Energy deposition clustering as a functional radiation quality descriptor for modeling relative biological effectiveness.

Purpose: To explore the use of the frequency of the energy deposition (ED) clusters of different sizes (cluster order, CO) as a surrogate (instead of, e.g., LET) classification of the physical characteristics of ionizing radiation at a nanometer scale, to construct a framework for the calculation of relative biological effectiveness (RBE) with cell survival as endpoint.

Methods: The frequency of cluster order f is calculated by sorting the ED sites generated with the Monte Carlo track structure code LIonTrack into clusters based on a single parameter called the cluster distance d being the maximum allowed distance between two neighboring EDs belonging to a cluster. Published cell survival data parameterized with the linear-quadratic (LQ) model for V79 cells exposed to 15 different radiation qualities (including brachytherapy sources, proton, and carbon ions) were used as input to a fitting procedure, designed to determine a weighting function w that describes the capacity of a cluster of a certain CO to damage the cell's sensitive volume. The proposed framework uses both f and w to construct surrogate based functions for the LQ parameters α and β from which RBE values can be derived.

Results: The results demonstrate that radiation quality independent weights w exist for both the α and β parameters. This enables the calculation of α values that correlate to their experimental counterparts within experimental uncertainties (relative residual of 15% for d = 2.5 nm). The combination of both α and β surrogate based functions, despite the higher relative residuals for β values, yielded an RBE function that correlated to experimentally derived RBE values (relative residual of 16.5% for d = 2.5 nm) for all radiation qualities included in this work.

Conclusions: The f cluster characterization of ionizing radiation at a nanometer scale can effectively be used to calculate particle and energy dependent α and β values to predict RBE values with potential applications to, e.g., treatment planning systems in radiotherapy.