Methods and algorithms for radiation therapy optimization under dose -volume restrictions

Ali T Tuncel, Purdue University

Abstract

According to the American Cancer Society, cancer accounts for almost one quarter of the deaths in the United States. Over a million new cases of cancer are diagnosed every year and about half of all cancer patients undergo radiation therapy at some point during the course of their treatment, making radiation therapy one of the most commonly used procedures in cancer treatment. In radiation therapy planning, the fluence map optimization (FMO) problem aims to determine optimal beamlet intensities to ensure that target tissues are sufficiently irradiated while nearby healthy tissues at risk are protected from excessive radiation. The desired levels of radiation dose distribution over the volume of each tissue are prescribed by physicians based on protocols. For each tissue, prescriptions typically specify minimum and maximum dose limits to be applied to the entire volume of the tissue. Moreover, prescriptions usually specify additional dose limits to be applied to some percentage of the tissue volume. The latter dose restrictions are known as dose-volume restrictions. Dose-volume restrictions yield non-convex FMO models that are typically hard to solve. This dissertation proposes novel methods that exploit the structure of FMO problems under dose-volume restrictions to efficiently derive provably globally optimal or near-globally optimal solutions. First, a mixed-integer programming (MIP) formulation for FMO is presented and several theoretical properties of the resulting model are analyzed. In particular, it is shown that, when subject to dose-volume restrictions, FMO problems are NP-hard and that the linear programming relaxation of their natural mixed integer programming formulation can be arbitrarily weak. A customized branch-and-cut algorithm is then proposed that can obtain provably optimal (or near-optimal) solutions of FMO problems. This branch-and-cut algorithm includes (i) problem-specific preprocessing methods that reduce the problem size, (ii) novel families of valid inequalities that strengthen problem formulation, and (iii) problem-specific enumeration methods that efficiently divide the feasible region of the problem. It is shown that the proposed framework significantly outperforms commercial MIP solvers and other methods for solving FMO instances arising from actual clinical cases.

Degree

Ph.D.

Advisors

Richard, Purdue University.

Subject Area

Operations research|Medicine

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