Radiotherapy quality assurance using statistical process control Diana Binny 1,2[0000-0002-9288-5496], Craig M Lancaster3[0000-0002-8797-9586], Tanya Kairn , Jamie V Trapp2[0000-0001-5254-0728], Scott B Crowe2,3 [0000-0001-70282,3[0000-0002-2136-6138]
6452] 1 Radiation Oncology Centres, Redlands, Australia Queensland University of Technology, Brisbane, Australia 3 Cancer Care Services, Royal Brisbane and Women’s Hospital, Brisbane, Australia 2
[email protected]
Abstract. Statistical process control (SPC) is an analytical decision-making tool that employs statistics to measure and monitor a system process. The fundamental concept of SPC is to compare current statistics in a process with its previous corresponding statistic for a given period. Using SPC, a control chart is obtained to identify random and systematic variations based on the mean of the process and trends are observed to see how data can vary in each evaluated period. An upper and lower control limit in an SPC derived control chart indicate the range of the process calculated based on the standard deviations from the mean, thereby points that are outside these limits indicate the process to be out of control. Metrics such as: process capability and acceptability ratios were employed to assess whether an applied tolerance is applicable to the existing process. SPC has been applied in this study to assess and recommend quality assurance tolerances in the radiotherapy practice for helical tomotherapy. Various machine parameters such as beam output, energy, couch travel as well as treatment planning parameters such as minimum percentage of open multileaf collimators (MLC) during treatment, planned pitch (couch travel per gantry rotation) and modulation factor (beam intensity) were verified against their delivery quality assurance tolerances to produce SPC based tolerances. Results obtained were an indication of the current processes and mechanical capabilities in the department rather than a vendor recommended or a prescriptive approach based on machine technicalities. In this study, we have provided a simple yet effective method and analysis results to recommend tolerances for a radiotherapy practice. This can help improve treatment efficiency and reduce inaccuracies in dose delivery using an assessment tool that can identify systematic and random variations in a process and hence avoid potential hazardous outcomes. Keywords: Radiation therapy, statistical process control, quality assurance, tomotherapy.
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1
Introduction
Recent advances in radiotherapy have sparked the need to reform quality check processes and tighten specifications set on treatment delivery systems[1]. Quality assurance (QA) of radiotherapy systems is a process to identify Type A and Type B errors against baseline or tolerance levels and is generally performed according to published guidelines and recommendations to ensure that the process quality conforms with existing standards [2-4]. The increased complexity of the treatment planning and delivery process requires thorough evaluation of QA procedures and subsequent dosimetric measurements to make informed decisions in the practice of radiation oncology[5, 6]. However, it is also necessary to determine the treatment system capabilities prior to imposing tolerances recommended by local or national standards[2, 7, 8]. With evolving treatment techniques, QA programs that ensure treatment dose is within a clinical tolerance are no longer sufficient and the process of quality assurance should include identifying and improving underlying uncertainties in the process to minimise variations [9]. Computational methods [10-12] have been applied in radiotherapy to verify if systems operate within their specifications. Statistical process control (SPC)[13] is one such tool that converts data into information to document, correct and improve system performance by testing if the mean and the dispersion of the measured data is stable over the period of analysis. TomoTherapy Hi-Art II system (Accuray, Inc., Sunnyvale, CA) is a hybrid between a 6MV linear accelerator and a helical megavoltage CT (MVCT) scanner capable of helically delivering intensity modulated radiation therapy (IMRT) combined with the advancing translational motion of a treatment couch [14]. The ratio of maximum to average of non-zero leaf open times is restricted to a particular value (also known as the modulation factor) between unity and five to enable optimised treatment delivery[14, 15]. Planning studies have demonstrated dosimetric advantages of using helical tomotherapy for sites such as breast, prostate, brain and head and neck over non-rotational treatment techniques [16-19]. However, delivery aspects of the treatment plan rely heavily on the user’s TPS input parameters, such as modulation factor (MF), field width (FW) and pitch [14, 20]. These parameters are modified in the TPS to produce an optimal plan. Despite the numerous amount of tomotherapy planning studies [14, 21-25] to recommend optimal parameters, no consensus was observed in recommendations to derive optimal plan parameters based on SPC methods. Additionally, no published data were found to recommend optimal dosimetric and mechanical tolerances in regard to machine output and tomotherapy couch position accuracy respectively. Knowledge of such a relationship would benefit quality assurance to improve treatment deliverability and detect possible flaws in the machine behaviour before an unforeseeable event. In this work, we demonstrate SPC utilisation for (i) dosimetric, (iii) mechanical and (iii) patient-specific QA for tomotherapy.
