Reconstruction of electron spectra using singular component decomposition

Abstract

Reconstruction of electron spectra of medical accelerators from measured depth dose distributions is an attractive tool for commissioning of a Monte Carlo treatment planning system. However, the reconstruction method is an inverse radiation transport problem which is poorly conditioned, in the sense it may become unstable due to small perturbations in the input data. Predicting the sharp (delta-like) peak in the electron spectrum provides an additional challenge for the numerical reconstruction technique. To improve efficiency and robustness of the reconstruction technique, we developed an algorithm based on a separation of the electron spectrum into singular and regular components. We approximate the singular peak of the spectrum by a narrow weighted Gaussian function. The parameters of this Gaussian function are sought using only the fall-off and toe regions of the depth-dose curve. Analytical representation of the spectral peak by a Gaussian has benefit since only one weight and the mean and variance must be derived from the depth-dose curve instead of multiple spectra weights. The regular part of the spectrum is reconstructed from the residual depth-dose distribution using a variational method combined with a regularization technique to avoid the nonphysical oscillations. The effectiveness of the method is demonstrated by comparing predictions to "benchmark" spectra and depth-dose distributions from Monte Carlo simulation of medical accelerators.

Angular correction in reconstruction of electron spectra from depth dose distributions

“…In our earlier article, 5 we presented similar comparisons except that we avoided the influence of the electron incident angular distribution upon the verification of our optimization algorithms by using depth-dose distributions for reconstruction that were simulated in the same parallel broad geometry as the monoenergetic depth-dose distributions. Therefore the agreement of incident and reconstructed spectra in the low energy region was perfect.…”

“…These procedures are based on the depth-dose data that assumes the electrons were at normal incidence to the surface of the absorbing medium. [2][3][4][5] This assumption is not a good one for clinical electron beams and so the electron spectra produced by a reconstruction procedure invoking this assumption will inherently contain a systematic error. Depthdose distributions from clinical electron beams are most affected in the shallow depth region by incident electrons having a large angular distribution.…”

“…In our first article on electron spectrum reconstruction from depth-dose distribution, 5 we discussed the efficiency of an optimization method for solving the governing integral Fredholm equation of the first kind used in the reconstruction procedure. We showed improved accuracy and robustness of the reconstruction technique when the electron spectrum is separated into singular and regular components.…”

Determinação de Espectros de Energia de Elétrons Clínicos a partir de Curvas de Porcentagem de Dose em Profundidade (PDP) utilizando o Método de Recozimento Simulado Clássico

“…Vários métodos [3][4][5][6][7]10 têm sido desenvolvidos a fim de extrair o espectro de elétrons da curva de PDP do eixo central, fazendo uso da equação (1), a causa de ser este um problema mal-posto 1,310 .…”

Phase space determination from measured dose data for intraoperative electron radiation therapy

“…This is not a strong simplification, as the bulk amount of dose in the region of interest in IOERT comes from the electrons, being the photons a very small fraction and, further, the role of photons will be replaced in the solution PHSP, at least to some extent, by electrons of low energy. In those cases where the photon contribution to the dose may be significant, it can be determined with the methods described in the literature (Faddegon et al 2000, Chvetsov andSandison 2002).…”