Optimization of the computational efficiency of a 3D, collapsed cone dose calculation algorithm for brachytherapy

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Abstract
Brachytherapy dose calculations based on point kernel superposition using the collapsed cone method have been shown to accurately model the influence from finite dimensions of the patient and effects from heterogeneities including those of high atomic numbers. The collapsed cone method is for brachytherapy applications most effectively implemented through a successive‐scattering approach, in which the dose from once and higher order of scattered photons is calculated separately and in successive scatter order. The calculation speed achievable is directly proportional to the number of directions used for point kernel discretization and to the number of voxels in the volume. In this work we investigate how to best divide the total number of directions between the two steps of successive‐scattering dose calculations. Results show that the largest fraction of the total number of directions should be utilized in calculating the first‐scatter dose. Also shown is how the number of directions required for keeping discretization artifacts at acceptably low levels decreases significantly in multiple‐source configurations, as a result of the dose gradients being less steep than those around single sources. Investigating the number of kernel directions required to keep artifacts low enough within the high dose region of an implant (i.e., for dose levels above approximately of the mean central target dose) reveals similar figures for brachytherapy as for external beam applications, where collapsed cone superposition is clinically used. Also shown is that approximating point kernels with their isotropic average leads to small dose differences at low and intermediate energies, implying that the collapsed cone calculations can be done in a single operation common to all sources of the implant at these energies. The current findings show that collapsed cone calculations can be achieved for brachytherapy with the same efficiency as for external beams. This, combined with recent results on gains in efficiency through implementing the algorithm on graphical card parallel hardware indicates that dose can be calculated with account for heterogeneities and finite dimensions within a few seconds for large voxel arrays and is therefore of interest for practical application to treatment planning.

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