Reconstruction of electron spectra from depth doses with adaptive regularization

Abstract

Electron spectral reconstruction of medical accelerators from measured depth doses is a practical method for providing the input initial phase space distribution at the patient surface that is required by Monte Carlo treatment planning systems. The posed inverse problem of spectral reconstruction is ill conditioned and this may lead to nonphysical oscillations in the reconstructed spectra. Use of a variational method of solution with a regularization technique removes the oscillations but tends to smooth the sharp (deltalike) energy peak that is a common feature in electron spectra generated by medical accelerators. Because the sharp peak contains a large percentage of the electrons in the spectrum, an accurate estimate of the peak width, height and position is critical to the success of the technique for spectrum reconstruction with regularization. We propose use of an adaptive regularization term as a special form of the general Tichonov regularization function. The variational method with the adaptive regularization term is applied to reconstruct electron spectra for the 6, 9, and 18 MeV electron beams of a Varian Clinac 2100C accelerator and proves to be a very simple, effective and accurate approach. Results using this variational method with adaptive regularization almost perfectly reconstruct electron spectra from depth dose distributions.

Beam modeling and beam model commissioning for Monte Carlo dose calculation‐based radiation therapy treatment planning: Report of AAPM Task Group 157

“…85 The energy distribution has been determined using spectral reconstruction algorithms, which find the spectrum that, when folded with monoenergetic depth dose curves, matches the measured depth dose curve. 48,65,86,87 This approach has been extended to determine multiple parameters of the beam model, including position of the virtual source. 88 The use of measurement-driven beam models obviates the need for beam simulation, and therefore circumvents the potential issues associated with the acquisition of detailed knowledge of the treatment head.…”

Sobre La Posibilidad De Usar El Método De Regularización De Tikhonov Para Reconstruir El Espectro De Energía De Un Haz Clínico De Electrones

“…Este método de regularización tiene por objeto transformar la ecuación integral de primer tipo (mal definida) en la ecuación integral de segundo tipo, (bien definida) [20], pretendiendo amortiguar los errores contenidos en los datos de entrada [22] y así alcanzar una soluciónútil y estable.…”

Beam generation and planar imaging at energies below 2.40 MeV with carbon and aluminum linear accelerator targets

“…This is due to the irregular electron spectra exiting the waveguide. Although the electron energy spectrum exiting the waveguide is often approximated as Gaussian, [14][15][16] in fact it can be highly asymmetric, 14,15 with a sharp decrease in electron population away from the nominal energy. An example of this can be seen in the work by Wei et al, 14 which gives electron spectra reconstructed from depth dose curves.…”

“…Although the electron energy spectrum exiting the waveguide is often approximated as Gaussian, [14][15][16] in fact it can be highly asymmetric, 14,15 with a sharp decrease in electron population away from the nominal energy. An example of this can be seen in the work by Wei et al, 14 which gives electron spectra reconstructed from depth dose curves. The results demonstrate that low-energy electrons, e.g., ranging from 1 to 3 MeV, are present in a 6 MeV spectrum; however, the relative fluence of these electrons is approximately one hundredth of that at the nominal energy.…”