The effect of MLC speed and acceleration on the plan delivery accuracy of VMAT

Abstract

Objective:

To determine a new metric utilizing multileaf collimator (MLC) speeds and accelerations to predict plan delivery accuracy of volumetric modulated arc therapy (VMAT).

Methods:

To verify VMAT delivery accuracy, gamma evaluations, analysis of mechanical parameter difference between plans and log files, and analysis of changes in dose–volumetric parameters between plans and plans reconstructed with log files were performed with 40 VMAT plans. The average proportion of leaf speeds ranging from l to h cm s⁻¹ (S_l–h and l–h = 0–0.4, 0.4–0.8, 0.8–1.2, 1.2–1.6 and 1.6–2.0), mean and standard deviation of MLC speeds were calculated for each VMAT plan. The same was carried out for accelerations in centimetre per second squared (A_l–h and l–h = 0–4, 4–8, 8–12, 12–16 and 16–20). The correlations of those indicators to plan delivery accuracy were analysed with Spearman's correlation coefficient (r_s).

Results:

The S_1.2–1.6 and mean acceleration of MLCs showed generally higher correlations to plan delivery accuracy than did others. The highest r_s values were observed between S_1.2–1.6 and global 1%/2 mm (r_s = −0.698 with p < 0.001) as well as mean acceleration and global 1%/2 mm (r_s = −0.650 with p < 0.001). As the proportion of MLC speeds and accelerations >0.4 and 4 cm s⁻² increased, the plan delivery accuracy of VMAT decreased.

Conclusion:

The variations in MLC speeds and accelerations showed considerable correlations to VMAT delivery accuracy.

Advances in knowledge:

As the MLC speeds and accelerations increased, VMAT delivery accuracy reduced.

Volumetric modulated arc therapy (VMAT) delivers a conformal prescription dose to the target volume while minimizing dose to normal tissues. This is accomplished by modulating photon beam intensities through the modulation of multileaf collimator (MLC) positions, gantry speeds and dose rates simultaneously at each control point (CP).^1–3 Although the modulation of photon beam intensity is a core feature of VMAT, excessive modulation of photon beam intensity increases uncertainty in the mechanical operation of the linear accelerator (linac) and also increases the number of small or irregular field shapes, resulting in differences in dose distributions between calculated and delivered plans.⁴ This can potentially cause not only poor tumour control but also damage to normal tissues. Therefore, pre-treatment quality assurance (QA) for each patient is routinely performed in the clinic for verification that the plan is delivered as intended.^3,5–9 Another method of verification to determine whether a VMAT plan is deliverable as intended or not is the analysis of dynamic log files registered in the linac control system during delivery.^10–14 As a further method of analysis, it has been suggested that the dose distribution in patient CT images be reconstructed with those dynamic log files and compared with that of the original treatment plan.¹⁵

On the other hand, several studies have suggested modulation indices for VMAT, which can quantify and evaluate the degree of modulation at the planning stage to verify the plan delivery accuracy.^4,16–24 Modulation indices have an advantage compared with pre-treatment QA or dynamic log file analysis in that clinical resources required to evaluate the degree of modulation of VMAT plans are spared. Masi et al¹⁸ suggested the modulation complexity score (MCS) for VMAT (MCS_v) as well as the leaf travel MCS (LTMCS) as modulation indices for VMAT, both of which focus on the MLC movement and the aperture shapes defined by MLCs. Li and Xing¹⁷ suggested a modulation index for VMAT (MI_SPORT) by combining the segmental monitor unit (MU) and variations in MLC positions. We also suggested a modulation index adopting previously suggested methodology by Webb²⁴ by quantifying MLC speeds, MLC accelerations, gantry rotation accelerations and dose-rate variations at each CP simultaneously.²⁵

In terms of the mechanical operation of linacs for VMAT, Nicolini et al²⁶ showed the reliability of variations in gantry rotational speed in relation to dose-rate variations for VMAT. In the previous study, we demonstrated that the effect of MLC movements on VMAT delivery accuracy was larger than that of gantry angle rotation or dose-rate variation.²⁵ It has been demonstrated that the modulation of MLC movement is a critical factor influencing plan delivery accuracy of VMAT.^9,18,25,26 Although considerable influence of MLC movement on plan delivery accuracy of VMAT is recognized, a more detailed relationship of VMAT plan delivery accuracy to the patterns of MLC movement, that is, variations in MLC speed and acceleration, is unclear. Thus, we investigated the effect of variations in MLC speeds and accelerations on plan delivery accuracy in this study. Furthermore, we tried to predict the plan delivery accuracy of VMAT with specific MLC speed and acceleration information.

