PV QA 3 - Poster Viewing Q&A 3
TU_18_3293 - Additional PTV margin for compensating rotational error is not a linear function of the distance between isocenter and treatment target.
Tuesday, October 23
1:00 PM - 2:30 PM
Location: Innovation Hub, Exhibit Hall 3
Additional PTV margin for compensating rotational error is not a linear function of the distance between isocenter and treatment target.
J. Chang; Radiation Medicine, Northwell Health, Lake Success, NY; Department of Physics and Astronomy, Hofstra University, Hempstead, NY
Purpose/Objective(s): The single isocenter for multiple targets (SIMT) technique is a popular treatment approach for multiple brain metastases but there is no consensus on how to compensate for the rotational error it introduces. Some suggested that the PTV expansion should be increased linearly with the distance between the isocenter and treatment target. In this study the author challenged these published margin recipes and hypothesized that the additional PTV margin is not a linear function as suggested. The purpose of this study was to derive the correct margin recipe for the SIMT technique using a previously developed statistical model that considers both translational and rotational uncertainties.
Materials/Methods: In the statistical model, both translational and rotational errors are assumed to follow the three-dimensional independent normal distribution with a zero mean, and standard deviations of respectively σS and σR, where σR = 0.01424 σD (rotation uncertainty in degree)× dI⇔T (distance in mm from isocenter to target). Based on this model, the author derived in this study the formulas for combined PTV margin, ME, and additional PTV margin, ΔM=ME-MS, required to maintain the same coverage probability when the rotational uncertainty is present, as a function of MS (initial PTV margin), σD and dI⇔T. Formulas for the maximal allowable dI⇔T and σD were also derived as a function of user-specified ΔMC/ MS, the fraction of MS below which the extra PTV margins can be ignored.
Results: Unlike other reported margin recipes, ΔM increases linearly with dI⇔T and σD only when there is no translational setup error, i.e., MS=0. When MS≠0, ΔM is a non-linear function of dI⇔T and σD but asymptotically approach a linear function for large dI⇔TσD. Using the derived formulas, values of ME and ΔM were calculated and plotted for commonly encountered clinical parameters including dI⇔T, MS or σD. It is observed from the plot that ΔM is insignificant when MS is dominant, and becomes more pronounced for larger dI⇔TσD. Cutoff value (dI⇔T σD)C for user specified ΔMC /MS is a linear function of σS with slope k(ΔMC/ MS), which is a function of ΔMC/ MS and is independent of the coverage probability. The following table lists k(ΔMC/ MS) values for a few selected ΔMC/MS with corresponding (dI⇔T σD)C (in mm·degree) for σs=0.71 mm. (dI⇔T)C or the maximally allowable dI⇔T (in mm) is also tabulated for two (0.3° and 0.45°) commonly encountered σD in clinics.
| ΔMC/ MS || 1% || 5% || 10% || 15% || 20% || 30% || 40% || 50% |
| k(ΔMC/ MS) || 10.0 || 22.5 || 32.2 || 39.9 || 46.6 || 58.3 || 68.8 || 78.5 |
| (dI⇔T σD)C in mm·degree for σs=0.71 mm || 7 || 16 || 23 || 28 || 33 || 41 || 49 || 56 |
| (dI⇔T)C in mm for σD=0.3°, σs=0.71 mm || 24 || 53 || 76 || 94 || 110 || 138 || 163 || 186 |
| (dI⇔T)C in mm for σD=0.45°, σs=0.71 mm || 16 || 35 || 51 || 63 || 73 || 92 || 109 || 124 |
Conclusion: The additional PTV margin, ΔM, is not a linear function of dI⇔T and σD, and can be ignored when MS is dominant. Cutoff value (dI⇔T σD)C is independent of coverage probability if it is specified as a function of ΔMC /MS. The presented data provide a convenient way for clinics to determine if additional PTV margin is needed for the SIMT technique.
Author Disclosure: J. Chang: None.