Mathematic modeling of the dose in water for calculating collimator scatter factor of flattening filter and flattening filter free megavoltage photon beams

This study presents an empirical method to model the percent depth dose (PDD) curves of flattening filter (FF) and FF-free (FFF) high-energy photon beams using a home-generated buildup function and tail function (buildup-tail function) in radiation therapy. The modeling parameters n and μ of the buildup-tail function were used to characterize the collimator scatter factor (Sc). The buildup function was a quadratic function in the form of d/ √(d2 + n) with main parameters of d (depth in water) and n, while the tail function was in the form of e−μd and was composed of an exponential function with d and μ. PDD was the product of buildup-tail function and characterized by the buildup-tail function by adjusting the parameters n and μ. The Sc of 6 and 10 MV in FF and FFF beams can be expressed simply by the modeling parameters n and μ. The main parameter n increases when photon energy increases. Its physical meaning expresses the beam hardening of photon energy in PDD. The parameter μ can be treated as an attenuation coefficient in the tail function, decreasing when photon energy increases. The values of n and μ obtained from the fitted buildup-tail function were applied into an analytical formula of Sc,FF = nE(S)0.63 μ E, Sc,FFF = nE(S)4.45 μ E to get the Sc of 6 and 10 MV in FF and FFF photon beams, with nE, μ E, S denoting n and μ at photon energy E of field size S. The calculated Sc was compared with the measured data and showed agreement, finding that the field difference was size within ±1%. This model can be used to parameterize the Sc for some clinical requirements. The modeling parameters n and μ can be used to predict the Sc in either FF or FFF beams for the treatment monitor unit in double-check dose calculation. The technique developed in this study can also be used for systematic or random errors in the quality assurance program, thus improving the clinical dose computation accuracy for patient treatment.