Statistical control of the spectral quality index in electron beams

Application and Challenges of Statistical Process Control in Radiation Therapy Quality Assurance

Quality assurance (QA) is important for ensuring precision in radiation therapy. The complexity and resource-intensive nature of QA has increased with the continual evolution of equipment and techniques. An effective approach is to improve the process control technology and resource optimization. Statistical process control is an economical and efficient tool that has been widely used to monitor, control, and improve quality management processes and is now being increasingly used for radiation therapy QA. This article reviews the development and methodology of statistical process control technology, evaluates its suitability in radiation therapy QA practices, and assesses its importance and challenges in optimizing radiation therapy QA processes.

Moving towards process-based radiotherapy quality assurance using statistical process control

Monitoring Radiotherapy Quality Assurance (QA) using Statistical Process Control (SPC) methods has gained wide acceptance. The significance of understanding the SPC methodologies has increased among the medical physics community with the release of Task Group (TG) reports from the American Association of Physicists in Medicine (AAPM) on patient-specific QA (PSQA) (TG-218) and Proton therapy QA (TG-224). Even though these reports recommend using SPC for QA analysis, physicists have ambiguities and doubts in choosing proper SPC tools and methodologies. This review article summarises the utilisation of SPC methods for different Radiotherapy QAs published in the literature, such as PSQA, routine Linac QA and patient positional verification. QA analysis using SPC could assist the user in distinguishing between 'special' and 'routine' sources of variations in the QA, which can aid in reducing actions on false positive QA results. For improved PSQA monitoring, machine-specific, site-specific, and technique-specific Tolerance Limits and Action Limits derived from a two-stage SPC-based approach can be used. Adopting a combination of Shewhart's control charts and time-weighted control charts for routine Linac QA monitoring could add more insights to the QA process. Incorporating SPC tools into existing image review modules or introducing new SPC software packages specifically designed for clinical use can significantly enhance the image review process. Proper selection and having adequate knowledge of SPC tools are essential for efficient QA monitoring, which is a function of the type of QA data available, and the magnitude of process drift to be monitored.

Guaranteed performance of individual control chart used in gamma passing rate-based patient-specific quality assurance

PURPOSE

To assess the effect of sampling variability on the performance of individual charts (I-charts) for PSQA and provide a robust and reliable method for unknown PSQA processes.

MATERIALS AND METHODS

A total of 1327 pretreatment PSQAs were analyzed. Different datasets with samples in the range of 20-1000 were used to estimate the lower control limit (LCL). Based on the iterative "Identify-Eliminate-Recalculate" and direct calculation without any outlier filtering procedures, five I-charts methods, namely the Shewhart, quantile, scaled weighted variance (SWV), weighted standard deviation (WSD), and skewness correction (SC) method, were used to compute the LCL. The average run length (ARL₀) and false alarm rate (FAR₀) were calculated to evaluate the performance of LCL.

RESULTS

The ground truth of the values of LCL, FAR₀, and ARL₀ obtained via in-control PSQAs were 92.31%, 0.135%, and 740.7, respectively. Further, for in-control PSQAs, the width of the 95% confidence interval of LCL values for all methods tended to decrease with the increase in sample size. In all sample ranges of in-control PSQAs, only the median LCL and ARL₀ values obtained via WSD and SWV methods were close to the ground truth. For the actual unknown PSQAs, based on the "Identify-Eliminate-Recalculate" procedure, only the median LCL values obtained by the WSD method were closest to the ground truth.

CONCLUSIONS

Sampling variability seriously affected the I-chart performance in PSQA processes, particularly for small samples. For unknown PSQAs, the WSD method based on the implementation of the iterative "Identify-Eliminate-Recalculate" procedure exhibited sufficient robustness and reliability.

Response of the ArcCHECK® device at 6 MV and 15 MV for VMAT and IMRT quality control

PURPOSE

To study the response of the ArcCHECK® device as VMAT and IMRT verification system.

METHODS

Various tests analyzing the linearity, the repeatability and the angular dependence of the device response, its dependence with the pulse repetition rate and the leakage losses were performed. The long-term response in dose measurements and the uniformity of the detectors conforming the system were controlled using a statistical process control program. The Elekta Infinity™ 6 and 15MV photon beams were used.

RESULTS

The device showed excellent repeatability and linearity. The differences between the responses obtained for any pair of angular incidences were less than 2%. The absorbed dose increased by 3% when the pulse repetition rate varied from 50 to 600MU/min. Results are in overall agreement with those found in previous works for the ArcCHECK®, in which a reduced number of the device diodes were analyzed, and for the MapCheck®, an older 2D device that used the same diodes. Charge losses were found to be negligible except for some of the diodes of the device. The statistical process control program is a very useful tool to control the correct functioning of the device in the long term.

