A Statistical Index for Evaluating the CTV Coverage Loss of Brain Stereotactic Radiosurgery When the PTV Margin Is Zero

Purpose: To develop a new statistical index “percent CTV (clinical target volume) coverage probability” (%CCP), defined as the probability that a specific percent (e.g., 95%) of the CTV can be reliably covered by the prescription dose, for evaluating the coverage loss of brain (fractionated) stereotactic radiosurgery (SRS/fSRS) when the PTV (planning target volume) margin is zero. Methods: The random variable Q for CTV percent coverage was derived using a previously developed model for CTV random motion that follows a three-dimensional (3D) independent normal distribution with a zero mean and a standard deviation of S σ (for translation) or δ σ (for rotation). Assuming both CTV and PTV are spherical with the same diameter d CTV , the cumulative distribution function of Q could be obtained analytically using the relation of sphere-sphere intersection. The %CCP was then derived as the reliability function of Q and was used to quantify the coverage loss for selected d CTV . Results: The 95% - 95% clinical goal (95% of the times, at least 95% of the CTV is covered) is not achievable with d CTV < 42 mm. For common CTVs (d CTV < 20 mm) encountered in SRS/fSRS, only 60% - 90% of the CTV could be reliably covered by the prescription dose 95% of the time. For 0.5 mm S σ = and 0.4 δ σ =  , the 95% CCP was the highest when the distance between the CTV and the isocenter 0 I T d ⇔ = and gradually decreased with the increasing I T d ⇔ . Conclusions: The %CCP was successfully derived for evaluating the CTV coverage loss for brain SRS/fSRS. When the PTV margin is zero, the 95% - 95% clinical goal cannot be achieved for most targets (d CTV < 42 mm).