Three Dimensional Expansion of Margins for Single-fraction Treatments: Stereotactic Radiosurgery Brain Cases

Purpose: To derive a clinically-practical margin formula between clinical target volume (CTV) and planning target volume (PTV) for single-fraction stereotactic radiosurgery (SRS).Methods: In previous publications on the margin between the CTV and the PTV, a Gaussian function with zero mean was assumed for the systematic error and the ma-chine systematic error was completely ignored. In this work we adopted a Dirac delta function for the machine system-atic error for a given machine with nonzero mean systematic error. Mathematical formulas for calculating the CTV-PTV margin for single-fraction SRS treatments were proposed. Results: Margins for single fraction treatments were derived such that the CTVs received the prescribed dose in 95% of the SRS patients. The margin defined in this study was machine specific and accounted for nonzero mean systematic error. The differences between our formulas and a previously published formula were discussed. Conclusion: Clinical margin formulas were proposed for deter-mining the margin between the CTV and the PTV in SRS treatments. Previous margin's recipes, being derived specifi-cally for conventional treatments, may be inappropriate for single-fraction SRS and could result in geometric miss of the target and even treatment failure for machines possessing of large systematic errors.