Fast Fourier transform convolution calculations of x-ray isodose distributions in homogeneous media

Convolution concepts were implemented using the discrete fast Fourier transform (FFT) to model the three-dimensional dose distribution due to x-rays produced by a medical linear accelerator. Convolution kernels were employed that had been calculated by Mackie using the EGS4 Monte Carlo code. The EGS4 code was also used to estimate initially the spectrum by simulating the production, filtering, and flattening of the beam in the collimator of the linear accelerator. The continuous bremsstrahlung spectrum was modeled using five discrete energies. The more subtle field-size effects of collimator scattering on the spectrum were obtained by calculating corrections to the spectral components using a least-squares search technique. Dose distributions were obtained using FFT convolutions of the kernels for each energy with the spectrally weighted fluence distributions for that energy. The dose distributions were compared with isodose distributions measured in a water phantom. The agreement was generally found to be better than 1% on the central axis. The calculation time for a single three-dimensional beam was approximately 20 min using a VAX/750 without an array processor. Methods were explored to reduce the calculation time using similar hardware, and estimates were made of how to reduce the calculation time using a more sophisticated computer system.