Computation of mean and variance of the radiotherapy dose for PCA-modeled random shape and position variations of the target

Radiotherapy dose delivery in the tumor and surrounding healthy tissues is affected by movements and deformations of the corresponding organs between fractions. The random variations may be characterized by non-rigid, anisotropic principal component analysis (PCA) modes. In this article new dynamic dose deposition matrices, based on established PCA modes, are introduced as a tool to evaluate the mean and the variance of the dose at each target point resulting from any given set of fluence profiles. The method is tested for a simple cubic geometry and for a prostate case. The movements spread out the distributions of the mean dose and cause the variance of the dose to be highest near the edges of the beams. The non-rigidity and anisotropy of the movements are reflected in both quantities. The dynamic dose deposition matrices facilitate the inclusion of the mean and the variance of the dose in the existing fluence-profile optimizer for radiotherapy planning, to ensure robust plans with respect to the movements.