Analysis and Development of Phenomenological Models for the Relative Biological Effectiveness in Proton Therapy

Abstract

Proton therapy is undergoing a rapid development making it increasingly popular as a treatment of cancer. Protons interact differently with the tissue compared to conventional radiation therapy with photons, resulting in a more beneficial dose distribution with greater dose conformation. The radiation quality is also different for protons and photons, as the ionisation density, often quantified by the linear energy transfer (LET), is higher for protons than for photons. Irradiation experiments on cells and animal models have shown that protons are slightly more effective in producing biological damage than photons. This difference in biological response is quantified by the relative biological effectiveness (RBE), which aid the comparison of the dose deposition from the two modalities and enables transferal of established clinical protocols from photon therapy to proton therapy. A conservative and constant RBE of 1.1 is used in proton therapy clinics, even though experiments have shown that the RBE can be both higher and lower, varying with different biological and physical quantities, including the LET value.

Phenomenological RBE models try to determine the various RBE dependencies from large experimental databases of cell irradiation experiments. In this work, existing phenomenological models were analysed and explored in a coherent manner: All models were parameterised and described by functions of the maximum RBE (RBEmax) and minimum RBE (RBEmin), the two model functions that make every model unique. The models were implemented in the FLUKA Monte Carlo code and used in estimation of the RBE and RBE-weighted dose for multiple patient plans and relevant dose parameters. The models were also analysed and compared regarding the underlying similarities and differences, which forms the basis for the unique definitions of RBEmax and RBEmin of each model. A new phenomenological RBE model was proposed, introducing the full LET spectrum as an input parameter for phenomenological models. Statistical methods were used to test whether a non-linear LET dependency of RBEmax would give a superior description of the experimental data compared to using the established linear dependency of the dose-averaged LET (LETd). Further, we analysed the LETd dependency of RBEmin in a two-step regression analysis, as the RBEmin function is most commonly assumed to be constant for all LETd values. Specifically, we analysed how restriction on the minimum dose of the underlying experimental database influenced RBEmin.

The estimation of the RBE and the RBE-weighted dose from the various models differed significantly. The largest deviations were seen for organs at risk (OAR) with low fractionation sensitivity ((α/β)x) and high LET. These variations are a result of the distributions of (α/β)x values and LETd values in the experimental databases, the assumptions for RBEmax and RBEmin and regression analysis method. The full LET spectrum was found to give a better representation of the experimental database included in our analysis. Regression weighted to the reported experimental uncertainties showed that a non-linear function (quartic function) gave a better fit to the data than a linear function. The RBEmin function was found to vary with the LETd value if dose constraints were added to the experimental database. By restricting the minimum dose in the database to be 1 Gy or lower, the analysis gave a non-negligible linear LETd dependency, while higher minimum doses indicated that the dependency is constant.

The deviations in the estimated RBE from the models can be traced back to the model differences in the database construction, the model assumptions and the regression techniques. Various methods were used in this thesis to develop novel models by reanalysing published data, such as construction of model databases with strict constraints, using the pure dose-survival data instead of only α and β values, statistical analysis of model assumptions, applying multiple regression techniques and recognition of the LET spectrum as a relevant input parameter. Together, these techniques could minimise the researcher bias and make more accurate RBE models, resulting in better dose predictions for clinically relevant scenarios.