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Int J Radiat Oncol Biol Phys. 1988 Nov;15(5):1251-6.

Quadtrees as a representation for irregularly shaped fields in radiotherapy applications.

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  • 1Joint Center for Radiation Therapy, Harvard Medical School, Boston, MA 02115.


The choice of data representations in treatment planning software impacts on the accuracy of the treatment plan and the total computation time. We present the quadtree data structure as one such representation for irregularly shaped fields in a three-dimensional electron pencil-beam algorithm. The quadtree subdivides the irregular field into pencil-beams of unequal size and considerably reduces the number of pencil-beams needed in the dose calculation while preserving the calculational accuracy. Small pencil-beams are concentrated around the field edges to provide optimal resolution and computational accuracy in penumbra regions. The quadtree simplifies the evaluation of the pencil-beam fluence at a given depth, and removes systematic errors present in alternative implementations. The quadtree algorithm results in a ten-fold performance improvement when compared to alternative implementations for the irregular field.

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