Mathematical model of the depth curve taking into account the entrance and exit problems

The central axis depth dose for high energy X-rays and γ-rays beams used in radiotherapy is a function of the photons energy, source-surface distance and field size. The standard depth-dose for an homogeneous medium clearly presents three different regions: one near the entrance surface, other near the exit surface and a third one in between. It is the purpose of the authors to present in this work a methodology for a general mathematical model that explains the globality of the absorbed dose curves, taking into account the build-up region (entrance surface) and the lack of backscattering at the exit surface. In this model all the terms have physical meanings, explaining the phenomena that might exist. Doses were measured using a Markus parallel plate ion chamber and a Mephystos dosimetric system. The studied energies were Co-60 and RX of 6, 8, 10 and 25 MV. We used source-surface distances between 60 and 120 cm and field sizes between 5x5 and 40x40 cm2. Using this mathematical model we have differences between experimental and predicted data smaller then 1.5%; extrapolating the curves to depth=0 we obtained values for the surface dose; differentiating the modelisation we obtain (for each energy, field and source-surface distance) the build-up depth