# Skull Thickness Calculation Using Thermal Analysis and Finite Elements
## 1 Introduction  
Since the human skull protects the brain, which is the most important part of our body, it is the most important bone structure making up our anatomy. This structure has important components such as the frontal, parietal, occipital, temporal, and sphenoidal components, and other small parts [1, 2]. These components are connected by connection points called sutures. Skull bones are complex shapes and have different compositions. Understanding them thoroughly requires explaining the relationship between their functions and forms. Skull bone thickness differs between the genders [3, 4]. Generally, a female skeleton tends to be smaller and less durable than a male skeleton. To better understand the mechanisms of head injuries, the mechanical properties of the skull are measured when an impact occurs [5] or when the skull is subjected to abnormal loads [6]. The mechanical resistance of the skull is highly dependent on skull thickness. Knowing the thicknessof patient-specific skull sections for plastic surgery can save workload and time during surgical operations [7]. Most of the studies on skull bone thickness use archeological materials. Many studies have reported that skull thickness varies greatly from one person to another [8]. In studies, mechanical measurements are generally performed with digital calipers on skulls with limited measurement points [9]. Moreover, such existing methods have only been used in laboratory environments (in vitro) or under artificial conditions. However, the thickness of the skull bones has been evaluated in two-dimensional limited sections on the basis of computed tomography (CT) scan slices [10; 11]. Another way to obtain thickness measurements is to create a three-dimensional (3D) model of the skull bone [12]. Modeling was performed on the basis of MRI data, which allowed the skull shape to be reconstructed, but this method also was not able to take into account the inner surface, and the skull thickness could not be evaluated at the desired level [13]. Skull thickness directly affects skull conductivity. The most important factor in epilepsy surgery is skull conductivity [14]. In a previous study, significant correlation information was obtained between skull thickness and skull conductivity [15]. Skull thickness is a very important factor in terms of skull deterioration and tendency to fracture [16]. The characterization of the thickness of the skull and understanding the manner in which this information changes with age are important steps in understanding the role of thickness in skull deterioration. Current methods for measuring skull thickness in adults are based on taking measurements using a saw at predetermined points in the skull. However, these methods may not give correct information about skull thickness. To address this issue, a different method was proposed to measure the skull thickness of adults using standardized anatomical points [17]. In another study, an automated approach to measuring skull thickness using CT images to determine soft tissue locations was presented [18]. In addition, a method for measuring skull thickness using after-death skull CT images of children was developed [19]. However, since the skull growth rate in children is extremely variable in this method, it is very difficult to determine a standard point from which to start the measurements. The finite element model of the skull is used to study the biomechanics of traumatic brain injury, and it is highly dependent on head geometry. In a study conducted using this information, a skull database containing information on the age-specific development of children's skulls was created with the help of the finite element model [20]. [PERSON] et al. proposed a method for defining the local thickness for an arbitrary structure without model assumptions [21]. According to this, the local thickness at the point of an arbitrary structure is determined by fitting maximal spheres to every point on the structure.