Introduction This study presents an empirical method to model the high-energy photon beam percent depth dose (PDD) curve by using the home-generated buildup function and tail function (buildup-tail function) in radiation therapy. The modeling parameters n and μ of buildup-tail function can be used to characterize the Collimator Scatter Factor (Sc) either in a square field or in the different individual upper jaw and lower jaw setting separately for individual monitor unit check. Methods and materials The PDD curves for four high-energy photon beams were modeled by the buildup and tail function in this study. The buildup function was a quadratic function in the form of dd2+n with the main parameter of d (depth in water) and n, while the tail function was in the form of e−μd and was composed by an exponential function with the main parameter of d and μ. The PDD was the product of buildup and tail function, PDD = dd2+n·e−μd. The PDD of four-photon energies was characterized by the buildup-tail function by adjusting the parameters n and μ. The Sc of 6 MV and 10 MV can then be expressed simply by the modeling parameters n and μ. Results The main parameters n increases in buildup-tail function when photon energy increased. The physical meaning of the parameter n expresses the beam hardening of photon energy in PDD. The fitting results of parameters n in the buildup function are 0.17, 0.208, 0.495, 1.2 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The parameter μ can be treated as attenuation coefficient in tail function and decreases when photon energy increased. The fitting results of parameters μ in the tail function are 0.065, 0.0515, 0.0458, 0.0422 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The values of n and μ obtained from the fitted buildup-tail function were applied into an analytical formula of Sc = nE(S)0.63μE to get the collimator to scatter factor Sc for 6 and 10 MV photon beam, while nE, μE, S denotes n, μ at photon energy E of field size S, respectively. The calculated Sc were compared with the measured data and showed agreement at different field sizes to within ±1.5%. Conclusions We proposed a model incorporating a two-parameter formula which can improve the fitting accuracy to be better than 1.5% maximum error for describing the PDD in different photon energies used in clinical setting. This model can be used to parameterize the Sc factors for some clinical requirements. The modeling parameters n and μ can be used to predict the Sc in either square field or individual jaws opening asymmetrically for treatment monitor unit double-check in dose calculation. The technique developed in this study can also be used for systematic or random errors in the QA program, thus improves the clinical dose computation accuracy for patient treatment.
Introduction: We developed a technique including preventing errors management method capable of dealing with the virtual source position delivered by different carbon ion energies from the pattern of spot scanning beam in this study. Materials and Methods: A homemade large-format complementary metal-oxide-semiconductor (CMOS) sensor and Gaf Chromic EBT3 films were used for the virtual source position measurement. The Gaf films were embedded in a self-designed rectangular plastic frame to tighten the films and set up on a treatment couch for irradiation in the air with the film perpendicular to the carbon ion beam at the nominal source-axis-distance (SAD) as well as upstream and downstream from the SAD. The horizontal carbon ion beam with five energies at a machine opening field size was carried out in this study. The virtual source position was determined mainly with a linear regression by back projecting the full width half maximum (FWHM) to zero at a distance upstream from the various source-film-distance and double checks additionally with a geometric convergent method to avoid any mistakes caused by manual measurement on FWHM. Results: The virtual source position for higher carbon ion energy has an obvious longer distance from the SAD since the more carbon ion beam energy, the less spreading affected by the horizontal and vertical magnetism, therefore, the distance of virtual source positions is decreased from SAD with high to low energy. Conclusion: The method for investigating the virtual source position in the carbon ion beam in this study can also be used for electrons and the proton. We have developed a technique capable of dealing with the virtual source position with a geometric convergent method to avoid any mistakes in spot scanning carbon ion beam.
Purpose. An experimental and mathematical study for determining the effective point of measurement ( P eff ) for a Farmer-type cylindrical chamber in a carbon ion passive scatter beam is presented. Methods. The ionization depth curves measured by the Bragg peak chamber were plotted according to the position of the inner surface of the entrance window, while the Farmer chamber was plotted at the tip of the cylindrical geometric center. The ionization depth curves measured by a cylindrical chamber in the 3D water phantom were then compared with a high-precision parallel-plate PTW Bragg peak chamber for inspecting the upstream shift correction of the cylindrical chamber in the carbon ion beam. A component of the vertical and horizontal integration method and the barrier model, cos φ = 1 − 2 α R L / 1 + α − R L , for analyzing the shift of effective point of measurement in different carbon ion energies and various field sizes, were studied. Results. The shift between the maximum peak of the Bragg peak chamber and the Farmer chamber in a field size of 10 cm × 10 cm with an energy of 330 MeV/u of carbon ion is 2.3 mm. This upstream shift corresponds to 0.744 ± 0.07 r , where r is the Farmer chamber inner radius of 3.05 mm. Carbon ion energy from 120 MeV/u to 400 MeV/u with different field sizes show different shifts of effective point of measurement in a range of 0.649 ± 0.02 r to 0.843 ± 0.06 r of 3 cm × 3 cm at an energy of 400 MeV/u and 10 cm × 10 cm at an energy of 120 MeV/u, respectively. The vertical and horizontal scatter analysis by the barrier model can precisely describe the shift of the effective point of measurement at different carbon ion energies with various field sizes. Conclusions. We conclude that the Farmer chamber can be used for a patient-specific dose verification check in carbon ion beam treatment if P eff is well calibrated.
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