ABSTRACT
Intensity-modulated radiation therapy (IMRT) is a modern cancer treatment technique aiming to deliver a prescribed conformal radiation dose to a target tumor while sparing the surrounding normal tissues and critical structures. In this chapter, we consider a set of combinatorial and geometric problems that arise in IMRT planning and delivery: (1) the static leaf sequencing problem, (2) the static leaf sequencing with error control problem, (3) the field splitting problem, (4) the dose simplification problem, (5) the dynamic leaf sequencing problem, and (6) the single-arc leaf sequencing problem. We discuss new efficient algorithms for these problems. The main ideas of the algorithms are to exploit the underlying geometric and combinatorial properties of the problems and transform them into graph problems such as shortest paths, optimal matchings, maximum flows, multicommodity demand flows, or linear programming problems. Some open problems and promising directions for future research are also given.
