Dose-Dependent LET Constraints and Constraint Resolution for Interpreting Proton Therapy Toxicity

Dose-averaged linear energy transfer (LET_D) has been increasingly implicated in normal tissue toxicity after proton therapy, yet LET_D-related constraints are commonly implemented as single-value thresholds. Such approaches neglect the coupled dependence of biological effect on dose and LET predicted by radiobiological models. We developed a probabilistic framework for dose-dependent LET constraints and evaluated its consistency with published clinical toxicity data.

Dose-LET_D constraint curves were derived using linear quadratic-based variable relative biological effectiveness (RBE) models with 4 published parametrizations. Uncertainty from RBE model selection, tissue radiosensitivity, and fractionation was incorporated by generating ensembles of constraint curves summarized as probabilistic envelopes. Published dose-LET_D data associated with 5 clinically relevant toxicities-brainstem necrosis, brain necrosis, radiation-induced brain image change, rib fracture, and osteoradionecrosis-were compared with the derived constraints. A constraint resolution metric based on voxel-level dose-LET_D sampling density and model uncertainty was introduced to assess whether constraints can be supported by available clinical data.

Probabilistic dose-LET_D constraints showed good agreement with published clinical constraints for brainstem necrosis, radiation-induced brain image, and osteoradionecrosis, with reported tolerance limits generally lying within or near the 95% confidence intervals. Dose-LET_D combinations observed in patients with toxicity consistently exceeded the upper bounds of the constraint envelopes. Agreement with clinical data was reduced when the most recent RBE model was used in isolation. Constraint resolution analysis demonstrated limited empirical support for constraint localization at higher LET values.

Dose-dependent probabilistic LET_D constraints provide a biologically consistent alternative to single-value LET_D thresholds in proton therapy.