Implementation of 3-D Anisotropy Corrected Fast Fourier Transform Dose Calculation around Brachytherapy Seeds

A routine dose computation around brachytherapy seeds employing the Fast Fourier Transform (FFT) has been demonstrated and likened to dose computations in a similar field based on the TG43 recommendations. In applying the FFT convolution model to dose computation, a dose convolution kernel which takes into consideration the anisotropy of the dose distribution around a brachytherapy source in the presence of tissue and applicator heterogeneities was presented. Resulting from the convolution kernel were functions with polynomial and exponential terms. The solution to the convolution integral was thus represented by the Fast Fourier transform. The versatility of the Fast Fourier Transform becomes evident with its speed of dose computation and accuracy evenly matched. It has also been described as ubiquitous; as successful procedures developed in one field could easily be adopted in other fields (E.g. external beam and brachytherapy). In typical dose computation procedures, the dose computation time is usually proportional to the number of sources or dwell positions required for the implants and relatively increases for large number of sources. With a dose convolution kernel developed for a 64x64x64 matrix size with wrap around ordering, the kernel was convoluted with the source distributions also in similar matrix size in 3D. Results from the analysis showed the FFT based convolution method in brachytherapy was comparable in speed with computerized treatment planning system whose model is based on the recommendations of the TG43. Further development on the FFT incorporating techniques such as the Monte Carlo simulation will be required to fine tune the potency of the FFT convolution in studying tumor growth and the aftermath upshots of radiation therapy.