Improved reconstruction methodology of clinical electron energy spectra based on Tikhonov regularization and generalized simulated annealing

Electron beam radiotherapy is the most widespread treatment modality todeal with superficial cancers. In electron radiotherapy, the energy spectrum isimportant for electron beam modelling and accurate dose calculation. Since thepercentage depth-dose (PDD) is a function of the beam’s energy, the reconstruction of the spectrum from the depth-dose curve represents an inverse problem.Thus, the energy spectrum can be related to the depth-dose by means of anappropriate mathematical model as the Fredholm equation of the first kind.Since the Fredholm equation of the first kind is ill-posed, some regularizationmethod has to be used to achieve a useful solution. In this work the Tikhonovregularization function was solved by the generalized simulated annealing optimization method. The accuracy of the reconstruction was verified by thegamma index passing rate criterion applied to the simulated PDD curves forthe reconstructed spectra compared to experimental PDD curves. Results showa good coincidence between the experimental and simulated depth-dose curvesaccording to the gamma passing rate better than 95% for 1% dose difference(DD)/1 mm distance to agreement (DTA) criteria. Moreover, the results showimprovement from previous works not only in accuracy but also in calculationtime. In general, the proposed method can help in the accuracy of dosimetryprocedures, treatment planning and quality control in radiotherapy.