Foundation of an analytical proton beamlet model for inclusion in a general proton dose calculation system

We have developed a model for proton depth dose and lateral distributions based on Monte Carlo calculations (GEANT4) and an integration procedure of Bethe-Bloch equation (BBE). The model accounts for the transport of primary and secondary protons, the creation of recoil protons and heavy recoil nuclei as well as lateral scattering of these contributions. The buildup, which is experimentally observed in higher energy depth dose curves, is modeled by an inclusion of two different origins: (1) secondary reaction protons with a contribution of ca. 65% of the buildup (for monoenergetic protons). (2) Landau tails as well as Gaussian type of fluctuations for range straggling effects. All parameters of the model for initially monoenergetic proton beams have been obtained from Monte Carlo calculations or checked by them. Furthermore, there are a few parameters, which can be obtained by fitting the model to the measured depth dose curves in order to describe individual characteristics of the beamline-the most important being the initial energy spread. We find that the free parameters of the depth dose model can be predicted for any intermediate energy from a couple of measured curves.