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Daily QA 3 device is suitable for routine daily and fortnightly quality ... У 2016 Published by Elsevier Ltd on behalf of Associazione Italiana di Fisica Medica. All.
Physica Medica xxx (2016) xxx–xxx

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Technical note

Monitoring Daily QA 3 constancy for routine quality assurance on linear accelerators Diana Binny a,b,⇑, Craig M. Lancaster a, Tanya Kairn b,c, Jamie V. Trapp b, Scott B. Crowe a,b a

Cancer Care Services, Royal Brisbane and Women’s Hospital, Brisbane, Australia Queensland University of Technology, Brisbane, Australia c Genesis Cancer Care Queensland, Brisbane, Australia b

a r t i c l e

i n f o

Article history: Received 13 May 2016 Received in Revised form 21 September 2016 Accepted 24 October 2016 Available online xxxx Keywords: Daily QA 3 Constancy Ionisation chamber Linear accelerator Quality assurance

a b s t r a c t The purpose of this study was to evaluate the suitability of the Daily QA 3 (Sun Nuclear Corporation, Melbourne, USA) device as a safe quality assurance device for control of machine specific parameters, such as linear accelerator output, beam quality and beam flatness and symmetry. Measurements were performed using three Varian 2300iX linear accelerators. The suitability of Daily QA 3 as a device for quality control of linear accelerator parameters was investigated for both 6 and 10 MV photons and 6, 9, 12, 15 and 18 MeV electrons. Measurements of machine specific using the Daily QA 3 device were compared to corresponding measurements using a simpler constancy meter, Farmer chamber and plane parallel ionisation chamber in a water tank. The Daily QA 3 device showed a linear dose response making it a suitable device for detection of output variations during routine measurements. It was noted that over estimations of variations compared with Farmer chamber readings were seen if the Daily QA 3 wasn’t calibrated for output and sensitivity on a regular eight to ten monthly basis. Temperature-pressure correction factors calculated by Daily QA 3 also contributed towards larger short term variations seen in output measurements. Energy, symmetry and flatness variations detected by Daily QA 3 were consistent with measurements performed in water tank using a parallel plate chamber. It was concluded that the Daily QA 3 device is suitable for routine daily and fortnightly quality assurance of linear accelerator beam parameters however a regular eight-ten monthly dose and detector array calibration will improve error detection capabilities of the device. Crown Copyright Ó 2016 Published by Elsevier Ltd on behalf of Associazione Italiana di Fisica Medica. All rights reserved.

1. Introduction Based on studies [1–5] from tumour control probability (TCP) and normal tissue complication probability (NTCP), it was concluded that deviations in dose delivery of 7–10% can result in clinically detectable effects on tumour and normal tissues. Hence various national and international protocols [4–10] recommend a clinical tolerance for linear accelerator output variation of ±3% in order to achieve planned tumour response. Retrospective studies [11–17] have also suggested the same threshold based on statistical analysis of random and systematic uncertainties and linear accelerator output trends. A constancy check device needs sufficient accuracy and precision to detect this level of variation [1]. ⇑ Corresponding author at: Department of Radiation Oncology, Royal Brisbane and Women’s Hospital, Cancer Care Services, Level 3, Joyce Tweddell Building, Butterfield Street, Herston 4029, Queensland, Australia. E-mail address: [email protected] (D. Binny).

Use of diode and ionisation chamber-based array detectors has become increasingly popular in the quality control of linear accelerator parameters. Although Daily QA 3 has been in clinical use for many years, there are no published studies verifying the performance of this device for linear accelerator constancy measurements. The aim of this study was to assess the performance of Daily QA 3 as a quality assurance tool and provide recommendations for its use. The Daily QA 3 (Sun Nuclear Corporation, Melbourne, USA) device consists of ionisation chambers and diode detectors with inherent build up designed for routine monitoring of linear accelerator beam parameters such as dose output, flatness, symmetry, energy and radiation and light field size checks. The Daily QA 3 device also contains software features to create baseline templates and a record of routine data after analysis for performance monitoring of linear accelerators.

http://dx.doi.org/10.1016/j.ejmp.2016.10.021 1120-1797/Crown Copyright Ó 2016 Published by Elsevier Ltd on behalf of Associazione Italiana di Fisica Medica. All rights reserved.

