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

The aim of this work is to investigate the influence of the statistical flu ctuations of Monte Carlo (MC) dose distributions on the dose volume histogr ams (DVHs) and radiobiological models, in particular the Poisson model for tumour control probability (tcp). The MC matrix is characterized by a mean dose in each scoring voxel, d, and a statistical error on the mean dose, si gma(d); whilst the quantities d and sigma(d) depend on many statistical and physical parameters, here we consider only their dependence on the phantom voxel size and the number of histories from the radiation source. Dose distributions from high-energy photon beams have been analysed. It has been found that the DVH broadens when increasing the statistical noise of the dose distribution, and the tcp calculation systematically underestimate s the real tumour control value, defined here as the value of tumour contro l when the statistical error of the dose distribution tends to zero. When i ncreasing the number of energy deposition events, either by increasing the voxel dimensions or increasing the number of histories from the source, the DVH broadening decreases and tcp converges to the 'correct' value. It is s hown that the underestimation of the tcp due to the noise in the dose distr ibution depends on the degree of heterogeneity of the radiobiological param eters over the population; in particular this error decreases with increasi ng the biological heterogeneity, whereas it becomes significant in the hypo thesis of a radiosensitivity assay for single patients, or for subgroups of patients. It has been found, for example, that when the voxel dimension is changed fr om a cube with sides of 0.5 cm to a cube with sides of 0.25 cm (with a fixe d number of histories of 10(8) from the source), the systematic error in th e tcp calculation is about 75% in the homogeneous hypothesis, and it decrea ses to a minimum value of about 15% in a case of high radiobiological heter ogeneity. The possibility of using the error on the rep to decide how many histories to run for a given voxel size is also discussed.