Radiotherapy And Immunotherapy In Cancer: A Mathematical Model

The rise of immunotherapy is a major breakthrough in oncology. Recently, the combination of radiotherapy with the blockade of immune checkpoint inhibitors such as the PD1-PDL1 axis or the CTLA4 pathway has shown a synergistic potential: in addition to the direct cell kill induced by irradiation, radiotherapy unleashes neoantigens that can further induce an anti-tumoral immune response. However, this immune response can be inhibited by the immunosuppressive nature of the tumor micro-environment (TME). Hence, radiotherapy combined with immune check-point inhibitors is a promising solution and is the subject of preclinical and clinical research. However, defining the most efficient scheduling between radiotherapy and immunotherapy is a crucial issue that cannot be properly addressed solely by empirical trial-and-error practices. Consequently, developing mathematical models that can describe the synergy between immune checkpoint inhibitors and radiotherapy is critical. Hence, we have built a pharmocodynamic model of the combination of radiotherapy with inhibitors of the PD1-PDL1 axis and/or the CTLA4 pathway. We describe a mathematical representation of how a growing tumor first elicits and then inhibits an anti-tumoral immune response. This anti-tumoral immune response is described by a primary and a secondary response. The primary immune response appears first and is down-regulated by the PD1-PDL1 axis, while the secondary immune response happens next and is down-regulated by the CTLA4 pathway. We describe the effects of irradiation by a slightly modified version of the Linear-Quadratic model. In particular, we explain the biphasic relationship between the size of a tumor and its immunogenicity, as measured by the abscopal immune response. The ability of the model to forecast pharmacodynamic endpoints was retrospectively validated by reproducing results from experimental studies investigating radiotherapy and immune checkpoint inhibitors. This model clarifies the issue of synchronisation of immunotherapy with radiotherapy and it also explains why the CTLA4 blockade often occurs with a delay. The model also explains why a sustained response to immunotherapy may or may not happen after treatment discontinuation. We believe that this mathematical model could be further used as a simulation tool to help decision-makers determine the optimal scheduling between radiotherapy and immunotherapy and could be a building block for the in-silico design of optimized multimodal strategies. Citation Format: Raphael Serre, Xavier Muracciole, Joseph Ciccolini, Sebastien Benzekry, Dominique Barbolosi. Radiotherapy and immunotherapy in cancer: A mathematical model. [abstract]. In: Proceedings of the 107th Annual Meeting of the American Association for Cancer Research; 2016 Apr 16-20; New Orleans, LA. Philadelphia (PA): AACR; Cancer Res 2016;76(14 Suppl):Abstract nr 2704.