Feasibility of a fast inverse dose optimization algorithm for IMRT via matrix inversion without negative beamlet intensities

Abstract

A fast optimization algorithm is very important for inverse planning of intensity modulated radiation therapy (IMRT), and for adaptive radiotherapy of the future. Conventional numerical search algorithms such as the conjugate gradient search, with positive beam weight constraints, generally require numerous iterations and may produce suboptimal dose results due to trapping in local minima. A direct solution of the inverse problem using conventional quadratic objective functions without positive beam constraints is more efficient but will result in unrealistic negative beam weights. We present here a direct solution of the inverse problem that does not yield unphysical negative beam weights. The objective function for the optimization of a large number of beamlets is reformulated such that the optimization problem is reduced to a linear set of equations. The optimal set of intensities is found through a matrix inversion, and negative beamlet intensities are avoided without the need for externally imposed ad-hoc constraints. The method has been demonstrated with a test phantom and a few clinical radiotherapy cases, using primary dose calculations. We achieve highly conformal primary dose distributions with very rapid optimization times. Typical optimization times for a single anatomical slice (two dimensional) (head and neck) using a LAPACK matrix inversion routine in a single processor desktop computer, are: 0.03 s for 500 beamlets; 0.28 s for 1000 beamlets; 3.1 s for 2000 beamlets; and 12 s for 3000 beamlets. Clinical implementation will require the additional time of a one-time precomputation of scattered radiation for all beamlets, but will not impact the optimization speed. In conclusion, the new method provides a fast and robust technique to find a global minimum that yields excellent results for the inverse planning of IMRT.