# Skull Thickness Calculation Using Thermal Analysis and Finite Elements
## 3 Proposed Skull Thickness Analysis Method  
In this study, a new method is developed to calculate bone thickness in all regions of the human skull on the basis of CT images using finite element analysis and thermal analysis methods. Images of skulls from people of different ages and genders were analyzed using CT scans. Analyses were performed with ANSYS [40], which is used in computer-aided engineering studies. Based on the finite element method, the ANSYS Workbench platform allows effective studies in different disciplines, such as mechanics, fluid dynamics, and heat transfer. Additionally, the thermal analysis method based on heat transfer, which is used in various engineering problems, was also used in this study, and the heat transfer was measured with respect to bone thickness. A graphical abstract of the proposed method is given in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Id** & **Gender** & **Age** & **Frames** & **PixelSpaceX** & **PixelSpaceY** & **PixelSpaceZ** & **Slice Thickness** \\ \hline
1 & M & 16.00 & 742 & 0.546 & 0.546 & 0.5 & 0.5 \\
2 & M & 16.00 & 305 & 0.488281 & 0.488281 & 0.625 & 0.625 \\
3 & F & 12.00 & 292 & 0.582031 & 0.582031 & 0.625 & 0.625 \\
4 & M & 14.00 & 766 & 0.546 & 0.546 & 0.5 & 0.625 \\
5 & F & 15.00 & 769 & 0.546 & 0.546 & 0.5 & 0.5 \\
6 & F & 16.00 & 303 & 0.492188 & 0.492188 & 0.625 & 0.625 \\
7 & M & 14.00 & 296 & 0.488281 & 0.488281 & 0.625 & 0.625 \\
8 & M & 13.00 & 650 & 0.546 & 0.546 & 0.5 & 0.5 \\
9 & M & 15.00 & 423 & 0.466797 & 0.466797 & 0.5 & 0.625 \\
10 & F & 11.00 & 288 & 0.488281 & 0.488281 & 0.625 & 0.625 \\ \hline \end{tabular} All data used in this study can be reached in Supplementary Materials part.  
\end{table}
Table 3: Skull CT data.  
Figure 9: Flowchart of the CT processing in the study.  
The proposed method includes the following main steps:  
1. Raw skull CT images are taken in DICOM format.
2. DICOM data are transformed into computer-based design models for analysis. In this transformation, the data are recorded in STL file format.
3. Some undesired bone particle regions obtained from CT should be removed. The STL files are cleared of errors caused by CT scanning in the SpaceClaim software, and these images are thereby made ready for analysis. Thus, the skull image is prepared for the mesh production process. Mesh production is performed using the appropriate  
Figure 10: Graphical abstract of the proposed method.  
number of nodes and elements. Thus, the meshed skull image is suitable for thermal analysis.
4. In this step, steady-state thermal analysis is carried out. Certain temperature values are applied to the inner and outer surfaces of the skull. In this paper, the internal temperature value is denoted as 0 \({}^{\circ}\)C. When the inner surface temperature value is set at 0 \({}^{\circ}\)C, the inner-outer temperature difference will automatically be equal to the outer surface temperature value. The temperature values on the outer surface of the skull images are taken along two perpendicular curves.
5. When obtaining bone thickness using temperature information, the distance between any skull point along the perpendicular curves and the closest inner surface point to this point is used. By using the Euclidean distance between these two points, the bone thickness information of the relevant point can be obtained.