Acceleration of intensity‐modulated radiotherapy dose calculation by importance sampling of the calculation matrices

Abstract

In inverse planning for intensity-modulated radiotherapy, the dose calculation is a crucial element limiting both the maximum achievable plan quality and the speed of the optimization process. One way to integrate accurate dose calculation algorithms into inverse planning is to precalculate the dose contribution of each beam element to each voxel for unit fluence. These precalculated values are stored in a big dose calculation matrix. Then the dose calculation during the iterative optimization process consists merely of matrix look-up and multiplication with the actual fluence values. However, because the dose calculation matrix can become very large, this ansatz requires a lot of computer memory and is still very time consuming, making it not practical for clinical routine without further modifications. In this work we present a new method to significantly reduce the number of entries in the dose calculation matrix. The method utilizes the fact that a photon pencil beam has a rapid radial dose falloff, and has very small dose values for the most part. In this low-dose part of the pencil beam, the dose contribution to a voxel is only integrated into the dose calculation matrix with a certain probability. Normalization with the reciprocal of this probability preserves the total energy, even though many matrix elements are omitted. Three probability distributions were tested to find the most accurate one for a given memory size. The sampling method is compared with the use of a fully filled matrix and with the well-known method of just cutting off the pencil beam at a certain lateral distance. A clinical example of a head and neck case is presented. It turns out that a sampled dose calculation matrix with only 1/3 of the entries of the fully filled matrix does not sacrifice the quality of the resulting plans, whereby the cutoff method results in a suboptimal treatment plan.

Development of the open-source dose calculation and optimization toolkit matRad

“…The pencil beam kernels, which account for dose contributions stemming from primary and scattered radiation, are precomputed for multiple SSDs. To reduce the memory requirements of the dose influence matrix used for optimization, matRad facilitates importance sampling as introduced by Ref …”

Online dose reconstruction for tracked volumetric arc therapy: Real‐time implementation and offline quality assurance for prostate SBRT

“…We could observe memory throughputs of 65–85 GB s, which is not far from the theoretical maximum bandwidth for the utilized CPU. The amount of data could potentially be decreased by a factor of three by applying dose‐influence sampling methods . This would decrease the amount of required RAM and speed up data loading times.…”

Multi-GPU implementation of a VMAT treatment plan optimization algorithm

“…For example, the importance sampling of the DDC matrix was reported to be able to reduce the matrix size to be ~1/3 of the complete matrix without sacrificing plan quality 33 . These methods could be combined with our multi-GPU implementation to allow us to keep DDC elements as many as possible or use even higher resolution in VMAT optimization on GPUs.…”

“…Although only penumbra elements for each beamlet dose were deleted, the accumulated dose contributed from all the deleted elements to a voxel inside PTV could still be relatively large. We would like to point out that there are algorithms developed to reduce the DDC matrix size, while better preserving the plan quality 33 . Here, we utilized a simple method for the purpose of focusing on the study about multi-GPU implementation.…”