Radiation Therapy Optimization Considering Uncertainties and Biological Effects



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The goal in radiation therapy is to maximize tumor cell killing while minimizing toxic effects on surrounding healthy tissues. A treatment protocol is generally used to decide on the treatment strategy and is a description of the desired radiation dose to the various regions of interest. Treatment planning then aims to find a plan as close to the treatment protocol as possible. Every step of radiation therapy is subject to some types of uncertainties (i.e., set-up uncertainty, patient motion, and tumor shrinkage), which may compromise the quality of a treatment. Therefore, this dissertation focuses primarily on optimization approaches to meet prescription requirements and manage the uncertainties in radiation therapy treatments. First, the problem of satisfying dose-volume constraints (DVCs) in the fluence map optimization (FMO) is explored. DVCs are normally used to prescribe and control the dose to the target and the healthy structures in a treatment protocol. Solving the FMO problem while satisfying DVCs often requires the use of tedious trial-and-error. Therefore, an automatic approach is proposed to satisfy DVCs using a multi-objective linear programming (LP) model for solving beamlet intensities. The plan quality and the satisfaction of the DVCs by the proposed algorithm are compared with two nonlinear approaches: a nonlinear FMO model and a commercial treatment planning system. Numerical results show that the proposed approach successfully improved the target coverage to meet the DVCs, while trying to keep OAR DVCs satisfied. Second, sharp gradients in intensity modulated proton therapy (IMPT) dose distributions can lead to treatment plans that are very sensitive to uncertainties. Robust optimization takes the uncertainties into account and leads to dose distributions that are resilient to uncertainties and of better quality than conventional approaches. The purpose of this study is to evaluate and compare the performance and effectiveness (in terms of plan quality, robustness, and delivery efficiency) of the two robust optimization approaches (worst case dose and minmax) and the conventional planning target volume (PTV)-based optimization using LP and NLP (nonlinear programming) models. The results show that LP-based methods are suitable for less challenging cancer cases where uncertainty scenarios are favorable for LP with tight constraints for finding a feasible solution. Moreover, plans generated using LP-based methods have notably fewer scanning spots than did those created using NLP-based methods, possibly leading to more efficient delivery. Third, A chance constrained programming (CCP) framework is proposed to handle uncertainties in radiation treatment planning that allows constraint violation up to a certain degree as it is the case in practice. The CCP framework can potentially be employed under different distributional assumptions. The goal of a CCP optimization model is to maximize the confidence level of the plans and the homogeneity of the dose distributions. To generalize CCP models, distributionally robust chance constrained programming is proposed when the probability distribution of the random parameter is not completely specified, but is only known to belong to a given class. Computationally tractable second-order cone programming counterparts of robust chance constraints are developed, assuming that only the first and second-order moments or the first-order moment and the support of the uncertain parameters are known. The performance of proposed models is verified by generating plans that are superior in terms of quality and robustness, homogeneity of dose distributions and confidence level of constraints. Lastly, the impact of incorporating variable relative biological effectiveness (RBE) in IMPT planning is investigated. The current practice of considering RBE in IMPT is to use a generic RBE value of 1.1 under all circumstances. However, it is shown that RBE can deviate significantly from this and contribute to unanticipated toxicities and recurrences. Therefore, the variability of RBE is exploited by optimization techniques in treatment planning so that higher RBE is confined within the target and critical structures are better spared compared to conventional planning with fixed RBE. For this purpose, RBE is systematically quantified and used to develop a nonlinear biological treatment planning model that is safer and more efficient. This resulted in improved tumor control when evaluating biologically equivalent dose, without sacrificing OAR sparing, for head and neck cancer patients.



Radiation therapy, Robust optimization, Chance Constrained Programming, Relative Biological Effectiveness, Dose-Volume Histogram, Dose-Volume Constraint


Portions of this document appear in: Zaghian, Maryam, Gino Lim, Wei Liu, and Radhe Mohan. "An automatic approach for satisfying dose-volume constraints in linear fluence map optimization for IMPT." Journal of cancer therapy 5, no. 2 (2014): 198.