A LAPLACE TRANSFORM PAIR MODEL TO DETERMINE BREMSSTRAHLUNG SPECTRA FROM ATTENUATION DATA (RADIATION, X-RAY, SPECTRAL MODELING)

Every x-ray attenuation curve inherently contains all the information necessary to extract the complete energy spectrum of a beam. To date, attempts to obtain accurate spectral information from attenuation data have been inadequate.^ This investigation presents a mathematical pair model, grounded in physical reality by the Laplace Transformation, to describe the attenuation of a photon beam and the corresponding bremsstrahlung spectral distribution. In addition the Laplace model has been mathematically extended to include characteristic radiation in a physically meaningful way. A method to determine the fraction of characteristic radiation in any diagnostic x-ray beam was introduced for use with the extended model.^ This work has examined the reconstructive capability of the Laplace pair model for a photon beam range of from 50 kVp to 25 MV, using both theoretical and experimental methods.^ In the diagnostic region, excellent agreement between a wide variety of experimental spectra and those reconstructed with the Laplace model was obtained when the atomic composition of the attenuators was accurately known. The model successfully reproduced a 2 MV spectrum but demonstrated difficulty in accurately reconstructing orthovoltage and 6 MV spectra. The 25 MV spectrum was successfully reconstructed although poor agreement with the spectrum obtained by Levy was found.^ The analysis of errors, performed with diagnostic energy data, demonstrated the relative insensitivity of the model to typical experimental errors and confirmed that the model can be successfully used to theoretically derive accurate spectral information from experimental attenuation data. ^

Electron intensity modulation for mixed-beam radiation therapy with an x-ray multi-leaf collimator

The current standard treatment for head and neck cancer at our institution uses intensity-modulated x-ray therapy (IMRT), which improves target coverage and sparing of critical structures by delivering complex fluence patterns from a variety of beam directions to conform dose distributions to the shape of the target volume. The standard treatment for breast patients is field-in-field forward-planned IMRT, with initial tangential fields and additional reduced-weight tangents with blocking to minimize hot spots. For these treatment sites, the addition of electrons has the potential of improving target coverage and sparing of critical structures due to rapid dose falloff with depth and reduced exit dose. In this work, the use of mixed-beam therapy (MBT), i.e., combined intensity-modulated electron and x-ray beams using the x-ray multi-leaf collimator (MLC), was explored. The hypothesis of this study was that addition of intensity-modulated electron beams to existing clinical IMRT plans would produce MBT plans that were superior to the original IMRT plans for at least 50% of selected head and neck and 50% of breast cases. Dose calculations for electron beams collimated by the MLC were performed with Monte Carlo methods. An automation system was created to facilitate communication between the dose calculation engine and the treatment planning system. Energy and intensity modulation of the electron beams was accomplished by dividing the electron beams into 2x2-cm2 beamlets, which were then beam-weight optimized along with intensity-modulated x-ray beams. Treatment plans were optimized to obtain equivalent target dose coverage, and then compared with the original treatment plans. MBT treatment plans were evaluated by participating physicians with respect to target coverage, normal structure dose, and overall plan quality in comparison with original clinical plans. The physician evaluations did not support the hypothesis for either site, with MBT selected as superior in 1 out of the 15 head and neck cases (p=1) and 6 out of 18 breast cases (p=0.95). While MBT was not shown to be superior to IMRT, reductions were observed in doses to critical structures distal to the target along the electron beam direction and to non-target tissues, at the expense of target coverage and dose homogeneity. ^