Investigation on the accuracy of field widths and the quantitative relationship with energy variations for dynamic jaws helical tomotherapy

Abstract Background and purpose TomoEDGE is an advanced technology for TomoTherapy treatment delivery by introducing a sliding‐window dynamic jaw motion. The front and back jaws move independently at the start and end of a target volume along the longitudinal couch direction to reduce the undesired dose to the normal tissues. The accuracy of field width is essential to treatment delivery in this regard. The purpose of this work was to analyze the performance of dynamic jaws on helical tomotherapy and investigate the relationship with energy variation. Methods The Tomotherapy‐Quality‐Assurance (TQA) Dynamic Field Width procedure was performed monthly across three tomotherapy machines. All field widths were analyzed, especially the FWHM of the 10 mm field width. Field width measurements were compared with the ratio of Percentage Depth Dose at 20 and 10 cm to render the value of correlation. Changes in beam FWHM and energy were further discussed. Two‐year data were collected for this purpose. Results On average, measured field widths in each unit agreed within 1% tolerance recommendation stated. The average absolute difference between reference and measured FWs in each unit was approximately 0.07 mm. An increase of 1.5% in the FW of the 10 mm nominal beam width was correlated with a 1% increase in PDD20,10 ratio, implying a positive correlation between the two factors (p < 0.002). Conclusions A positive correlation between nominal 10 mm FW and PDD20,10 was observed. In the case that the PDD20,10 marginally passes the QA tests, users are recommended to consider further verification on Dynamic Jaws to ensure the smallest field width to be within tolerance, which is essential to maintain effective treatment in TomoEDGE system. Since the regression of this study was a single‐factor model, other confounding factors such as the focal spot size of linear accelerator should also be considered when evaluating the machine status.


INTRODUCTION
In TomoTherapy system, a linear accelerator is mounted on a circular gantry.Treatment is delivered in a helical mode comprising the rotating radiation beam along with concurrent couch movement.A fan-beam geometry is shaped by adjustable jaws which are further modulated (inplane) by a binary multileaf collimator.The radiation field width is defined by the jaws in the longitudinal (IEC-y) direction.In TomoTherapy machines without TomoEDGE option, treatment was delivered by static jaws at fixed field width,either 10,25,or 50 mm at isocenter during the entire treatment.Thus, the field penumbra along the longitudinal direction was approximately identical to the field size on both cranial-caudal sides of the target volume. 1Further to this beam characteristic, it is essential to limit the dose to organ at risk (OAR) by delivering the treatment with MLC collimated sub-fields under the drawback of increasing treatment time.
TomoEDGE is an advanced technology for treatment delivery by introducing a sliding-window dynamic jaw motion. 2 The front and back jaws, defining the beam width on the negative IEC-y and positive IEC-y direction respectively, move independently at the start and end of a target volume along the longitudinal couch direction.Figure 1 illustrates the concept of slidingwindow dynamic jaw motion.At the start of treatment, the jaws are set close to the minimum width to move across the cranial border of the target.As the target continues to move into the radiation beam, the back jaw keeps opening until the full treatment field size at the center portion of the target is being treated.Then, the front jaws start closing sequentially and reach the minimum jaw width at the caudal border of the target.The treatment delivery is said to be finished when the target volume leaves the radiation beam completely.
With the introduction of dynamic jaw feature, the dose distribution within the target is identical to that with fixed field width but the dose penumbra at cranial and caudal ends of the target is close to the 10 mm field width, irrespective of field size selection.It serves the purpose of reducing the extra dose on patients.
TomoEDGE beam model consists of four symmetric and six asymmetric longitudinal profiles.Full width at half maximum (FWHM) of the beam profile is an important parameter directly related to the accuracy and reproducibility of the dose delivery during tomotherapy treatment. 3For the standard governing the quality assurance of helical tomotherapy, AAPM task group 306 (TG-306) states the importance of measured FWHMs and recommends regular monitoring of the beam parameter to guarantee the agreement with the beam model. 4 previous study by Katayama et al. compared the performance between standard static mode and TomoEDGE technique in terms of beam-on time, average dose on target and dose conformity. 5Urso et al. attempted to evaluate the performance in terms of accuracy and precision of the dynamic jaws by measuring all 10 commissioned beam profiles of TomoEDGE technology for a 2-year duration. 6 Step-Wedge Helical) were the most susceptible to beam energy fluctuation. 9Until now, no published studies on the evaluation concerning the relationship between TomoEDGE dynamic jaws field width and the energy variations.
This study aims to firstly analyze the performance of the dynamic jaws of all 10 commissioned field widths on an approximately monthly basis on three Radixact tomotherapy units licensed with TomoEDGE for a 2-year duration.Dynamic jaw performance is defined by the quantitative comparison of FWHM between the golden standard reference and the field width measured in the present study.Secondly, ratio of percentage depth dose (PDD) measured at 20 and 10 cm depth along the static beam central axis in SolidWater are obtained within the same study period.The correlation between the dynamic jaw field width and energy variation is statistically evaluated.

