Comparing the Microdosimetric Kinetic Model-Predicted Proton RBE Values Using Constant and Variable Quadratic Beta Coefficients

Abstract

In the current microdosimetric kinetic model (MKM) model for predicting the biological effects of therapeutic particles, the quadratic beta coefficient is assumed to be a constant independent of radiation types. However, many cell irradiation experiments have shown the variable beta coefficients for different beam qualities. The purpose of this study is to compare the predicted relative biological effectiveness (RBE) of protons using the MKM model with a constant beta value and beam quality (i.e., the microdosimetric quantity lineal energy) dependent beta values. We have spatially mapped the biological effects along the path of a mono-energetic 81.4 MeV proton beam using the high-throughput method. Clonogenic cell survival curves with twelve different beam qualities (dose mean lineal energy, yD) were obtained for the non-small cell lung cancer (NSCLC) cell line H460. The Cs-137 photon source was used as the reference. The microdosimetric data were obtained from the track-structure Monte Carlo simulations using Geant4-DNA with a water sphere (d = 2 μm) as the target. The alpha and beta coefficients for protons and reference photons were obtained from the linear-quadratic fit results of each survival curve. The beta coefficient of photons was selected as the constant beta value for MKM predictions. We calculated the alpha coefficient using the constant beta first and then using the variable beta for each proton beam quality. The MKM model predicted RBE values as a function of beam quality were then compared with the experimental RBE. The twelve evenly sampled yD values of the proton beam ranges from 1.38 to 21.77 keV/μm with the value of 12.93 keV/μm at the Bragg peak. The alpha and beta coefficients from Cs-137 photon source are 0.23 Gy-1 and 0.10 Gy-2. Our experiments have shown a general trend that the alpha and beta values of protons from experimental survival curves increase with the increase of yD. The experimental RBE increases from 0.99 (yD = 1.38 keV/μm) to 2.85 (yD = 21.77 keV/μm) in a rather non-linear way. Using the constant beta based MKM model, the predicted RBE (cell surviving fraction = 0.1) only varies from 1.00 to 1.12, nearly independent of the beam quality. In contrast, using the variable beta based MKM model, the predicted proton RBE increases as a function of yD and varies from 1.00 to 2.73. The relative difference between variable beta based MKM model prediction and the experimental RBE is within ±10%. From the results in this study, we conclude that using the experimentally determined variable beta values, MKM model can better predict the biological effects of protons. However, more experiments for different beam qualities and different cell lines are needed to further consolidate the conclusion made here.