Proton beam secondary depth-dose calculation with a secondary propagation model

Purpose: This study aimed to construct a proton beam secondary depth-dose calculation model to improve the depth-dose accuracy in proton therapy.Methods: The secondary dose contributed by secondary particles was investigated in this study. A secondary propagation model (SPM) was constructed to calculate the absolute secondary depth-dose. The transport of secondary particles was considered by introducing a dose propagation function. An approximated linear formula of the propagation function was applied, replacing an accurate but complex Bragg curve function to simplify the calculation process. The primary depth-dose was also calculated using a straight-track approximation model, and the total calculated result (primary plus secondary) was evaluated by gamma analysis referring to the Geant4 simulation result.Results: Proton beams with initial energies of 50, 100, 150, and 200 MeV were calculated and verified. The inelastic secondary proton dose and elastic recoiled proton dose had a similar trend and were close to the simulation result. The inelastic alpha dose deviated between the calculation and simulation at the entrance of the primary beam and decreased along the depth. Under the given gamma tolerance (2% max/1 mm), the calculated and simulated total doses showed an acceptable gamma index below one in the entire beam range.Conclusion: The secondary propagation model improved the depth-dose distribution accuracy. The SPM com-bined with a primary calculation model will help make more accurate treatment plan calculations.