Continuous leaf optimization for IMRT leaf sequencing

Purpose: Conventional step-and-shoot intensity modulated radiation therapy leaf sequencing methods, where a nonhomogeneous fluence map is converted to a set of apertures and associated intensities, assume that target fluence is stratified into a fixed number of discrete levels and/or aperture leaf positions are restricted to a discrete set of locations. These assumptions induce a deviation from the planned fluence map and/or reduce the feasible region of potential plans, respectively. A continuous leaf optimization (CLO) framework is developed as a postprocessing methodology to improve upon conventional leaf sequencing so that the resulting plan avoids these two main drawbacks. Methods: The CLO model directly represents leaf positions and aperture intensities with continuous variables with the goal of reproducing some target fluence profile. Fluence through leaf edges is modeled using the error function, and continuous fluence is approximated using a 0.1 mm discretization across the aperture opening. Conventional leaf sequencing methods provide feasible solutions to the CLO model, and a first-order descent algorithm is used to converge onto a locally optimal solution. Results: As a proof-of-concept, the authors test this framework on 1D (single leaf pair) fluence maps. The CLO model was applied to conventional leaf sequencing and direct aperture optimization solutions. Consistent improvements to existing leaf sequencing methods were found when tested on 232 generated instances of potential target fluence. In addition to improvements in matching the target fluence, the CLO model was able to keep MUs at similar values to the initial conventional sequence. Conclusions: The CLO model can improve upon existing leaf sequencing methods by avoiding the restrictions of fluence stratification and discretized leaf positions. This study lays the foundation for future models and solution methodologies that can incorporate continuous leaf positions explicitly into the treatment planning model.