The speeds of each MLC between each CP were calculated with clinically acceptable VMAT plans and divided into several groups according to the magnitude of MLC speed. The same was carried out for MLC acceleration. After that, the ratios of the CP numbers in a group to the total number of CPs were calculated. The correlations of those calculated values to the plan delivery accuracy were analysed using the Spearman's rank correlation coefficient (r_s). The plan delivery accuracy was evaluated using two-dimensional (2D) global and local gamma-index methods with various gamma criteria. The global gamma index calculates the difference in dose relative to a specific dose, such as the maximum dose, while the local gamma index calculates dose difference relative to the current measurement point.²⁷ Dynamic log file analysis and changes in dose–volumetric parameters between the original treatment plans and plans reconstructed with log files were also investigated. Through evaluation of the correlations of each group to plan delivery accuracy, the effects of variations in MLC speeds and accelerations on VMAT plan delivery accuracy were investigated.

METHODS AND MATERIALS

Volumetric modulated arc therapy planning

The VMAT plans analysed in our previous study were also used in this study.²⁵ Randomly, 20 head and neck (H&N) and 20 prostate VMAT plans were retrospectively selected from plans previously used for patient treatment in the Department of Radiation Oncology, Seoul National University Hospital. For the generation of both prostate and H&N VMAT plans, 6-MV photon beams of Trilogy^® with Millennium^TM 120 MLC (Varian^® Medical Systems, Palo Alto, CA) were used. All VMAT plans were generated using two full arcs with the Eclipse system (Varian Medical Systems). The progressive resolution optimizer 3 (PRO3, v. 10; Varian Medical Systems) was used for optimization. For the calculation of dose distributions, the Anisotropic Analytic Algorithm v. 10 (Varian Medical Systems) was used with a calculation grid of 2.5 mm. For the patients with prostate cancer in our institution, a primary plan delivering 50.4 Gy (daily, 1.8 Gy) to the primary target volume and a boost plan delivering 30.6 Gy (daily, 1.8 Gy) to the boost target volume were generated. Only primary plans were analysed in this study. A primary target volume was defined with a margin of 2 cm from the prostate and seminal vesicles in all directions except the inferior and posterior directions. To reduce dose to the rectal wall, a margin of 1 cm was added to the inferior and posterior directions. In the case of H&N VMAT plans, the simultaneous integrated boost technique was used with a total of three target volumes. A margin of 0.3 cm was added in all directions from the clinical target volume. Prescription doses of 67.5 Gy (daily, 2.25 Gy), 54 Gy (daily, 1.8 Gy) and 48 Gy (daily, 1.6 Gy) were delivered to Targets 1, 2 and 3, respectively.

Verification of volumetric modulated arc therapy plan delivery accuracy

A total of three types of verification methods used in our previous study²⁵ were adopted to evaluate the VMAT delivery accuracy in this study.

Gamma-index method with MapCHECK2^TM detector array

2D dose distributions of each VMAT plan were measured with a MapCHECK2 detector array (Sun Nuclear Corporation, Melbourne, FL). When measuring 2D dose distributions, the MapCHECK2 detector array was inserted into a MapPHAN^TM (Sun Nuclear Corporation), which is a solid water phantom with a hole for insertion of the MapCHECK2 detector array. For comparison, the reference planar dose distributions of each VMAT plan were calculated in a virtual water phantom with a calculation grid of 1 mm, which is the finest resolution of the Eclipse system. The mass density of that virtual water phantom in the Eclipse system was manually modified and assigned to match the calculated and measured values with the MapCHECK2 detector array inserted into MapPHAN, in accordance with manufacturer recommendations. Before the measurement of 2D dose distributions for gamma evaluations, the output of the linac was calibrated with a measured value based on the American Association of Physicists in Medicine Task Group 51 protocol.²⁸ After that, the absolute reading of the MapCHECK2 detector array was calibrated following the manufacturer provided protocol. The relative readings of each detector in the MapCHECK2 detector array were also calibrated according to the protocol provided by the manufacturer. After measurements of the VMAT plan dose distributions, both global and local gamma evaluations were performed with SNC patient software v. 6.1.2 (Sun Nuclear Corporation). Gamma criteria of 2%/2, 1%/2 and 2%/1 mm were used for gamma evaluation. As recommended by previous studies for pre-treatment QA for VMAT, gamma criteria of 3%/3 and 1%/1 mm were not used in this study.^7,8,29 Any values that were <10% of the maximum dose were not evaluated when performing gamma evaluations as often cited in the literature.^8,30,31

Analysis of log files generated during volumetric modulated arc therapy delivery

During the acquisition of planar dose distributions with the MapCHECK2 detector array, dynamic log files, which are records of actual gantry angles and delivered MUs at each CP of a VMAT plan, were acquired. Simultaneously, DynaLog files (Varian Medical Systems), which are a record of MLC positions every 50 ms, were acquired for each VMAT plan. These two types of log files were combined using an in-house program written in MATLAB^® v. 8.1 (MathWorks^®, Natick, MA) to generate digital imaging and communications in medicine-radiotherapy (DICOM-RT)-formatted VMAT plan files. For each VMAT plan, the differences in MLC positions, gantry angles and delivered MUs at each CP between the original treatment plan and the DICOM-RT-formatted VMAT plan were calculated.

