Deep learning for dose-averaged linear energy transfer estimation in pencil-beam scanning and double scattering...

Accounting for the linear energy transfer (LET) in proton radiotherapy may reduce treatment-related side effects. When Monte Carlo (MC) simulations are unavailable, deep-learning (DL) surrogate models can be applied. We develop DL LET models for brain tumour patients and assess their uncertainty for an external dataset lacking LET reference.

A multi-institutional dataset of 570 patients with 605 treatment plans was used for model development and evaluation. DL models predicting dose-averaged LET (LET ${}_d$ ) were trained separately for pencil-beam scanning (PBS) and double scattering (DS) treatments, as well as a combined PBS+DS model. Deviations from MC reference were evaluated by median and 98th percentile voxelwise absolute errors (VAE) in organs at risk and the treatment target. Uncertainty was evaluated via deep ensemble variance and latent space distance, correlated with the median VAE, and applied to an external DS cohort without LET ${}_d$ reference.

The PBS+DS model achieved average median VAEs below 0.42 keV/ $\mu$ m. Ensemble variance and latent space distance showed positive correlations with error, with the strongest association observed for ensemble variance (up to $\rho$ $=$ 0.88). Both uncertainty metrics indicated an estimated average median VAE below 0.54 keV/ $\mu$ m for the DS model on the external DS data.

DL models accurately approximate LET ${}_d$ for PBS and DS proton radiotherapy. Uncertainty estimation provides indirect evidence of model reliability and enables performance estimation in cohorts lacking LET ${}_d$ reference, supporting safer application in retrospective analyses and clinical research.