Monte Carlo dose calculations and radiobiological modelling: analysisof the effect of the statistical noise of the dose distribution on theprobability of tumour control

Abstract

The aim of this work is to investigate the influence of the statisticalfluctuations of Monte Carlo (MC) dose distributions on the dose volumehistograms (DVHs) and radiobiological models, in particular the Poisson modelfor tumour control probability (tcp). The MC matrix is characterized by a meandose in each scoring voxel, d, and a statistical error on the mean dose,σd; whilst the quantities d and σd depend on manystatistical and physical parameters, here we consider only their dependence onthe phantom voxel size and the number of histories from the radiation source.Dose distributions from high-energy photon beams have been analysed. It hasbeen found that the DVH broadens when increasing the statistical noise of thedose distribution, and the tcp calculation systematically underestimates thereal tumour control value, defined here as the value of tumour control whenthe statistical error of the dose distribution tends to zero. When increasingthe number of energy deposition events, either by increasing the voxeldimensions or increasing the number of histories from the source, the DVHbroadening decreases and tcp converges to the `correct' value. It is shownthat the underestimation of the tcp due to the noise in the dose distributiondepends on the degree of heterogeneity of the radiobiological parameters overthe population; in particular this error decreases with increasing thebiological heterogeneity, whereas it becomes significant in the hypothesis ofa radiosensitivity assay for single patients, or for subgroups of patients.It has been found, for example, that when the voxel dimension is changed froma cube with sides of 0.5 cm to a cube with sides of 0.25 cm (with a fixednumber of histories of 108 from the source), the systematic error in thetcp calculation is about 75% in the homogeneous hypothesis, and it decreasesto a minimum value of about 15% in a case of high radiobiologicalheterogeneity. The possibility of using the error on the tcp to decide howmany histories to run for a given voxel size is also discussed.