Analysis of dose–volumetric parameters

The DICOM-RT-formatted VMAT plans were imported into the Eclipse system, and dose distributions in patient CT image sets identical to those used for treatment planning were calculated for each VMAT plan. The DICOM-RT-formatted VMAT plans included information of every MLC position, gantry angles and MUs at each CP. Using the PRO3 algorithm, each plan had a total of 178 CPs per full arc, thus the CP intervals were 2.0341°. Just as in original VMAT plans generated in the Eclipse system, the DICOM-RT-formatted plans used discrete information from each CP to calculate the dose distributions in the CT image set of a patient. Calculation grids of 2.5 mm, identical to the original treatment plans, were used for dose calculation. After calculation of dose distributions, clinically significant dose–volumetric parameters were calculated with identical structure sets as those used for treatment planning. For the target volume, the dose received by 95% of the target volume (D_95%), D_5%, minimum, maximum and mean dose to the target volume were calculated. For prostate organs at risk (OARs), D_20% of rectal wall and bladder, mean dose to the rectal wall, bladder and femoral head, and D_50% of femoral head were calculated. For H&N OARs, mean dose to each parotid gland and the maximum dose to the spinal cord, the brain stem, each lens, optic chiasm and each optic nerve were calculated. The differences in dose–volumetric parameters between original treatment plans and the DICOM-RT-formatted plans were calculated.

Analysis on the MLC speeds and accelerations of VMAT plans

CPs in VMAT plans (RapidArc^®; Varian Medical Systems) are defined in gantry rotation intervals of 2.0341°, therefore adjacent CPs do not necessarily have equal time intervals, thus the time between CPs must be calculated in advance to allow determination of MLC speeds and accelerations. According to manufacturer specifications, the maximum gantry speed and the maximum dose rate were 4.8° s⁻¹ and 600 MU min⁻¹ (i.e. 10 MU s⁻¹), respectively, thus we calculated time between each CP based on this information. The maximum MU able to be delivered without slowing down the gantry rotation is (2.0341 × 10 MU s⁻¹)/(4.8° s⁻¹) = 4.238 MU. If it is necessary to deliver MU >4.238 MU, the gantry rotation speed should be decreased. In this case, the dose rate is maintained at the maximum of 600 MU min⁻¹. Therefore, (1) if the value of MU is ≤4.238 MU at a given CP, the time between CP is 2.0341°/(4.8° s⁻¹) = 0.424 s, while (2) if the value of MU is >4.238 MU, the time is (the MU at that CP)/(10 MU s⁻¹). With this time information, the speed of each leaf (Leaf speed_i) at each CP was calculated as follows.

$${\text{Leaf\hspace{0.17em}speed}}_i\hspace{0.17em}=\hspace{0.17em}\frac{\left|{\text{Leaf}}_i-{\text{Leaf}}_{i+1}\right|}{{\text{Time}}_i}$$ (1)

where Leaf_i is the position of the leaf at the ith CP, and Time_i is the time between the ith CP and the (i+1)th CP.

For each leaf, the number of CPs with Leaf speeds ranging from l to h cm s⁻¹ were counted and divided by the total number of CPs for each VMAT plan (S_l–h). Since no Leaf speed_i >2 cm s⁻¹ was observed in VMAT plans analysed in this study, the combinations of l and h in this study were from 0 to 0.4 cm s⁻¹ (S_0–0.4), from 0.4 to 0.8 cm s⁻¹ (S_0.4–0.8), from 0.8 to 1.2 cm s⁻¹ (S_0.8–1.2), from 1.2 to 1.6 cm s⁻¹ (S_1.2–1.6) and from 1.6 to 2.0 cm s⁻¹ (S_1.6–2.0). After that, the average value of S_l–h of every MLC for each section was calculated for each VMAT plan.

To take acceleration into account, the acceleration of each leaf (Leaf accel_i) at each CP was calculated as follows.

$${\text{Leaf\hspace{0.17em}accel}}_i=\frac{\left|{\text{Leaf\hspace{0.17em}speed}}_i-{\text{Leaf\hspace{0.17em}speed}}_{i+1}\right|}{{\text{Time}}_{i+1}}$$ (2)

For each leaf, the number of CPs with leaf accelerations ranging from l to h cm s⁻² were counted and divided by the total number of CPs for each VMAT plan (A_l–h). Since no Leaf accel_i >20 cm s⁻² was observed in VMAT plans analysed in this study, the combinations of l and h in this study were from 0 to 4 cm s⁻² (A_0–4), from 4 to 8 cm s⁻² (A_4–8), from 8 to 12 cm s⁻² (A_8–12), from 12 to 16 cm s⁻² (A_12–16) and from 16 to 20 cm s⁻² (A_16–20). After that, average values of A_l–h of every MLC for each section were calculated for each VMAT plan.

For each VMAT plan, mean values and standard deviations (SDs) of every Leaf speed_i in centimetre per second unit and Leaf accel_i in centimetre per second square unit were also calculated.

