A Monte Carlo study of different LET definitions and calculation parameters for proton beam therapy

The strong in vitro evidence that proton Relative Biological Effectiveness (RBE) varies with Linear Energy Transfer (LET) has led to an interest in applying LET within treatment planning. However, there is a lack of consensus on LET definition, Monte Carlo (MC) parameters or clinical methodology. This work aims to investigate how common variations of LET definition may affect potential clinical applications. MC simulations (GATE/GEANT4) were used to calculate absorbed dose and different types of LET for a simple Spread Out Bragg Peak (SOBP) and for four clinical PBT plans covering a range of tumour sites. Variations in the following LET calculation methods were considered: (i) averaging (dose-averaged LET (LETd) & track-averaged LET); (ii) scoring (LETd to water, to medium and to mass density); (iii) particle inclusion (LETd to all protons, to primary protons and to particles); (iv) MC settings (hit type and Maximum Step Size (MSS)). LET distributions were compared using: qualitative comparison, LET Volume Histograms (LVHs), single value criteria (maximum and mean values) and optimised LET-weighted dose models. Substantial differences were found between LET values in averaging, scoring and particle type. These differences depended on the methodology, but for one patient a difference of similar to 100% was observed between the maximum LETd for all particles and maximum LETd for all protons within the brainstem in the high isodose region (4 keV mu m(-1) and 8 keV mu m(-1) respectively). An RBE model using LETd including heavier ions was found to predict substantially different LET-weighted dose compared to those using other LET definitions. In conclusion, the selection of LET definition may affect the results of clinical metrics considered in treatment planning and the results of an RBE model. The authors' advocate for the scoring of dose-averaged LET to water for primary and secondary protons using a random hit type and automated MSS.