Three Essays on Radiotherapy Treatment Planning Optimization

Radiation therapy is one of the most common and effective methods of treating cancer. There are two main types: external and internal. External to the patient, a linear accelerator aims beams of radiation toward the patient; internal to the patient, radioactive sources are placed temporarily or permanently at the treatment site to deposit dose locally. Both methods of treatment can deliver complex dose distributions to a patient. The radiation damages both tumorous tissue and nearby healthy organs; treatment planning optimization determines how to deliver a dose distribution that maximizes tumor kill while sparing nearby healthy organs as much as possible. This thesis studies three treatment planning problems: the first two are in the context of external radiation therapy and the third is in the context of internal radiation therapy. Conventional planning is based on only the physical geometry of the patient anatomy. In chapter II, we propose two models that incorporate (additional) liver function information for planning liver cancer treatment to preserve as much post-treatment liver function as possible and compare this to a conventional approach that ignores liver function information. Conventional plans assume the patient geometry does not change between the time of patient imaging and later treatments. Although the patient geometry can be updated at treatment for plan adaptation, current practice may lead to plans that result in significantly worse quality than originally intended due to its myopic nature. In chapter III, we propose a model that produces a plan that caters to each potential patient geometry while considering both day-of and cumulative impact. In high-dose rate brachytherapy, the patient undergoes anesthesia due to the need to implant catheters for radiation source placement before planning. Consideration of multiple conflicting criteria in treatment planning results in challenging optimization problems. Current commercial systems require iterative guess-and-checking of optimization input parameters to make trade-offs among criteria, but a plan must be finalized quickly to minimize anesthesia administration. In chapter IV, we develop a practical optimization engine that generates a trade-off surface and feeds into a graphical user interface that provides the clinician more control to make trade-offs without trial-and-error optimizations.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/140827/1/vwwu_1.pd

Reducing Conservatism in Pareto Robust Optimization

Robust optimization (RO) is a sub-field of optimization theory with set-based uncertainty. A criticism of this field is that it determines optimal decisions for only the worst-case realizations of uncertainty. Several methods have been introduced to reduce this conservatism. However, non of these methods can guarantee the non-existence of another solution that improves the optimal solution for all non-worse-cases. Pareto robust optimization ensures that non-worse-case scenarios are accounted for and that the solution cannot be dominated for all scenarios. The problem with Pareto robust optimization (PRO) is that a Pareto robust optimal solution may be improved by another solution for a given subset of uncertainty. Also, Pareto robust optimal solutions are still conservative on the optimality for the worst-case scenario. In this thesis, first, we apply the concept of PRO to the Intensity Modulated Radiation Therapy (IMRT) problem. We will present a Pareto robust optimization model for four types of IMRT problems. Using several hypothetical breast cancer data sets, we show that PRO solutions decrease the side effects of overdosing while delivering the same dose that RO solutions deliver to the organs at risk. Next, we present methods to reduce the conservatism of PRO solutions. We present a method for generating alternative RO solutions for any linear robust optimization problem. We also demonstrate a method for determining if an RO solution is PRO. Then we determine the set of all PRO solutions using this method. We denote this set as the ``Pareto robust frontier" for any linear robust optimization problem. Afterward, we present a set of uncertainty realizations for which a given PRO solution is optimal. Using this approach, we compare all PRO solutions to determine the one that is optimal for the maximum number of realizations in a given set. We denote this solution as a ``superior" PRO solution for that set. At last, we introduce a method to generate a PRO solution while slightly violating the optimality of the optimal solution for the worst-case scenario. We define these solutions as ``light PRO" solutions. We illustrate the application of our approach to the IMRT problem for breast cancer. The numerical results present a significant impact of our method in reducing the side effects of radiation therapy

Personalized Medicine in Chronic Disease Management.

Chronic diseases are persistent medical conditions which affect half of all adults in the United States. The nature of these long-term chronic conditions present monitoring and treatment challenges to practicing clinicians and medical researchers: (1) how to use information learned about each patient's disease characteristics over time to tailor monitoring and treatment decisions, (2) how to make sequential decisions when each decision has strong implications for future decisions, and (3) how to incentivize adherence to prescribed medications. By combining operations research with the principles of personalized medicine, this work develops novel mathematical models to answer high impact clinical questions faced when managing patients with chronic conditions. We begin our research by understanding how information about a single patient can be used to personalize the patient's forecasted disease dynamics and likelihood of disease progression. Next, we consider how models of heterogeneity in disease characteristics and patient behavior can be embedded within an optimization framework to design individualized treatment plans. Finally, we develop a model for copayment restructuring to improve patient adherence to individualized treatment plans.PhDIndustrial and Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111447/1/schellg_1.pd