Correlation analysis

To investigate the effect of MLC speed and acceleration on the VMAT plan delivery accuracy, correlations of S_l–h, A_l–h, mean values and SDs of Leaf speed_i and Leaf accel_i to the plan delivery accuracy were analysed with Spearman's rank correlation coefficient (r_s). To examine the statistical significance of the values of r_s, p-values were acquired using a two-tailed unpaired parameter condition. Since the data in this study represented a relatively small sample size, and did not consider missing values, p-values were computed with the exact permutation distributions. Plan delivery accuracy in this study was characterized using three separate methods as mentioned above.²⁵ The first method was to use both global and local gamma passing rates with 2%/2, 1%/2 and 2%/1 mm. The second method was to investigate mechanical parameter differences such as MLC positional differences, gantry angle differences and MU differences at each CP between original treatment plans and DICOM-RT files generated with the log files. Finally, dose-volumetric parameter differences between the original plans and DICOM-RT reconstructed VMAT plan files. For the correlation tests of both gamma passing rates and mechanical parameter differences, a total of 40 VMAT plans were used, including both prostate and H&N VMAT plans, while a total of 20 VMAT plans were used to test the correlations with dose–volumetric differences as the OARs of the prostate plans were different from those of the H&N plans.

RESULTS

The values of S_l–h, A_l–h and mean values of Leaf speed_i and Leaf accel_i

The values of S_l–h, A_l–h and mean values of Leaf speed_i and Leaf accel_i are shown in Table 1. As mentioned above, no values of Leaf speed_i and Leaf accel_i >2 and 20 cm s⁻², respectively, were observed. Therefore, the summed value of S_l–h of every section in a VMAT plan was always 1. The same applied for A_l–h. To illustrate the differences in the patterns of MLC speed variations according to the plan delivery accuracy, examples of the two plans showing the highest delivery accuracy (prostate VMAT 1 and 2) and the two showing the worst delivery accuracy (H&N VMAT 1 and 2) are shown in Figure 1. Highly modulated VMAT plans contained larger proportions of CPs with high MLC speeds than did lowly modulated VMAT plans. For MLC accelerations, representative examples of the two VMAT plans that showed the highest plan delivery accuracy (prostate VMAT 1 and 2), as well as those of the two VMAT plans that showed the worst plan delivery accuracy (H&N VMAT 1 and 2) are shown in Figure 2. Highly modulated VMAT plans contained larger proportions of CPs with MLC accelerations >4 cm s⁻² than did lowly modulated VMAT plans. The values of S_l–h calculated with prostate VMAT plans were always different from those calculated with H&N VMAT plans with statistical significance, as displayed in Table 1 (p < 0.001). With the exception of S_0–0.4, the values of S_l–h of H&N VMAT plans were always higher than those of prostate VMAT plans. The mean value of MLC speeds of H&N VMAT plans was higher than that of prostate VMAT plans (p < 0.001). All values of A_l–h of H&N VMAT plans, except A_0–4, were equal to or higher than those of prostate VMAT plans with statistical significances (p < 0.001). The mean value of MLC acceleration of H&N VMAT plans was higher than that of prostate VMAT plans (p < 0.001).

Table 1.

The average proportion of control point (CP) numbers belonging to particular sections according to the magnitude of multileaf collimator (MLC) speed and acceleration and average values of mean MLC speed and acceleration

Plan type	MLC speed
	S0–0.4	S0.4–0.8	S0.8–1.2	S1.2–1.6	S1.6–2.0	Mean speed
Prostate VMAT	0.637 ± 0.026	0.139 ± 0.011	0.050 ± 0.006	0.028 ± 0.003	0.147 ± 0.014	0.476 ± 0.672
H&N VMAT	0.434 ± 0.033	0.181 ± 0.011	0.082 ± 0.007	0.050 ± 0.007	0.253 ± 0.025	0.772 ± 0.745
p-value	<0.001	<0.001	<0.001	<0.001	<0.001	<0.001

Plan type	MLC acceleration
	A0–4	A4–8	A8–12	A12–16	A16–20	Mean acceleration
Prostate VMAT	0.903 ± 0.016	0.080 ± 0.013	0.017 ± 0.004	0.000 ± 0.000	0.000 ± 0.000	1.311 ± 1.849
H&N VMAT	0.853 ± 0.015	0.123 ± 0.011	0.025 ± 0.004	0.000 ± 0.000	0.000 ± 0.000	1.825 ± 2.075
p-value	<0.001	<0.001	<0.001	0.416	0.932	<0.001

A_l–h, the proportion of number of CPs of MLC accelerations ranging from l to h cm s⁻²; H&N, head and neck; p-value, p-values showing statistical significances of differences between S_l–h (A_l–h) of prostate plans and S_l–h (A_l–h) of H&N plans; S_l–h, the proportion of number of CPs with MLC speeds ranging from l to h cm s⁻²; VMAT, volumetric modulated arc therapy.

Figure 1.

The number of control points in a volumetric modulated arc therapy (VMAT) plan are plotted according to the speeds of multileaf collimator (MLC). VMAT plans for prostate cancer, which showed superior plan delivery accuracy (a, b), as well as VMAT plans for head and neck cancer, which showed inferior plan delivery accuracy (c, d), are shown.

