AbstractID: 7144 Title: Accuracy and Efficiency Comparisons between Three-Dimensional Multigroup
Discrete Ordinates and Voxel Based Monte Carlo Methods for Dosimetric Modeling of the Model 6702
¹²⁵I seed.
The Discrete Ordinates Method (DOM) is a deterministic solver of the Boltzmann equation, governing photon transport,
which is, in principle, as accurate as competing Monte Carlo methods. We have evaluated the accuracy and efficiency of
DOM simulations for 3D modeling of a Model 6702 125I seed dose distribution relative to a voxel-based Monte Carlo
(3DMC) code. Because the mathematical basis of the two methods is so different (deterministic DOM versus stochastic
3DMC), this comparison is a unique and extremely complex task. Both methods exhibit systematic errors of different origin
(finite-differencing errors in DOM, voxel volume-averaging errors in 3DMC) while the 3DMC results have statistical
uncertainties varying significantly both with voxel size and local dose. To support a fair and comprehensive comparison of
the two methods, we have developed a statistical approach, which models both the systematic and random error and predicts
the fraction of points whose errors exceed tolerance thresholds. For 3DMC, this model is used to identify the run time and
voxel size at each distance that satisfy these criteria, while for DOM, it is used to identify a spatial mesh satisfying the same
systematic accuracy constraint of 5%.
The results show that with similar accuracy, 3D DOM is an order of magnitude faster than 3DMC in our three-dimensional
simulations, which uses a very efficient expected track-length estimator. The DOM computational times of about 1 hour
demonstrate the method’s potential for implementing the solution of the photon transport equations in patient’s treatment
planning.
Supported by NIH Grant R01 CA46640.