The effect of Monte Carlo statistical uncertainties on the evaluation of dose distributions in radiation treatment planning

This paper discusses the effect of statistical uncertainties present in Monte Carlo (MC) calculated dose distributions on the evaluation of a 'cost function' that expresses the suitability of a treatment plan for the intended treatment. The mathematical derivations given are valid for any 'well-behaved' cost function. The validity of the general expressions is demonstrated using numerical examples. It is shown that random dose uncertainties lead to statistical and systematic uncertainties on the cost function. The balance between the two types of uncertainty and the desired accuracy on the cost function presents a clear criterion for the maximum acceptable MC dose uncertainties. It is demonstrated that it is possible to remove the systematic cost function uncertainty. Finally, it is shown that when the dose distribution is close to a true optimum, MC calculations of the cost function converge to the true result as one over the number of particles simulated, i.e. much faster than the individual close uncertainties.