Difference in LET-based biological doses between IMPT optimization techniques: Robust and PTV-based optimizations

Abstract

Purpose: While a large amount of experimental data suggest that the proton relative biological effectiveness (RBE) varies with both physical and biological parameters, current commercial treatment planning systems (TPS) use the constant RBE instead of variable RBE models, neglecting the dependence of RBE on the linear energy transfer (LET). To conduct as accurate a clinical evaluation as possible in this circumstance, it is desirable that the dosimetric parameters derived by TPS ( $D^{\text{RBE}=1.1}$ ) are close to the "true" values derived with the variable RBE models ( $D^{v\text{RBE}}$ ). As such, in this study, the closeness of $D^{\text{RBE}=1.1}$ to $D^{v\text{RBE}}$ was compared between planning target volume (PTV)-based and robust plans.

Methods: Intensity-modulated proton therapy (IMPT) treatment plans for two Radiation Therapy Oncology Group (RTOG) phantom cases and four nasopharyngeal cases were created using the PTV-based and robust optimizations, under the assumption of a constant RBE of 1.1. First, the physical dose and dose-averaged LET (LET_d ) distributions were obtained using the analytical calculation method, based on the pencil beam algorithm. Next, $D^{v\text{RBE}}$ was calculated using three different RBE models. The deviation of $D^{v\text{RBE}}$ from $D^{\text{RBE}=1.1}$ was evaluated with D₉₉ and D_max , which have been used as the evaluation indices for clinical target volume (CTV) and organs at risk (OARs), respectively. The influence of the distance between the OAR and CTV on the results was also investigated. As a measure of distance, the closest distance and the overlapped volume histogram were used for the RTOG phantom and nasopharyngeal cases, respectively.

Results: As for the OAR, the deviations of $D_{max}^{v\text{RBE}}$ from $D_{max}^{\text{RBE}=1.1}$ were always smaller in robust plans than in PTV-based plans in all RBE models. The deviation would tend to increase as the OAR was located closer to the CTV in both optimization techniques. As for the CTV, the deviations of $D_{99}^{v\text{RBE}}$ from $D_{99}^{\text{RBE}=1.1}$ were comparable between the two optimization techniques, regardless of the distance between the CTV and the OAR.

Conclusion: Robust optimization was found to be more favorable than PTV-based optimization in that the results presented by TPS were closer to the "true" values and that the clinical evaluation based on TPS was more reliable.

Keywords: plan comparison; proton therapy; robust optimization; variable RBE.