Split exponential track length estimator for Monte-Carlo simulations of small-animal radiation therapy

We propose the split exponential track length estimator (seTLE), a new kerma-based method combining the exponential variant of the TLE and a splitting strategy to speed up Monte Carlo (MC) dose computation for low energy photon beams. The splitting strategy is applied to both the primary and the secondary emitted photons, triggered by either the MC events generator for primaries or the photon interactions generator for secondaries. Split photons are replaced by virtual particles for fast dose calculation using the exponential TLE. Virtual particles are propagated by ray-tracing in voxelized volumes and by conventional MC navigation elsewhere. Hence, the contribution of volumes such as collimators, treatment couch and holding devices can be taken into account in the dose calculation. We evaluated and analysed the seTLE method for two realistic small animal radiotherapy treatment plans. The effect of the kerma approximation, i.e. the complete deactivation of electron transport, was investigated. The efficiency of seTLE against splitting multiplicities was also studied. A benchmark with analog MC and TLE was carried out in terms of dose convergence and efficiency. The results showed that the deactivation of electrons impacts the dose at the water/bone interface in high dose regions. The maximum and mean dose differences normalized to the dose at the isocenter were, respectively of 14% and 2% . Optimal splitting multiplicities were found to be around 300. In all situations, discrepancies in integral dose were below 0.5% and 99.8% of the voxels fulfilled a 1%/0.3 mm gamma index criterion. Efficiency gains of seTLE varied from 3.2 × 10⁵ to 7.7 × 10⁵ compared to analog MC and from 13 to 15 compared to conventional TLE. In conclusion, seTLE provides results similar to the TLE while increasing the efficiency by a factor between 13 and 15, which makes it particularly well-suited to typical small animal radiation therapy applications. (paper)