Biologically-based radiation therapy planning and adjustable robust optimization

Radiation therapy is one of the main treatment modalities for various different cancer types. One of the core components of personalized treatment planning is the inclusion of patient-specific biological information in the treatment planning process. Using biological response models, treatment parameters such as the treatment length and dose distribution can be tailored, and mid treatment biomarker information can be used to adapt the treatment during its course. These additional degrees of freedom in treatment planning lead to new mathematical optimization problems. This thesis studies various optimization aspects of biologically-based treatment planning, and focuses on the influence of uncertainty. Adjustable robust optimization is the main technique used to study these problems, and is also studied independently of radiation therapy applications

Pareto Adaptive Robust Optimality via a Fourier-Motzkin Elimination Lens

We introduce the concept of Pareto Adaptive Robust Optimality (PARO) for linear Adaptive Robust Optimization (ARO) problems. A worst-case optimal solution pair of here-and-now decisions and wait-and-see decisions is PARO if it cannot be Pareto dominated by another solution, i.e., there does not exist another such pair that performs at least as good in all scenarios in the uncertainty set and strictly better in at least one scenario. We argue that, unlike PARO, extant solution approaches -- including those that adopt Pareto Robust Optimality from static robust optimization -- could fail in ARO and yield solutions that can be Pareto dominated. The latter could lead to inefficiencies and suboptimal performance in practice. We prove the existence of PARO solutions, and present particular approaches for finding and approximating such solutions. We present numerical results for a facility location problem that demonstrate the practical value of PARO solutions. Our analysis of PARO relies on an application of Fourier-Motzkin Elimination as a proof technique. We demonstrate how this technique can be valuable in the analysis of ARO problems, besides PARO. In particular, we employ it to devise more concise and more insightful proofs of known results on (worst-case) optimality of decision rule structures.Comment: Revised version. 38 pages, 2 figure

Biologically-based radiation therapy planning and adjustable robust optimization

Radiation therapy is one of the main treatment modalities for various different cancer types. One of the core components of personalized treatment planning is the inclusion of patient-specific biological information in the treatment planning process. Using biological response models, treatment parameters such as the treatment length and dose distribution can be tailored, and mid treatment biomarker information can be used to adapt the treatment during its course. These additional degrees of freedom in treatment planning lead to new mathematical optimization problems. This thesis studies various optimization aspects of biologically-based treatment planning, and focuses on the influence of uncertainty. Adjustable robust optimization is the main technique used to study these problems, and is also studied independently of radiation therapy applications

HIFUtk: visual analytics for high intensity focused ultrasound simulation

Magnetic Resonance-guided High Intensity Focused Ultrasound (MR-HIFU) is a novel and non-invasive therapeutic method. It can be used to locally increase the temperature in a target position in the human body. HIFU procedures are helpful for the treatment of soft tissue tumors and bone metastases. In vivo research with HIFU systems poses several challenges, therefore, a flexible and fast computer model for HIFU propagation and tissue heating is crucial. We introduce HIFUtk, a visual analytics environment to define, perform, and visualize HIFU simulations. We illustrate the use of HIFUtk by applying HIFU to a rabbit bone model, focusing on two common research questions related to HIFU. The first question concerns the relation between the ablated region shape and the focal point position, and the second one concerns the effect of shear waves on the temperature distribution in bone. These use cases demonstrate that HIFUtk provides a flexible visual analytics environment to investigate the effects of HIFU in various type of materials