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2. Materials and methods All measurements were carried out using Varian 2300iX linear accelerators VA 1 (2013–2015), VA 2 (2014–2015) and VA 3 (2012–2015) at Royal Brisbane and Women’s Hospital for photon energies 6 and 10 MV as well as electron energies 6, 9, 12, 15 and 18 MeV. All three linear accelerators operate at maximum dose rate of 600 MU/min for photons and 400 MU/min for electrons. Fortnightly quality assurance (QA) results from Daily QA 3 for the three Varian linear accelerators (VA1–3) ranging across a period of 3 years (2012–2015) were compared to the corresponding ionisation chamber measurements for output, symmetry, flatness and energy. Measurement devices used in this report, manufacturers and their purposes with the tolerance applied are presented in Table 1. Analysis was carried out using variations from baselines collected during commissioning and/or annual service of the linear accelerator. 2.1. Daily QA 3 device The Daily QA 3 device (see Fig. 1) consists of 13 vented and fully guarded primary ionisation chambers and 12 secondary diode detectors for penumbral measurements with an inherent effective build-up of 1.0 ± 0.1 g/cm2 over ion chambers and actual acrylic build-up of 1.1 cm over diode detectors and an inherent acrylic backscatter of 2.3 cm [18]. The device also consists of temperature and pressure sensors located within the build-up material to correct

output [18]. Measurement data are transferred to a PC for storage and trend analysis. The application version used in this study is 2.5.1. The Daily QA 3 device was used to perform fortnightly constancy checks of output, flatness, symmetry, energy and lightradiation coincidence on each of the three linear accelerators used in this study. Baselines were reset during annual QA on each of the linear accelerators directly after performing absolute calibrations on all energies. All Daily QA 3 baseline and fortnightly measurements were performed at a field size of 20  20 cm2 at a 100SSD for 150 MU. The vendor recommends recalibration of the baseline template if there is a drift in the linear accelerator output over time, incorrect temperature-pressure calibration or if there is an error in the initial linear accelerator output calibration [18]. Linacheck and ionisation chamber fortnightly measurements were made using 10  10 cm2 field size at a 100 SSD for 150 MU. 2.2. Short-term reproducibility and linearity Reproducibility and linearity of the device were first assessed to ensure the capability of Daily QA 3 to detect small variations in output. Linearity was tested by delivering set Monitor Units (MU) to the Daily QA 3 device with no additional build-up in the interval between 140 and 160 MU at 2 MU increments and a standard 20 cm  20 cm2 field size at 100 cm SSD at all available energies. This was then compared to a corresponding linearity test done using a Farmer ionisation chamber. For the purpose of comparing the different devices, the detected signal was normalised to 100%

Table 1 Measurement devices, their manufacturers, purpose and tolerance used during this study. Device

Manufacturer

Purpose

Tolerance

Daily QA 3 Linacheck (no build up) 30013 Farmer ionisation chamber in build-up cap 23343 Markus parallel plate ionisation chamber in water tank

Sun Nuclear Corporation, Melbourne, USA PTW GmbH, Freiburg, Germany PTW, Freiburg, Germany PTW, Freiburg, Germany

Output, beam quality, symmetry, flatness Output Output Flatnessa, symmetryb, beam qualityc

3% 3% 2% a, b = 2%, c = 1%

Fig. 1. Schematic of the Daily QA 3 device featuring locations and functions of the several detectors used for checking various beam parameters.

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for a specified number of MUs (150). Long and short-term reproducibility were tested for a set number of MUs using both Daily QA 3 and Farmer ionisation chamber detectors and a percentage standard deviation was derived from these measurements. A previous study [1] had already been carried out to assess linearity and reproducibility in PTW Linacheck for assessing its suitability as a constancy device.

35  35 cm2 for photons and a depth of maximum dose (dmax) using a 25  25 cm2 field size for electrons. Measurements made using a PTW Markus chamber were analysed using the Mephysto software (PTW, Freiburg, Germany). Percentage dose ratio for deriving flatness of a beam is shown below:

