R₅₀ as a beam quality specifier for selecting stopping‐power ratios and reference depths for electron dosimetry

Abstract

For electron beam reference dosimetry in radiotherapy, it is shown that by choosing the reference depth as dref = 0.6R(50)-0.1 cm, where R50 is the half-value depth in centimeters, the Spencer-Attix water-to-air stopping-power ratio at dref is given by (Llp)airw = 1.2534 - 0.1487 (R50)0.2144. This is derived from data for (Llp)airw obtained from realistic Monte Carlo simulations for 24 clinical beams. The rms deviation of this expression from the Monte Carlo calculations is 0.16%, with a maximum deviation of 0.26%. This approach fully takes into account the spectral differences between real electron beams of the same R50 and allows an absorbed-dose calibration at a standards laboratory to be easily and accurately transferred to a reference clinical beam. Using a single parameter to specify (Llp)airw, rather than the two parameters (R50 and depth) needed when the reference depth is chosen as the depth of dose maximum, has the potential to greatly simplify electron beam dosimetry protocols and allows the use of a similar formalism for photon and electron beam dosimetry. For use in converting a depth-ionization curve into a depth-dose curve, a somewhat less accurate but general expression for (Llp)w(air) as a function of R50 and depth is presented.

Comparison between TG‐51 and TG‐21: Calibration of photon and electron beams in water using cylindrical chambers

“…The discrepancies are somewhat larger than those for photon beams, approaching 2% at 16 MeV. Note the electron stopping power data used in TG‐51 are based on realistic clinical electron beams, 5 whereas the data used in TG‐21 are based on mono‐energetic electrons. This may explain a somewhat larger discrepancy for electrons than that seen for photons.…”

Total skin electron beam therapy using an inclinable couch on motorized table and a compensating filter

“…Thus, we corrected the value that was extrapolated from the h pl that was calculated at the reference depth (d ref ) of various energies in solid phantom by Araki. 10 The stopping power which is an important factor was also calculated from the equation of Burn et al 11 The correction factors of P TP , P pol , and P ion were previously measured. Percentage depth ionization (PDI) was converted to PDD by multiplying various correction factors, which are mentioned above, and stopping power for quality of ionization.…”

TG‐51: Experience from 150 institutions, common errors, and helpful hints

“…For photons it is the question of whether or not the $0.6r_{\text{cav}}$ shift is incorporated. For electrons it is the question of whether the electron stopping‐power data used are from TG‐51 (Burns et al 7 ) or TG‐21 tables (this is discussed later).There is confusing labeling of several chambers in the $k_{\mathrm{normalR}50}^{\prime }$ figures: (i) PR‐06C/G chambers are identified with two groups of chambers in Fig. 5.…”

“…For photons it is the question of whether or not the $0.6r_{\text{cav}}$ shift is incorporated. For electrons it is the question of whether the electron stopping‐power data used are from TG‐51 (Burns et al 7 ) or TG‐21 tables (this is discussed later).…”

“…TG‐51 recommends incorporating updated stopping power ratios from Burns et al 7 This impacts on output at $d_{max}$ because it changes the depth‐dose data. Physicists continue to ask us what the impact would be if they did not convert their clinical depth dose data to incorporate the Burns stopping power data.…”