Electron spectra measurements in linear accelerators via neural network reconstruction from percentage depth dose (PDD) data.

This work presents a novel methodology for the indirect measurement of electron energy spectra produced by a linear accelerator, in which artificial neural networks are applied to solve a first-kind Fredholm integral equation linking percentage depth dose (PDD) curves to the underlying electron energy spectrum in water. A training corpus was generated by convolving mathematically defined spectra with a response matrix obtained via Monte Carlo simulations, and two Multi-Layer Perceptron (MLP) neural networks were trained on this dataset. Subsequently, experimental PDD curves produced by electron beams at nominal energies of 4, 6, and 9 MeV were measured using an Elekta Precise linear accelerator and processed through the trained networks to reconstruct the corresponding electron spectra. The reconstructed spectra were used to simulate PDD curves via Monte Carlo calculations, which were then compared with the measured ones. To evaluate the agreement, two figures of merit were applied: the Normalized Average Relative Difference (NARD) and the Kullback-Leibler Distance, both yielding values below 0.01. In addition, a residual analysis based on z-scores was performed to assess the statistical significance of the discrepancies between measured and simulated PDD curves. This methodology enables accurate spectrum reconstruction using only standard clinical measurements, without requiring access to the internal design of the accelerator, offering a practical tool for beam characterization and quality assurance in radiotherapy. Notably, the neural network implicitly learns to resolve ill-posed and underdetermined problems by approximating their inversion, effectively emulating a generalized Moore-Penrose pseudoinverse in scenarios where the number of unknowns exceeds the number of equations.