Clonogenic Survival RBE Calculations in Carbon Ion Therapy: The Importance of the Absolute Values of α and β in the Photon Dose-Response Curve and a Strategy to Mitigate Their Anticorrelation

The computation of the relative biological effectiveness (RBE) is a fundamental step in the planning of cancer radiotherapy treatments with accelerated ions. Numerical parameters derived analyzing the dose response of the chosen cell line after irradiation to photons (i.e., α and β, namely the linear and quadratic terms of the linear-quadratic model of cell survival) are generally used as input to biophysical models to predict the ion RBE. The α/β ratio for the photon exposure is generally regarded as an indicator of cell radiosensitivity. However, previous studies suggest that α/β might not be a sufficient parameter to model the RBE of relatively high linear energy transfer (LET) radiation such as carbon ions. For a fixed α/β, the effect of the absolute values of α and β on the computed RBE is underexplored. Furthermore, since α and β are anticorrelated during the fit of the photon-exposed in vitro survival data, different linear-quadratic fits could produce different sets of α and β, thus affecting the RBE calculations. This article reports the combined effect of the α/β ratio and the absolute values α and β on the RBE computed with the Mayo Clinic Florida microdosimetric kinetic model (MCF MKM) for 12C ions of different LET. Furthermore, we introduce a theory-based strategy to potentially mitigate the anticorrelation between α and β during the fit of the photon dose-response biological data.