A workflow to select local tolerance limits by combining statistical process control and error curve model.

Abstract

Background: Patient-specific quality assurance (QA) is a complicated process specific to personnel, equipment, and procedure. The universal or commonly used tolerance limits may not be applicable to local situations. Therefore, it is a need for a medical physicist to establish appropriate local tolerance limits based on actual situations and quantitatively evaluate the error sensitivity of selected tolerance limits to determine their availability in clinical practice.

Purpose: This study aims to develop a comprehensive and scientifically sound methodology for determining appropriate local tolerance limits in patient-specific QA.

Methods and materials: A total of 214 RapidArc plans for cervical cancer were selected. Systematic multi-leaf collimator (MLC) positional errors were simulated across eighteen offsets ranging from ± 0.2 to ± 5 mm. Dose verification was conducted on 808 RapidArc plans, and a retrospective review was carried out. Firstly, six commonly used QA metrics in gamma and DVH analysis were extracted from the QA results of 196 error-free RapidArc plans. These QA metrics included GP₁₀ (gamma passing rates [GPRs] at 3%/2mm, 10% dose threshold), GP₅₀ (GPRs at 3%/2mm, 50% dose threshold), µGI₅₀ (mean gamma index at 3%/2mm, 50% dose threshold), PTV₉₅ (dose received by 95% of PTV), PTV₅ (dose received by 5% of PTV) and PTV_mean (mean dose received by PTV). Secondly, the statistical process control was used to establish the corresponding tolerance limits for each metric. Then, six error curve models were created based on 360 error-introduced plans to record changes in QA metrics under different magnitudes of MLC positional error. The error range of theoretical detection limits for systematic MLC positional errors was investigated to assess error sensitivity quantitatively using the error curve model. Finally, the process-based tolerance limits of six single QA metrics and four combined QA metrics were validated by using 252 sets of test data. The binary classification performance (error-free/error-introduced) was assessed based on detection rate, accuracy, precision, recall, and f1-score.

Results: The theoretical detection limits for process-based tolerance limits of GP₁₀, GP₅₀, µGI₅₀, PTV₉₅, PTV_mean, and PTV₅ were 2.19 mm, 2.71 mm, 3.52 mm, 1.93 mm, 3.20 mm, and 2.15 mm, respectively. In the validation phase, the process-based tolerance limits for PTV₉₅ effectively identified systematic MLC positional errors exceeding 0.6 mm with a detection rate of 76.19%, displaying superior performance in binary classification among six single metrics. Regarding combined metrics, the joint evaluation of process-based tolerance limits for GP₁₀ and PTV₉₅ showed a higher detection rate of 80.16% for systematic MLC positional errors exceeding 0.6 mm.

Conclusion: The proposed workflow integrates the establishment and validation of tolerance limits. It not only provides a practical tool for setting local tolerance limits based on actual clinical scenarios but also offers a quantitative method for medical physicists to understand the error sensitivity of the selected local tolerance limits.