# Skin Absorbed Dose Coefficients for Human Legs from Beta Radiation as a Function of Height
## 2 Materials and Methods
The International Commission on Radiological Protection (ICRP), in report 116, has recommended a thickness of 50 microns for the basal layer. They also recommended considering the start of the basal layer at a depth of 50 microns from the surface of the skin [51]. This modeling assumes that most basal cells are placed within 25 percent of the mean epidermal thickness at any desired area of the skin [52]. The mean values of epidermal thickness for different parts of the body were compared by [PERSON] et al. They showed that the basal layer of skin in the human leg starts at a depth of 40 \(\upmu\)m from the skin surface to the depth of 93 \(\upmu\)m, which is close to the recommended estimation from ICRP report 116 in terms of both placement and thickness [53]. Furthermore, ICRP Report 116 has suggested that basal cells should not be represented using reference voxel geometries when modeling the phantom for simulations. The phantom of the human leg in the Geant4 Monte Carlo Simulation was modeled as 50 different truncated cones made of soft human tissue, as shown in Figure 2. The percentage of elements and the density of the skin tissue are considered to be the same as the soft tissue; they are presented in Table 1.  
In the modeling, the foot is modeled by three different cuboids stacking over each other, and it is assumed that the foot is covered by a leather shoe that is 6 cm in height in total. Table 1 shows the elemental composition of the materials. The phantom leg starts from 6 cm above the ground until 106 cm. The segmented cells are made of three upside-down, truncated cones inside each other and are 2 cm high. The innermost truncated cones represent the mixture of bones and muscles; they are also assumed to be made from soft tissue; the central truncated cone represents the basal cell layer (50 \(\upmu\)m); and the outer truncated cone represents the surface layer (the dead layer cell of the skin), which is also considered 50 \(\upmu\)m thick. Both the basal and the dead cell layers (the epidermis layer) are made from soft tissue; the basal layers (middle truncated cones) are considered to be detectors in the Geant4 simulations, and the absorbed dose to these parts of the cell is measured (Figure 3). The bottom radius, r, of the n-th truncated cones is calculated as follows:  
\[r_{(\upmu m)}=4+0.08\times(n-1) \tag{7}\]  
In this calculation, each cone's bottom radius equals the top radius of the underneath cone cell. Figure 3: Cell layers for each truncated cone. Figure 2: Leg phantom model. The negatively charged beta particles (primary electrons), secondary electrons, and generated photos were tracked during the simulation. The number of particles that hit the basal cell layer, as well as the deposited energy from these particles, were tallied and calculated using the \"G4 SDManager\" class. For this purpose, a sensitive detector from this class was assigned to the basal layer in the leg phantom. Furthermore, the particles were eliminated if they hit the sphere border (Figure 1). The default physics simulator in Geant4 for intermediate energy particles (G4 EmStandardPhysics) was acquired since the maximum beta particle was set to 4 MeV. This physics list processes ionization, bremsstrahlung, multiple scattering, the photoelectric effect, Compton scattering, and pair production. The physics parameters were set to the default values in the Geant4 simulation. GENT4 version 10-04-patch-02 with multi-threading was used to obtain the results. The simulation time for the total of 2 \(\times\) 10\({}^{9}\) iterations in Geant4 was very high, especially for the energy sources with more than 2.5 MeV. However, using the multi-threaded simulations in Geant4 further reduced the time of simulations while increasing the required processors and memory to perform the task. Using the C++ libraries makes Geant4 a fast toolkit in terms of using the multi-thread CPUs as well as the assigned memory, which helped in the simulations for this paper.