Photon field quantities and units for kernel based radiation therapy planning and treatment optimization

Abstract

The problem of choosing radiation quantities and units for energy deposition kernels and their associated kernel densities is treated with the aim of making them consistent with related classical radiation quantities and units such as restricted mass stopping powers and mass attenuation coefficients. It is shown that it is very useful to define the kernels, h(r), in terms of the quotient of the mean specific energy imparted to the medium by the radiant energy incident on a volume element centred at the origin of the kernel. The basic building block used to generate these kernels is the point energy deposition kernel, hp, describing the spatial distribution of the energy imparted by a photon interacting at a point in a medium. This will allow the kernels to be regarded as generalizations of the traditional mass stopping and attenuation coefficients, which in detail describe the spatial distribution of the mean energy deposition around an interaction site. As a consequence, the irradiation of kernel density, f(r), should be expressed in terms of the radiant energy incident per unit volume of the medium. It is shown that the kernel density is equal to minus the divergence of the incident unattenuated vectorial energy fluence, and it therefore acts as an irradiation density for the incident vectorial energy fluence.