A model predictive control approach for discovering nonstationary fluence-maps in cancer radiotherapy fractionation

We consider an optimization problem in radiotherapy, where the goal is to maximize the biological effect on the tumor of radiation intensity profiles across multiple treatment sessions, while limiting their toxic effects on nearby healthy tissues. We utilize the standard linear-quadratic dose-response model, which yields a nonconvex quadratically constrained quadratic programming (QCQP) formulation. Since nonconvex QCQPs are in general computationally difficult, recent work on this problem has only considered stationary solutions. This restriction allows a convex reformulation, enabling efficient solution. All other generic convexification methods for nonconvex QCQPs also yield a stationary solution in our case. While stationary solutions could be sub-optimal, currently there is no efficient method for finding nonstationary solutions. We propose a model predictive control approach that can, in principle, efficiently discover nonstationary solutions. We demonstrate via numerical experiments on head-and-neck cancer that these nonstationary solutions could produce a larger biological effect on the tumor than stationary.