Multistage Stochastic Fractionated Intensity Modulated Radiation Therapy Planning

Intensity modulated radiation therapy (IMRT) is a widely used cancer treatment technique as it can deliver highly complex beam distributions, targeting malignant cells while avoiding or limiting exposure of healthy organs and tissues. To further increase the destructive effect on tumor cells and reduce side effects, radiotherapy is usually divided into several treatments called fractions and delivered over several weeks. The fractionated IMRT planning refers to treatment planning over multiple fractions, which extends the typical goal of finding optimal beamlet intensities at a single treatment session, where interfractional motion-related uncertainties arise in addition to intrafractional ones. We propose a novel multistage stochastic programming (MSP) modeling framework for this problem that can appropriately incorporate the sequential decision-making nature and prevailing stochasticity in cancer treatment. We solve a sample average approximation of our model via stochastic dual dynamic programming, and consider a variety of risk measures. We conduct computational experiments on five test cases that are generated based on clinical data. Through extensive simulations, we show that our MSP model generates higher quality treatment plans compared to its deterministic counterpart based on multiple performance measures. In particular, our model leads to a higher rate of tumor cover- age and a lower rate of radiation exposure for healthy tissues. Accordingly, the proposed MSP framework can greatly contribute to the clinical practice in fractionated IMRT.

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