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Purpose:   Setting a proper margin is crucial for not only delivering the required radiation dose to a target volume, but also reducing the unnecessary radiation to the adjacent organs at risk. This study investigated the independent one‐dimensional symmetric and asymmetric margins between the clinical target volume (CTV) and the planning target volume (PTV) for linac‐based single‐fraction frameless stereotactic radiosurgery (SRS).Methods:   The authors assumed a Dirac delta function for the systematic error of a specific machine and a Gaussian function for the residual setup errors. Margin formulas were then derived in details to arrive at a suitable CTV‐to‐PTV margin for single‐fraction frameless SRS. Such a margin ensured that the CTV would receive the prescribed dose in 95% of the patients. To validate our margin formalism, the authors retrospectively analyzed nine patients who were previously treated with noncoplanar conformal beams. Cone‐beam computed tomography (CBCT) was used in the patient setup. The isocenter shifts between the CBCT and linac were measured for a Varian Trilogy linear accelerator for three months. For each plan, the authors shifted the isocenter of the plan in each direction by ±3 mm simultaneously to simulate the worst setup scenario. Subsequently, the asymptotic behavior of the CTV V 80%  for each patient was studied as the setup error approached the CTV‐PTV margin.Results:   The authors found that the proper margin for single‐fraction frameless SRS cases with brain cancer was about 3 mm for the machine investigated in this study. The isocenter shifts between the CBCT and the linac remained almost constant over a period of three months for this specific machine. This confirmed our assumption that the machine systematic error distribution could be approximated as a delta function. This definition is especially relevant to a single‐fraction treatment. The prescribed dose coverage for all the patients investigated was 96.1% ± 5.5% with an extreme 3‐mm setup error in all three directions simultaneously. It was found that the effect of the setup error on dose coverage was tumor location dependent. It mostly affected the tumors located in the posterior part of the brain, resulting in a minimum coverage of approximately 72%. This was entirely due to the unique geometry of the posterior head.Conclusions:   Margin expansion formulas were derived for single‐fraction frameless SRS such that the CTV would receive the prescribed dose in 95% of the patients treated for brain cancer. The margins defined in this study are machine‐specific and account for nonzero mean systematic error. The margin for single‐fraction SRS for a group of machines was also derived in this paper.

Three independent one‐dimensional margins for single‐fraction frameless stereotactic radiosurgery brain cases using CBCT