The purpose of this work was to investigate the response of prostate cancer to different radiotherapy schedules, including hypofractionation, to evaluate potential departures from the linear–quadratic (LQ) response, to obtain the best-fitting parameters for low-(LR), intermediate-(IR), and high-risk (HR) prostate cancer and to investigate the effect of ADT on the radiobiological response. We constructed a dataset of the dose–response containing 87 entries/16,536 patients (35/5181 LR, 32/8146 IR, 20/3209 HR), with doses per fraction ranging from 1.8 to 10 Gy. These data were fit to tumour control probability models based on the LQ model, linear–quadratic–linear (LQL) model, and a modification of the LQ (LQmod) model accounting for increasing radiosensitivity at large doses. Fits were performed with the maximum likelihood expectation methodology, and the Akaike information criterion (AIC) was used to compare the models. The AIC showed that the LQ model was superior to the LQL and LQmod models for all risks, except for IR, where the LQL model outperformed the other models. The analysis showed a low α/β for all risks: 2.0 Gy for LR (95% confidence interval: 1.7–2.3), 3.4 Gy for IR (3.0–4.0), and 2.8 Gy for HR (1.4–4.2). The best fits did not show proliferation for LR and showed moderate proliferation for IR/HR. The addition of ADT was consistent with a suppression of proliferation. In conclusion, the LQ model described the response of prostate cancer better than the alternative models. Only for IR, the LQL model outperformed the LQ model, pointing out a possible saturation of radiation damage with increasing dose. This study confirmed a low α/β for all risks.

PurposeTo investigate the response of prostate cancer to different radiotherapy schedules, including hypofractionation, and to evaluate potential departures from the linear-quadratic (LQ) response. To obtain best-fitting parameters for low (LR), intermediate (IR), and high risk (HR) prostate cancer.Methods and MaterialsWe have constructed a dataset of dose-response containing 87 entries (35 LR, 32 IR, 20 HR), with doses per fraction ranging from 1.8 to 10 Gy. These data were fitted to tumor control probability models based on the LQ model, linear-quadratic-linear (LQL), and a modification of the LQ (LQmod) accounting for increasing radiosensitivity at large doses. Fits were performed with the maximum likelihood expectation methodology, and the Akaike-Information-Criterion (AIC) was used to compare models.ResultsThe AIC shows that the LQ model is superior to the LQL and LQmod for all risks, except for IR where the LQL outperforms the other models. The analysis shows a low α/β for all risks: 2.01 Gy for LR (95% confidence interval 1.74-2.26), 3.44 Gy for IR (2.99-4.02), and 2.78 Gy for HR (1.43-4.18). Best-fits do not show proliferation for LR, and only moderate proliferation for IR/HR.ConclusionsIn general, the LQ model describes the response of prostate cancer better than the alternative models. Only for IR the LQL outperforms the LQ. This study confirms a lowα/βfor all risks, with doses per fraction ranging from <2 Gy up to 10 Gy.

There is evidence of synergy between radiotherapy and immunotherapy. Radiotherapy can increase liberation of tumor antigens, leading to activation of antitumor T-cells. This effect can be boosted with immunotherapy. Radioimmunotherapy is therefore a very promising therapeutic combination against cancer, with potential to increase tumor control rates. Biomathematical response models of radioimmunotherapy may help clinicians to design optimal treatment schedules. In this work we present a biomathematical model of tumor response to radioimmunotherapy. The model uses the linear-quadratic response of tumor cells to radiation, and builds on previous developments to include the radiation-induced immune effect. We have focused this study on the combined effect of radiotherapy and αPDL1/αCTL4 therapies. The model fits recent preclinical data of volume dynamics and control obtained with different dose fractionations and αPDL1/αCTL4. A biomathematical study of optimal combination strategies suggests that a good understanding of the biological delays associated to radoimmunotherapy, the biokinetics of the immunotherapy drug, and the interplay among them, may be of paramount importance to design optimal radioimmunotherapy schedules. Biomathematical models like the one we present can help to interpret experimental data on the synergy between radiotherapy and immunotherapy, and to assist in the design of more effective treatments, could potentially boost the implementation of radioimmunotherapy.