Intensity modulated radiation therapy (IMRT) is a standard and optimal technique for tumor treatment [1,2]. The latest IMRT technique is volumetric modulated arc therapy (VMAT). VMAT performs dynamic multi-leaf collimator (MLC) IMRT by rotating 360° once or twice, allowing for continuous control of the linear accelerator’s rotation speed and dose rate [3]. As the impact of IMRT, which controls MLC modulation, increases in radiation therapy, the correlation between leaf location accuracy and interleaf or adjacent leaf transmission as well as the accuracy of delivered IMRT fields have been a subject of research [4]. The American Association of Physicists in Medicine Task group reports also referred the importance of quality assurance (QA) protocol for IMRT [5,6]. TG-142 recommends testing the MLC system, including the leaf position accuracy, for gantry rotation as it may affect leaf motion due to gravitational effects imposed on the leaf carriage system.

The picket fence test can be used to qualitatively assess positional accuracy [7]. Additionally, the dose rate and gantry speed, which can affect the leaf carriage system, can be monitored by comparing the picket fence dose distribution and the open beam. Analysis methods include evaluating the MLC travel speed by using the MLC log files or vendor software, but electric portal imaging device (EPID) can also be used for immediate quantitative analysis [5,8-10]. Using EPID, the distance of leaves from junction to junction and the picket fence length can be measured by detecting changes in each position of the image acquired with subpixel precision. Leaf transmission can also be evaluated by calculating the area of the region of interest (ROI) representing the calibrated unit (CU) value in each case.

However, when using EPID, the distance of the leaves from junction to junction is measured by the eye with the highest CU value at the leaf junction. Thus, the results of this method may be subjective, not quantitative. In contrast, radiological imaging technology^® (RIT), which is a representative software that can perform MLC QA, can analyze not only the length of leaf junctions but also the full width at half maximum in the leaf pair junction [11]. To utilize this software, a reference EPID template is required for each linear accelerator, and the discrepancy is analyzed through comparison with the reference template. In this study, we developed an analytical method for EPID picket fence images using Python and their packages. Rather than simply obtaining the max value or performing interpolation, the value was obtained by performing linear fitting up to the 5th order and estimating the extreme value. Additionally, the areas of the open beam and picket fence, which can determine the contribution of gantry speed and dose rate to the motion of the MLC, were analyzed in Python.

MLC QA was performed for the Halcyon^TM linear accelerator, which contains a 6-MV flattening filter free and a dual-layer MLC [12]. Halcyon^TM was equipped with an EPID imager that records 1,280×1,280-pixel transmission images during treatment. The MLC of the Halcyon^TM linear accelerator was a 1.0-cm wide double-layered collimator with low leakage and transmission of radiation, making it optimal for IMRT and VMAT [13]. The MLC QA was comprised of four sections depending on the variable of interest: picket fence test, dose rate, gantry speed, and leaf speed; this was offered by Varian Medical Systems for the machine QA program. The MLC operating direction of all plans was from patient right to patient left (PL), and the operating conditions of each plan are summarized in Table 1. The picket fence patterns were designed to assess the accuracy of MLC leaf positions. As the gantry rotates, the leaves create a junction at 1.5-mm intervals, irradiate for approximately 4 seconds, and then move 1.5 cm in the PL direction to create 10 junctions and create EPID images. EPID images were extracted by digital imaging and communications in medicine format and written by Python 3.6. Pandas 1.1.5, Numpy 1.19.5, Sympy, and Scikit-learn packages were used for analysis.

Table 1 . Plan parameters for the MLC QA.

MLC QA plan	Delivered MU	Gantry rotation	Dose rate
Picket fence test	480.0	179.0°–187.0°	800 MU/s
Dose rate	61.1	179.0°–242.8°	~800 MU/s (variation)
Gantry speed	383.0	179.0°–242.8°	800 MU/s
Leaf speed	245.0	179.0°–187.0°	800 MU/s

MLC, multi-leaf collimator; QA, quality assurance; MU, monitor unit..

