A fast inverse direct aperture optimization algorithm for intensity‐modulated radiation therapy

PURPOSE: The goal of this work was to develop and evaluate a fast inverse direct aperture optimization (FIDAO) algorithm for IMRT treatment planning and plan adaptation. METHODS: A previously proposed fluence map optimization algorithm called fast inverse dose optimization (FIDO) was extended to optimize the aperture shapes and weights of IMRT beams. FIDO is a very fast fluence map optimization algorithm for IMRT that finds the global minimum using direct matrix inversion without unphysical negative beam weights. In this study, an equivalent second-order Taylor series expansion of the FIDO objective function was used, which allowed for the objective function value and gradient vector to be computed very efficiently during direct aperture optimization, resulting in faster optimization. To evaluate the speed gained with FIDAO, a proof-of-concept algorithm was developed in MATLAB using an interior-point optimization method to solve the reformulated aperture-based FIDO problem. The FIDAO algorithm was used to optimize four step-and-shoot IMRT cases: on the AAPM TG-119 phantom as well as a liver, prostate, and head-and-neck clinical cases. Results were compared with a conventional DAO algorithm that uses the same interior-point method but using the standard formulation of the objective function and its gradient vector. RESULTS: A substantial gain in optimization speed was obtained with the prototype FIDAO algorithm compared to the conventional DAO algorithm while producing plans of similar quality. The optimization time (number of iterations) for the prototype FIDAO algorithm vs the conventional DAO algorithm was 0.3 s (17) vs 56.7 s (50); 2.0 s (28) vs 134.1 s (57); 2.5 s (26) vs 180.6 s (107); and 6.7 s (20) vs 469.4 s (482) in the TG-119 phantom, liver, prostate, and head-and-neck examples, respectively. CONCLUSIONS: A new direct aperture optimization algorithm based on FIDO was developed. For the four IMRT test cases examined, this algorithm executed approximately 70-200 times faster without compromising the IMRT plan quality.