Implementation of FFT convolution and multigrid superposition models in the FOCUS RTP system

In radiotherapy treatment planning, convolution/superposition algorithms currently represent the best practical approach for accurate photon dose calculation in heterogeneous tissues. In this work, the implementation, accuracy and performance of the FFT convolution (FFTC) and multigrid superposition (MGS) algorithms are presented. The FFTC and MGS models use the same 'TERMA' calculation and are commissioned using the same parameters. Both models use the same spectra, incorporate the same off-axis softening and base incident lateral fluence on the same measurements. In addition, corrections are explicitly applied to the polyenergetic and parallel kernel approximations, and electron contamination is modelled. Spectra generated by Monte Carlo (MC) modelling of treatment heads are used. Calculations using the MC spectra were in excellent agreement with measurements for many linear accelerator types. To speed up the calculations, a number of calculation techniques were implemented, including separate primary and scatter dose calculation, the FFT technique which assumes kernel invariance for the convolution calculation and a multigrid (MG) acceleration technique for the superposition calculation. Timing results show that the FFTC model is faster than MGS by a factor of 4 and 8 for small and large field sizes, respectively. Comparisons with measured data and BEAM MC results for a wide range of clinical beam setups show that (a) FFTC and MGS doses match measurements to better than 2% or 2 mm in homogeneous media; (b) MGS is more accurate than FFTC in lung phantoms where MGS doses are within 3% or 3 mm of BEAM results and (c) FFTC overestimates the dose in lung by a maximum of 9% compared to BEAM.