Optimization methods for spatiotemporally fractionated radiotherapy planning
The goal in radiotherapy, as one of the main modalities for cancer treatment, is to deliver sufficient radiation dose to the tumor region to eradicate the disease while sparing the surrounding healthy tissues to the largest extent possible. To achieve this goal, radiotherapy plans for individual cancer patients are designed to deliver the desired spatial dose distribution to the patient. The radiotherapy plan will be then used on a daily basis to deliver a daily fraction of the prescribed radiation dose over the course of treatment. However, there is biological evidence suggesting that additional therapeutic gain may be achieved if we allow for temporal variation in the radiotherapy plan. This treatment paradigm is known as spatiotemporal fractionation, which is the topic of this dissertation. In this research, we first develop mathematical models and solution methods to show the existence of the potential therapeutic benefit of spatiotemporal plans over conventional plans for stylized cancer cases. Then, we focus on the computational challenges of optimizing spatiotemporally fractionated plans for clinical cancer cases. The main challenge is the non-convex and large-scale nature that arises in the proposed optimization models. We develop customized solution methods that use sequential quadratic/linear programming in a constraint generation framework. We also provide optimality bounds on the found feasible solutions by solving Lagrangian relaxation using a column generation approach. We also extend our spatiotemporal planning approach to explicitly account for a major source of uncertainty that may compromise the potential therapeutic benefit achievable from spatiotemporal fractionation. Specifically, we incorporate the uncertainty associated with inter- and intra-patient variability in the radio-biological parameter values. To account for such uncertainties, we propose a robust optimization approach, which optimizes over a range of possible realization of the uncertain parameters. We test the computational performance of the proposed solution methods using stylized as well as de-identified clinical cancer cases.
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