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An Improved Method of Heterogeneity Compensation for the Convolution / Superposition Algorithm

Purpose: To improve the accuracy of convolution/superposition (C/S) in heterogeneous material by developing a new algorithm: heterogeneity compensated superposition (HCS). Methods: C/S has proven to be a good estimator of the dose deposited in a homogeneous volume. However, near heterogeneities electron disequilibrium occurs, leading to the faster fall-off and re-buildup of dose. We propose to filter the actual patient density in a position and direction sensitive manner, allowing the dose deposited near interfaces to be increased or decreased relative to C/S. We implemented the effective density function as a multivariate first-order recursive filter and incorporated it into GPU-accelerated, multi-energetic C/S implementation. We compared HCS against C/S using the ICCR 2000 Monte-Carlo accuracy benchmark, 23 similar accuracy benchmarks and 5 patient cases. Results: Multi-energetic HCS increased the dosimetric accuracy for the vast majority of voxels; in many cases near Monte-Carlo results were achieved. We defined the per-voxel error, %|mm, as the minimum of the distance to agreement in mm and the dosimetric percentage error relative to the maximum MC dose. HCS improved the average mean error by 0.79 %|mm for the patient volumes; reducing the average mean error from 1.93 %|mm to 1.14 %|mm. Very low densities (i.e. < 0.1 g / cm3) remained problematic, but may be solvable with a better filter function. Conclusions: HCS improved upon C/S's density scaled heterogeneity correction with a position and direction sensitive density filter. This method significantly improved the accuracy of the GPU based algorithm reaching the accuracy levels of Monte Carlo based methods with performance in a few tenths of seconds per beam. Acknowledgement: Funding for this research was provided by the NSF Cooperative Agreement EEC9731748, Elekta / IMPAC Medical Systems, Inc. and the Johns Hopkins University. James Satterthwaite provided the Monte Carlo benchmark simulations.