@article {1432,
	title = {The determination of optimal treatment plans for Volumetric Modulated Arc Therapy (VMAT)},
	journal = {European Journal of Operational Research},
	volume = {272},
	year = {2019},
	pages = {372-388},
	abstract = {<p>The success of radiation therapy depends on the ability to deliver the proper amount of radiation to cancerous cells while protecting healthy tissues. As a natural consequence, any new treatment technology improves quality standards concerning primarily this issue. Similar to the widely used Intensity Modulated Radiation Therapy (IMRT), the radiation resource is outside of the patient{\textquoteright}s body and the beam is shaped by a multi-leaf collimator mounted on the linear accelerator{\textquoteright}s head during the state-of-the-art Volumetric Modulated Arc Therapy (VMAT) as well. However, unlike IMRT, the gantry of the accelerator may rotate along one or more arcs and deliver radiation continuously. This property makes VMAT powerful in obtaining high conformal plans in terms of dose distribution; but the apertures are interdependent and optimal treatment planning problem cannot be decomposed into simpler independent subproblems as a consequence. In this work, we consider optimal treatment planning problem for VMAT. First, we formulate a mixed-integer linear program minimizing total radiation dose intensity subject to clinical requirements embedded within the constraints. Then, we develop efficient solution procedures combining Benders decomposition with certain acceleration strategies. We investigate their performance on a large set of test instances obtained from an anonymous real prostate cancer data.</p>},
	keywords = {algorithms, Benders decomposition, integer programming, Radiation therapy, VMAT},
	issn = {0377-2217},
	doi = {https://doi.org/10.1016/j.ejor.2018.06.023},
	url = {https://www.sciencedirect.com/science/article/pii/S0377221718305514},
	author = {P{\i}nar Dursun and Z C Ta{\c s}k{\i}n and I. Kuban Altinel}
}
@article {1429,
	title = {Using branch-and-price to determine optimal treatment plans for volumetric modulated arc therapy (VMAT)},
	journal = {Computers \& Operations Research},
	volume = {110},
	year = {2019},
	pages = {1-17},
	abstract = {<p>Volumetric Modulated Arc Therapy (VMAT) is the state-of-the-art technique for external radiation therapy treatment. In this method, radiation can be delivered continuously on one or more arcs during the rotation of the gantry of the linear accelerator. This property makes VMAT powerful in obtaining high conformal plans in terms of dose distribution within short treatment times. However, the apertures composed by the leaves of the multileaf collimator (MLC) system that shapes continuously the radiation are interdependent, which makes treatment planning hard. We propose a mixed integer linear programming model for VMAT planning problem and exact branch-and-price algorithms to solve it. The objective of the model is to minimize total radiation that is delivered to the patient, and pricing subproblem is decomposable by rows of the MLC and can be solved as a shortest path problem. We generate a large set of test instances from a real data set and evaluate the performance of the proposed branch-and-price algorithm. Computational results reveal that new algorithms are efficient and capable of finding optimal solutions for large problem instances.</p>},
	keywords = {Branch-and-price, Column generation, integer programming, Radiation therapy, Shortest path problem, VMAT},
	issn = {0305-0548},
	doi = {https://doi.org/10.1016/j.cor.2019.05.018},
	url = {https://www.sciencedirect.com/science/article/pii/S0305054819301315},
	author = {P{\i}nar Dursun and Z C Ta{\c s}k{\i}n and I. Kuban Altinel}
}
