Kinetic-diffusion-rotation algorithm for dose estimation in electron beam therapy

Monte Carlo methods are state-of-the-art when it comes to dosimetric computations in radiotherapy. However, the execution time of these methods suffers in high-collisional regimes. We address this problem by introducing a kinetic-diffusion particle tracing scheme. This algorithm, first proposed in the context of neutral transport in fusion energy, relies on the explicit simulation of the exact kinetic motion in low-collisional regimes and dynamically switches to an approximate random walk in high-collisional regimes. The random walk corresponds to an advection-diffusion process that preserves the first two moments (mean and variance) of the kinetic motion. We derive an analytic formula for the mean kinetic motion and discuss the addition of a multiple scattering distribution to the algorithm. In contrast to neutral transport, the electron beam therapy setting does not readily admit to an analytical expression for the variance of the kinetic motion, and we therefore resort to the use of a lookup table. We test the algorithm for dosimetric computations in electron beam therapy on a 2D CT scan of a lung patient. Using a simple particle model, our Python implementation of the algorithm is nearly 33 times faster than an equivalent kinetic simulation at the cost of a small modeling error.