The effect of statistical uncertainty on inverse treatment planning based on Monte Carlo dose calculation

The effect of the statistical uncertainty, or noise, in inverse treatment p lanning for intensity modulated radiotherapy (IMRT) based on Monte Carlo do se calculation was studied. Sets of Monte Carlo beamlets were calculated to give uncertainties at D-max ranging from 0.2% to 4% for a lung tumour plan . The weights of these beamlets were optimized using a previously described procedure based on a simulated annealing optimization algorithm. Several d ifferent objective functions were used. It was determined that the use of M onte Carlo dose calculation in inverse treatment planning introduces two er rors in the calculated plan. In addition to the statistical error due to th e statistical uncertainty of the Monte Carlo calculation, a noise convergen ce error also appears. For the statistical error it was determined that app arently successfully optimized plans with a noisy dose calculation (3% 1 si gma at D-max), which satisfied the required uniformity of the dose within t he tumour, showed as much as 7% underdose when recalculated with a noise-fr ee dose calculation. The statistical error is larger towards the tumour and is only weakly dependent on the choice of objective function. The noise co nvergence error appears because the optimum weights are determined using a noisy calculation, which is different from the optimum weights determined f or a noise-free calculation. Unlike the statistical error, the noise conver gence error is generally larger outside the tumour, is case dependent and s trongly depends on the required objectives.