Master of Science (MS)


Physics and Astronomy

Document Type



In this study, a proton pencil beam dose calculation algorithm was developed for a parallel, monoenergetic beam incident on a homogeneous water phantom. Fermi-Eyges theory (Eyges 1948) was used to transport pencil beams, and the characteristic width of elastic scatter events was modeled using the differential Moliere scattering power (Gottschalk 2010). The incorporation of this scattering power formalism allowed our model to account for multiple Coulomb scattering, single scattering, plural scattering, and rigorously accounted for material effects on scatter. Nonelastic nuclear interactions were incorporated into an additional pencil beam model. The attenuation of primary fluence due to nuclear events was accounted for using a weighted sum of primary and nuclear pencil beam components (Pedroni et al. 2005, Soukup et al. 2005). Free parameters of the nuclear pencil beam model were determined by a non-linear least squares fit to narrow field Monte Carlo data. Our dose calculation model was commissioned using central-axis depth dose data extracted from Monte Carlo simulations. Analytical corrections were incorporated to ensure that all input central-axis data satisfied side scatter equilibrium.

The dose calculation model was evaluated against Monte Carlo simulations of dose in a simplified beamline. Proton beam energies of 50, 100, 150, 200, and 250 MeV and field sizes of 4x4 cm2 and 10x10 cm2 were evaluated in three geometries: (1) flat phantom; (2) step phantoms (step heights of 1 and 4 cm); and (3) oblique phantom (rotation angle of 45°). All geometries evaluated with Monte Carlo dose calculations yielded 100% of points passing distance-to-agreement (DTA) ≤ 1 mm or Percent Dose Difference ≤ 3%. At least 99% of points passed with a DTA ≤ 1 mm or Percent Dose Difference ≤ 2%. The pencil beam dose calculation model provided excellent results when compared with Monte Carlo data.



Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Fontenot, Jonas