Determination of the beam quality index of high-energy photon beams under nonstandard reference conditions

At some modern radiotherapy machines it is not possible to achieve reference conditions for the measurement of beam quality indices used in dosimetry codes of practice, such as IAEA TRS-398 and AAPM TG-51. This work aims at providing self-consistent and simpler expressions and more accurate fits for a limited range of beams of interest than have been proposed previously for deriving these beam quality indices from measurements.

The starting point is a formula proposed by Sauer [Med. Phys. 36, 4168-4172 (2009)] for deriving the beam quality index used in IAEA TRS-398, TPR(20,10), from a measurement of the tissue phantom ratio at depths of 20 cm and 10 cm in water for an s × s cm(2) (equivalent) square field, TPR(20,10)(s). First, a self-consistent version of this formula is established followed by a simpler version by making a linear approximation. A similar approach is proposed to derive the beam quality index used in AAPM TG-51, %dd(10)(X), from a measurement of PDD(10)(s), the percentage depth dose at 10 cm for a square field with size s. All models were fitted to subsets of relevant data from BJR supplement 25.

The linear models for TPR(20,10)(s) and exponential models for PDD(10)(s) as a function of the (equivalent) square field size can reproduce the beam quality within 0.3% and beam quality correction factors within 0.05% for square field sizes ranging from 4 cm to 12 cm and nominal photon energies from 4 MV to 12 MV. For higher energy beams the errors are only slightly worse but for %dd(10)(X), an additional uncertainty component has to be considered for the electron contamination correction.

The models proposed here can be used in practical recommendations for the dosimetry of small and nonstandard fields.