A pencil‐beam photon dose algorithm for stereotactic radiosurgery using a miniature multileaf collimator

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Abstract
A computer-controlled miniature multileaf collimator (MMLC) with 4 mm leaf width and a maximum field size of 6 cm X 6 cm has been designed as a tertiary beam-shaping device for linac-based stereotactic radiosurgery. The purpose of this study is to develop an accurate and efficient dose calculation model for use with the MMLC. A pencil-beam based algorithm using a sum of three Gaussian kernels was developed to model the off-axis ratio of MMLC fields. Because the kernel integration over a rectangular field can be solved in closed form, dose to any point from an arbitrary MMLC field can be calculated efficiently by summing dose contribution from a set of rectangular apertures and transmission blocks that model individual leaf openings or leaf transmissions. The model uses an effective rectangular field and equivalent square method for determination of depth dose and dose output. Results showed that the calculated percentage depth dose was within 1% and output factor was within 1.5% of measured data. The parameters of the pencil beam kernels were extracted by fitting measured off-axis profiles for a few field sizes at a few depths. The accuracy of the calculated off-axis ratio was tested by comparison with measured data for a number of MMLC fields. The algorithm was shown to be accurate to within 1.5% or 1 mm for off-axis ratios. The algorithm computes at a speed of 34,600 data points per second on a DEC Alpha server model 2000/433 (Digital Equipment Corp., Maynard, MA), which is about 15 times faster than a Clarkson-type summation method.