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

Abstract

Electron beam radiotherapy is the most widespread treatment modality to
deal with superficial cancers. In electron radiotherapy, the energy spectrum is
important for electron beam modelling and accurate dose calculation. Since the
percentage 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 an
appropriate mathematical model as the Fredholm equation of the first kind.
Since the Fredholm equation of the first kind is ill-posed, some regularization
method has to be used to achieve a useful solution. In this work the Tikhonov
regularization function was solved by the generalized simulated annealing optimization method. The accuracy of the reconstruction was verified by the
gamma index passing rate criterion applied to the simulated PDD curves for
the reconstructed spectra compared to experimental PDD curves. Results show
a good coincidence between the experimental and simulated depth-dose curves
according to the gamma passing rate better than 95% for 1% dose difference
(DD)/1 mm distance to agreement (DTA) criteria. Moreover, the results show
improvement from previous works not only in accuracy but also in calculation
time. In general, the proposed method can help in the accuracy of dosimetry
procedures, treatment planning and quality control in radiotherapy.