Decomposition of pencil beam kernels for fast dose calculations in three‐dimensional treatment planning

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Abstract
A method for the calculation of three‐dimensional dose distributions for high‐energy photon beams is presented. The main features are (i) the calculation is fast enough to allow interactive three‐dimensional treatment planning, and (ii) irregularly shaped or compensated fields, which are required to fit three‐dimensional dose distributions to target volumes, are adequately taken into consideration. The method is based on the pencil beam convolution technique and shares its features concerning accuracy. A considerable gain in speed is achieved by decomposing the pencil beam kernel into three separated terms, thus reducing the required number of two‐dimensional convolutions. The convolutions are performed in the frequency domain via the fast Hartley transform. Using these techniques, the calculation time for the convolutions is only about 8 s on a DEC VAX station 3100. This is one‐fourth to one‐third of the calculation time for the ray tracing through the three‐dimensional CT data set, which has to be performed in any case. Results of the calculation are compared with measurements in a homogeneous phantom for 15 MV photons. Two irregular fields shaped with a multileaf collimator are considered. The deviations between measured and calculated absolute dose values are smaller than ±2%.

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