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2
Method and Materials
During an SPC analysis, a control chart is obtained that shows how a process varies over time [1, 26]. A bold center line (CL) in this control chart corresponds to the mean of the process which is also the reference for data point dispersion. The upper control limit (UCL) and lower control limit (LCL) indicate the range of the process. When the data fall within the UCL and LCL, the process is said to be within control (with only random or Type A causes affecting the process) and out of control (due to Type B or non-random causes) when the points fall outside the range. The control limits are calculated from equations (1 – 3)[27]. UCL = X + 3
(1)
√
(2)
CL = X LCL = X − 3
(3)
√
where R is the range of the group, 𝑑 is a constant and depends on the continuous set of n measurements. For all cases considered in this study, n is 1 and 𝑑 is 1.128[28]. 𝑚𝑅 is the average of the moving range or the absolute values of the difference between two consecutive measurements (mRi = |𝑥 − 𝑥 |) and 𝑋 is the mean of the dataset. As a pre-requisite to use control charts the data was tested for normal distribution. The Ander-Darling [29, 30] (AD) statistic was used to test the hypothesized distribution F(x) for normality according to the below equation: A
= −n − ∑
[ln(FX )) + ln(1 − F(X
))]
(4)
where (X1 < … < Xn) are the ordered sample data points and n is the number of data points in the data distribution. In the AD test, the decision to reject a null hypothesis (H0) is based on comparing the p-value [31] for the hypothesis (h) test with the specified significance level of 5% such that a h value of 0 would indicate that the distribution is normal and 1 otherwise. The process capability, 𝑐 is used to compare the variation process of the data with respect to the upper and lower specified limits relative to the dispersion of process data and is calculated from equation (5)[12]. c =
(5)
where, USL and LSL are upper and lower user specified limits and σ is the standard deviation of the data distribution. A 𝑐 value of 1 would indicate that the process is within action limits and a 𝑐 > 1 would mean that the process is well within specification limits. A 𝑐 value less than 1 indicates the process is outside a permissible range for a given action limit. However, in some cases a high 𝑐 process can still perform poorly[1, 12, 28], therefore process acceptability index 𝑐 is also used to assess if the
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process center is relative to the user specified limit and is calculated from equation (6)[12] c
= min
,
(6)
SPC was used to assess tomotherapy rotational and static beam output and energy. Rotational output difference for two tomotherapy machines T1 and T2 were plotted against time for a period of three years. Out of process control points were investigated and post correction control charts were obtained again to verify process stability. TomoTherapy translational couch movement was also tested using SPC and variations (offsets) in its IEC X, Y and Z directions were assessed using SPC over a fouryear period. Baseline comparisons for IEC offset measurements using the Step-wedge Helical module were set at user specified action levels of ±2 mm and process indices for action levels of ±1 mm. Since there is no current protocol to adhere to for these limits, process indices 𝑐 and 𝑐 were employed to quantify the process behaviour. SPC was also used on set of 28 head and neck, 19 pelvic and 23 brain pre-treatment plans verified using 3D diode array ArcCHECK (Sun Nuclear Corporation (SNC), Melbourne, FL) and an Exradin A1SL ionisation chamber (Standard Imaging, Middleton, WI) placed at the center of the ArcCHECK in a polymethyl methacrylate (PMMA) cylinder for relative fluence and absolute dose measurements respectively. Gamma [32] and point dose variations (planned versus measured dose) were compared against parameters such as %LOT, sinogram segments, gantry period, modulation factor actual, etc. The normality, capability and acceptability values with their corresponding probability were calculated from the measurement data using the MATLAB 2016a program (The MathWorks, Natick, NA, USA).
