On the value of a multistage optimization approach for intensity-modulated radiation therapy planning*

Objective. Intensity-modulated radiation therapy (IMRT) aims to distribute a prescribed dose of radiation to cancerous tumors while sparing the surrounding healthy tissue. A typical approach to IMRT planning uniformly divides and allocates the same dose prescription (DP) across several successive treatment sessions. A more flexible fractionation scheme would lend the capability to vary DPs and utilize updated CT scans and future predictions to adjust treatment delivery. Therefore, our objective is to develop optimization-based models and methodologies that take advantage of adapting treatment decisions across fractions by utilizing predictions of tumor evolution. Approach. We introduce a nonuniform generalization of the uniform allocation scheme that does not automatically assume equal DPs for all sessions. We develop new deterministic and stochastic multistage optimization-based models for such a generalization. Our models allow us to simultaneously identify optimal DPs and fluence maps for individual sessions. We conduct extensive numerical experiments to compare these models using multiple metrics and dose-volume histograms. Main results. Our numerical results in both deterministic and stochastic settings reveal the restrictive nature of the uniform allocation scheme. The results also demonstrate the value of nonuniform multistage models across multiple performance metrics. The improvements can be maintained even when restricting the underlying fractionation scheme to small degrees of nonuniformity. Significance. Our models and computational results support multistage stochastic programming (SP) methodology to derive ideal allocation schemes and fluence maps simultaneously. With technological and computational advancements, we expect the multistage SP methodologies to continue to serve as innovative optimization tools for radiation therapy planning applications.