A new concept of pencil beam dose calculation for 40–200 keV photons using analytical dose kernels

Purpose: The advent of widespread kV-cone beam computer tomography in image guided radiation therapy and special therapeutic application of keV photons, e.g., in microbeam radiation therapy (MRT) require accurate and fast dose calculations for photon beams with energies between 40 and 200 keV. Multiple photon scattering originating from Compton scattering and the strong dependence of the photoelectric cross section on the atomic number of the interacting tissue render these dose calculations by far more challenging than the ones established for corresponding MeV beams. That is why so far developed analytical models of kV photon dose calculations fail to provide the required accuracy and one has to rely on time consuming Monte Carlo simulation techniques. Methods: In this paper, the authors introduce a novel analytical approach for kV photon dose calculations with an accuracy that is almost comparable to the one of Monte Carlo simulations. First, analytical point dose and pencil beam kernels are derived for homogeneous media and compared to Monte Carlo simulations performed with the Geant4 toolkit. The dose contributions are systematically separated into contributions from the relevant orders of multiple photon scattering. Moreover, approximate scaling laws for the extension of the algorithm to inhomogeneous media are derived. Results: The comparison of the analytically derived dose kernels in water showed an excellent agreement with the Monte Carlo method. Calculated values deviate less than 5% from Monte Carlo derived dose values, for doses above 1% of the maximum dose. The analytical structure of the kernels allows adaption to arbitrary materials and photon spectra in the given energy range of 40–200 keV. Conclusions: The presented analytical methods can be employed in a fast treatment planning system for MRT. In convolution based algorithms dose calculation times can be reduced to a few minutes.