Column Generation-Based Techniques for Intensity-Modulated Radiation Therapy (IMRT) and Volumetric Modulated Arc Therapy (VMAT) Treatment Planning

The statistics have estimated about 18.1 million cancer cases in 2018 around the world, which is expected to increase to 24 million by 2035. Radiation therapy is one of the most important cancer treatment methods, which about 50% of patients receive during their illness. This method works by damaging the genetic material within cancerous cells and destroying their ability to reproduce. However, normal cells are also affected by radiation; therefore, the treatment should be performed in such a way that it maximizes the dose of radiation to tumors, while simultaneously minimizing the adverse effects of radiations to healthy tissues. The optimization techniques are useful to determine where and how much radiation should be delivered to patient's body. In this project, we address the intensity-modulated radiation therapy (IMRT) as a widelyused external radiotherapy method and also a novel form called volumetric modulated arc therapy (VMAT). In IMRT, a finite number of directions are determined for the beam radiation, while in VMAT, the linear accelerator rotates around the patient's body while the beam is on. These technologies give us the ability of changing the beam shape and the dose rate dynamically during the treatment. The treatment planning problem consists of selecting a delivery sequence of beam shapes, optimizing the dose rate of the beam, and determining the rotation speed of the gantry, if required. In this research, we take advantages of the column generation technique, as a leading optimization method specifically for large-scale problems, to improve the treatment time and non-linear non-convex clinical objectives in VMAT treatment planning, and also develop a new multi-objective column generation framework for IMRT. In the first essay, we develop a novel column generation algorithm optimizing the trade-off between delivery time and treatment quality for VMAT treatment planning. To this end, simultaneous column-and-row generation is developed to relate the configuration of beam apertures in columns to the treatment time restriction in the rows of the model. Moreover, we propose a modified clustering technique to aggregate similar volume elements of the patient's body and efficiently reduce the number of constraints in the model. The computational results show that a high-quality treatment is achievable using a four-thread CPU. In the second essay, we develop an automatic planning approach integrating dose-volume histogram (DVH) criteria, the most common method of treatment evaluation in practice, for VMAT treatment planning. We take advantage of the iterative procedure of column generation to adjust the model parameters during aperture generation and meet nonlinear DVH criteria without considering hard constraints in the model. The results on clinical cases show that our methodology had significant improvement to obtain clinically acceptable plans without human intervention in comparison to simple VMAT optimization. In addition, the comparison to an existing commercial treatment planning system shows the quality of the obtained plans from the proposed method, especially for the healthy tissues, is significantly better while the computational time is less. In the third essay, we address the IMRT treatment planning, which is formulated as a large scale convex optimization problem with simplex feasibility space. We first integrate a novel Frank-Wolfe-based solution approach, so-called Blended Conditional Gradients, into the column generation to improve the computational performance for the method. We then propose a multi-objective column generation technique to directly obtain apertures that approximate an efficient non-dominated set of treatment plans. To this end, we find lower and upper bounds for the Pareto front and generate a column with a pre-assigned or new weight-vector of the objectives, reducing the maximum distance of two bounds. We prove this algorithm converges to the Pareto front. The results in a two-dimensional objective space to find the trade-off plans between the treat of target volumes and sparing the healthy structures show the efficiency of the algorithm to approximate the Pareto front with deliverable treatment plans in about 3 minutes, avoiding a large number of columns. This method is also applicable for other classes of convex optimization problems requiring both column generation and multi-objective optimization.