Determination of scatter factor parameters and electron disequilibrium for monoenergetic photon beams

The tissue-phantom-ratio (TPR) is expressed as the product of the phantom scatter factor (SF), an electron disequilibrium factor, and an attenuation factor, equal to the zero-area TPR. The scatter factor, as a function of depth d and field size s, has been described by two parameters a and w, SF(d,s) = 1 + asd/(ws + d). We have determined the parameters a and w for 20 monoenergetic photon beams between 1 and 20 MeV. Pencil-beam energy-deposition kernels were obtained using Monte Carlo simulations. The kernels were used to calculate broad-beam depth-dose data, which were converted to TPR and fitted to the equation above using an iterative search over a-w space. The parameter a is nearly equal to the attenuation coefficient for all energies while the parameter w increases with energy. The resulting a and w compare favorably to values determined for clinical photon beams, as a function of the measured attenuation coefficient. With the scatter factor determined, we isolated the electron disequilibrium factor for each monoenergetic beam. It can be characterized as a quadratic function of the depth. The coefficients of the quadratic function can be related to the range of the most energetic secondary electron produced.