Using the Proton Energy Spectrum and Microdosimetry To Model Proton Relative Biological Effectiveness

PURPOSE: We introduce a methodology to calculate the microdosimetric quantity dose-mean lineal energy for input into the microdosimetric kinetic model (MKM) to model the relative biological effectiveness (RBE) of proton irradiation experiments.

METHODS AND MATERIALS: The data from seven individual proton RBE experiments were included in this study. In each experiment, the RBE at several points along the Bragg curve was measured. Monte Carlo (MC) simulations to calculate the lineal energy probability density function of 172 different proton energies were carried out with use of Geant4 DNA. We calculated the fluence-weighted lineal energy probability density function (fw(y)), based on the proton energy spectra calculated through MC at each experimental depth, calculated yD¯ for input into the MKM, and then computed the RBE. The radius of the domain (rd) was varied to reach the best agreement between the MKM-predicted RBE and experimental RBE. A generic RBE model as a function of dose averaged linear energy transfer (LETD) with one fitting parameter was presented and fit to the experimental RBE data as well, to facilitate a comparison to the MKM.

RESULTS: Both the MKM and LETD based models modeled the RBE from experiments well. Values for rd were similar to those of other cell lines under proton irradiation that were modeled with the MKM. Analysis of the performance of each model revealed neither model was clearly superior to the other.

CONCLUSIONS: Our three key accomplishments include the following: (1) Developed a method that uses the proton energy spectra and lineal energy distributions of those protons to calculate dose-mean lineal energy. (2) Demonstrated that our application of the MKM provides theoretical validation of proton irradiation experiments that show that RBE is significantly greater than 1.1. (3) Showed that there is no clear evidence that the MKM is better than LETD based RBE models.