Accelerated prompt gamma estimation for clinical proton therapy simulations

There is interest in the particle therapy community in using prompt gammas (PGs), a natural byproduct of particle treatment, for range verification and eventually dose control. However, PG production is a rare process and therefore estimation of PGs exiting a patient during a proton treatment plan executed by a Monte Carlo (MC) simulation converges slowly. Recently, different approaches to accelerating the estimation of PG yield have been presented. Sterpin et al (2015 Phys. Med. Biol. 60 4915-46) described a fast analytic method, which is still sensitive to heterogeneities. El Kanawati et al (2015 Phys. Med. Biol. 60 8067-86) described a variance reduction method (pgTLE) that accelerates the PG estimation by precomputing PG production probabilities as a function of energy and target materials, but has as a drawback that the proposed method is limited to analytical phantoms. We present a two-stage variance reduction method, named voxelized pgTLE (vpgTLE), that extends pgTLE to voxelized volumes. As a preliminary step, PG production probabilities are precomputed once and stored in a database. In stage 1, we simulate the interactions between the treatment plan and the patient CT with low statistic MC to obtain the spatial and spectral distribution of the PGs. As primary particles are propagated throughout the patient CT, the PG yields are computed in each voxel from the initial database, as a function of the current energy of the primary, the material in the voxel and the step length. The result is a voxelized image of PG yield, normalized to a single primary. The second stage uses this intermediate PG image as a source to generate and propagate the number of PGs throughout the rest of the scene geometry, e.g. into a detection device, corresponding to the number of primaries desired. We achieved a gain of around 10(3) for both a geometrical heterogeneous phantom and a complete patient CT treatment plan with respect to analog MC, at a convergence level of 2% relative uncertainty in the 90% yield region. The method agrees with reference analog MC simulations to within 10(-4), with negligible bias. Gains per voxel range from 10(2) to 10(4). The presented generic PG yield estimator is drop-in usable with any geometry and beam configuration. We showed a gain of three orders of magnitude compared to analog MC. With a large number of voxels and materials, memory consumption may be a concern and we discuss the consequences and possible tradeoffs. The method is available as part of Gate 7.2.