2.3. Long-term reproducibility and output constancy

where Dmax and Dmin are maximum and minimum dose values within the central 80% of the profile curve measured at 100 SSD and 10 cm depth. Prior to using the PTW Markus chamber, profile comparisons (flatness, symmetry and percentage depth doses) were made for photon and electron beams using a PTW Advanced Markus chamber and a maximum variation of 90%) to minimize measurement uncertainties in the build-up region. Backscatter studies were not performed as all detectors used the same set-up to derive variations from baselines. 2.4. Temperature-pressure correction factor The Daily QA 3 device contains five thermistors and one temperature sensor. Four of the thermistors are located beside each of the curved ionisation chambers used for measuring photon energy and one is located close to the CAX chamber. The temperature sensor is located outside the measuring detector near the electronics. In the current version (2.5.1) of the Daily QA 3 device, temperature corrections are performed using the thermistor located next to CAX chamber. The pressure sensor is a temperature compensated on-chip bipolar operational amplifier with a thin film resistor network. Pressure measurements are recorded from the slope transfer function between the output voltage and supply voltage as per the Daily QA 3 manual [18]. Calibration of temperature and pressure was performed prior to the collection of baseline values on all machines. Temperature was measured externally using an alcohol based thermometer and the pressure was measured using an electronic marine barometer (Weems & Plath, Annapolis, USA). All measuring devices were kept in the bunker for approximately 30–45 min to thermally equilibrate prior to use. The temperature-pressure correction factor (kTP) for the two detectors (Daily QA 3 and ionisation chamber) were compared at the same temperature and pressure (22 °C and 1013.25 hPa) to investigate the ionisation chamber response due to variations in ambient temperature and pressure recordings. 2.5. Flatness The Daily QA 3 device measures flatness using 5 primary ionisation chambers (as shown in Fig. 1 as CAX, T, B, L and R) [18]. The maximum (QMAX) and minimum (QMIN) charge measured by the five ionisation chambers are used to calculate flatness (QAF), as:

QAF ¼ 

QMAX  QMIN  100% QMAX þ QMIN

ð1Þ

Flatness of a beam profile measured during annual QC is based on the IEC [19] definition of percentage dose ratio using a PTW 3D water tank at a depth of 10 cm for photons and a field size of

Flatness ¼

Dmax  100% Dmin

ð2Þ

2.6. Symmetry Axial and Transverse symmetry measurements are expressed as a percentage in Daily QA 3 and are calculated from:

      T B RL  AX þ ð1ÞOR   ð1  AXÞ AxSym ¼ ð1Þ1OR  CAX CAX  100%

ð3Þ       T B RL TrSym ¼ ð1Þ1OR   ð1  AXÞ þ ð1ÞOR   AX CAX CAX  100% ð4Þ where uncorrected Top (T), Bottom (B), Left (L), Right (R) and Central (CAX) detector readings are used in conjunction with axial (AX) value for the detector axis in the set. This value is set as ‘‘Axial” = 1 and ‘‘Transverse” = 0. OR refers to the orientation value for the measurement set such that ‘‘Target” and ‘‘Right” = 1 and ‘‘Gun” and ‘‘Left” = 0. Symmetry measurements as specified by the IEC [19] were made during annual QA, in a water tank at dmax at 100 cm SSD and a field size of 35  35 cm2 for photons and 25  25 cm2 for electrons. Maximum dose ratio within the central 80% of the beam profile was calculated from:



Symmetry ¼

DðxÞ DðxÞ



 100%

ð5Þ

max

where D(x) and D(x) refer to the maximum dose value along the beam profile on either side. Variations from baselines set up during commissioning were then compared to Daily QA 3 variations. 2.7. Electron beam quality The ability of the Daily QA 3 device to detect electron beam energy variations was investigated by comparing energy measurements made using the Daily QA 3 device against energy measurements from regular annual QA. The Daily QA 3 device uses five ionisation chambers (e-chambers) to check electron energy. The five ionisation chambers include the 0.3 cc detector at the centre and four 0.6 cc detectors placed at 5.6 cm from the centre on the diagonals. Three 0.6 cc detectors use different build-up disk thickness of copper (5.5 mm), aluminium (5.5 mm) and steel (3.8 mm) in conjunction with a water equivalent build-up on all five detectors. This setup allows the measurement at five different points with a single exposure and the ratio of each e-chamber reading to the CAX chamber

