The collapsed cone superposition algorithm applied to scatter dose calculations in brachytherapy

Abstract

Methods for scatter dose calculations in brachytherapy have been developed based on the collapsed cone superposition algorithm. The methods account for effects on the scatter dose caused by the three-dimensional distribution of heterogeneities in the irradiated volume and are considerably faster than methods based on straightforward superposition of kernels or direct Monte Carlo simulations. Use of a successive-scattering approach, in which the dose contribution from once- and multiply scattered photons are calculated separately, was found superior to conventional superposition using a single point kernel for all scatter generations. Use of the successive-scattering approach significantly reduces artifacts stemming from steep fluence gradients, typical of the brachytherapy geometry and critical for the collapsed cone approximation. The algorithm is tested versus Monte Carlo simulations for point sources of energies 28.4, 100, 350, and 662 keV. Results agree well for both a homogeneous water phantom and an air-water half-phantom.

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

“…16 Residual-scatter kernels at these energies have already in previous work been approximated as isotropic. 12,13 In this work the possibility of also approximating the first-scatter point kernels as isotropic will be investigated. Problems with the isotropic assumption might arise for kernels in high atomic number materials which show a pronounced forward directed peak stemming from elastically scattered photons.…”

“…It has previously been shown that calculations using the two steps of successive scattering can use a smaller number of total directions for similar levels of kernel discretization artifacts in the end result than what is achievable through calculation of the total scatter dose in a single step. 12 Optimizing computational efficiency, hence, translates into searching the minimum number of total transport directions that result in acceptable approximations in dose from discretization artifacts, and how these directions are best split between the steps for first and residual scatter. In the current work, the calculations are done in homogeneous phantoms but the algorithm considers heterogeneities and finite patient dimensions both in deriving the primary dose, the distribution of released scatter energy, and through kernel-scaling corrections.…”

“…14 The CC approach is a kernel superposition method which has been optimized for speed through discretizing the angular part of the point kernel by collapsing the angular cone binning onto a suitably designed lattice of transport lines. 11,20,21 By use of a successive-scattering approach, 12,16 the transport is divided into separate steps for first and residual scatter, respectively, as illustrated in Fig. 1.…”

“…In the current work, the calculations are done in homogeneous phantoms but the algorithm considers heterogeneities and finite patient dimensions both in deriving the primary dose, the distribution of released scatter energy, and through kernel-scaling corrections. 12,13 The calculation time scaling in Eq. ͑1͒ is therefore valid for both homogeneous and heterogeneous geometries.…”

“…Several methods have been proposed, such as Monte Carlo ͑MC͒ simulations, [7][8][9] 3D implementa-tion of the discrete ordinates method to solve the transport equation analytically, 10 and the collapsed cone kernel superposition algorithm adopted for brachytherapy ͑CC͒. 11,12 The CC approach has been used to model the effects of finite phantom dimensions, 12 heterogeneities including those of high Z materials, 13 and source data connectivity to dose distributions around clinical sources. 14 The CC algorithm has recently been demonstrated to run very efficiently on mainframe parallel hardware like multicore processors and graphical processor units.…”