3
Results and Discussion
3.1
Dosimetric QA
Figure 1 shows tomotherapy output variations for a six-week period in which a magnetron was changed. A Type B or systematic uncertainty was observed and was subsequently investigated. Analysis and machine log book recordings found this to be a malfunctioning magnetron which was replaced following which the system appeared to be back in control.
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Fig. 1. T2:SPC analysis for static output measurement variation during a six-week period before and after magnetron replacement. Red circle indicates a higher output during the period which the magnetron was replaced. (Adapted from Binny, Diana, et al. "Investigating output and energy variations and their relationship to delivery QA results using Statistical Process Control." Physica Medica 38 (2017): 105-110.)
3.2
Mechanical QA
Figure 2 shows T2 IECZ axis offset measurements were retrospectively assessed using SPC for the first 180 observations. Machine logbooks indicated that the z-axis encoder was calibrated when the system reported an out of tolerance measurement at the end of first 90 observations. Calculated 𝑐 and 𝑐 indices showed that ± 2 mm was the most appropriate tolerance for the given dataset.
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Fig. 2. Retrospective (a) pre-and (b) post-z-axis encoder calibration measurements assessed using SPC for unit T2 for the first 180 observations. Black arrows indicate out of control points below the user-specified limit of ±2 mm. Red circle indicates out of control point above ±2 mm action limit. Blue dashed lines represent the user specified limit of ±2 mm. ( Adapted from Binny, Diana, et al. "Statistical process control and verifying positional accuracy of a cobra motion couch." Journal of applied clinical medical physics 18.5 (2017): 70-79.)
SPC analysis performed on the dataset showed that systematic variations (as indicated by the data points greater than the calculated LCL of -1.6 mm in figure 2(a)) were present prior to the out of tolerance behaviour (> 2 mm) and could have been repaired prior to couch failure. This further demonstrates the need for a statistical process control QA.
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Table 1. Control chart based parameters for a three-monthly couch analysis period for units T1 and T2. (Adapted from Binny, Diana, et al. "Statistical process control and verifying positional accuracy of a cobra motion couch." Journal of applied clinical medical physics 18.5 (2017): 70-79.)
IEC Offsets SPC Parameters
T1 X
Y
T2 Z
X
Y
UCL (mm)
0.65
0.342
0.566
0.818
0.539
0.236
LCL (mm)
-0.775
-0.421
-1.298
-0.725
-0.192
-1.996
CL (mm)
-0.062
-0.039
-0.366
0.046
0.174
-0.88
σ
0.3436
0.165
0.377
0.295
0.171
0.542
AD*
Not Normal
Normal
Not Normal
Normal
Normal
Normal
No. of observations
90
Table 1 shows calculated LCL and UCL limits derived using SPC for the existing couches for T1 and T2 which are lower than the pre-set tolerance of 2 mm on the system. 3.3
Z
Patient-specific QA
Fig. 3. Brain SPC Analysis: Modulation factor (actual).
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Figure 4. Head and Neck Analysis: Modulation factor (actual)
Based on SPC analysis on planning parameters, it was concluded that different treatment sites have varied MLC distribution patterns and hence different parameters to aid in achieving optimal dose distribution. Recommendations were provided based on machine performance (assessed using gamma delivery and point dose variations from plan) for each patient specific site analysed in this study. An example of the difference in a plan parameter (Modulation factor (actual)) specific to treatment site is shown in figures 3 and 4. Therefore, a single recommendation for gamma % pass rate or % point dose tolerance in addition to various plan parameters may not be sufficient.
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Conclusion
This study investigated the usefulness of SPC methods for dosimetric, mechanical and patient-specific QA parameters for tomotherapy. Our results have highlighted that treatment and machine specific tolerances should be used in addition to conforming to various clinical standards. SPC analysis can help in identifying special cause of variations thereby optimising tomotherapy system maintenance and aiding in improved treatment delivery outcomes.
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Conflict of interest
This research did not receive any grant from funding agencies in the public, commercial, or not-for-profit sectors. The authors have no conflict of interest to declare.
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