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 machine systematic error was completely ignored. In this work we adopted a Dirac delta function for the machine systematic 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 determining the margin between the CTV and the PTV in SRS treatments. Previous margin’s recipes, being derived specifically 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.

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