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

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, h(p), 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 or 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. The microscopic kernels or the irradiation density may thus be viewed as a perfect 'sink' distribution to the required incident photon energy fluence which is totally absorbed at f(r), and instead replaced by the kernels which describe the detailed energy deposition in the medium in coordinates centred at the sinks. From these definitions the required incident energy fluence from an external radiation source used for treatment realization can be determined directly by projecting the irradiation density on the relevant positions of the radiation source. This procedure has the valuable property that maximal calculational accuracy is achieved in the tumour because the irradiation density has non-zero values only in the tumour, and the accuracy of the kernel is highest at its origin.