Fast modelling of spectra and stopping-power ratios using differentiated fluence pencil kernels

Modern radiotherapy steadily utilizes more of the available degrees of freedom provided by radiotherapy equipment, raising the need for the dosimetric methods to deliver reliable measurements for situations where the spectral properties of the radiation field may also vary. A kernel-based superposition method is presented for which the spectra from any field modulation can be instantly calculated, thus facilitating the determination of dosimetric quantities at arbitrary locations. A database of fluence pencil kernels describing the fluence resulting from point monodirectional monoenergetic beams incident onto a water phantom has been calculated with the PENELOPE-2005 Monte Carlo package. Spectra calculated by means of the kernels are presented for various 6 MV fields. The spectra have been used to investigate depth and lateral variations of water-to-air stopping-power ratios. Results show that the stopping-power ratio decreases with depth, and that this effect is more pronounced for small fields. These variations are clearly connected to spectral variations. For a 10 x 10 cm(2) field, the difference between the stopping-power ratio at 2.5 cm depth and 30 cm depth is less than 0.3% while for a 0.3 x 0.3 cm(2) field this difference is 0.7%. Ratios outside the field were found to be sensitive to the collimator leakage spectral variations.