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reading is used to measure changes in energy [18]. The reported energy value is the slope weighted average of the energy measured by the four ratios as per the Daily QA 3 manual [18]. Variations from baseline energy values from Daily QA 3 measurements were compared to variations from baseline R50,Ion (50% values from a depth ionisation curve) values acquired from water tank scans. Depth ionisation scans were acquired for electrons at 100 am SSD for a field size of 10  10 cm2. 2.8. Photon beam quality Photon energy is checked by Daily QA 3 by assessing variations in the flatness of the beam from one measurement to the next using the four curved ionisation chambers (located 11.3 cm from

the centre) and the CAX chamber. All photon energy detectors have a volume of 0.3 cc as per the Daily QA 3 manual [18]. Photon energy measurements performed using water tank scans also looked at variations in flatness of the profiles acquired at dmax compared to baseline values. Water tank scans were acquired at 100 cm SSD and field size of 35  35 cm2 using a PTW Markus chamber. External modifications were made to alter the beam characteristics such as flatness, symmetry and energy to assess Daily QA 3 sensitivity to non-standard beams. Photon beam characteristics were altered using a 15⁰ wedge at a 270⁰ orientation (transverse direction) to change transverse symmetry and flatness and a 5 mm wax build up was placed on the entire detector to change the energy. Electron beams were modified using wax half blocks

Fig. 2. Linearity measurement results for Daily QA 3 and Farmer ionisation chamber (140–160 MU) at a dose rate of 600 MU/min for (a) 6 MV and (b) 9 MeV.

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on detector (WHBD) of varying thicknesses in the transverse direction of the beam to modify flatness and symmetry and the energy was varied using 5 mm RMI-457 solid water (SW). 3. Results

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compared against Farmer chamber readings to within ±0.15 Gy. The range 140–160 MU was chosen to ensure no odd effects are seen in the most relevant range of use for this device. The coefficient of determination (R2) for measured dose (cGy) against MU for 6 MV and 9 MeV were 0.9998 and 0.9996 respectively.

3.1. Short-term reproducibility and linearity 3.2. Long-term reproducibility and output constancy As discussed in the earlier section, a short-term reproducibility of Daily QA 3 was tested using a set MU of 150 for 10 consecutive 6 MV readings using 20  20 cm2 field size at 100 cm SSD. The coefficient of variation for Daily QA 3 reproducibility was found to be 0.06%. As shown in Fig. 2, Daily QA 3 readings were linear for all measured energies with set monitor units (140–160 MU) when

To test long-term reproducibility, Daily QA 3 and Farmer ionisation chamber measurement were compared on 18 occasions over an 8-month period. Over this period an increase of 1.3% was seen in the Farmer ionisation chamber readings (95% confidence interval: 0.001–0.007, two tailed t-test, p = 0.01). In the same period Daily QA 3 showed an increase of 1.6% (95% confidence interval:

Fig. 3. Output constancy variations from baselines for Daily QA 3, Farmer ionisation chamber and PTW Linacheck device for VA 3 linear accelerator (6 MV).

Fig. 4. Output constancy variations from baselines for Daily QA 3, Farmer ionisation chamber and PTW Linacheck device for VA 2 linear accelerator (18 MeV).

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0.003–0.01, two-tailed t-test, p = 0.001). This is consistent with the output variations observed in linear accelerators [1,20,21] and both devices have identified comparable variations.

This shows that the Daily QA 3 device can produce reproducible and consistent results for a period of up to eight months. Over and under estimations were seen after this period (discussed in later

Table 2 Maximum (Max), mean and standard deviations (SD) for Daily QA 3 output variation (%) when compared to Farmer ionisation chamber for three linear accelerators VA 1, 2 and 3. Energy

6X 10X 6E 9E 12E 15E 18E

VA 1 (2013–2015)

VA 2 (2013–2015)

VA 3 (2012–2015)

Max

Mean

SD

Max

Mean

SD

Max

Mean

SD

2.2 1.9 1.6 1.8 1.8 1.4 2.1

0.4 0.0 0.2 0.2 0.2 0.2 0.1

0.7 0.5 0.5 0.6 0.5 0.5 0.4

1.4 1.5 1.1 1.1 1.1 0.9 1.2

0.1 0.1 0.1 0.1 0.1 0.1 0.1

0.4 0.4 0.2 0.3 0.3 0.2 0.3

2.0 1.2 2.6 1.4 1.7 1.1 0.8

0.2 0.1 0.2 0.2 0.1 0.0 0.1

0.6 0.4 0.6 0.4 0.3 0.3 0.2

Fig. 6. 18 MeV (a) Individual detector baseline variations when compared to ionisation chamber variations with time. (Dark arrows indicate the period when Daily QA 3 baselines for dose and sensitivity were reset). (b) Daily QA 3 and Linacheck baseline variations against the corresponding IC variations.

