Deterministic photon kerma distribution based on the Boltzmann equation for external beam radiation therapy.

A photon transport algorithm for fully three-dimensional radiotherapy treatment planning has been developed based on the discrete ordinates (SN) solution of the Boltzmann equation. The algorithm is characterized by orthogonal adaptive meshes, which place additional points where large gradients occur and a procedure to evaluate the collided flux using the representation of spherical harmonic expansion instead of the summation of the volume-weighted contribution from discrete angles. The Boltzmann equation was solved in the form of SN spatial, energy, and angular discretization with mitigation of ray effects by the first-collision source method. Unlike existing SN codes, which were designed for general purpose for multiparticle transport in areas such as nuclear engineering, our code is optimized for medical radiation transport. To validate the algorithm, several examples were employed to calculate the photon flux distribution. Numerical results show good agreement with the Monte Carlo calculations using EGSnrc.