Figure 2.

The number of control points in a volumetric modulated arc therapy (VMAT) plan are plotted according to the accelerations of multileaf collimator (MLC). Volumetric modulated arc therapy plans for prostate cancer, which showed superior plan delivery accuracy (a, b) as well as VMAT plans for head and neck cancer, which showed inferior plan delivery accuracy (c, d) are shown.

Gamma passing rates vs variations in multileaf collimator movements

Gamma passing rates vs variations in multileaf collimator speed

The values of r_s and corresponding p-values for S_l–h, mean values and SDs of MLC speeds to both global and local gamma passing rates are shown in Table 2.

Table 2.

Spearman's rank correlation coefficients between gamma passing rates and S_l–h

Metric	2%/2 mm		1%/2 mm		2%/1 mm
	rs	p-value	rs	p-value	rs	p-value
Global gamma passing rates
S0–0.4	0.479	0.002	0.674	<0.001	0.301	0.059
S0.4–0.8	−0.458	0.003	−0.644	<0.001	−0.258	0.108
S0.8–1.2	−0.511	0.001	−0.690	<0.001	−0.338	0.033
S1.2–1.6	−0.489	0.001	−0.698	<0.001	−0.319	0.045
S1.6–2.0	−0.471	0.002	−0.662	<0.001	−0.283	0.076
Mean speed	−0.470	0.002	−0.674	<0.001	−0.283	0.077
SD speed	−0.417	0.007	−0.611	<0.001	−0.220	0.172
Local gamma passing rates
S0–0.4	0.540	<0.001	0.584	<0.001	0.522	0.001
S0.4–0.8	−0.489	0.001	−0.554	<0.001	−0.404	0.010
S0.8–1.2	−0.526	<0.001	−0.559	<0.001	−0.512	0.001
S1.2–1.6	−0.508	0.001	−0.546	<0.001	−0.489	0.001
S1.6–2.0	−0.498	0.001	−0.553	<0.001	−0.491	0.001
Mean speed	−0.536	<0.001	−0.579	<0.001	−0.515	0.001
SD speed	−0.420	0.007	−0.475	0.002	−0.413	0.008

r_s, Spearman's rho; SD, standard deviation; S_l–h, the proportion of number of control points with multileaf collimator speeds ranging from l to h cm s⁻².

The r_s values of S_l–h as well as mean values and SDs of MLC speeds to global gamma passing rates with 2%/2 and 1%/2 mm were always statistically significant showing p-values <0.008. In the cases of local gamma passing rates, all values of r_s were statistically significant to gamma passing rates with every gamma criterion (p < 0.02). For both global and local gamma passing rates, the r_s values of S_0–0.4 always had positive signs, while those of the other S_l–h always had negative signs. Therefore, as the values of S_0–0.4 increased, the values of both global and local gamma passing rates increased. However, as the proportion of CPs with MLC speeds >0.4 cm s⁻¹ increased, the values of both global and local gamma passing rates decreased. As mean values and SDs of MLC speeds increased, both global and local gamma passing rates decreased. The highest r_s value was observed between S_1.2–1.6 and global gamma passing rates with 1%/2 mm (r_s = −0.698 with p < 0.001).

Gamma passing rates vs variations in multileaf collimator accelerations

The values of r_s and corresponding p-values for A_l–h, mean values and SDs of MLC accelerations to both global and local gamma passing rates are shown in Table 3.

Table 3.

Spearman's rank correlation coefficients between gamma passing rates and A_l–h

Metric	2%/2 mm		1%/2 mm		2%/1 mm
	rs	p-value	rs	p-value	rs	p-value
Global gamma passing rates
A0–4	0.477	0.002	0.643	<0.001	0.267	0.096
A4–8	−0.468	0.002	−0.644	<0.001	−0.264	0.100
A8–12	−0.350	0.027	−0.473	0.002	−0.182	0.261
A12–16	−0.226	0.161	−0.293	0.066	−0.197	0.223
A16–20	−0.225	0.163	−0.253	0.116	−0.323	0.042
Mean accel.	−0.476	0.002	−0.650	<0.001	−0.253	0.115
SD accel.	−0.407	0.009	−0.575	<0.001	−0.228	0.158
Local gamma passing rates
A0–4	0.468	0.002	0.510	0.001	0.456	0.003
A4–8	−0.465	0.003	−0.505	0.001	−0.447	0.004
A8–12	−0.368	0.019	−0.370	0.019	−0.378	0.016
A12–16	−0.362	0.022	−0.289	0.070	−0.426	0.006
A16–20	−0.224	0.166	−0.272	0.089	−0.372	0.018
Mean accel.	−0.516	0.001	−0.543	<0.001	−0.479	0.002
SD accel.	−0.447	0.004	−0.454	0.003	−0.455	0.003

accel., acceleration; A_l–h, the proportion of number of control points of multileaf collimator accelerations ranging from l to h cm s⁻²; r_s, Spearman's rho; SD, standard deviation.