Measurement of dynamic jaws field width
In this study, three Radixact tomotherapy machines licensed with TomoEDGE were used and Tomotherapy Quality Assurance (TQA) Field Width Dynamic Jaws procedure was employed.It is a standard procedure which performs open-field measurement of all 10 commissioned longitudinal field width beam profiles sequentially and automatically.In order to measure the topographic field width procedure, an Exradin A1SL ion chamber was inserted into a 5 cm virtual solid water slab phantom.Another 0.5 cm SolidWater slab phantom was positioned on top of the slab containing the ion chamber to ensure the point of measurement was at a depth of 1.5 cm.The slab phantom was placed at a source-to-surface distance (SSD) of 85 cm.The height of the couch tabletop was adjusted until the surface of slab phantom was aligned with the gantry bore laser.The setup is illustrated in Figure 2.
To minimize the intrinsic variability in measurement, the same set of ion chambers and SolidWater slab phantom were used throughout the whole study.The beam profiles were collected by the TomoTherapy Elec-troMeter Measurement System (TEMS) software by sampling the electrometer reading at regular time intervals when the couch travelled with a constant velocity to move the ion chamber across the radiation beam along the longitudinal direction.Figure 3 shows the typical plot of a TQA Field Width Dynamic Jaws measurement.
For the asymmetric field width, POS notation defined the front jaw and back jaw to be both set on the positive IEC-y direction with respect to the radiation isocenter while the jaws for NEG were both set on the negative IEC-y direction.
After the acquisition of beam profile data, MATLAB (MathWorks, Natick, MA) was used as the analyzing tool for those reference profiles.Different combinations of Gaussian model were used to fit the profile data and FWHM of each profile was calculated.Figure 4 demonstrates the example of the fitted curve with a field width of 10 mm.The FWHM results between measured and reference profile were then compared.As recommended by AAPM Task Group 306, the difference between profile's FWHM for symmetric field should not be differed by more than 1% while using an absolute tolerance of 0.5 mm for asymmetric field widths. 4

Measurement of energy variations
Percentage depth dose (PDD) is an indicator for assessing the beam quality in radiotherapy megavoltage photon beams.On a weekly basis, the PDD ratio of 20 to 10 cm is measured with two Exradin A1SL ion chambers in SolidWater slab phantoms with static beam mode in order to monitor any energy variation of the machines.One of the ion chambers is regarded as a reference chamber to compensate output fluctuations while another is used as the field chamber to measure dose at different depths.

Energy variations study
In this study, the PDD ratio was then used as a metric for the beam energy variation with which measured dynamic jaw field widths were compared.The field widths were plotted against the PDD ratios and were fitted linearly.Pearson's correlation coefficient (denoted as |r|) and the p-values for testing the hypothesis that there was no relationship between the observed phenomena (null hypothesis) were evaluated.A correlation on dynamic jaw field width variation FW can be found based on a two-year retrospective analysis as below, where PDD 20,10 is the energy variation obtained using an ionization chamber and virtual solid water phantoms at depths 20 and 10 cm,  1 is the regression coefficient and  0 is the constant.This equation can thus help to obtain a quantitative study on how the energy variation affects the actual field width in all 10 commissioned field widths.

Verification on the accuracy of dynamic jaws field width
The result of the FWHM comparison for three Radixact tomotherapy units was summarized in Table  to be within 1% tolerance while the absolute differences of all measured asymmetric field widths were within 0.5 mm tolerance.The absolute differences between reference and measured FWs in Radixact A and C are on average 0.06 mm while that in Radixact B is around 0.09 mm.Among the measurements of the four symmetric beam profiles, 10 mm FW demonstrated the largest variation between the reference and measured values in all three Radixact units.Percentage of FWHM measurements exceeding the 1% tolerance level (symmetric) or the 0.5 mm tolerance level (asymmetric) in 10 mm FW were listed Table 2.According to AAPM TG-306, 10 mm symmetric treatment slice width was the most unstable field width to comply with the 1% FWHM tolerance and the test was sensitive to the setup variation. 4The failed measurements were repeated promptly after the setup verification such as the examination of the alignment between the surface of slab phantom and the gantry bore laser and couch speed uniformity.
Figure 5 shows the FWHM results of 10 mm symmetric and asymmetric field width in three units graphically.
F G E 5 Box plots showing the measured FWHMs (10 mm symmetric and asymmetric) of Radixact Units with the order of Radixact A, B and C. FWHMs were along the vertical axis in mm.On each box, the central mark represented the median, while the top and bottom edges of the box represented the 75 th and 25 th percentiles, respectively.The outliers were plotted individually using the "+" marker symbol.Standard reference FWHMs were indicated by the central blue solid lines, while dotted and dotted-dashed lines indicated the ± 1% and ± 2% from standard reference values.Interquartile range (IQR) is measured by the length of the Tukey boxplot indicating the level of distribution on the measurement.The greater the IQR, the more spread out the measurement.It could be observed that the IQRs of 10 mm symmetric FW were relatively larger in all three Radixact units.Data was tabulated in Table 3.

