Fast patient-specific Monte Carlo brachytherapy dose calculations via the correlated sampling variance reduction technique

Purpose: To demonstrate potential of correlated sampling Monte Carlo (CMC) simulation to improve the calculation efficiency for permanent seed brachytherapy (PSB) implants without loss of accuracy. Methods: CMC was implemented within an in-house MC code family (PTRAN) and used to compute 3D dose distributions for two patient cases: a clinical PSB postimplant prostate CT imaging study and a simulated post lumpectomy breast PSB implant planned on a screening dedicated breast cone-beam CT patient exam. CMC tallies the dose difference, D, between highly correlated histories in homogeneous and heterogeneous geometries. The heterogeneous geometry histories were derived from photon collisions sampled in a geometrically identical but purely homogeneous medium geometry, by altering their particle weights to correct for bias. The prostate case consisted of 78 Model-6711 ¹²⁵I seeds. The breast case consisted of 87 Model-200 ¹⁰³Pd seeds embedded around a simulated lumpectomy cavity. Systematic and random errors in CMC were unfolded using low-uncertainty uncorrelated MC (UMC) as the benchmark. CMC efficiency gains, relative to UMC, were computed for all voxels, and the mean was classified in regions that received minimum doses greater than 20, 50, and 90 of D ₉₀, as well as for various anatomical regions. Results: Systematic errors in CMC relative to UMC were less than 0.6 for 99 of the voxels and 0.04 for 100 of the voxels for the prostate and breast cases, respectively. For a 1 1 1 mm³ dose grid, efficiency gains were realized in all structures with 38.1- and 59.8-fold average gains within the prostate and breast clinical target volumes (CTVs), respectively. Greater than 99 of the voxels within the prostate and breast CTVs experienced an efficiency gain. Additionally, it was shown that efficiency losses were confined to low dose regions while the largest gains were located where little difference exists between the homogeneous and heterogeneous doses. On an AMD 1090T processor, computing times of 38 and 21 sec were required to achieve an average statistical uncertainty of 2 within the prostate (1 1 1 mm³) and breast (0.67 0.67 0.8 mm³) CTVs, respectively. Conclusions: CMC supports an additional average 38-60 fold improvement in average efficiency relative to conventional uncorrelated MC techniques, although some voxels experience no gain or even efficiency losses. However, for the two investigated case studies, the maximum variance within clinically significant structures was always reduced (on average by a factor of 6) in the therapeutic dose range generally. CMC takes only seconds to produce an accurate, high-resolution, low-uncertainly dose distribution for the low-energy PSB implants investigated in this study.