An approximate analytical solution of the Bethe equation for charged particles in the radiotherapeutic energy range

摘要: Charged particles such as protons and carbon ions are an increasingly important tool in radiotherapy. There however unresolved physics issues impeding optimal implementation, including estimation of dose deposition non-homogeneous tissue, essential aspect treatment optimization. Monte Carlo (MC) methods can be employed to estimate radiation profile, whilst powerful, these computationally expensive, limiting practicality. In this work, we start from fundamental the form Bethe equation yield a novel approximate analytical solution for particle range, energy linear transfer (LET). The is given terms exponential integral function with relativistic co-ordinate transform, allowing application at radiotherapeutic levels (50–350 MeV protons, 100–600 Mev/a.m.u ions). Model results agreed closely carbon-ions (mean error within ≈1%) literature values. Agreement was high along track, some discrepancy manifesting track-end. model presented has applications charged radiotherapy optimization framework rapid method LET estimation, capable accounting heterogeneity electron density ionization potential.