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

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.

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.

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.

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.