Lateral electron disequilibrium in radiotherapy treatment planning

Abstract

Lateral electron disequilibrium on the central-axis of small-diameter circular beams is investigated using the EGS4 Monte Carlo system, for 10 MV photons. Monte Carlo results generated using the reciprocity technique are presented. In water, disequilibrium is found to occur for beams with diameters of less than approximately 4 cm. In lung of density 0.25 g cm⁻³, disequilibrium occurs for diameters less than approximately 16 cm. The lateral electron equilibrium factor is defined and used to quantify the degree of disequilibrium. Convolution dose calculation for 10 MV photons, using polyenergetic energy deposition kernels, gives a slight error in central-axis dose, due to beam hardening with depth. Primary and scattered polyenergetic kernels formed for a surface primary photon spectrum contain less and more fractional energy respectively than primary and scattered kernels formed for a beam hardened spectrum. A beam hardening correction to the kernels used in the convolution is proposed. This correction improves the agreement of convolution results with Monte Carlo predictions. A superposition algorithm is developed and used to calculate dose in a lung phantom for 10 MV photons. Results show an overestimate in dose in the lung for a 5 cm square field when compared with experiment and Monte Carlo results. Disagreement is due to the assumption made in the density scaling method that secondary electrons travel in straight lines. A modification to the interaction voxel weighting in the density scaling procedure improves the result. The superposition method for 4 MV and 10 MV photons has been incorporated into the GRATIS treatment planning system. Two and three-dimensional electron pencil beam algorithms are used to calculate the dose distribution in a water medium containing a small cavity for a 12 MeV electron beam. The measured hot spot beneath the cavity is 122%. The 2-D method predicts 114% and the 3-D method predicts 127%. Both profile and depth dose curves produced by the 3-D method are superior to those produced by the 2-D method. The 3-D pencil beam algorithm has been incorporated into the GRATIS treatment planning system.