The validity of the density scaling method in primary electron transport for photon and electron beams

In the convolution/superposition method of photon beam dose calculations, inhomogeneities are usually handled by using some form of scaling involving the relative electron densities of the inhomogeneities. In this paper the accuracy of density scaling as applied to primary electrons generated in photon interactions is examined. Monte Carlo calculations are compared with density scaling calculations for air and cork slab inhomogeneities. For individual primary photon kernels as well as for photon interactions restricted to a thin layer, the results can differ significantly, by up to 50%, between the two calculations. However, for realistic photon beams where interactions occur throughout the whole irradiated volume, the discrepancies are much less severe. The discrepancies for the kernel calculation are attributed to the scattering characteristics of the electrons and the consequent oversimplified modeling used in the density scaling method. A technique called the kernel integration technique is developed to analyze the general effects of air and cork inhomogeneities. It is shown that the discrepancies become significant only under rather extreme conditions, such as immediately beyond the surface after a large air gap. In electron beams all the primary electrons originate from the surface of the phantom and the errors caused by simple density scaling can be much more significant. Various aspects relating to the accuracy of density scaling for air and cork slab inhomogeneities are discussed.