The energy-dependent electron loss model for pencil beam dose kernels

The 'monoenergetic' electron loss model was derived in a previous work to account for pathlength straggling in the Fermi-Eyges pencil beam problem. In this paper, we extend this model to account for energy-loss straggling and secondary knock-on electron transport in order to adequately predict a depth dose curve. To model energy-loss straggling, we use a weighted superposition of a discrete number of monoenergetic pencil beams with different initial energies where electrons travel along the depth-energy characteristics in the continuous slowing down approximation (CSDA). The energy straggling spectrum at depth determines the weighting assigned to each monoenergetic pencil beam. Supplemented by a simple transport model for the secondary knock-on electrons, the 'energy-dependent' electron loss model predicts both lateral and depth dose distributions from the electron pencil beams in good agreement with Monte Carlo calculations and measurements. The calculation of dose distribution from a pencil beam takes 0.2 s on a Pentium III 500 MHz computer. Being computationally fast, the 'energy-dependent' electron loss model can be used for the calculation of 3D energy deposition kernels in dose optimization schemes without using precalculated or measured data. (author)