Distributionally Robust Chance Constraints for Radiotherapy Treatment Planning under Geometric Uncertainty

Abstract

Radiation therapy is a popular treatment modality for cancer which benefits from optimization. Mainstream approaches define a margin around the tumor called the planning target volume (PTV) to account for changes in patient anatomy throughout the course of treatment. However, the PTV concept does not adequately address uncertainty in the position of the tumor or in the probability distribution of its shifts.

In this thesis, we develop a distributionally robust optimization framework for radiation therapy treatment planning under inter-fraction geometric uncertainty of the clinical target volume (CTV) where the underlying probability distribution of rigid shifts is not well known. To achieve this, we begin with a deterministic model, then augment it using chance-constrained optimization. Next, we consider an ambiguous chance constraint and apply its robust reformulation to treatment planning models.

We first apply these three frameworks to a basic fluence map optimization model. Then, we include machine deliverability constraints and formulate a direct aperture optimization model. Due to the large-scale combinatorial structure, these models cannot be solved efficiently at a clinical scale, making them unusable for modern treatment approaches such as volumetric-modulated arc therapy. Therefore, we extend a sequential convex programming algorithm to include robust and distributionally robust optimization.

Through experiments on two lung cancer patients, we show that the novel distributionally robust treatment planning model can achieve better tumor coverage than the robust model as well as better healthy tissue sparing than the standard PTV approach. We also show that adding robust and distributionally robust optimization does not degrade the quality of the convex approximation. We conclude with a discussion on limitations and present ideas for future research projects.