The determination of treatment plans for volumetric modulated arc therapy

Volumetric modulated arc therapy is the state-of-the-art technique for external radiation therapy treatment, where radiation can be delivered continuously during the rotation of the linear accelerator's gantry. This property makes this technique powerful in obtaining high conformal plans requiring short treatment times. However, the multileaf collimator system shapes the radiation beam continuously, thus the resulting apertures are interdependent due to leaf motion limitations, which makes treatment planning hard. In this thesis, we first propose two mixed integer linear programming formulations minimizing total radiation delivered to the patient subject to the geo- metrical and clinical requirements. Then, we develop exact solution algorithms that combine Benders decomposition with certain acceleration strategies and implement branch-and-price method where pricing subproblem is decomposable by rows of multileaf collimator and can be solved as a shortest path problem. We investigate their performance on a large set of test instances obtained from an anonymous real prostate cancer data. The computational results reveal that they are efficient and outperform a widely used commercial solver. In particular, branch-and-price implementation is capable to find optimal solutions for larger problem instances. However, they cannot provide realistic plans for real clinical problems because of their large size. In order to address this issue, we develop a two-phase column generation based heuristic that tunes the parameters of dose-volume requirements and yields an automated treatment planning environment, which does not require any human intervention. We test its performance on real prostate data sets and compare the quality of the generated plans with those obtained by a widely used commercial treatment planning system. Results show that it can obtain medically acceptable plans requiring significantly less radiation in reasonable computation times.