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

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.