Use of fast Fourier transforms in calculating dose distributions for irregularly shaped fields for three‐dimensional treatment planning

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Abstract
In three‐dimensional radiation treatment planning, essentially all fields are irregular and compensated. Consequently, it is important to predict accurately dose for such fields to ensure adequate coverage of the target region and sparing of healthy tissues. Traditional approaches, namely, those involving scatter integration and extended source and those utilizing negatively weighted fields, are inaccurate, especially near the boundaries defined by blocks and collimators. In the method presented in this paper, dose distributions for arbitrarily shaped beams are calculated by two‐dimensional convolution of the relative primary photon fluence distributions and kernels representing the cross‐sectional profiles of a pencil beam at a series of depths. The pencil beam dose distributions are computed, once and for all, with the Monte Carlo method for photon energy spectrum for each treatment machine. The finite size of the source, which is important for cobalt machines, is also taken into account using convolution of the source with the relative primary fluence distribution. Convolutions are performed using fast Fourier transforms on an array processor. Results of calculations are in excellent agreement with measured data. While no data are presented for fields modified by compensators, the method of calculation should apply at least as well for such fields since the variations in fluence distribution for compensated fields are not as sharp as for points near the block boundaries.