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.

Fig. 1

(a) Schematic diagram of the transverse plane of the RTOG benchmark phantom. (b) An example of the transverse plane of the nasopharyngeal case, Case A. Orange arrows indicate the direction of the proton beams. RTOG, Radiation Therapy Oncology Group.

Fig. 2

(a, b) Biological dose distributions displayed by the TPS (RBE = 1.1) for PTV‐based and robust plans created for the RTOG phantom with an OAR radius of 15 mm. (c, d) LET_d distributions corresponding to (a) and (b), respectively. LET, linear energy transfer; OARs, organs at risk; PTV, planning target volume; RBE, relative biological effectiveness; RTOG, Radiation Therapy Oncology Group; TPS, treatment planning systems.

Fig. 3

Comparison of the $\mathrm{\Delta }{D}_{max}$ for the OARs between PTV‐based (blue) and robust (red) plans in the nasopharyngeal case: (a) brainstem and (b) spinal cord. OARs, organs at risk; PTV, planning target volume.

Fig. 4

Comparison of the $\mathrm{\Delta }{D}_{99}$ for the CTV between PTV‐based (blue) and robust (red) plans in the nasopharyngeal case: (a)${\left(\alpha /\beta \right)}_x=3$ and (b) ${\left(\alpha /\beta \right)}_x=12$. CTV, clinical target volume; PTV, planning target volume.

Fig. 5

Comparison of the $\mathrm{\Delta }{D}_{max}$ for the OARs between PTV‐based (blue) and robust plans (red) in the nasopharyngeal case: (a) Brainstem, (b) Spinal cord. From left to right in each set of bars, the results calculated with RBE models proposed by Wilkens et al., Wedenberg et al., and McNamara et al. are shown. OARs, organs at risk; PTV, planning target volume; RBE, relative biological effectiveness.

Fig. 6

Comparison of the $\mathrm{\Delta }{D}_{99}$ for the CTV between PTV‐based (blue) and robust plans (red) in the nasopharyngeal case: (a)${\left(\alpha /\beta \right)}_x=3$, (b) ${\left(\alpha /\beta \right)}_x=12$. From left to right in each set of bars, the results calculated with RBE models proposed by Wilkens et al., Wedenberg et al., and McNamara et al. are shown. CTV, clinical target volume; PTV, planning target volume; RBE, relative biological effectiveness.