Motion-encoded dose calculation through fluence/sinogram modification.

Conventional radiotherapy treatment planning systems rely on a static computed tomography (CT) image for planning and evaluation. Intra/inter-fraction patient motions may result in significant differences between the planned and the delivered dose. In this paper, we develop a method to incorporate the knowledge of intra/inter-fraction patient motion directly into the dose calculation. By decomposing the motion into a parallel (to beam direction) component and perpendicular (to beam direction) component, we show that the motion effects can be accounted for by simply modifying the fluence distribution (sinogram). After such modification, dose calculation is the same as those based on a static planning image. This method is superior to the "dose-convolution" method because it is not based on "shift invariant" assumption. Therefore, it deals with material heterogeneity and surface curvature very well. We test our method using extensive simulations, which include four phantoms, four motion patterns, and three plan beams. We compare our method with the "dose-convolution" and the "stochastic simulation" methods (gold standard). As for the homogeneous flat surface phantom, our method has similar accuracy as the "dose-convolution" method. As for all other phantoms, our method outperforms the "dose-convolution." The maximum motion encoded dose calculation error using our method is within 4% of the gold standard. It is shown that a treatment planning system that is based on "motion-encoded dose calculation" can incorporate random and systematic motion errors in a very simple fashion. Under this approximation, in principle, a planning target volume definition is not required, since it already accounts for the intra/inter-fraction motion variations and it automatically optimizes the cumulative dose rather than the single fraction dose.