Optimal use of limited proton resources for liver cancer patients in combined proton-photon treatments.

Objective: Liver cancer patients may benefit from proton therapy through increase of the tumor control probability (TCP). However, proton therapy is a limited resource and may not be available for all patients. We consider combined proton-photon liver SBRT treatments (CPPT) where only some fractions are delivered with protons. It is investigated how limited proton fractions can be used best for individual patients and optimally allocated within a patient group. Approach: Photon and proton treatment plans were created for five liver cancer patients. In CPPT, limited proton fractions may be optimally exploited by increasing the fraction dose compared to photon fraction dose. To determine a patient's optimal proton and photon fraction dose, we maximize the target BED while constraining the mean normal liver BED, which leads to an up- or downscaling of the proton and photon plan, respectively. The resulting CPPT balances the benefits of fractionation in the normal liver versus exploiting the superior proton dose distributions. After converting the target BED to TCP, the optimal number of proton fractions per patient is determined by maximizing the overall TCP of the patient group. Main results: For the individual patient, a CPPT treatment that delivers a higher fraction dose with protons than photons allows for dose escalation in the target compared to delivering the same proton and photon fraction dose. On the level of a patient group, CPPT may allow to distribute limited proton slots over several patients. Through an optimal use and allocation of proton fractions, CPPT may increase the average patient group TCP compared to a proton patient selection strategy where patients receive single-modality proton or photon treatments. Significance: Limited proton resources can be optimally exploited via CPPT by increasing the target dose in proton fractions and allocating available proton slots to patients with the highest TCP increase. .