Opportunity Loss Minimization and Newsvendor Behavior

To study the decision bias in newsvendor behavior, this paper introduces an opportunity loss minimization criterion into the newsvendor model with backordering. We apply the Conditional Value-at-Risk (CVaR) measure to hedge against the potential risks from newsvendor’s order decision. We obtain the optimal order quantities for a newsvendor to minimize the expected opportunity loss and CVaR of opportunity loss. It is proven that the newsvendor’s optimal order quantity is related to the density function of market demand when the newsvendor exhibits risk-averse preference, which is inconsistent with the results in Schweitzer and Cachon (2000). The numerical example shows that the optimal order quantity that minimizes CVaR of opportunity loss is bigger than expected profit maximization (EPM) order quantity for high-profit products and smaller than EPM order quantity for low-profit products, which is different from the experimental results in Schweitzer and Cachon (2000). A sensitivity analysis of changing the operation parameters of the two optimal order quantities is discussed. Our results confirm that high return implies high risk, while low risk comes with low return. Based on the results, some managerial insights are suggested for the risk management of the newsvendor model with backordering

Robust Direct Aperture Optimization Methods for Cardiac Sparing in Left-Sided Breast Cancer Radiation Therapy

Designing conformal and equipment-compatible radiation therapy plans is essential for ensuring high-quality treatment outcomes for cancer patients. Intensity modulated radiation therapy (IMRT) is a commonly-used method of radiation delivery for cancer patients, wherein beams of radiation are individually contoured to cover a patient’s tumour cells while avoiding healthy cells and organs. In IMRT for left-sided breast cancer, the goal is to irradiate all cells in the breast tissue while avoiding the neighbouring, and extremely radiation-sensitive, heart cells. To add to the complexity of this treatment, the entire dose must be delivered while the patient is breathing, causing the location of the heart and target organs to move and deform unpredictably. The search for a plan that is of the highest quality for a specified set of parameters is called treatment plan optimization. One method of treatment plan optimization that provides an optimal radiation distribution, even under the worst-case realization of a patient’s motion uncertainty, uses a framework called robust optimization. A drawback of using this robust optimization framework, however, is that it does not immediately output physically deliverable IMRT plans. Rather, a subsequent, non-trivial post-processing phase must be applied to the output intensity distributions in order to generate an equipment-compatible plan; a process which can substantially degrade the treatment quality. In this thesis, a holistic approach that combines enforcement of delivery constraints with robust optimization is introduced. The process for creating deliverable plans is called direct aperture optimization (DAO), and the combined model is called robust DAO (RDAO). Novel modelling strategies for integrating the DAO requirements into a robust framework are presented, leading to a large-scale difficult-to-solve mixed integer programming problem. To contend with the complexity of the problem, additional modelling approaches are suggested for improving solution efficiency. These approaches include a hybrid heuristic-optimization technique, which provides good quality, but non-optimal treatment plans. Clinicians may use the output of this hybrid technique as is, or apply it as a warm start for the RDAO model. The models are implemented in C++ and CPLEX and results are presented, first using a one-dimensional phantom, and then a three-dimensional clinical patient dataset. While the full RDAO model is quite time-consuming to run, high-quality plans are ultimately produced. These plans are both clinically deliverable and mitigate the risk of underdosing a patient’s cancerous cells under motion uncertainty, demonstrating their value over plans that did not account for motion uncertainty

Optimization Problems in Radiation Therapy Treatment Planning.

Radiation therapy is one of the most common methods used to treat many types of cancer. External beam radiation therapy and the models associated with developing a treatment plan for a patient are studied. External beams of radiation are used to deliver a highly complex so-called dose distribution to a patient that is designed to kill the cancer cells while sparing healthy organs and normal tissue. Treatment planning models and optimization are used to determine the delivery machine instructions necessary to produce a desirable dose distribution. These instructions make up a treatment plan. This thesis studies four problems in radiation therapy treatment plan optimization. First, treatment planners generate a plan with a number of competing treatment plan criteria. The relationship between criteria is not known a priori. A methodology is developed for physicians and treatment planners to efficiently navigate a clinically relevant region of the Pareto frontier generated by trading off these different criteria in an informed way. Second, the machine instructions for intensity modulated radiation therapy, a common treatment modality, consist of the locations of the external beams and the non-uniform intensity profiles delivered from each of these locations. These decisions are traditionally made with separate, sequential models. These decisions are integrated into a single model and propose a heuristic solution methodology. Third, volumetric modulated arc therapy (VMAT), a treatment modality where the beam travels in a coplanar arc around the patient while continuously delivering radiation, is a popular topic among optimizers studying treatment planning due to the difficult nature of the problem and the lack of a universally accepted treatment planning method. While current solution methodologies assume a predetermined coplanar path around the patient, that assumption is relaxed and the generation of a non-coplanar path is integrated into a VMAT planning algorithm. Fourth, not all patient information is available when developing a treatment plan pre-treatment. Some information, like a patient's sensitivity to radiation, can be realized during treatment through physiological tests. Methodologies of pre-treatment planning considering adaptation to new information are studied.PhDIndustrial and Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113366/1/troylong_1.pd