1. Picket fence test

Fig. 1 shows the picket fence test performed under the conditions in Table 1. ROIs were determined for 49 leaf pairs by referring to the Halcyon templet for RIT software. There were 10 junctions, and each pixel value was fitted with a 5th-order polynomial equation centered on the peak point as follows:

Figure 1. Electric portal imaging device image for picket fence test written by Python. X and Y axes represent the pixel number. A white vertical line in the figure is a leaf junction.

where p(x_i)=y_j for each i, j∈{0, 1, 2,..., n} and n is the number of data. The solution was obtained to the value that minimized the sum squared error, ${\displaystyle {\sum }_{i=1}^n{\left(y_i-y_i^{\text{'}}\right)}^2}$. The inflection point of each fitted function was set as the peak, and the minimum and maximum values were obtained by measuring the distance between peak points at each junction. The data with fitted function were described at Fig. 2. The results are summarized in Table 2. We compared our results with a method measuring the distance between the maximum pixels of each leaf junction and that obtained by the RIT software. Ours and the RIT’s results were measured within tolerance, and the method of measuring distance was using the maximum pixels over or under-estimated.

Table 2 . Comparison of the mathematics method by fitting with a general method using pixel value.

Method	Min (mm)	Max (mm)
A 5th-order polynomial equation	14.54	15.68
Maximum pixel value distance	13.86	16.06
RIT software	14.10	15.53

Figure 2. Fitting curve samples are represented by the blue line, the pixel number (data) is the blue dot, and the red dot is the peak value at junction, where J_{N (N=1, 2, 3,…, 10)} is the junction and L_{M (M=1, 2, 3,…, 49)} is the leaf pair of the picket fence test.

2. Dose rate, gantry speed, and leaf speed variation

Dose rate, gantry speed, and leaf speed plan were performed and compared with the open beam plan offered by Varian Medical Systems for the machine QA program as shown in Fig. 3. The open beam plans stand in for static field and did not include the MLC movement. We compared the areas of the open beam and MLC plan for each ROI, and results are summarized in Tables 3–5. R_corr represents the dynamic multi-leaf collimator value/open value×100 as the corrected reading. The number of ROIs was set to be Figs. 3d, e, f at each bend shaped pair.

Table 3 . Results of gantry speed plan for MLC QA.

ROI measurement point	DMLC value (CU)	Open value (CU)	Rcorr	Difference to average (%)	Average deviation (%)
Pair 1	0.37623	2.73410	13.76	0.50	0.24
Pair 2	0.42164	3.09327	13.63	−0.45
Pair 3	0.46441	3.39585	13.68	−0.12
Pair 4	0.48495	3.54020	13.70	0.04
Pair 5	0.46472	3.39341	13.69	−0.02
Pair 6	0.42198	3.09005	13.66	−0.27
Pair 7	0.37614	2.73917	13.73	0.29

MLC, multi-leaf collimator; QA, quality assurance; ROI, region of interest; DMLC, dynamic multi-leaf collimator; CU, calibrated unit..

Table 4 . Results of dose rate plan for MLC QA.

ROI measurement point	DMLC value (CU)	Open value (CU)	Rcorr	Difference to average (%)	Average deviation (%)
Pair 1	0.06974	0.50712	13.75	0.74	0.41
Pair 2	0.07296	0.53877	13.54	−0.79
Pair 3	0.07583	0.55791	13.59	−0.43
Pair 4	0.07700	0.56434	13.65	−0.04
Pair 5	0.07618	0.55791	13.65	0.03
Pair 6	0.07344	0.53888	13.63	−0.16
Pair 7	0.06973	0.50754	13.74	0.65

MLC, multi-leaf collimator; QA, quality assurance; ROI, region of interest; DMLC, dynamic multi-leaf collimator; CU, calibrated unit..

Table 5 . Results of leaf speed plan for MLC QA.

ROI measurement point	DMLC value (CU)	Open value (CU)	Rcorr	Difference to average (%)	Average deviation (%)
Pair 1	0.05153	1.81094	2.85	−1.43	0.96
Pair 2	0.06059	2.10309	2.88	−0.20
Pair 3	0.06641	2.26161	2.94	1.72
Pair 4	0.06094	2.09697	2.91	0.67
Pair 5	0.05170	1.80512	2.87	−0.76

MLC, multi-leaf collimator; QA, quality assurance; ROI, region of interest; DMLC, dynamic multi-leaf collimator; CU, calibrated unit..

Figure 3. Electric portal imaging device images of open beam and each intensity modulated radiation therapy plan for the multi-leaf collimator quality assurance. (a) and (d) are for the dose rate plan, (b) and (e) are for the gantry speed plan, and (c) and (f) are for the leaf speed plan.

