A time discretized mathematical model and heuristic for sliding windows IMRT

Sliding-window intensity-modulated radiation therapy is a cancer treatment method whereby a high-energy beam is modulated by a multileaf collimator that uses pairs of opposing leaves that move unidirectionally across the beam field to irradiate cancerous tissue. We formulate a mixed-integer nonlinear (MINLP) program to optimize the delivery of treatment, wherein the optimal motion of the leaves is determined. To alleviate the complexity of the proposed model, we present a linear reformulation and a rapid heuristic that produces high-quality feasible solutions. Using retrospective patient datasets, we demonstrate that the proposed model generates a valid sequence of apertures that account for all deliverability criteria and can, therefore, be directly implemented in clinical treatment planning software to assist planners. We also show, empirically, that the heuristic provides high-quality feasible solutions that can be used as a strong incumbent to warm-start the original mathematical model.