# Skull Thickness Calculation Using Thermal Analysis and Finite Elements
## 4 Experimental Results  
To perform thermal analysis of CT data in the ANSYS program, they must first be defined in SpaceClaim software. These identified data are STL-type files known as \"Stereolithography\". STL is a format created by dividing the surfaces of the 3D-designed model into multiple triangles in a mathematical array [41]. This format allows the storage and transmission of the volume information of a 3D skull without any color or texture information. Two-dimensional section images of the human skull are created with the help of computed tomography. These images are overlaid and then made into a 3D model using appropriate software. In this study, RadiAnt DICOM Viewer software is used as the first step to rearrange the surface geometries of skull CT images [42]. CT data is then saved in STL format and meshed using RadiAnt software. When the STL file format is prepared, the number of meshes created on the surface of the skull is directly proportional to the skull's resolution. STL files prepared in the second step are transferred to SpaceClaim software. Thus, the meshed skull images are analyzed and prepared for ANSYS. Before being taken to ANSYS for thermal analysis, all of the mesh bodies with multiple unconnected regions on the skull surface are separated. The separation of mesh bodies is an important operation for ANSYS analysis. Figure 11 shows an example of unconnected regions on the skull image. All unconnected regions are removed from the skull for a more robust analysis. Access to the inner surface is necessary in order to determine the skull's thickness. Therefore, as seen in Figure 12, the facial region of the skull is removed by drawing a curve from the forehead to the neck. Thus, access to the meshed  
Figure 11: (**a**) Unconnected mesh body. (**b**) All unconnected mesh bodies (orange color). (**c**) Skull without unconnected mesh body. Then thermal analysis is performed using ANSYS Workbench. The temperature value of the skull's inner surface is assumed to be 0 \({}^{\circ}\)C. Thus, the temperature value of any point on the skull's outer surface gives the temperature difference directly. The heat transfer is performed within one second. There is no difference between simulating for one second or for longer with respect to the heat transfer image. In this study, the play duration for the animation was selected as one second. Simulation time does not directly inform surgical practices. In Figure 13, the left side and top views of the skull are shown. These thermal analysis results were taken in different periods of heat transfer. The color distributions in the thermal images correspond to different bone thicknesses. The red color indicates the region with the greatest bone thickness. The green color indicates the region with the thinnest bone thickness. Other colors show intermediate values of bone thickness in red and green regions. Thanks to the developed method, the bone thickness information of any desired point on the skull can be obtained numerically. Figure 12: (**a**) Surface separation curve. (**b**) Removal of the facial region. (**c**) Internal region of skull surface. Figure 13: _Cont._  
It is well known that the main bone structures in the skull include the frontal, parietal, occipital, and temporal bones. The thickness information at any point of these bones is critical for medical operations. If geometric curves passing over these bones can be found, the thickness information of the desired point can be easily obtained by using the proposed method. Therefore, random points are chosen along two curves that intersect each other as perpendicular axes. The first geometric curve starts from the left temporal bone of the skull, passes over the parietal bone, and ends in the right temporal bone. While the temporal bone forms the sides of the skull, the parietal bone is the bone at which the skull edges and roof join. It was determined on the basis of the temperature differences that the temporal bone is thinner than the parietal bone.