Monte Carlo simulations are widely used, but it has been argued that a grid-based Boltzmann solution should have the same computational complexity. In addition, transport equation models have two advantages: Reduced models can be derived in a systematic manner, and analytical expressions for gradient can be obtained, which is useful for optimization.
We present recent advances in the modeling of dose calculation and treatment plan optimization using transport equations and reduced models. Computational results will be presented as 3D videos.