With the exception of A_12–16 and A_16–20, the r_s values of A_l–h as well as mean and SDs of MLC accelerations to global gamma passing rates with 2%/2 and 1%/2 mm were always statistically significant (p < 0.03). In the cases of local gamma passing rates, all r_s values were statistically significant except r_s between A_12–16 and passing rates with 1%/2 mm and A_16–20 and passing rates with 2%/2 and 1%/2 mm. The r_s values of A_0–4 always had positive signs, while those of the other A_l–h always had negative signs to both global and local gamma passing rates, showing the same tendency as S_l–h. The highest r_s values were observed between mean acceleration of MLC and passing rates with global 1%/2 mm (r_s = −0.650 with p < 0.001).

Differences in mechanical parameters between original plans and log files vs variations in MLC movements

Differences in mechanical parameters between original plans and log files vs variations in MLC speeds

The values of r_s and corresponding p-values of S_l–h, mean values and SDs of MLC speeds to the differences in mechanical parameters between plan and delivery are shown in Table 4. All r_s values of S_l–h, mean speed and SD of MLC to the MLC positional errors and gantry angle errors were statistically significant, always showing p < 0.001. No statistically significant correlation of those indicators to MU errors was observed (p > 0.05). The r_s value between S_0–0.4 and MLC errors showed a negative correlation, while the r_s values between the other S_l–h and MLC errors showed positive correlations. This tendency was opposite in gantry angle errors. Therefore, as the proportion of CPs with MLC speeds <0.4 cm s⁻¹ increased, the MLC error decreased but gantry angle error increased. On the other hand, as the proportion of CPs with MLC speeds >0.4 cm s⁻¹ increased, the MLC error increased but gantry angle error decreased. For MLC errors, the highest r_s value was observed with S_0–0.4 (r_s = −0.927 with p < 0.001). For gantry angle errors, the highest correlation was observed at S_1.2–1.6 (r_s = −0.694 with p < 0.001).

Table 4.

Spearman's rank correlation coefficients between mechanical parameter differences at each control point (CP) and S_l–h as well as A_l–h

Metric	MLC position		Gantry angle		MU
	rs	p-value	rs	p-value	rs	p-value
S0–0.4	−0.927	<0.001	0.615	<0.001	0.096	0.557
S0.4–0.8	0.760	<0.001	−0.531	<0.001	−0.057	0.726
S0.8–1.2	0.878	<0.001	−0.675	<0.001	−0.119	0.466
S1.2–1.6	0.869	<0.001	−0.694	<0.001	−0.195	0.229
S1.6–2.0	0.902	<0.001	−0.626	<0.001	−0.138	0.397
Mean speed	0.915	<0.001	−0.621	<0.001	−0.126	0.437
SD speed	0.857	<0.001	−0.622	<0.001	−0.095	0.562
A0–4	−0.835	<0.001	0.669	<0.001	0.196	0.225
A4–8	0.843	<0.001	−0.677	<0.001	−0.184	0.256
A8–12	0.688	<0.001	−0.564	<0.001	−0.131	0.421
A12–16	0.202	0.211	−0.034	0.834	−0.110	0.501
A16–20	0.255	0.112	−0.177	0.276	0.085	0.602
Mean accel.	0.840	<0.001	−0.659	<0.001	−0.172	0.288
SD accel.	0.799	<0.001	−0.631	<0.001	−0.118	0.467

accel., acceleration; A_l–h, the proportion of number of CPs of MLC accelerations ranging from l to h cm s⁻²; MLC, multileaf collimator; MU, monitor unit; r_s, Spearman's rho; SD, standard deviation; S_l–h, the proportion of number of CPs with MLC speeds ranging from l to h cm s⁻².

Differences in mechanical parameters between original plans and log files vs variations in MLC accelerations

The values of r_s and corresponding p-values of A_l–h, mean values and SDs of MLC accelerations to the differences in mechanical parameters between the original treatment plan and log files recorded during delivery are shown in Table 4. All r_s values of A_l–h, mean MLC accelerations and SDs of MLC accelerations to the MLC positional errors and gantry angle errors were statistically significant (p < 0.001) except A_12–16 and A_16–20. Similar to the results of MLC speed, no statistically significant correlation to MU errors was observed (p > 0.05). The r_s value between A_0–4 and MLC errors showed a negative correlation, while the r_s values between the other A_l–h and MLC errors showed positive correlations. Just as in the results of the MLC speed analysis, this tendency was opposite for gantry angle errors. For both MLC errors and gantry angle errors, the highest r_s values were observed with A_4–8 (r_s = 0.843 with p < 0.001 and r_s = −0.677 with p < 0.001, respectively).

Differences in dose–volumetric parameters between the original treatment plan and plans reconstructed with log files vs variations in MLC movements

Volumetric modulated arc therapy plans for prostate cancer

The statistically significant r_s values and corresponding p-values of the S_l–h, A_l–h, mean values and SDs of MLC speed and accelerations to the differences in dose–volumetric parameters between original treatment plans and plans reconstructed with log files for prostate cancer are shown in Table 5.