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sections) which indicates that Daily QA 3 calibrations every six to eight months can improve consistency of the detector. Output variations observed between Daily QA 3 and Farmer chamber were within 2% for photons and electrons for all VA 1, 2 and 3 linear accelerators in the period 2012–2015 as shown in Figs. 3 and 4 and Table 2. Sensitivity of Daily QA 3 ionisation chambers observed for this period were seen to worsen if detector calibrations were not performed annually. Sensitivity changes attributed to error percentages in the form of either over or under estimations to the baseline value. Linacheck baseline variations when compared to Farmer chamber and Daily QA 3 were seen to be within ±2% (See Fig. 6 and Supplementary material: Fig. 5) It was observed that overall agreements between Farmer chamber and Daily QA 3 in variations from baseline generally showed the same pattern for electrons and photons (See Table 2 and Figs. 3, 4, 6 including Supplemental material: Fig. 5) with a mean variation of ±1% in the first 8 months of resetting baselines (two-tailed t-test, t (18) = 2.1, p < 0.001). During this period, it was also observed that Daily QA 3 results correlate more closely with the ionisation chamber results than the corresponding Linacheck readings. Variations in the sensitivity and calibration of the Linacheck device may have contributed to the mean statistical differences observed (F-test for variance, F > F Critical, p = 0.02, a = 0.05). Higher Daily QA 3 variations (>±1.5%) were seen when compared to the ionisation chamber, if the detector was not calibrated on an annual basis. From the above mentioned observations it was concluded that in order to keep the output variations to a minimum a six to eight monthly detector sensitivity calibration would be essential. Dose recalibration (i.e. resetting of baselines) of the detector is also a must after every change in the machine beam characteristics as per the Daily QA 3 manual. Daily QA 3 sensitivity can be also improved if the ionisation chambers and diode detectors are routinely calibrated.

3.3. Temperature-pressure correction factor (kTP) It was observed that the temperature-pressure correction factors applied to the output dose in Daily QA 3 played a small role in increasing or reducing detector sensitivity (See Figs. 7 and 8).

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Daily QA 3 kTP relative mean variations up to ±1.6% were seen when compared to ionisation readings analysed for all machines. This indicates that there is a variation in the ambient temperature and pressure recording in the electronics of Daily QA 3. This also contributes to the output variation seen between the two detectors as discussed earlier sections (Output Constancy) of this study. Temperature-pressure variations can be effectively reduced by performing calibrations for the same while resetting detector dose baselines and should be regularly checked against departmental standards (See Fig. 8). 3.4. Flatness and symmetry The Daily QA 3 flatness variations from baselines were compared to corresponding water tank measurements during regular annual QA (See Supplemental material: Fig. 9). Retrospective flatness analysis for all machines showed a maximum difference from baselines between measurements produced by the two systems to be within ±0.5% for all energies considered in this study. Transverse and axial symmetry measurement variation from baselines were also seen to be consistent with the annual water tank scans within ±1.5% for all energies checked on all machines. The two detectors agreed to within ±2% with water tank measurements. No systematic trend was seen in the direction of the error variations (i.e. positive or negative). Daily QA 3 was able to detect asymmetry in the beam profile which was further confirmed with water tank scans and adjusted back to baselines (See Supplemental material: Fig. 10). 3.5. Beam quality Daily QA 3 measures variations in energy for photons and electrons. As discussed in the earlier sections Daily QA 3 utilises ionisation chambers and checks for variations between them to detect energy changes. Electron energy variations measured using the results produced by the detectors were within ±1.5% using the current average slope weighted method in Daily QA 3. Measurements made using water tank scans showed that all machines measured within ±0.5% of the

Fig. 7. Daily QA 3 vs Farmer ionisation chamber temperature-pressure correction factors plotted against time period for VA 3.

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Fig. 8. Daily QA 3 temperature-pressure correction factors variations from ionisation chamber (%) plotted against time period for VA 3. The dark arrow indicates the period when Daily QA 3 temperature and pressure was recalibrated.

