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A novel stochastic optimization method for handling misalignments of proton and photon doses in combined treatments

Objective. Combined proton–photon treatments, where most fractions are delivered with photons and only a few are delivered with protons, may represent a practical approach to optimally use limited proton resources. It has been shown that, when organs at risk (OARs) are located within or near the tumor, the optimal multi-modality treatment uses protons to hypofractionate parts of the target volume and photons to achieve near-uniform fractionation in dose-limiting healthy tissues, thus exploiting the fractionation effect. These plans may be sensitive to range and setup errors, especially misalignments between proton and photon doses. Thus, we developed a novel stochastic optimization method to directly incorporate these uncertainties into the biologically effective dose (BED)-based simultaneous optimization of proton and photon plans. Approach. The method considers the expected value Eb and standard deviation σb of the cumulative BED b in every voxel of a structure. For the target, a piecewise quadratic penalty function of the form bmin−Eb−2σb+2 is minimized, aiming for plans in which the expected BED minus two times the standard deviation exceeds the prescribed BED bmin. Analogously, Eb+2σb−bmax+2 is considered for OARs. Main results. Using a spinal metastasis case and a liver cancer patient, it is demonstrated that the novel stochastic optimization method yields robust combined treatment plans. Tumor coverage and a good sparing of the main OARs are maintained despite range and setup errors, and especially misalignments between proton and photon doses. This is achieved without explicitly considering all combinations of proton and photon error scenarios. Significance. Concerns about range and setup errors for safe clinical implementation of optimized proton–photon radiotherapy can be addressed through an appropriate stochastic planning method.