Table 5.

Statistically significant Spearman's rank correlation coefficients of the differences in dose–volumetric parameters between treatment plan and delivery to S_l–h and A_l–h of prostate volumetric modulated arc therapy plans

Dose–volumetric parameter		S0–0.4	S0.4–0.8	S1.2–1.6	S1.6–2.0	Mean speed	Standard deviation speed	A4–8	A16–20	Mean accel.
Target volume
D95%	rs	–	0.529	0.563	–	0.512	–	0.460	0.464	0.461
	p-value	–	0.017	0.010	–	0.021	–	0.041	0.040	0.041
D5%	rs	–	0.533	–	–	–	–	–	–	–
	p-value	–	0.016	–	–	–	–	–	–	–
Maximum dose	rs	–	–	0.490	–	–	–	–	–	–
	p-value	–	–	0.028	–	–	–	–	–	–
Mean dose	rs	–	0.548	–	–	–	–	–	0.473	–
	p-value	–	0.012	–	–	–	–	–	0.035	–
Organs at risk
Rectal wall D20%	rs	−0.452	0.472	0.527	0.507	0.534	0.501	0.461	–	–
	p-value	0.046	0.036	0.017	0.023	0.015	0.024	0.041	–	–
Femoral head mean dose	rs	–	–	–	–	–	–	–	0.449	–
	p-value	–	–	–	–	–	–	–	0.047	–

accel., acceleration; A_l–h, the proportion of number of CPs of MLC accelerations ranging from l to h cm s⁻²; CP, control point; D_n%, dose received by n% of volume of structure; r_s, Spearman's rho; S_l–h, the proportion of number of CPs with MLC speeds ranging from l to h cm s⁻².

In the case of MLC speed, S_0.4–0.8 showed statistically significant correlations to the changes in dose–volumetric parameters most frequently (four cases). The highest correlation was observed between S_1.2–1.6 and D_95% of target volume (r_s = 0.563 with p = 0.01). The r_s values of S_0–0.4 had negative signs and the other S_l–h had positive signs, just as in the results of gamma passing rates and mechanical parameter differences.

For MLC acceleration, A_16–20 showed statistically significant correlations to the changes in dose–volumetric parameters most frequently (three cases). The highest correlation was observed between A_16–20 and mean dose to target volume (r_s = 0.473 with p = 0.035).

Volumetric modulated arc therapy plans for head and neck cancer

The statistically significant values of r_s and corresponding p-values of the S_l–h, A_l–h, mean values and SDs to MLC speed and accelerations to the differences in dose–volumetric parameters between original treatment plans and the plans reconstructed with log files for H&N cancer are shown in Table 6. For both MLC speeds and accelerations, statistically significant r_s values were observed more frequently in H&N VMAT plans than in prostate VMAT plans.

Table 6.

Statistically significant Spearman's rank correlation coefficients of the differences in dose–volumetric parameters between treatment plan and delivery to S_l–h and A_l–h of head and neck volumetric modulated arc therapy plans

Dose–volumetric parameter		S0–0.4	S0.4–0.8	S0.8–1.2	S1.2–1.6	S1.6–2.0	Mean speed	A0–4	A4–8	A16–20	Mean acceleration
Target 1
D95%	rs	–	–	0.677	0.464	–	–	–	–	–	0.464
	p-value	–	–	0.001	0.039	–	–	–	–	–	0.039
D5%	rs	–	–	0.648	0.541	–	–	–	–	–	0.462
	p-value	–	–	0.002	0.014	–	–	–	–	–	0.040
Mean	rs	–	–	0.675	0.616	–	–	–	–	–	0.495
	p-value	–	–	0.001	0.004	–	–	–	–	–	0.026
Target 2
D95%	rs	–	–	0.467	0.451	–	–	–	–	–	0.480
	p-value	–	–	0.038	0.046	–	–	–	–	–	0.032
D5%	rs	–	–	0.702	0.552	–	–	−0.529	0.531	–	0.675
	p-value	–	–	0.001	0.013	–	–	0.018	0.017	–	0.001
Mean	rs	–	–	0.647	0.670	–	–	−0.461	0.465	–	0.623
	p-value	–	–	0.002	0.001	–	–	0.041	0.039	–	0.003
Target 3
D95%	rs	–	–	0.519	0.515	–	–	–	–	0.481	0.563
	p-value	–	–	0.023	0.024	–	–	–	–	0.037	0.012
D5%	rs	–	–	0.674	0.597	–	–	−0.476	0.473	–	0.552
	p-value	–	–	0.002	0.007	–	–	0.039	0.041	–	0.014
Min.	rs	−0.569	–	0.651	0.579	0.628	0.586	−0.577	0.630	–	0.694
	p-value	0.011	–	0.003	0.009	0.004	0.008	0.010	0.004	–	0.001
Max.	rs	–	–	0.579	0.747	–	–	−0.543	0.574	–	0.546
	p-value	–	–	0.009	<0.001	–	–	0.016	0.010	–	0.016
Mean	rs	–	−0.540	0.541	0.569	–	–			–	–
	p-value	–	0.017	0.017	0.011	–	–			–	–
Organs at risk
Brain stem max.	rs	–	–	–	–	–	–	–	–	–	0.467
	p-value	–	–	–	–	–	–	–	–	–	0.038
Left parotid gland mean	rs	−0.484	–	–	–	–	0.478	–	–	–	–
	p-value	0.031	–	–	–	–	0.033	–	–	–	–
Left optic nerve max.	rs	–	–	–	–	–	–	–	–	−0.480	–
	p-value	–	–	–	–	–	–	–	–	0.032	–

