Coupled Path Planning, Region Optimization, and Applications in Intensity-Modulated Radiation Therapy

The couple path planning (CPP) problem seeks the motion paths of the leaves of a multileaf collimator, to optimally reproduce the prescribed dose in intensity-modulated radiation therapy (IMRT). We study two versions of the CPP problem, constrained and unconstrained CPP, based on whether the starting and ending locations of the sought paths are prespecified. The unconstrained CPP problem models the leaf sequencing problem in dynamic IMRT delivery, while the set of all constrained CPP problem instances, in which all combinations of the starting and ending locations are considered, plays a key role in an emerging IMRT technique called arc-modulated radiation therapy. We give efficient algorithms for both the constrained and unconstrained CPP problems, and for computing the set of all constrained CPP problem instances. Our results are based on several new ideas and geometric observations, and substantially improve the solutions based on standard techniques. Implementation results show that our CPP algorithms run fast and produce better IMRT treatment plans than current methods.