James F. Dempsey, H. Edwin Romeijn, Jonathan G. Li, Daniel A. Low, Jatinder R. Palta
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 irregardless 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. It is predicted and validated
that an isotropic dose grid with < 2.5 mm spacing is sufficient to prevent dose errors larger than a
percent. However, it is noted that in practice this resolution is mostly needed in high dose target
regions. Finally, an empirical analysis demonstrated that this resolution is needed most in high
dose targets and a multi-resolution 2-4-6 mm spacing model is developed where these spacings
are applied to targets, structures, and tissue, respectively.