## 2 Materials and Methods  
This study employed the Particle and Heavy Ion Transport Code System (PHITS) simulation program to develop a detailed model of the mandibular structure, encompassing all anatomical layers. PHITS is commonly used in various fields, such as medical physics, space radiation, nuclear engineering, and materials science. It can simulate the transport of all types of particles in a wide range of energies, from thermal neutrons to high-energy heavy ions. The code is particularly useful for calculating radiation dose distributions in complex geometries, such as the human body or complex machines. It allows the user to define materials and geometries in detail and simulate particle-matter interactions. PHITS also includes a variety of physical models to handle different types of interactions and processes, making it an effective tool for research [23]. The format of the PHITS simulation code is presented in Figure 1.  
In this study, the simulation process involved configuring each component of the mandibular model using two distinct scenarios, one employing specific chemical compositions to accurately represent real tissues and the other using their corresponding tissue-equivalent materials, which are explained in Table 1. The chemical composition, atomic density, and density values of the real tissues are sourced from the SRIM Database. In this study, a material is considered tissue-equivalent based on several key parameters. These include the chemical composition, density, and atomic structure of the material, which are matched as closely as possible to the corresponding properties of the real tissues. Specifically, we focused on replicating the atomic number, electron density, and X-ray attenuation coefficients of the materials to ensure that their radiation interaction properties align with those of biological tissues. For example, materials like PMMA (Polymethyl Methacrylate) were chosen for soft tissues due to their similar elemental composition and attenuation characteristics. Likewise, Parylene N was selected for muscle tissue and Teflon for bone structures, as these materials show comparable absorption behavior under X-ray exposure. The parameters we used were sourced from databases such as the SRIM and were carefully verified to ensure that the chosen materials mimic the behavior of real tissues as accurately as possible in the specified energy range of 50-100 keV. The following materials were assigned to each layer: PMMA for the skin, parotid gland, Superficial Musculoaponeurotic System (SMAS), mucosa and gum tissues; Parylene N for masseter muscle tissue; polyethylene for buccal fat tissue; water for saliva tissue; and Teflon for cortical bone and cancellous bone. These materials were meticulously selected based on their physical properties to ensure accurate simulation of the tissue layers. On the other hand, in the simulation program, the source characteristics, including X-ray photon energies ranging from 50 to 100 keV, the exposure time of 10 s, and the distance between the source and the phantom, which was set to 20 cm, were adjusted according to the general conditions for taking a panoramic dental X-ray [24]. In this study, the X-rays used had photon energies ranging from 50 to 100 keV. The corresponding wavelengths were calculated for each energy level using the relation \(\lambda=\frac{\hbar c}{E}\), where \(\lambda\) is the wavelength, \(h\) is [PERSON]'s constant, \(c\) is the speed of light, and \(E\) is the photon energy. The calculated wavelengths for the energy range are as follows: 50 keV: 0.0248 nm, 60 keV: 0.0207 nm, 70 keV: 0.0177 nm, 80 keV: 0.0155 nm, 90 keV: 0.0138 nm, and 100 keV: 0.0124 nm. These values provide the wavelength for each energy level used in the simulations. In this study, the focus was primarily on simulating the major tissue types within the mandible, such as bone, muscle, and soft tissues.