# Skull Thickness Calculation Using Thermal Analysis and Finite Elements
## 1 Introduction
The application of this theory led researchers to the development of a number of different application techniques due to its high computational costs. The disadvantage of the Hildebrand method is that it does not work directly on the 3D volume. The results obtained from the 2D projection of a 3D volume object are processed. With the Beam Propagation method, ultrasound measurements of beam-based thickness are performed [22]. In this method, phase aberrations and differences due to high levels of absorption occur. Poor focusing and higher energy loss occur, especially at higher ultrasound frequencies. The main issue faced by the Beam Propagation and Hildebrand methods that has not been addressed previously, and which could be important, is the inability of these methods to deal with 3D medical images and pediatric skulls. Not all state-of-the-art methods can do it, but in any case, it would be interesting to explain why this is the case, and whether this problem can be solved by FEM-based thermal analysis of CT images. It is possible to apply our method to all skull regions separately, and to subsequently combine their results. FEM-based thermal analysis provides more descriptive distance information about skull thickness through the Euclidean function. Existing methods of measuring skull thickness in adults require improvement. Most of them do not give accurate results for pediatric skulls [23]. Therefore, a method that can accurately calculate both pediatric and adult skull thicknesses is required. In our study,both pediatric and adult skull thicknesses can be calculated numerically. There is currently no relevant literature investigating the evolution of skull thickness across all growth stages. This paper proposes a fast and reliable method for determining skull thickness on the basis of CT images. In the proposed method, the thickness of the desired area of the skull can be calculated by using the finite element method and the thermal heat method, without the application of any surgical procedures. It should be pointed out that this feature makes the proposed method appropriate in scenarios where automatic determination of skull thickness is required. In the literature, there is no specific study in the field of head imaging presenting the use of the FEM and thermal heat methods together. Another gap seen in the literature is the lack of methods that can numerically calculate both pediatric and adult skull thicknesses. In our study, it is shown that the proposed method makes it easier to evaluate how skull thickness changes with age. Thus, owing to the generation of an effective skull mesh map with the finite element method, the bone thicknesses of all human skulls can be calculated, independently of gender and age. The paper is structured as follows. In Section 2, the determination of the thickness of a solid object using the thermal analysis method is shown using ANSYS finite element software 2020 R1. In Section 3, comprehensive information about the skull images used in this paper is given. Then, the proposed skull bone thickness calculation method based on the proposed thermal analysis is described. Finally, Section 4 includes the experimental results and recommendations.