Adjoint methods for radiation therapy treatment planning

Michael Kowalok, University of Wisconsin


The propagation of neutral particles (neutrons or gammas) through matter is described by the linear form of the Boltzmann transport equation. The conventional use of this equation is to transport particles from a source and solve for the distribution of particle flux within a system. Conversely, the mathematical adjoint to the Boltzmann equation describes the propagation of “adjoint particles” from a detector with a certain response function. The distribution of adjoint flux is used to predict the response of the detector to an arbitrary source introduced at any position in the system. The adjoint flux from the detector may also be interpreted as an “importance function” because it shows the importance of each source parameter to the magnitude of the detector’s response.

In this work, we investigate the use of forward and adjoint transport for external beam radiation therapy treatment planning. The goal for such planning is to devise a set of beams that will deliver a prescribed radiation dose to tumor tissue, yet spare nearby normal tissue structures as much as possible. We perform adjoint Monte Carlo calculations for each tumor and for each normal tissue structure. These calculations provide an estimate of which beams are most important for achieving the goals of the treatment plan. Based on this information, forward simulations are performed to accurately calculate the dose distributions for the most important beams. Iterations of forward and adjoint calculations are used to refine the set of beams for the treatment plan. This iterative method has shown the potential to increase the efficiency of the treatment planning process by focusing computational resources on the most important elements of the source field.

Abstract Author(s): M. Kowalok, R. Jeraj, T. Bohm, T.R. Mackie, D. Henderson