Calculation of stopping-power ratios using realistic clinical electron beams

The Spencer-Attix water/air restricted mass collision stopping-power ratio is calculated in realistic electron beams in the energy range from 5-50 MeV for a variety of clinical accelerators including the Varian Clinac 2100C, the Philips SL75-20, the Siemens KD2, the AECL Therac 20, and the Scanditronix Medical Microtron 50. The realistic clinical beams are obtained from full Monte Carlo simulations of the clinical linear accelerators using the code BEAM. The stopping-power ratios calculated using clinical beams are compared with those determined according to the AAPM and the IAEA protocols which were calculated by using monoenergetic parallel beams. Using the energy-range relationship of Rogers and Bielajew [Med. Phys. 13, 687-694 (1986)] leads to the most consistent picture in which the stopping-power ratios at dmax derived from mono-energetic calculations underestimate the stopping-power ratios calculated with the realistic beam by 0.3% at 5 MeV and up to 1.4% at 20 MeV. The stopping-power ratios at dmax determined according to the AAPM TG-21 protocol (1983) are shown to overestimate the realistic stopping-power ratios by up to 0.6% for a 5-MeV beam and underestimate them by up to 1.2% for a 20-MeV beam. Those determined according to the IAEA (1987) protocol overestimate the realistic stopping-power ratios by up to 0.3% for a 5-MeV beam and underestimate them by up to a 1.1% for a 20-MeV beam at reference depth. The causes of the differences in the stopping-power ratios between the realistic clinical mono-energetic beams are analyzed quantitatively. The changes in the stopping-power ratios at dmax are mainly due to the energy spread of the electron beam and the contaminant photons in the clinical beams. The effect of the angular spread of electrons is rather small except at the surface. Data are presented which give the corrected stopping-power ratios at dmax or reference depth starting from those determined according to protocols for any energy of clinical electron beams with scattering foils. For scanned clinical electron beams the correction to stopping-power ratios determined according to protocols is found to be less than 0.5% at dmax or reference depth for all beam energies studied. We quantify the differences in the stopping-power ratios determined using the depth of 50% ionization level and the depth of 50% dose level. The differences are very small except for very-high-energy beams (50 MeV) where they can be up to 0.8%.