Incorporating the rotational setup uncertainty into the planning target volume margin expansion for the single isocenter for multiple targets technique.

Abstract

The single isocenter for multiple targets (SIMT) technique has become a popular treatment approach for multiple brain metastases. However, the rotational error that is introduced is usually not considered in planning target volume (PTV) expansion. We have developed a statistical model that takes into account both translational and rotational uncertainties. In this study, we incorporated the rotational error into PTV margin expansion for the clinical use of the SIMT technique. In the statistical model, both translational and rotational errors are assumed to follow the 3-dimensional, independent, normal distribution with a zero mean and standard deviations of σ_S and σ_R, where σ_R = 0.01424σ_D (rotational uncertainty in degree)×d_I ⇔ T (distance in mm from isocenter to target). Based on this model, we derived in this study the additional PTV margin, ∆M, that is required to maintain the same coverage probability when the rotational uncertainty is present as a function of M_S (initial PTV margin), σ_D, and d_I ⇔ T. The maximum allowable d_{I ⇔ T, C} and σ_{D, C} were also calculated as a function of user-specified ∆M_c/M_S, the fraction of M_S below which the extra PTV margins can be ignored. Combined PTV margin, M_E, and additional PTV margin, ∆M, were plotted for commonly encountered clinical parameters including d_I ⇔ T, M_S, or σ_D. Unlike other reported margin recipes, ∆M is not a linear function of any of these 3 parameters. In addition, the rate of increase for ∆M is quite slow for small d_I ⇔ T and becomes more significant for larger d_I ⇔ T. Cutoff values d_{I ⇔ T, C} and σ_{D, C} were also plotted for various ∆M_c/M_S, which can be used to determine if an additional PTV margin is needed for the SIMT technique. The presented data provide a convenient way for clinics to determine the appropriate PTV margin for the SIMT technique.