Calculation of Electron Stopping Power in Human Skin and Bone Cortical (100–260 MeV)

Abstract

The aim of this study is to assess the mass stopping power for human skin and bone in the range of energies from 100 to 260 MeV with an emphasis on the relevance of reliable estimates of mass stopping power to very high-energy electron (VHEE) radiotherapy. Units mass electronic stopping power (MeV·cm²/g) versus electron energy (MeV). Theoretical calculations for collisional and radiative degradation, including the density-effect correction, were performed in MATLAB 2025, and results were compared with the data from NIST ESTAR database. An energy electrons and three-parameter semi-empirical expression (H = 2.4515, b = 1.0092, and G = 225) was also fitted to estimate the stopping power as a function of electron kinetic energy. Excel 2024 calculations yielded a high correlation coefficient (R = 1) for both skin and bone, with percentage errors of 3.46% for skin and the correlation coefficient between the semi-empirical equation and the practical ESTAR data is R = 0.975 with an error percentage of ( MAPE = 5.90%) for bone cortical using the semi-empirical fit [9]. In contrast, the theoretical Bethe–Bloch equations showed very weak correlations with semi-empirical equation data, with (MAPE = 93.55%) for skin and (MAPE = 98.15%) for bone. These discrepancies may be associated with the limitations of the theoretical model in accounting for energy-loss mechanisms such as bremsstrahlung and material polarization effects These differences emphasize the necessity of proper representation of the radiative loss and material-dependent density effects at high energies. The semi-empirical approach could give a convenient estimate within the energy range under investigation, but must be further validated and numerical implementation and the definition of the parameters carefully checked before clinical use.