It has been recently shown that an additional therapeutic gain may be achieved if a radiotherapy plan is altered over the treatment course using a new treatment paradigm referred to in the literature as spatiotemporal fractionation. Because of the nonconvex and large-scale nature of the corresponding treatment plan optimization problem, the extent of the potential therapeutic gain that may be achieved from spatiotemporal fractionation has been investigated using stylized cancer cases to circumvent the arising computational challenges. This research aims at developing scalable optimization methods to obtain high-quality spatiotemporally fractionated plans with optimality bounds for clinical cancer cases. In particular, the treatment-planning problem is formulated as a quadratically constrained quadratic program and is solved to local optimality using a constraint-generation approach, in which each subproblem is solved using sequential linear/quadratic programming methods. To obtain optimality bounds, cutting-plane and column-generation methods are combined to solve the Lagrangian relaxation of the formulation. The performance of the developed methods are tested on deidentified clinical liver and prostate cancer cases. Results show that the proposed method is capable of achieving local-optimal spatiotemporally fractionated plans with an optimality gap of around 10%–12% for cancer cases tested in this study. Summary of Contribution: The design of spatiotemporally fractionated radiotherapy plans for clinical cancer cases gives rise to a class of nonconvex and large-scale quadratically constrained quadratic programming (QCQP) problems, the solution of which requires the development of efficient models and solution methods. To address the computational challenges posed by the large-scale and nonconvex nature of the problem, we employ large-scale optimization techniques to develop scalable solution methods that find local-optimal solutions along with optimality bounds. We test the performance of the proposed methods on deidentified clinical cancer cases. The proposed methods in this study can, in principle, be applied to solve other QCQP formulations, which commonly arise in several application domains, including graph theory, power systems, and signal processing.

The majority of cancer-related fatalities are due to metastatic disease. Chemotherapeutic agents are administered along with radiation in chemoradiotherapy (CRT) to control the primary tumor and systemic disease such as metastasis. This work introduces a mathematical model of CRT treatment scheduling to obtain optimal drug and radiation protocols with the objective of minimizing metastatic cancer cell populations at multiple potential sites while maintaining a desired level of control on the primary tumor. Dynamic programming framework is used to determine the optimal radiotherapy fractionation regimen and the drug administration schedule. We design efficient DP data structures and use structural properties of the optimal solution to reduce the complexity of the resulting DP algorithm. We derive closed-form expressions for optimal chemotherapy schedules in special cases. The results suggest that if there is only an additive and spatial cooperation between the chemotherapeutic drug and radiation with no interaction between them, then radiation and drug administration schedules can be decoupled. In that case, regardless of the chemo- and radio sensitivity parameters, the optimal radiotherapy schedule follows a hypofractionated scheme. However, the structure of the optimal chemotherapy schedule depends on model parameters such as chemotherapy-induced cell kill at primary and metastatic sites, as well as the ability of primary tumor cells to initiate successful metastasis at different body sites. In contrast, an interactive cooperation between the drug and radiation leads to optimal split-course concurrent CRT regimens. Additionally, under dynamic radio sensitivity parameters due to the reoxygenation effect during therapy, we observe that it is optimal to immediately start the chemotherapy and administer a few large radiation fractions at the beginning of the therapy, while scheduling smaller fractions in later sessions. We quantify the trade-off between the new and traditional objectives of minimizing the metastatic population size and maximizing the primary tumor control probability, respectively, for a cervical cancer case. The trade-off information indicates the potential for significant reduction in the metastatic population with minimal loss in the primary tumor control.

Beam-on time is an important measure of the delivery efficiency in intensity-modulated radiation therapy (IMRT). Traditionally, minimizing beam-on time has been postponed until the leaf sequencing stage, where the treatment plan quality is already determined and fixed. However, there is a trade-off between the beam-on time and the treatment plan quality. The aim of this study is to incorporate the beam-on time into the treatment plan optimization stage using a direct aperture optimization approach that allows for explicitly quantifying the trade-off. The proposed approach can provide clinicians with valuable information for each patient case so that they can design clinically attractive yet efficient treatment plans. Using the special structure of the problem, we propose an exact solution approach that sequentially characterizes segments of the Pareto-efficient frontier. In addition, an approximate solution technique that is applicable to more classes of evaluation criteria is developed. Our approximate technique is tested on clinical cancer cases, and its performance is compared with the general approximation techniques that are available for convex bicriteria optimization problems. The results of our experiments validate that our approach can achieve a more accurate representation of the Pareto-efficient frontier with less computational effort.