Large-Scale Optimization Approaches for Radiation Therapy

Abstract

Radiation therapy treatment planning (RTTP) is a medically important, multistage clinical problem that poses a number of challenges in practice. This daily clinical task is full of highly-complex, large-scale operations research problems which make it difficult to both find and evaluate the highest quality plans. Modern-day planning software is often equipped with reliable but sub-optimal internal calculators and heuristics. While these heuristics may give up on some quality, they are practically and clinically viable for achieving fast results. In an ideal world, however, optimality would not need to be sacrificed in the name of clinical viability.

The goal of this thesis is to move towards the clinical viability of integrating optimal RTTP processes. There are a number of novel frameworks proposed within this document, as well as several first implementations. The largest contribution is a comprehensive look at uncertainty in radiation therapy for breast cancer treatment. In the past, uncertainty has been approached using a number of techniques, including stochastic optimization, robust optimization (RO), and plan-averaging. This thesis advances the robust field, providing an exploration of integrating faster robust approaches into both continuous and integer portions of general RO, as well as the more specific RTTP models. Promising improvements were made in terms of integration at the continuous level, but the results also suggested that the methods were less effective for integration into more complex integer models.

The thesis details a mechanism for trading off some of the conservatism characteristic of RO, for greater expected performance, without sacrificing the robustness guarantees in a light Pareto robust optimal (LPRO) framework. The document includes one of the first studies to include LPRO, and it uses the method to generate high-quality plans for radiation therapy. It also outlines the first integration of tumour-control via conditional value at risk with Pareto and light Pareto robust optimization. The LPRO method is shown to not only work effectively, but to provide meaningful treatment benefit without adding significant complexity to the underlying RO approaches.

The thesis also takes a novel, structural perspective on two notoriously difficult RTTP problems; beam angle optimization (BAO) and direct aperture optimization (DAO). The framework for BAO comes from the field of rotational geometry, and contains the steps taken to derive several potential branch and price sub problems in an effort to improve tractability. The DAO framework is inspired by the field of decision diagrams, and is the first framework to integrate aperture limitation directly into a graphical model, which is hypothesized to make the solution speed far faster and more practical for integrating into clinical planning software.

The final major study regards down-sampling in RTTP. Down-sampling is an approach that is used implicitly in planning software, and performed explicitly in most RTTP operations research papers, however, there is no agreed-upon method to perform this process. A system for comparing down-sampling approaches is introduced along with a small-scale demonstration using patient data. This study is intended to provide the basis for a larger-scale future comparison with more patient data. Finally, the thesis concludes in a proposal for future work in the field of RTTP.