Energy variation study
In this section, the relationship between the FWHM and energy variation was evaluated.To assess the energy variation, a two-year retrospective study on the measurement of PDD ratio of 20 to 10 cm depth using SolidWater phantoms was performed.
The purpose of the evaluation on PDD 20,10 ratio was to monitor the energy stability in regular time intervals.Linear regression model was fitted to inspect the dependence of energy fluctuation indicated by the PDD ratio of 20 to 10 cm depth on the change of FWHM.Measurements were dependent on several parameters such as the setup, the sensitivity of the ionization chamber and FW.Therefore, same chambers and Solid-Water phantoms should be used during the whole study period.The results on the linear regression depicted that an increase in the PDD ratio resulted in a greater measurement on 10 mm symmetric FW, implying a positive correlation between the two factors (p < 0.002).Figure 6-8 shows the energy variation relationship between the measured FWHM of the 10 mm symmetric FW and PDD 20,10 ratio in Radixact A-C respectively.The regression coefficients in nominal 10 mm symmetric FW for three Radixact units were summarized in Table 4.The measured FWHM in nominal 10mm symmetric FW showed an increase of 1.5% when PDD 20,10 ratio was increased by 1%.

Accuracy of dynamic jaws field width
The findings in this study demonstrated the precision and accuracy of the TomoEDGE beam model.Urso et al. have investigated the performance of TomoEDGE technology using a single TomoHDA machine.The results of our study are on the same order with the study presented by Urso et al., where the average absolute difference between reference and measured FWHWs in each Radixact unit was approximately 0.07 mm.It can be observed that around one-third of the measurement in the small symmetric field width (10 mm nominal FW) did not comply with the 1% tolerance level.As stated by AAPM TG-306, smaller field width was more sensitive to the external factors of the dynamic jaw movement, for example, the mechanical deviation caused by the noise generated in couch velocity affecting the precision of couch move.Besides,as mentioned by the manufacturer (Accuray Incorporated, Sunnyvale, CA), the dynamic jaw encoder built inherently with an absolute position tolerance of 0.05 mm. 10 The inherent tolerance was already being one-half of the recommended 1% tolerance for the field width.As a result, the inherent and external factors contributed to the frequent non-compliance on the performance of small field width.

Energy variation study
Output energy stability and beam field width are both considered as the important beam parameters in quality assurance procedure of Tomotherapy machine.Binny et al. have evaluated the relationship between the energy variations detected using step-wedge helical and static modules. 7A correlation to patient delivery QA results was demonstrated, suggesting that minor energy fluctuation can affect the dose deliverability.In the aspect of increasing the beam field, the coverage of the total irradiated area increases, and thus extra dose is delivered to the patient which is undesirable.Therefore, monitoring both the energy variation and beam field width are considered as critically important in limiting the extra patient dose.In this study, the relationship of FWHM and energy variation was carefully investigated.The results depicted that an increase in the PDD ratio resulted in an increase in FWHM on 10 mm symmetric FW, implying a positive correlation between the two factors (p < 0.002).
The evaluation on PDD 20,10 ratio was used to monitor the energy stability regularly.According to the guideline by the manufacturer (Accuray Incorporated, Sunnyvale, CA), the absorbed dose at depth 20 cm to the maximum absorbed dose at depth 1.5 cm should be in the range 0.315 to 0.327 (0.321 ± 2%) while that at depth 10 cm to 1.5 cm should be in the range of 0.593 to 0.618 (0.6055 ± 2%). 11The acceptable criteria of PDD 20,10 ratio was 0.520 to 0.541 (0.530 ± 2%).It can be demonstrated that even if the ratio of PDD 20,10 increases but not exceeding the permissible level, it is possible that the beam field width falls outside the 1% tolerance.It is desirable to adjust the range of PDD 20,10 ratio to verify whether the beam field width pass as well.Based on the linear regression models on three Radixact units, the constrained PDD 20,10 ratios for Radixact A and B should be 0.524 to 0.528 while that for Radixact C is 0.526 to 0.531.The constraints are machine specified but the range of 0.524 to 0.528 is chosen as the recommended criteria.For the case that the PDD 20,10 QA marginally passes the constrained range, it is recommended to perform the Dynamic Jaw QA immediately to ensure the smallest field width to be within tolerance, which is essential to maintain effective treatment in TomoEDGE system.
From our study, it can be illustrated that there is a large variation of the measured field width on a small difference of the PDD ratio.The study by Chen et al. revealed that the large variation in measured FWHM for a similar PDD 20,10 ratio can be the result of multiple factors.The focal spot size of the linear accelerator acts as the major role in affecting the penumbra region.The consequence is especially severe for small fields. 12Since the regression of this study was a single-factor model, other confounding factors such as the focal spot size of linear accelerator should also be considered when evaluating the machine status.
To assess the clinical impact of the variations in beam energy, a circular 2D electronic device was utilized.Nine patient-specific treatment plans, which carried >90% γ passing rate, were further analyzed.The reference dose was intentionally adjusted by 1% to simulate a slight change in beam energy.γ passing criteria 3% dose/3 mm DTA was set.One out of nine plans reflected a change in passing rate below 90% which would require further investigation in normal clinical settings.

