Empirical modeling of the percent depth dose for megavoltage photon beams

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 p of buildup-tail function can be used to characterize the Collimator Scatter Factor (So 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 d/root d(2)+n with the main parameter of d (depth in water) and n, while the tail function was in the form of e(-mu d) and was composed by an exponential function with the main parameter of d and mu. The PDD was the product of buildup and tail function, PDD = d/root d(2)+n . e(-mu d). The PDD of four-photon energies was characterized by the buildup-tail function by adjusting the parameters n and mu. The S-c of 6 MV and 10 MV can then be expressed simply by the modeling parameters n and mu. 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 mu can be treated as attenuation coefficient in tail function and decreases when photon energy increased. The fitting results of parameters p 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 mu obtained from the fitted buildup-tail function were applied into an analytical formula of S-c = n(E) (S)(0.63)mu to get the collimator to scatter factor S-c for 6 and 10 MV photon beam, while n(E), mu(E), S denotes n, mu at photon energy E of field size S, respectively. The calculated S-c 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 S-c factors for some clinical requirements. The modeling parameters n and mu can be used to predict the S-c 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.