Optimization of Radiation Therapy Treatment Planning Considering Setup Uncertainty and Radiobiological Effects

The clinical goal of radiation therapy is to maximize tumor cell killing while minimizing toxic effects on surrounding healthy tissues. A treatment protocol is 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 (Romeijn and Dempsey (2008)). Every step of radiation therapy is subject to some types of uncertainties (i.e., setup uncertainty, patient motion, and tumor shrinkage), which may compromise the quality of treatment. Basically, in treatment planning, a region of the patient where both tumor and organs at risk (OARs) are located with a certain probability is irradiated with a lower dose than the prescribed tumor dose. However, under uncertainty, the nearby healthy organs that should be irradiated by lower dose are always occupied by tumor voxels with a higher dose. Although the more ambitious goal is to damage the tumor cells so as to guarantee total tumor coverage for treatment, severe patient complications can occur when the surrounding healthy tissues receive an excessive amount of the radiation dose. Therefore, it is desired to develop an optimization approach to meet prescription requirements and tackle the uncertainties in radiation therapy treatments. The proposed research attempts to overcome these limitations and find optimal beamlet intensity that will deliver a dose distribution close to the prescribed dose lead to a better sparing of healthy tissues. First, to control the safety of the critical organs at risk during radiation as well as to provide sufficient tumor coverage, a Chance Constrained Programming (CCP) (Charnes and Cooper (1959)) approach is presented to handle setup uncertainty in radiation treatment planning that allows constraint violation up to a certain degree as it is the case in practice. We assume the uncertain dose distribution is governed by a known probability function and demonstrate that the proposed CCP model can solve the treatment planning problems efficiently. Second, a CCP framework for radiation therapy treatment planning is considered, in which the probability distribution of the random dose contribution is not completely specified, but is only known to belong to a given class of distributions. Sometimes, the information on hand for the random parameter might be limited to mean, covariance, and/or support of the uncertain data. In these situations, Distributionally Robust Chance Constrained Programming (DRCCP) (Calafiore and El Ghaoui (2006)) can be considered as a natural way to deal with uncertainties. An explicit convex condition is provided that guarantees the satisfaction of the probabilistic treatment planning constraints for any realization of the distribution within the given class. Third, to systematically quantify the biological effects of radiation beams, a linear energy transfer (LET) is incorporated into the optimization of intensity modulated proton therapy (IMPT) plans. Because increased LET correlates with increased biological effectiveness of protons, high LETs in target volumes and low LETs in critical structures and normal tissues are preferred in an IMPT plan. Conventionally, the IMPT optimization criteria only includes dose-based objectives in which the relative biological effectiveness (RBE) is assumed to have a constant value of 1.1. In this study, we added LET-based objectives for maximizing LET in target volumes and minimizing LET in critical structures and normal tissues. We then explore the effect of this optimization to not only produce satisfactory dose distributions but also to achieve reduced LET distributions (thus lower biologically effective dose distributions) in critical structures and increased LET in target volumes compared to plans created using conventional objectives. Moreover, to effectively treat a cancer patient with radiotherapy, an effective treatment strategy must be in place that considers dose delivery history and the patients’ on-treatment biological changes. However, assessing the biological impacts of radiation on a tumor and the nearby healthy structures is not an easy task. But, the response of the cells to the radiation can be categorized by volume change, and these changes can be investigated by mathematical models that approximate reality. In this study, we seek to understand the importance of considering tumor shrinkage and proliferation during radiation treatment and how this affects the optimal prescribed dose in each fraction. We propose a stochastic sequential optimization structure under setup uncertainty of dose delivery, that optimizes the dose in various fractions of an adaptive radiation therapy treatment plan by comparing the damage in tumor cells against the damage to the normal tissues volumetrically. Thus, while not prescribing specific strategies, this report provides the framework and guidance physicians to make appropriate decisions in implementing a safe and efficient treatment plan in their clinics on an individual patient.