SU‐E‐T‐508: A Novel Method of Heterogeneity Compensation for the Convolution / Superposition Algorithm

Purpose: We developed a better method of accounting for the effects of heterogeneity in convolution algorithms. We integrated this method into our GPU‐accelerated, multi‐energetic convolution/superposition (C/S) implementation. In doing so, we have created a new dose algorithm: heterogeneity compensated superposition (HCS). Methods: Convolution in the spherical density‐scaled distance space, a.k.a. 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 faster fall‐off and re‐buildup than predicted by C/S. 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 traditional C/S. We implemented the effective density function as a multivariate first‐order recursive filter. We compared HCS against traditional C/S using the ICCR 2000 Monte‐Carlo accuracy benchmark, 23 similar accuracy benchmarks and 5 patient cases. For the patient cases, we created custom routines capable of using the discrete material mappings used by Monte‐Carlo. C/S normally considers each voxel to be a mixture of materials based on a piecewise‐linear density look‐up table. Results: Multi‐energetic HCS increased the dosimetric accuracy for the vast majority of voxels; in many cases near Monte‐Carlo results were achieved. HCS improved the mean Van Dyk error by 0.79 (% of Dmax or mm) on average for the patient volumes; reducing the mean error from 1.93%|mm to 1.14%|mm. We found a mean error difference of up to 0.30 %|mm between linear and discrete material mappings. Very low densities (i.e. <0.1 g / cm³) remained problematic, but may be solvable with a better filter function. Conclusions: We have developed a novel dose calculation algorithm based on the principals of C/S that better accounts for the electron disequilibrium caused by patient heterogeneity. This work was funded in part by the National Science Foundation under Grant No. EEC9731748, in part by Johns Hopkins University internal funds and in part by Elekta.