Smoothing Monte Carlo calculated dose distributions by iterative reduction of noise

A smoothing algorithm based on an optimization procedure is presented and evaluated for single electron and photon beams and a full intensity modulated radiation therapy (IMRT) delivery. The algorithm iteratively reduces the statistical noise of Monte Carlo (MC) calculated dose distributions. It is called IRON (iterative reduction of noise). By varying the dose in each voxel, the algorithm minimizes the second partial derivatives of dose with respect to X, Y and Z. An additional restoration term ensures that too large dose changes are prevented. IRON requires a MC calculated one-dimensional or three-dimensional dose distribution with or without known statistical uncertainties as input. The algorithm is tested using three different treatment plan examples, a photon beam dose distribution in water, an IMRT plan of a real patient and an electron beam dose distribution in a water phantom with inhomogeneities. It is shown that smoothing can lead to an additional reduction of MC calculation time by factors of 2 to 10. This is especially useful if MC dose calculation is part of an inverse treatment planning system. In addition to this, it is shown that smoothing a noisy dose distribution may introduce some bias into the final dose values by converting the statistical uncertainty of the dose distribution into a systematic deviation of the dose value.