LET-based approximation of the microdosimetric kinetic model for proton radiotherapy

Phenomenological relative biological effectiveness (RBE) models for proton therapy, based on the dose-averaged linear energy transfer (LET), have been developed to address the apparent RBE increase towards the end of the proton range. The results of these phenomenological models substantially differ due to varying empirical assumptions and fitting functions. In contrast, more theory-based approaches are used in carbon ion radiotherapy, such as the microdosimetric kinetic model (MKM). However, implementing microdosimetry-based models in LET-based proton therapy treatment planning systems poses challenges.

This work presents a LET-based version of the MKM that is practical for clinical use in proton radiotherapy.

At first, we derived an approximation of the Mayo Clinic Florida (MCF) MKM for relatively-sparsely ionizing radiation such as protons. The mathematical formalism of the proposed model is equivalent to the original MKM, but it maintains some key features of the MCF MKM, such as the determination of model parameters from measurable cell characteristics. Subsequently, we carried out Monte Carlo calculations with PHITS in different simulated scenarios to establish a heuristic correlation between microdosimetric quantities and the dose averaged LET of protons.

A simple allometric function was found able to describe the relationship between the dose-averaged LET of protons and the dose-mean lineal energy, which includes the contributions of secondary particles. The LET-based MKM was used to model the in vitro clonogenic survival RBE of five human and rodent cell lines (A549, AG01522, CHO, T98G, and U87) exposed to pristine and spread-out Bragg peak (SOBP) proton beams. The results of the LET-based MKM agree well with the biological data in a comparable or better way with respect to the other models included in the study. A sensitivity analysis on the model results was also performed.

The LET-based MKM integrates the predictive theoretical framework of the MCF MKM with a straightforward mathematical description of the RBE based on the dose-averaged LET, a physical quantity readily available in modern treatment planning systems for proton therapy.