Monte-Carlo-derived insights into dose-kerma-collision kerma inter-relationships for 50 keV-25 MeV photon beams in water, aluminum and copper.

The relationships between D, K and Kcol are of fundamental importance in radiation dosimetry. These relationships are critically influenced by secondary electron transport, which makes Monte-Carlo (MC) simulation indispensable; we have used MC codes DOSRZnrc and FLURZnrc. Computations of the ratios D/K and D/Kcol in three materials (water, aluminum and copper) for large field sizes with energies from 50 keV to 25 MeV (including 6-15 MV) are presented. Beyond the depth of maximum dose D/K is almost always less than or equal to unity and D/Kcol greater than unity, and these ratios are virtually constant with increasing depth. The difference between K and Kcol increases with energy and with the atomic number of the irradiated materials. D/K in 'sub-equilibrium' small megavoltage photon fields decreases rapidly with decreasing field size. A simple analytical expression for X̅, the distance 'upstream' from a given voxel to the mean origin of the secondary electrons depositing their energy in this voxel, is proposed: X̅(emp) ≈ 0.5R(csda)(E̅(0)), where E̅(0) is the mean initial secondary electron energy. These X̅(emp) agree well with 'exact' MC-derived values for photon energies from 5-25 MeV for water and aluminum. An analytical expression for D/K is also presented and evaluated for 50 keV-25 MeV photons in the three materials, showing close agreement with the MC-derived values.