The use of variable grid spacing to accelerate dose calculations

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Abstract
Planning radiation therapy using three‐dimensional patient data is a very time consuming process with current hardware and software. When calculating a three‐dimensional dose distribution, the standard technique is to cover the volume of interest with a uniformly spaced matrix of points at which the dose is calculated. It is obvious that the dose is usually quite slowly varying in a large proportion of the region of interest; namely, in those regions which are either well inside or well outside the geometrical boundaries of the field. We have developed an algorithm which allows us to reduce the number of calculation points, and hence the time of calculation of the entire dose distribution, manyfold. We use a nonuniform grid of calculated points, based on the fact that the only regions which are troublesome for accurate doseinterpolation are those in which large values of the second derivative of the dose as a function of position occur. We demonstrate that, at most grid points, the dose can be determined without decreasing accuracy below acceptable limits by simple linear interpolation between grid points much further apart than is usual in conventional techniques. We investigated our algorithm for one‐, two‐, and three‐dimensional examples and for Co‐60, 25‐MV photon, and 160‐MV proton beams. In situations for which an accuracy of about 1% in dose and 1.6 mm in position was desired, we found gain factors for the number of points needing direct calculation of approximately 3 (one‐dimension), 6 to 10 (two‐dimensions) and 16 (three‐dimensions).