Coupled reduced order model and adjoint methodologies for proton therapy

Abstract

The goal of this project is to see if we can improve the treatment plan for proton therapy by using reduced order models and adjoint theory for proton therapy. We shall use a singular value decomposition on a dose distribution matrix to obtain the modes from which we can reconstruct every dose distribution. Using adjoint methodologies for proton therapy, we will define a response from which we can find the sensitivities, or gradient, in order to fit a Hermite interpolation polynomial on multidimensional simplices. The results show that the Hermite interpolation polynomial is a useful tool to find responses for low dimensional problems. For errors in one or two dimensions, the Hermite polynomial was able to reconstruct all dose distributions with R²=1. However, for an error in three dimensions the Hermite polynomial sometimes fails to reconstruct the dose distribution to within acceptable margins. We conclude that the combination of a ROM and adjoint method to find Hermite interpolation polynomial is a promising tool in order to further improve the proton therapy treatment plan. Further research should be done in order to determine whether Hermite interpolation can be used in every scenario, or if it fails if the grid becomes irregular. Finally, the extrapolating qualities of the Hermite polynomial should be tested.