Modeling scatter-to-primary dose ratio for megavoltage photon beams

Purpose: A three-parameter semiempirical model for scatter-to-primary dose ratio (SPR) is proposed to fit PDD (or TPR) and S_p beam data. The SPR formula proposed in this study is more accurate than the previously published formula utilizing two parameters, especially for lower energy megavoltage photon beams, because the effect of backscattered photons is now taken into account. Methods: Monte Carlo (MC) calculated SPR for photon energy spectrum between ⁶⁰Co and 24 MV are used to evaluate the accuracy of the models. Based on fitting the MC data, the dependence of the SPR parameters (a₀, w₀, d₀) with the attenuation coefficients of the photon beams is obtained and they were incorporated into the authors' optimization routine. The ability of the optimization routine to fit measured clinic data is examined for photon energies ranging from ⁶⁰Co to 25 MV for all major cobalt and linear accelerator manufacturers. Results: The authors' model successfully fits the measured photon beam data for field size (E/3-40 cm), where E is photon energy in MV and for clinically usable depths, d_max to 20 cm for ⁶⁰co, d_max to 30 cm for 4 MV, and d _max to 40 cm for 6 MV and higher photon energies. The maximum error among these fits is better than 2% for photon energies above ⁶⁰co Conclusions: The new SPR formula, along with the optimization routine, can serve as an efficient tool for performing quality control of x-ray beam data that conforms to AAPM Radiation Therapy Committee TG40 and Therapy Physics Committee TG142 reports on beam data requirement.