The accuracy of the MLC movement can be assessed by the picket fence test with an error standard of <1 mm. It is determined by comparing the measurement with the planned leaf junctions at a spacing of 1.5 cm. However, if the brightest part of the leaf junction in the EPID image or the maximum pixel value was chosen, the movement of the MLC cannot be evaluated accurately. Also, when we monitored monthly, it was difficult to decide the origin of the deflective movement.

As shown in Table 2, the method of comparing the general pixel values mentioned above lead to over- or under-estimation depending on the EPID pixel number. Junctions for those cases are shown in Fig. 4. There were discontinuous pixel values in the EPID image, which might be caused by the calibration of EPID’s a-silicon detector or due to limitations in resolution. These values can also cause confusion in monitoring trends in MLC movement.

Figure 4. Over- or under-estimation of cases of the general method using pixel value. The blue solid line is the 5th-order polynomial fitting function, and the red dot is the inflection point of the fitting function. The red arrow represents over- or under-estimated cases if the maximum pixel value distance method was used.

Next, EPID images were obtained by analyzing the dose rate, gantry speed, and leaf speed plan offered by Varian Medical Systems for the machine QA program. The ability of Halcyon^TM to modulate the dose rate and gantry speed to achieve the specified values was evaluated. Next, the MLC leaf speed control was evaluated after having validated the MLC accuracy and Halcyon’s ^TM ability to vary the dose rate and gantry speed. The procedures were intended to determine whether there was a problem with the performance of the MLC by analyzing quantitative changes in EPID measurement values, including movements of the open beam and MLC, through ratio values. Varian Medical System presented a tolerance of ±3.0% for each difference value and 1.5% for the average deviation of all difference values. It was possible to determine that these three factors of IMRT treatment had little effect on MLC movement, and that accurate treatment would be performed.

The leaf pair trend of peak values of each junction, as measured by the presented method, is shown in Fig. 5. The peak value of each junction shows a tendency to move in the PL direction as it goes down for each leaf pair. It can be inferred that this is because the movement of the fence in the plan is irradiated while moving in the PL direction, but it is judged to be a meaningless and infinitesimal movement of <0.5 mm. Analysis of these MLC movements will be helpful for future monitoring and will be beneficial data for making decisions when problems arise.

Figure 5. Peak values trend as measured by setting the inflection point corresponding to the leaf pair. S, superior; PL, patient left; I, inferior; PR, patient right.

The MLC currently plays the most important role in IMRT and VMAT treatment, and its accuracy is related to the accuracy of treatment. The major items of the MLC QA are the picket fence test, dose rate, gantry speed, and leaf speed variation. The aim of the picket fence test is to determine whether the MLC can be accurately driven to the correct position according to the IMRT plan. Generally, the picket fence test is performed by measuring the distance between the brightest parts, with the maximum CU value of the leaf junction created by the MLC QA plan. However, this may be obtained as a discontinuous value due to limitations in EPID pixel resolution, resulting in under- or over-estimation of the value of the distance between leaf junctions. The mathematical method of fitting the value of the leaf junction presented in this study to the 5th order and finding the peak value based on the extrema complemented and yielded reasonable results. The QA of the remaining items (dose rate, gantry speed, and leaf speed variation) were performed by calculating each ROI’s area and comparing the values when the MLC is driven and not driven during open beam. The method presented in this study will enable the MLC QA to be appropriately analyzed and will help monitor its operation.

The authors have nothing to disclose.

All relevant data are within the paper and its Supporting Information files.

Conceptualization: Chang Heon Choi, Jung-in Kim. Data curation: Jin Jegal, Hyojun Park. Formal analysis: Jin Jegal. Investigation: Jin Jegal, Hyojun Park. Methodology: Seonghee Kang. Project administration: Chang Heon Choi. Resources: Chang Heon Choi, Jung-in Kim. Software: Jin Jegal, Hyojun Park. Supervision: Jung-in Kim, Chang Heon Choi. Validation: Seonghee Kang, Chang Heon Choi. Visualization: Jin Jegal, Hyojun Park. Writing – original draft: Jin Jegal. Writing – review & editing: Seonghee Kang, Chang Heon Choi, Jung-in Kim.