Inverse reconstruction of energy spectra of clinical electron beams using the generalized simulated annealing method

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In radiotherapy, the electron spectrum should be considered for accurate dose calculation. There are mainly three approaches to obtain the central axis electron energy spectrum, namely: (i) radiation source modeling; (ii) direct measurement and (iii) inverse reconstruction. To determine the electron spectra, it is proposed to use the inverse reconstruction approach. Inverse reconstruction consists in deriving the electron spectra from measured depth dose distributions. Since inverse reconstruction is a poorly conditioned problem the Tikhonov regularization is implemented to avoid the nonphysical oscillations inherent to this problem. Generalized simulated annealing method is used for minimizing the Tikhonov function in order to find the electron spectra. The effectiveness of the spectral reconstruction is verified by the gamma index criterion. Gamma Index defines the degree of agreement between two depth-dose distributions based on predefined tolerances in terms of distance-to-agreement (DTA) and difference dose (DD). Results show a good agreement between provided (measured in a water phantom) and reproduced (simulated from a reconstructed spectrum) depth dose curves within the gamma index tolerance level defined by >95% passing rate with 1% difference dose/1 mm distance to agreement. In addition, it is possible to evidence an acceptable agreement between provided and reproduced dose profiles according to >95% with 2%/2 mm for every beam, excepting the lowest energy beam. Therefore, it is concluded that generalized simulated annealing is able to reconstruct central-axis electron spectra incident on water phantom surface within restrictive limits of gamma index clinical acceptance.