CONCLUSIONS

The results of the analysis carried out indicate that the working and stability conditions of the ArcCHECK® device are adequate for its purpose. The dependence with the pulse repetition rate should be considered when VMAT or similar treatments are evaluated. A control program for the statistical monitoring of the device would be desirable and useful.

A Bayesian control chart based on the beta distribution for monitoring the two-dimensional gamma index pass rate in the context of patient-specific quality assurance

PURPOSE

In the context of quality assurance in intensity modulated radiation therapy (IMRT), the aim of this work was two-fold: (a) to show that the beta distribution characterizes the two-dimensional gamma index pass rate (GIPR), and that the quantiles of the distribution should be used in order to compute the control limit (CL) for the detection of abnormally low GIPR, and (b) to introduce a Bayesian control chart that allows calculation of CLs from the first measurement.

METHODS

In order to enable monitoring of the GIPR from the first measurement, we developed a Bayesian control chart based on the beta distribution, elaborated according to the following two steps: (a) an iterative bayesian inference approach without any prior information on the GIPR distribution was used at the start of monitoring and the CL was progressively updated; and (b) when sufficient in-control arcs had been recorded and the estimators of the parameters of the beta distribution were sufficiently accurate, the CL of the chart was fixed to a constant value corresponding to the quantile of the beta distribution. The clinical utility of this approach is illustrated through a real data case study: monitoring the GIPR of patients treated with a moving gantry IMRT technique RapidArc^TM on a Novalis TrueBeam STx (Varian Medical Systems) linear accelerator equipped with an aS1200 electronic portal imager device.

RESULTS

We showed that some commonly used distributions for monitoring GIPR in the literature, such as normal or logarithm transformation, are not appropriate. We compared the CLs of those solutions with the CL of our chart based on the BD (CL = 95.14%). The comparison revealed that the CL for the normal law (CL = 97.62%) generated too many false positives, and that the CL of the Logarithm transformation (CL = 83.74%) could fail to efficiently detect (i.e., sufficiently early on or faster) changes in the process.

CONCLUSIONS

Successful GIPR monitoring requires careful and rigorous application of well-established statistical concepts in the field of statistical process control. In this paper, we stress the importance of carefully analyzing the distribution of the monitored characteristic that is plotted on the control chart. We propose a Bayesian control chart that can be viewed as a practical solution for early implementation of GIPR monitoring, starting from the first arc. We demonstrate that beta distribution is a better method for characterizing the GIPR, and thus, the use of this approach is expected to improve patient-specific quality assurance plans in radiotherapy.

Evaluation of Elekta Agility multi-leaf collimator performance using statistical process control tools

Purpose

To evaluate the performance and stability of Elekta Agility multi‐leaf collimator (MLC) leaf positioning using a daily, automated quality control (QC) test based on megavoltage (MV) images in combination with statistical process control tools, and identify special causes of variations in performance.

Methods

Leaf positions were collected daily for 13 Elekta linear accelerators over 11‐37 months using the automated QC test, which analyzes 23 MV images to determine the location of MLC leaves relative to radiation isocenter. Leaf positioning stability was assessed using individual and moving range control charts. Specification levels of ±0.5, ±1, and ±1.5 mm were tested to determine positional accuracy. The durations between out‐of‐control and out‐of‐specification events were determined. Peaks in out‐of‐control leaf positions were identified and correlated to servicing events recorded for the whole duration of data collection.

Results

Mean leaf position error was −0.01 mm (range −1.3–1.6). Data stayed within ±1 mm specification for 457 days on average (range 3–838) and within ±1.5 mm for the entire date range. Measurements stayed within ±0.5 mm for 1 day on average (range 0–17); however, our MLC leaves were not calibrated to this level of accuracy. Leaf position varied little over time, as confirmed by tight individual (mean ±0.19 mm, range 0.09–0.43) and moving range (mean 0.23 mm, range 0.10–0.53) control limits. Due to sporadic out‐of‐control events, the mean in‐control duration was 2.8 days (range 1–28.5). A number of factors were found to contribute to leaf position errors and out‐of‐control behavior, including servicing events, beam spot motion, and image artifacts.

Conclusions

The Elekta Agility MLC model was found to perform with high stability, as evidenced by the tight control limits. The in‐specification durations support the current recommendation of monthly MLC QC tests with a ±1 mm tolerance. Future work is on‐going to determine if performance can be optimized further using high‐frequency QC test results to drive recalibration frequency.

