Electron loss model with energy straggling for therapeutic beam dose calculations

An analytical transport model to account for pathlength and energy-loss straggling of an electron pencil beam is presented. The pathlength straggling is taken into account by incorporating into the Fermi-Eyges equation an angle and depth dependent absorption cross-section that governs the loss of electrons with depth and the saturation of the mean squared spatial spread. The energy-loss straggling problem is solved by use of a weighted superposition of discrete elementary pencil beams that lose energy according to the CSDA. These elementary pencil beams have slightly different initial energies and thus slightly different ranges of penetration. The energy straggling spectrum determines the weighting. Our model predicts both lateral and depth dose distributions from the electron pencil beams close to EGS4 Monte-Carlo calculations and measurements