The population percentile allowance method for determining systematic spatial error tolerances for temporary intensity modulated brachytherapy

Abstract

Background: Multiple approaches are under development for delivering temporary intensity modulated brachytherapy (IMBT) using partially shielded applicators wherein the delivered dose distributions are sensitive to spatial uncertainties in both the applicator position and shield orientation, rather than only applicator position as with conventional high-dose-rate brachytherapy (HDR-BT). Sensitivity analyses to spatial uncertainties have been reported as components of publications on these emerging technologies, however, a generalized framework for the rigorous determination of the spatial uncertainty tolerances of dose-volume parameters is needed. Purpose: To derive and present the population percentile allowance (PPA) method, a generalized mathematical and statistical framework to evaluate the tolerance of temporary IMBT approaches to spatial uncertainties in applicator position and shield orientation. Methods: A mathematical formalism describing geometric applicator position and shield orientation shifts was derived that supports straight and curved applicators and applies to serial and helical rotating shield brachytherapy (RSBT) and direction modulated brachytherapy (DMBT). The PPA method entails defining the percentage of a patient population receiving a given therapy that is, allowed to receive dose-volume errors in the target volume and specified organs at risk of a defined percentage or less, then determining what combinations of applicator position and shield orientation systematic errors would be expected to produce that outcome in the population. The PPA method was applied to the use case of multi-shield helical 169Yb-based RSBT for cervical cancer, with 45° and 180° shield emission angles. A total of 37 cervical cancer patients were considered in the population, with average (± 1 standard deviation) HR-CTV volumes of 79 cm3 ± 37 cm3 and optimized baseline treatment plans (no spatial uncertainties applied) created for each patient to meet dose-volume requirements of 85 GyEQD2 (equivalent uniform dose in 2 Gy fraction), with D2cc tolerance doses of 90 GyEQD2, 75 GyEQD2, and 75 GyEQD2 for bladder, rectum, and sigmoid colon, respectively. Results: For the PPA requirement that 90% of cervical cancer patients receiving multi-shield helical RSBT could have a maximum dose-volume uncertainty of 10% for high-risk clinical target volume (HR-CTV) D90 (minimum dose to hottest 90%) and bladder, rectum, and sigmoid colon D2cc (minimum dose to hottest 2 cm3), the tolerance systematic applicator position and shield orientation uncertainties were approximately ± 1.0 mm and ± 4.25°, respectively. For ± 1.5 mm and ± 5° systematic applicator position and shield orientation tolerances, 90% of the patients considered would have a maximum dose-volume uncertainty of 12.8% or less. Conclusion: The PPA method was formalized to determine the temporary IMBT spatial uncertainty tolerances that would be expected to result in an allowed percentage of a population of patients receiving relative dose-volume errors above a defined percentage. Multi-shield, helical 169Yb-based RSBT for cervical cancer was evaluated and tolerances determined, which, if applied on each treatment fraction, would represent an extreme situation. The PPA method is applicable to a variety of temporary IMBT approaches and can be used to rigorously determine the design parameters for the delivery systems such as mechanical driver motor accuracy, shield angle backlash, applicator rotation, and applicator fixation stability.