‘Dirty dose’-based proton variable RBE models - performance assessment on in vitro data

Abstract

Background

In clinical proton radiotherapy, a constant relative biological effectiveness (RBE) of 1.1 is typically applied. Due to abundant evidence of variable RBE effects from in vitro data, multiple variable RBE models have been suggested, typically by describing the $\alpha$ and $\beta$ parameters in the linear quadratic (LQ) model as a function of dose averaged linear energy transfer (${\text{LET}}_d$).

Purpose

This work introduces a new variable RBE model based on the dirty dose concept, where dose deposited in voxels with a corresponding LET exceeding a specific threshold is considered “dirty” in the sense that it has a biological effect above the one predicted by a constant RBE of 1.1. As only one LET level, corresponding to a specific energy for a given particle in a given medium, needs to be monitored, this offers several advantages, such as simplified calculations by removing the need for intricate end of range LET calculations and averaging procedures, as well as opening up for more efficient experimental assessment of the cell specific model parameters.

Methods

Previously published in vitro data were utilized, where surviving fraction (SF), dose and ${\text{LET}}_d$ were reported for a pristine proton beam with varying physical PMMA thicknesses placed upstream of the cells. The setup was re-simulated to extract dirty dose metrics for the corresponding reported ${\text{LET}}_d$-values. Models were created by setting the $\alpha$ parameter of the LQ model as a function of the fraction of dirty dose and subsequently benchmarked against models based on other radiation quality metrics by comparing the root-mean-square-error (RMSE) of the predicted and actual cell surviving fraction.

Results

Variable RBE models based on dirty dose perform on par with conventional radiation quality metrics with a RMSE of 0.38 for a dirty dose-based model with a threshold of 7 $\mathrm{keV}/\mu m$, compared to 0.42 and 0.36 for a ${\text{LET}}_d$-based and $Q_{\mathrm{eff},d}$-based model, respectively. Higher chosen LET thresholds typically performed better and lower performed worse.

Conclusion

The results indicate that models based on dirty dose metrics perform equally well as conventional radiation quality metrics. Due to the simplified calculations involved and the potential for more efficient measurement techniques for data generation, dirty dose-based models might be the most conservative and practical approach for creating future proton variable RBE models.