CONCLUSIONS
Through this long-term retrospective study, the performance of TomoEDGE technology has been evaluated in three Radixact tomotherapy machines by statistical method.All measured symmetric field widths in each unit demonstrated to be within 1% tolerance while the absolute differences of all measured asymmetric field widths were within 0.5 mm tolerance recommendation stated by AAPM TG-306.The correlation between FWHM and PDD 20,10 ratio has been investigated.It is noticeable that an increase in FWHM on nominal 10 mm symmetric FW showed an increase of 1.5% when PDD 20,10 ratio was increased by 1%.Besides, even the ratio of PDD 20,10 increases but to be still well within the permissible level,it is possible that the beam field width falls outside the 1% tolerance level.Hence, it is desirable to adjust the range of PDD 20,10 ratio from 0.524 to 0.528 to verify whether the beam field width also passes as well.Slight deviation in beam quality QA may be considered as a signal to the change in field width.For the case that the PDD 20,10 QA marginally passes the constrained range, user is recommended to consider further verification QA on Dynamic Jaw to ensure the smallest field width to be within tolerance, which is essential to maintain effective treatment in TomoEDGE system.Since the regression of this study was a single-factor model, other confounding factors such as the focal spot size of linear accelerator should also be considered when evaluating the machine status.

AC K N OW L E D G M E N T S
The authors have nothing to report.This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors declare no conflicts of interest.

R E F E R E N C E S
Binny et al. have demonstrated the correlation between the output or energy variations on different delivery modes and patient delivery QA results 7 while Ferris et al. investigated the effects of variable-width jaw motion on the beam characteristics for Radixact Synchrony®. 8Choi et al. have presented the correlation between TomoTherapy Quality Assurance (TQA) data trend and TomoHD functional status, showing that the exit detector flatness among all four TQA modules (Basic Dosimetry, System Monitor, Step-Wedge Static and

F I G U R E 2
Illustration of the phantom and ion chamber setup.

3 4
Typical normalized plot of a TQA field width dynamic jaws measurement with the field width order of 50 mm, 25 mm, 20 mm, 10 mm, 25 mm POS, 25 mm NEG, 20 mm POS, 20 mm NEG, 10 mm POS, 10 mm NEG.Example of 10 mm field width profile with normalization.

6
Plot of measured FWHM of nominal 10 mm symmetric FW against PDD 20,10 for Radixact Unit A.

7
Plot of measured FWHM of nominal 10 mm symmetric FW against PDD 20,10 for Radixact Unit B.
AU T H O R C O N T R I B U T I O N SH.M. Poon-Experiment, data analysis, writing-Original draft.T.L. Chiu-Experiment, data analysis, writing-Review & Editing, supervision.S.K. Yu-Conceptualization, resources Field Width FWHM comparison for Radixact Units throughout a 2-year duration.
TA B L E 1Note: The comparison between the golden standard reference and the measured FWHM in dynamic jaw motion beam model.All values were shown in mm.
. All measured symmetric field widths in each unit demonstrated Percentage of individual FWHM measurement exceeding the 1% tolerance level of symmetric FW or 0.5 mm tolerance level of asymmetric FW recommendation by AAPM TG-306.
Note: 10 mm symmetric treatment slice widths were the most sensitive to the 1% FWHM tolerance and the setup should be verified promptly.
Plot of measured FWHM of nominal 10 mm symmetric FW against PDD 20,10 for Radixact Unit C.