Table 3 External modification details that were made to alter standard beams for Daily QA 3 detection in the form of variations from baselines (%) for beam flatness, symmetry and energy of all available energies. Materials used

6X 15° physical wedge 270° (left) + 5 mm wax build up on detector

10X

6E 5 mm SW + 5 mm WHBD

9E 5 mm SW + 8 mm WHBD

12E 5 mm SW + 12 mm WHBD

15E 5 mm SW + 16 mm WHBD

18E 5 mm SW + 19 mm WHBD

Flatness (%) Symmetry (%) Energy (%)

10.25 24.59 4.28

7.23 20.15 6.82

1.99 5.94 13.53

2.77 5.96 15.07

2.23 5.18 13.04

1.4 3.34 21.36

2.2 1.7 27.78

current baseline (See Supplemental material: Fig. 11). Although the sample size from annual QA measurements in this analysis is small, the errors observed were generally being over-estimated in the same direction of error variations. Photon energy measurement variations for both Daily QA 3 and water tank scans showed no obvious trend but were within ±2% of each other for all machines. External modifications were made to alter the beam characteristics and the percentage variations from baselines were noted (See Table 3). As discussed earlier in the section, the Daily QA 3 manual states that changes in energy for photons are measured by changes in the symmetry adjusted flatness. In the case of photons, it was seen that the energy measurements were also sensitive to depth and Daily QA 3 was capable of detecting the variations in flatness and symmetry due to the presence of the physical wedge. Electron energy measurements also proved that the detector was sensitive to a small variation in energy introduced by the 5 mm SW placed on the entire detector. Flatness and symmetry changes were also observed by increasing WHBD thicknesses. This section of the study concludes that Daily QA 3 is capable of detecting modifications made to the beam by reporting relative changes from baseline data.

4. Discussion In this study, the Daily QA 3 constancy device has been characterised using linear accelerator parameters and we have discussed

factors influencing measurement capabilities such as temperaturepressure corrections, ionisation chamber measurement techniques and specifications. Other factors like set-up variations, error in baseline template measurements, linear accelerator not being warmed up prior to measurements, reduced sensitivity of the ionisation chambers, etc. can also cause higher variations in measurement. Therefore, to reduce these uncertainties, it is recommended to properly re-calibrate Daily QA 3 for dose and detector sensitivity within 6–8 months of use or as soon as a drift above ±1% from ionisation chamber is seen. This can be done by introducing tighter tolerances for the error detection within the software. This study recommends the use of Daily QA 3 as a secondary check device only and a primary method of measuring radiation parameters should always be maintained. 5. Conclusions This study has verified the suitability of the Daily QA 3 device for regular quality control of linear accelerator output, flatness, symmetry and energy. The device has good linearity and reproducibility and it produces similar results to Farmer and Markus ionisation chamber measurements. Temperature-pressure correction factors calculated for both ionisation chamber and Daily QA 3 have been seen to vary by up to ±1.6% in some cases which indicates that there may be variations in the correction factor calculations in the device that can influence linear accelerator output measurements. Therefore, it is imperative that temperaturepressure calibration be accurate from initial use and be checked/ calibrated out on a regular basis while performing QA.

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The results presented in this study are retrospective analyses only and there is potential scope for testing the Daily QA 3 device for manual changes in temperature-pressure, symmetry and energy which would give more confidence in the detection of non-standard beams. Acknowledgements The authors would like to thank all staff from the radiotherapy physics group (Cancer Care Services, Royal Brisbane and Women’s Hospital, Queensland, Australia) especially Steven Sylvander and Robert Fitchew for all assistance and constructive remarks in the analysis undertaken during this study. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.ejmp.2016.10. 021. References [1] McDermott GM, Buckle AH. Monitoring linear accelerator output constancy using the PTW Linacheck. Med Dosim 2011;36:71–4. [2] Warkentin BJ, Stavrev P, Stavreva N, Field C, Fallone BG. A TCP-NTCP estimation module using DVHs and known radiobiological models and parameter sets. J Appl Clin Med Phys 2004;5. [3] Baumann M, Petersen C. TCP and NTCP: a basic introduction. Rays 2004;30:99–104. [4] Dutreix A. When and how can we improve precision in radiotherapy? Radiother Oncol 1984;2:275–92. [5] Thwaites DI, Mijnheer B, Mills JA. Quality assurance of external beam radiotherapy. Radiation oncology physics: a handbook for teachers and students. Vienna: International Atomic Energy Agency; 2005. 407-450. [6] Mayles W, Lake R, McKenzie A, Macaulay E, Morgan H, Jordan T, et al. Physics aspects of quality control in radiotherapy. Institute of Physics and Engineering in Medicine (IPEM) IPEM Report 811999.

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