Implementation and validation of the method for the energy spectra reconstruction of electron beams generated by the AQURE mobile accelerator.

Background: The energy spectrum is the main component of the Monte Carlo model of the electron beam. One possible method to obtain it is a backward reconstruction from the measured depth dose distribution, owing to solving the inverse first-degree Fredholm integral equation with appropriate regularisation. This study aimed to reconstruct and validate energy spectra for mobile intraoperative accelerators. Materials and methods: The Geant4 package was used to simulate percentage depth dose (PDD) distributions. The micro-Diamond detector and the BeamScan water phantom were used to measure PDD. 160 PDDs were simulated for quasi-monoenergetic beams with energies from 0 to 20 MeV for a 10 cm diameter applicator. Using the simulated and measured PDDs, energy spectra were reconstructed for all available nominal energies by solving the inverse Fredholm equation. A single Gaussian peak was used as a reference solution, and the regularisation parameter λ was set to 0.05. Obtained spectra were used to simulate PDD for 5 and 6 cm applicators and compared with the measurements. Results: Simulated and measured PDDs were compared using the gamma analysis method with 2% DD and 2 mm distance to agreement (DTA) criteria. Measured and simulated PDDs agree perfectly for the 4 MeV beam. For higher energies, the PDDs agree at all depths except for depths less than 2 mm. Conclusion: The numerical solution of the inverse Fredholm equation with Tikhonov regularisation using simulated annealing optimisation is a reliable method to reconstruct the energy spectrum for electron beams produced by mobile intraoperative accelerators.