A fourier analysis of the dose grid resolution required for accurate IMRT fluence map optimization

We present a theoretical and empirical analysis of the errors associated with the spatial discretization of the dose grid employed in optimized intensity modulated radiation therapy (IMRT) treatment plans. An information theory based Fourier analysis of the accuracy of discrete representations of three-dimensional dose distributions is presented. When applied to beamlet-based IMRT dose distributions, the theory produces analytic integrals that can bound worst case aliasing errors that can occur regardless of the location and orientation of the dose grid. The predictions of this theory are compared to empirical results obtained by solving a linear-programming based fluence-map optimization model to global optimality. A reasonable agreement between worst case estimates and the empirical results is attributed to the fact that the optimization takes advantage of aliasing to produce an optimal plan. We predicted and empirically demonstrated that an isotropic dose grid with <2.5 mm spacing is sufficient to prevent dose errors larger than a percent. However, we noted that in practice this resolution is mostly needed in high-dose target regions. Finally, a multiresolution 2-4-6 mm spacing model was developed and empirically tested where these spacings were applied to targets, structures, and tissue, respectively.