title: An improved physics-based approach for unfolding megavoltage bremsstrahlung spectra using transmission analysis.
abstract: OBJECTIVE
  To develop a physics-based approach to improve the accuracy and robustness of the ill-conditioned problem of unfolding megavoltage bremsstrahlung spectra from transmission data.
  
  
  METHODS
  Spectra are specified using a rigorously-benchmarked functional form. Since ion chambers are the typical detector used in transmission measurements, the energy response of a Farmer chamber is calculated using the EGSnrc Monte Carlo code, and the effect of approximating the energy response on the accuracy of the unfolded spectra is studied. A proposal is introduced to enhance spectral sensitivity by combining transmission data measured with multiple detectors of different energy response and by combining data from multiple attenuating materials. Monte Carlo methods are developed to correct for nonideal exponential attenuation (e.g., scatter effects and secondary attenuation). The performance of the proposed methods is evaluated for a diverse set of validated clinical spectra (3.5-25 MV) using analytical transmission data with simulated experimental noise.
  
  
  RESULTS
  The approximations commonly used in previous studies for the ion-chamber energy response lead to significant errors in the unfolded spectra. Of the configurations studied, the one with best spectral sensitivity is to measure four full transmission curves using separate low-Z and high-Z attenuators in conjunction with two detectors of different energy response (the authors propose a Farmer-type ion chamber, once with a low-Z, and once with a high-Z buildup cap material), then to feed the data simultaneously to the unfolding algorithm. Deviations from ideal exponential attenuation are as much as 1.5% for the smallest transmission signals, and the proposed methods properly correct for those deviations. The transmission data with enhanced spectral sensitivity, combined with the accurate and flexible spectral functional form, lead to robust unfolding without requiring a priori knowledge of the spectrum. Compared with the commonly-used methods, the accuracy is improved for the unfolded spectra and for the unfolded mean incident electron kinetic energy by at least factors of three and four, respectively. With simulated experimental noise and a lowest transmission of 1%, the unfolded energy fluence spectra agree with the original spectra with a normalized root-mean-square deviation, %Δ(ψ), of 2.3%. The unfolded mean incident electron kinetic energies agree, on average, with the original values within 1.4%. A lowest transmission of only 10% still allows unfolding with %Δ(ψ) of 3.3%.
  
  
  CONCLUSIONS
  In the presence of realistic experimental noise, the proposed approach significantly improves the accuracy and robustness of the spectral unfolding problem for all therapy and MV imaging beams of clinical interest.
authors.affiliation: Department of Physics, Carleton University, Ottawa, Ontario, Canada. eali@physics.carleton.ca
authors.forename: E S M
authors.initials: ES
authors.lastname: Ali
authors.forename: D W O
authors.initials: DW
authors.lastname: Rogers
mesh_terms: D004583:Electrons; D017785:Photons; D010825:Physics / Q000379:methods*; D013057:Spectrum Analysis