Intensity modulation under geometrical uncertainty: a deconvolution approach to robust fluence

A deconvolution algorithm has been developed to obtain robust fluence for external beam radiation treatment under geometrical uncertainties. Usually, the geometrical uncertainty is incorporated in the dose optimization process for inverse treatment planning to determine the additional intensity modulation of the beam to counter the geometrical uncertainty. Most of these approaches rely on dose convolution which is subject to the error caused by patient surface curvature and internal inhomogeneity. In this work, based on an 1D deconvolution algorithm developed by Ulmer and Kaissl, a fluence-deconvolution approach was developed to obtain robust fluence through the deconvolution of the nominal static one given by any treatment planning system. It incorporates the geometrical uncertainty outside the dose optimization procedure and therefore avoids the error of dose convolution. Robust fluences were calculated for a 4 x 4 cm flat field, a prostate IMRT and a head and neck IMRT plan in a commercial treatment planning system. The corresponding doses were simulated for 30 fractions with the random Gaussian distribution of the iso-centers showing good agreement with the nominal static doses. The feasibility of this deconvolution approach for clinical IMRT planning has been demonstrated. Because it is separated from the optimization procedure, this method is more flexible and easier to integrate into different existing treatment planning systems to obtain robust fluence.