Robust intensity-modulated proton therapy to reduce high linear energy transfer in organs at risk

Abstract

Purpose: We propose a robust treatment planning model that simultaneously considers proton range and patient setup uncertainties and reduces high linear energy transfer (LET) exposure in organs at risk (OARs) to minimize the relative biological effectiveness (RBE) dose in OARs for intensity-modulated proton therapy (IMPT). Our method could potentially reduce the unwanted damage to OARs.

Methods: We retrospectively generated plans for 10 patients including two prostate, four head and neck, and four lung cancer patients. The "worst-case robust optimization" model was applied. One additional term as a "biological surrogate (BS)" of OARs due to the high LET-related biological effects was added in the objective function. The biological surrogate was defined as the sum of the physical dose and extra biological effects caused by the dose-averaged LET. We generated nine uncertainty scenarios that considered proton range and patient setup uncertainty. Corresponding to each uncertainty scenario, LET was obtained by a fast LET calculation method developed in-house and based on Monte Carlo simulations. In each optimization iteration, the model used the worst-case BS among all scenarios and then penalized overly high BS to organs. The model was solved by an efficient algorithm (limited-memory Broyden-Fletcher-Goldfarb-Shanno) in a parallel computing environment. Our new model was benchmarked with the conventional robust planning model without considering BS. Dose-volume histograms (DVHs) of the dose assuming a fixed RBE of 1.1 and BS for tumor and organs under nominal and uncertainty scenarios were compared to assess the plan quality between the two methods.

Results: For the 10 cases, our model outperformed the conventional robust model in avoidance of high LET in OARs. At the same time, our method could achieve dose distributions and plan robustness of tumors assuming a fixed RBE of 1.1 almost the same as those of the conventional robust model.

Conclusions: Explicitly considering LET in IMPT robust treatment planning can reduce the high LET to OARs and minimize the possible toxicity of high RBE dose to OARs without sacrificing plan quality. We believe this will allow one to design and deliver safer proton therapy.

Keywords: biological optimization; intensity-modulated proton therapy (IMPT); linear energy transfer (LET); robust optimization.

Figure 1

Comparison of dose distribution assuming a fixed RBE of 1.1 (top row) and LET distribution (bottom row) for case 2 in the nominal scenario. (a) and (b):distribution of dose assuming a fixed RBE of 1.1. (c) and (d):distribution of the LET (unit: kev/μm). (a) and (c) are the results from the conventional model RO; (b) and (d) are the results from our new model RO(BS). Clinical target volume (CTV) and spinal cord are contoured by red (top middle enclosed area) and cyan lines (bottom enclosed area), respectively. In RO(BS), the high LET distribution in spinal cord (comparing (c) and (d)) is considerably reduced, while the physical dose distribution of the tumor is very similar. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 2

Difference of doses from the results of the plan derived from the RO(BS) model minus the results of the plan derived from the RO model assuming a fixed RBE of 1.1. A representative transverse slice of case 2 under nominal scenario is shown. For two beams with their directions indicated by white arrows, the RO(BS) model clearly will reduce the intensity of beamlets of the lower beam deposited at the proximal edge of the target (red contour and top enclosed area) when brainstem (yellow contour and bottom enclosed area) is proximal to the target. This effect will lead to an decrease of physical dose (blue area and left bottom gray area) from the RO(BS) model compared with the RO model. Correspondingly, the beamlet intensities in the upper beam parallel to the brain stem will increase to compensate the physical dose in the target. This causes an increase of the physical dose in the red area (top right dark area). [Color figure can be viewed at wileyonlinelibrary.com]

Figure 3

Comparison of DVH curves generated by the per‐voxel maximum (red and dark) and minimum (blue and gray) l doses of tumor assuming a fixed RBE of 1.1 derived from the models with and without BS terms for the head‐and‐neck cancer case. The new model RO(BS) is represented by solid curves and the conventional model RO by dashed curves. The difference between the DVH curves generated by the per‐voxel maximum and minimum doses of tumor indicates plan robustness. The difference of plan quality and plan robustness is only minor between the two models. [Color figure can be viewed at wileyonlinelibrary.com]

Figure A2

The xBD ‐volume histograms of the cases 1–5 (in the nominal scenario) for RO (dashed Line) and RO(BS) (solid Line), respectively. The curves from our new robust model RO(BS) were drawn as solid lines and ones from the conventional model RO as dashed lines. The RO model can reduce xBD , although the degree of reduction varies from patient to patient and organ to organ. [Color figure can be viewed at wileyonlinelibrary.com]