Leaf-sequencing for intensity-modulated arc therapy using graph algorithms

Intensity-modulated arc therapy (IMAT) is a rotational IMRT technique. It uses a set of overlapping or nonoverlapping arcs to create a prescribed dose distribution. Despite its numerous advantages, IMAT has not gained widespread clinical applications. This is mainly due to the lack of an effective IMAT leaf-sequencing algorithm that can convert the optimized intensity patterns for all beam directions into IMAT treatment arcs. To address this problem, we have developed an IMAT leaf-sequencing algorithm and software using graph algorithms in computer science. The input to our leaf-sequencing software includes (1) a set of (continuous) intensity patterns optimized by a treatment planning system at a sequence of equally spaced beam angles (typically 10 degrees apart), (2) a maximum leaf motion constraint, and (3) the number of desired arcs, k. The output is a set of treatment arcs that best approximates the set of optimized intensity patterns at all beam angles with guaranteed smooth delivery without violating the maximum leaf motion constraint. The new algorithm consists of the following key steps. First, the optimized intensity patterns are segmented into intensity profiles that are aligned with individual MLC leaf pairs. Then each intensity profile is segmented into k MLC leaf openings using a k-link shortest path algorithm. The leaf openings for all beam angles are subsequently connected together to form 1D IMAT arcs under the maximum leaf motion constraint using a shortest path algorithm. Finally, the 1D IMAT arcs are combined to form IMAT treatment arcs of MLC apertures. The performance of the implemented leaf-sequencing software has been tested for four treatment sites (prostate, breast, head and neck, and lung). In all cases, our leaf-sequencing algorithm produces efficient and highly conformal IMAT plans that rival their counterpart, the tomotherapy plans, and significantly improve the IMRT plans. Algorithm execution times ranging from a few seconds to 2 min are observed on a laptop computer equipped with a 2.0 GHz Pentium M processor.