Inclusion of geometrical uncertainties in radiotherapy treatment planning by means of coverage probability.

PURPOSE: Following the ICRU-50 recommendations, geometrical uncertainties in tumor position during radiotherapy treatments are generally included in the treatment planning by adding a margin to the clinical target volume (CTV) to yield the planning target volume (PTV). We have developed a method for automatic calculation of this margin. METHODS AND MATERIALS: Geometrical uncertainties of a specific patient group can normally be characterized by the standard deviation of the distribution of systematic deviations in the patient group (Sigma) and by the average standard deviation of the distribution of random deviations (sigma). The CTV of a patient to be planned can be represented in a 3D matrix in the treatment room coordinate system with voxel values one inside and zero outside the CTV. Convolution of this matrix with the appropriate probability distributions for translations and rotations yields a matrix with coverage probabilities (CPs) which is defined as the probability for each point to be covered by the CTV. The PTV can then be chosen as a volume corresponding to a certain iso-probability level. Separate calculations are performed for systematic and random deviations. Iso-probability volumes are selected in such a way that a high percentage of the CTV volume (on average > 99%) receives a high dose (> 95%). The consequences of systematic deviations on the dose distribution in the CTV can be estimated by calculation of dose histograms of the CP matrix for systematic deviations, resulting in a so-called dose probability histogram (DPH). A DPH represents the average dose volume histogram (DVH) for all systematic deviations in the patient group. The consequences of random deviations can be calculated by convolution of the dose distribution with the probability distributions for random deviations. Using the convolved dose matrix in the DPH calculation yields full information about the influence of geometrical uncertainties on the dose in the CTV.
RESULTS: The model is demonstrated to be fast and accurate for a prostate, cervix, and lung cancer case. A CTV-to-PTV margin size which ensures at least 95% dose to (on average) 99% of the CTV, appears to be equal to about 2Sigma + 0.7sigma for three all cases. Because rotational deviations are included, the resulting margins can be anisotropic, as shown for the prostate cancer case.
CONCLUSION: A method has been developed for calculation of CTV-to-PTV margins based on the assumption that the CTV should be adequately irradiated with a high probability.