Geometric algorithms for leaf sequencing problems in intensity modulated radiation therapy

Intensity-modulated radiation therapy (IMRT) is a modern cancer treatment technique, aiming to deliver a lethal radiation dose to a targeted tumor while sparing the surrounding normal tissues and critical structures. A key to performing IMRT is the accurate and efficient delivery of discrete dose distributions using the linear accelerator (LINAC) and the multileaf collimator (MLC). In this thesis, we study the static leaf sequencing (SLS) problems that arise in IMRT delivery, whose goal is to compute a treatment plan that determines the delivery of prescribed dose distributions in the minimum amount of time. Existing leaf sequencing algorithms, both in commercial planning systems and in medical literature, are all heuristics and do not guarantee any good quality of the computed treatment plans, which in many cases result in prolonged delivery time and compromised treatment quality. In this thesis, we present several new MLC leaf sequencing algorithms and software. Our new algorithms, based on a novel unified approach and geometric optimization techniques, are very efficient and guarantee the optimal quality of the output treatment plans. Our ideas include formulating the leaf sequencing problems as computing shortest paths, maximum matchings, and path covers in a weighted directed acyclic graph and building the graph by computing optimal bipartite matchings and minimum cost flows on various geometric objects. Specifically, we have developed algorithms for the SLS problem in one, two, and three dimensions, and with machine delivery error control and MLC model generalizations. We have also studied the impact of the various MLC mechanical constraints on the delivery time, which may provide insights into the design of future MLC systems. Comparisons between our SLS software and commercial treatment planning systems and well-known SLS algorithms in medical literature have shown significant improvements. The IMRT plans produced by our SLS software not only take significantly shorter delivery times (up to 75% less), but also have a much better treatment quality. This proves the clinical feasibility of our software and has led to its use for treating cancer patients in the Department of Radiation Oncology, University of Maryland Medical Center, Baltimore, MD and the Helen P. Denit Cancer Center, Montgomery General Hospital, Olney, MD.