Radiation therapy treatments for cancer aim to deliver a toxic dose of radiation to malignant tumors, while controlling the dose to healthy tissues and organs. In external beam therapy, radiation is delivered by a linear accelerator, and a Multileaf Collimator (MLC) is used to change the shape of the beam opening, or aperture. A treatment plan for each patient is designed by specifying the apertures and timing and source intensity decisions for each beam angle used in the treatment. Mathematical optimization models are commonly used in modern radiation treatment planning, and rely on mathematical models of the dose distribution delivered to the patient by the portions of the beams exposed by the apertures. Volumetric Modulated Arc Therapy (VMAT) and Tomotherapy are two of the highly utilized forms of external-beam radiation therapy, each with unique features of the MLCs. For both modalities, the current standard treatment planning methodology is prone to creating a discrepancy between the doses that are intended, and the doses that are actually delivered to the patient. The goal of our research is to develop improved treatment planning strategies that reduce this divergence. In tomotherapy, the MLC consists of binary leaves alternating between fully open and closed states, while the beam traces a helicoidal trajectory around the patient. Dosimetric discrepancies in tomotherapy have been attributed to the lack of accurate models of leaf motion and dose delivery during leaf transitions between states, with their impact exacerbated by short leaf open times (LOTs). Moreover, the discretization of beam motion currently used for dose calculations is relatively coarse, which also contributes to the dosimetric errors. We propose a new treatment planning delivery and modeling paradigm for tomotherapy that allows us to impose lower bounds on minimum and average LOTs, while allowing for arbitrarily finer discretization of beam motion --- both features absent from existing approaches. VMAT treatments use a rectangular MLC, with leaves that can open and close partially, creating complex two-dimensional aperture shapes, while the beam moves along pre-specified trajectories, or arcs. Current VMAT treatment planning approaches tend to create plans with complex and irregular apertures with small areas and excessive edge lengths. The dose delivery models for such apertures are less accurate than for apertures with simpler, rounder shapes; therefore discrepancies between planned and delivered dose are frequently observed in VMAT treatments as well. Our proposed optimization model for VMAT treatment planning considers a tradeoff between the quality of the planned treatment with respect to the clinical goals and a penalty on irregularly-shaped apertures. This model extends and combines a VMAT planning model with a new edge metric penalty with favorable mathematical properties compared to penalties studied in the literature. Due to the complexities of VMAT delivery, the resulting optimization models require development of heuristic solution approaches. We develop a significant extension of a heuristic algorithm for VMAT treatment planning applicable to the new model. We test the models and algorithms proposed in this thesis on clinical cases, demonstrating improvements in treatment characteristics of the resulting treatment plans --- LOTs and discretization levels in tomotherapy and aperture shape metrics in VMAT. While the precise reductions in dosimetric discrepancies resulting from these changes will need to be confirmed by dosimetric studies, these favorable characteristics should lead to clinical treatments that are more effective and safer for the patients.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153340/1/wilmer_1.pdf