/s1](https://www.mdpi.com/article/10.3390/app112110483/s1)), Table S1: All skull CT data, Video S1: Heat transitions of the model 1 s, Video S2: Heat transitions of the model 4 s.  
Conceptualization, M.C., M.F.T., D.Y.P., K.G. ; Methodology, M.C., M.F.T. ; Software, M.C., M.F.T. ; Manual Measurement, M.C., M.F.T. ; Investigation, M.C., M.F.T. ; Writing--Review and Editing, M.C., M.F.T., D.Y.P., K.G. ; Visualization, M.C., M.F.T. ; Supervision, M.F.T. ; Funding Acquisition, D.Y.P., K.G. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The study was conducted according to the protocol approved by the Inonu University, Turkey (project code: 2016/16-278). All procedures performed in studies involving human participants were in accordance with the ethical standards of Firat University Hospital Committee and with the 1964 Helsinki declaration or comparable ethical standards.