Electron beam energy QA - a note on measurement tolerances

Monthly QA is recommended to verify the constancy of high‐energy electron beams generated for clinical use by linear accelerators. The tolerances are defined as 2%/2 mm in beam penetration according to AAPM task group report 142. The practical implementation is typically achieved by measuring the ratio of readings at two different depths, preferably near the depth of maximum dose and at the depth corresponding to half the dose maximum. Based on beam commissioning data, we show that the relationship between the ranges of energy ratios for different electron energies is highly nonlinear. We provide a formalism that translates measurement deviations in the reference ratios into change in beam penetration for electron energies for six Elekta (6‐18 MeV) and eight Varian (6‐22 MeV) electron beams. Experimental checks were conducted for each Elekta energy to compare calculated values with measurements, and it was shown that they are in agreement. For example, for a 6 MeV beam a deviation in the measured ionization ratio of ±15% might still be acceptable (i.e., be within ±2 mm), whereas for an 18 MeV beam the corresponding tolerance might be ±6%. These values strongly depend on the initial ratio chosen. In summary, the relationship between differences of the ionization ratio and the corresponding beam energy are derived. The findings can be translated into acceptable tolerance values for monthly QA of electron beam energies.

PACS number(s): 87.55, 87.56

Statistical process control for electron beam monitoring

PURPOSE

To assess the electron beam monitoring statistical process control (SPC) in linear accelerator (linac) daily quality control. We present a long-term record of our measurements and evaluate which SPC-led conditions are feasible for maintaining control.

METHODS

We retrieved our linac beam calibration, symmetry, and flatness daily records for all electron beam energies from January 2008 to December 2013, and retrospectively studied how SPC could have been applied and which of its features could be used in the future. A set of adjustment interventions designed to maintain these parameters under control was also simulated.

RESULTS

All phase I data was under control. The dose plots were characterized by rising trends followed by steep drops caused by our attempts to re-center the linac beam calibration. Where flatness and symmetry trends were detected they were less-well defined. The process capability ratios ranged from 1.6 to 9.3 at a 2% specification level. Simulated interventions ranged from 2% to 34% of the total number of measurement sessions. We also noted that if prospective SPC had been applied it would have met quality control specifications.

CONCLUSIONS

SPC can be used to assess the inherent variability of our electron beam monitoring system. It can also indicate whether a process is capable of maintaining electron parameters under control with respect to established specifications by using a daily checking device, but this is not practical unless a method to establish direct feedback from the device to the linac can be devised.

A method to relate StarTrack(®) measurements to R50 variations in clinical linacs

The relation between the data recorded with any device for the daily checking of the behavior of a clinical linac and the reference magnitudes to be monitored may be unknown. An experimental method relating the energy stability of the electron beam measured with StarTrack(®) to the R50 beam quality index is proposed. The bending magnet current is varied producing a change in the exit energy window and, therefore, a modification of the R50 value. For different values of this current, the output data of StarTrack(®) and the R50, obtained from depth doses measured in a water phantom are determined. A linear fit between both sets of data allows the identification of the StarTrack(®) output that provides the best way to obtain the quality index R50, for each beam nominal energy. Using these fits, an historical datum series is used to analyze the method proposed in the daily quality control. The ouput data of the StarTrack(®) and the R50 values show a good linear correlation. It is possible to establish a methodology that allows the monitoring of R50 by direct use of the daily quality control data measured with StarTrack(®). A method to monitor R50 in the daily quality control using the StarTrack(®) device has been developed. The method may be applied to similar devices in which the statistical control variable does not show a linear behavior with R50.

Control chart analysis of data from a multicenter monitor unit verification study

BACKGROUND AND PURPOSE

This study aims to investigate the process of monitor unit verification using control charts. Control charts is a key tool within statistical process control (SPC), through which process characteristics can be visualized, usually chronologically with statistically determined limits.

MATERIAL AND METHODS

Our group has developed a monitor unit verification software that has been adopted at several Swedish institutions for pre-treatment verification of radiotherapy treatments. Deviations between point dose calculations using the treatment planning systems and using the independent monitor unit verification software from 9219 treatment plans and five different institutions were included in this multicenter study. The process of monitor unit verification was divided into subprocesses. Each subprocess was analyzed using probability plots and control charts.

RESULTS

Differences in control chart parameters for the investigated subprocesses were found between different treatment sites and different institutions, as well as between different treatment techniques. 19 of 37 subprocesses met the clinical specification (± 5%), i.e. process capability index was equal to or above one.

CONCLUSIONS

Control charts were found to be a useful tool for continuous analysis of data from the monitor unit verification software for patient specific quality control, as well as for comparisons between different institutions and treatment sites. The derived control chart limits were in agreement with AAPM TG114 guidelines on action levels.