Dose-volume-based IMRT fluence optimization: A fast least-squares approach with differentiability

AbstractIn intensity-modulated radiation therapy (IMRT) for cancer treatment, the most commonly used metric for treatment prescriptions and evaluations is the so-called dose-volume constraint (DVC). These DVCs induce much needed flexibility but also non-convexity into the fluence optimization problem, which is an important step in the IMRT treatment planning. Currently, the models of choice for fluence optimization in clinical practice are weighted least-squares models. When DVCs are directly incorporated into the objective functions of least-squares models, these objective functions become not only non-convex but also non-differentiable. This non-differentiability is a problem when software packages designed for minimizing smooth functions are routinely applied to these non-smooth models in commercial IMRT planning systems. In this paper, we formulate and study a new least-squares model that allows a monotone and differentiable objective function. We devise a greedy approach for approximately solving the resulting optimization problem. We report numerical results on several clinical cases showing that, compared to a widely used existing model, the new approach is capable of generating clinically relevant plans at a much faster speed. This improvement can be more than one-order of magnitude for some large-scale problems

On a Problem of Weighted Low-Rank Approximation of Matrices

We study a weighted low rank approximation that is inspired by a problem of constrained low rank approximation of matrices as initiated by the work of Golub, Hoffman, and Stewart (Linear Algebra and Its Applications, 88-89(1987), 317-327). Our results reduce to that of Golub, Hoffman, and Stewart in the limiting cases. We also propose an algorithm based on the alternating direction method to solve our weighted low rank approximation problem and compare it with the state-of-art general algorithms such as the weighted total alternating least squares and the EM algorithm