Optimizing the movement of a single absorber for 1D non-uniform dose delivery by (fast) simulated annealing

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Abstract
A new simplified technique for 1D non-uniform dose delivery using a single dynamic absorber, driven by a computer system, has been recently proposed together with a simple analytic algorithm. This technique uses an optimized 'stepped' absorber's speed profile and the generated fluence profile is an approximation of the desired radiation beam. In the case of non-uniform beam profiles with multiple maxima/minima, the original proposed 'stepping algorithm' has some limitations and produces a too rough approximation of the desired profiles. In order to increase the agreement between desired and generated profiles, more sophisticated optimization schemes are required. In this paper we have applied a variant of simulated annealing (SA) as a statistical optimization algorithm to further investigate the possibilities and the limits of the single-absorber technique in the field of 1D intensity modulation. In the current application the cost function used is the mean square root of the percentage differences between desired and generated profiles, the absorber's resting times have been chosen as optimization variables and at each iteration just one variable is randomly changed, adding an incremental 'grain'. A Cauchy generating function is used, different cooling schedules are evaluated; constraints related to our apparatus are introduced and starting annealing parameters are set after some initial optimization tests. The method is tested in reproducing theoretical non-uniform beams, by comparing desired modulated fluence profiles with calculated fluence profiles obtainable with the single absorber after the derivation of optimized speed profiles by the proposed SA approach. The results of these simulations show that the application of the SA method optimizes the single absorber's performance and that clinically important modulated beams useful for conformal radiotherapy can be accurately reproduced.