Relationship between %dd(10)x and stopping-power ratios for flattening filter free accelerators: a Monte Carlo study

The relationship between the photon beam quality specifier %dd(10)x and the Spencer-Attix water water to air restricted mass collision stopping-power ratio, (L/rho))air(water), is studied using Monte Carlo simulation with realistic beams in contrast to the previously used realistic but uniform spectra from an isotropic point source. The differences between accelerators with and without flattening filters are investigated since flattening filter free accelerators appear to be useful for IMRT. Our results show that the standard relationship between %dd(10)x and (L/rho)air(water), which is used in the TG-51 protocol to calculate the quality conversion factor kQ, is acceptable for beams with or without a flattening filter with a maximum error of 0.4%, although a fit to the new data would reduce the maximum error to 0.2%. Reasons for differences between the individual values of %dd(10)x and (L/ rho)air(water) with and without a flattening filter are studied. Specifically the differences due to the softening of the beam, the change in shape of the profile, and the inclusion of radial variations in the photon energy spectra, are investigated. It is shown that if TPR10(20) is used as a beam quality specifier, there are two different relationships between TPR10(20) and (L/rho)air(water) which differ by 0.4%-1%. When using TPR10(20) as a beam quality specifier in a beam without a flattening filter, one should subtract 0.5% from the value of kQ for a given value of TPR10(20).