A_l–h, the proportion of number of CPs of MLC accelerations ranging from l to h cm s⁻²; CP, control point; D_n%, dose received by n% of volume of structure; Max., maximum dose; Mean, mean dose; Min., minimum dose; r_s, Spearman's rho; S_l–h, the proportion of number of CPs with MLC speeds ranging from l to h cm s⁻².

In the case of MLC speed, S_0.8–1.2 and S_1.2–1.6 showed statistically significant correlations to the changes in dose–volumetric parameters most frequently (both 11 cases). The highest correlation was observed between S_1.2–1.6 and the maximum dose to Target 3 (r_s = 0.747 with p < 0.001). The r_s values of S_0–0.4 and S_0.4–0.8 had negative signs, while the other S_l–h had positive signs.

In the case of MLC acceleration, mean acceleration showed statistically significant correlations to the dose–volumetric parameters most frequently (11 cases). The highest correlation was observed between mean acceleration and the minimum dose to Target 3 (r_s = 0.694 with p = 0.001). The r_s values of A_0–4 had negative sign, and the other A_l–h had positive signs, showing the identical tendency as the other results.

DISCUSSION

As demonstrated by Kerns et al,³² restricting the maximum MLC speed can improve VMAT delivery accuracy. In this study, by correlation analysis, we demonstrated that not only MLC speeds but also MLC accelerations could affect the VMAT delivery accuracy. Both mean MLC speed and acceleration showed considerable correlations to the results acquired from various VMAT verification methods. As the MLC speed and MLC acceleration increased, VMAT delivery accuracy decreased. This result is consistent with results demonstrated in our previous study.²⁵ As a detailed analysis, the r_s values of S_l–h and A_l–h to VMAT delivery accuracy indicated that the VMAT delivery accuracy became worse if the proportions of MLC speeds 0.4 cm s⁻¹ or accelerations >4 cm s⁻² increased. When these proportions increased, both global and local gamma passing rates decreased, MLC positional errors increased and the magnitude of changes in dose–volumetric parameters increased, indicating a decrease in plan delivery accuracy. The global gamma passing rates with 1%/2 mm vs S_0–0.4 and A_0–4 as well as MLC positional errors vs S_0–0.4 and A_0–4 are plotted in Figure 3. This seems to be owing to the increased uncertainty in MLC movements by the increased MLC speeds and accelerations. Large uncertainties in MLC positions would cause the MLC positional errors and this might cause not only poor gamma passing rates but also large changes in dose–volumetric parameters between plan and delivery. Although poor gamma passing rates came from not only delivery errors but also TPS (eclipse) commissioning errors, the tendency of correlations of gamma passing rates to both MLC speeds and accelerations were similar with those of MLC positioning errors, which is irrelevant to the TPS commissioning errors.

Figure 3.

The global gamma passing rates with 1%/2 mm vs S_0–0.4 (a), S_1.2–1.6 (c), A_0–4 (e) and mean accelerations (g) are plotted. The multileaf collimator (MLC) positional errors vs S_0–0.4 (b), S_1.2–1.6 (d), A_0–4 (f) and mean accelerations (h) are also plotted.

Correlations of MLC speeds and MLC accelerations to the gantry angle errors showed the opposite tendency as that observed in gamma passing rates, MLC errors and changes in dose–volumetric parameters between plan and delivery. That is, gantry angle errors decreased as MLC speeds and accelerations increased. VMAT plans tend to be delivered with maximum gantry rotation speed if possible.^26,33 If it is necessary to deliver large MUs at a specific sector of an arc, which cannot be delivered even with the maximum dose rate, the gantry rotation speed should be lowered.^26,33 In that case, MLCs might not have to move fast compared with the case of the maximum rotation speed of gantry since more time would be given to MLCs to move for modulation of photon beams owing to slowing down of gantry rotation speed. Therefore, not all but some low MLC speeds and accelerations at certain CPs might indicate the changes in the gantry rotation speed, which could make more gantry angle errors. We guess that the opposite tendency of correlations where gantry angle errors decreased as MLC speeds and accelerations increased was owing to this reason. Further analysis on the relationship between MLC speeds and MLC accelerations with gantry angle errors will be performed as a future work.

In the case of the relationship of MU errors with MLC speeds and accelerations, no statistically significant correlations were observed. The average MU errors of the prostate and H&N VMAT plans in this study were only 0.160 ± 0.002 and 0.140 ± 0.130, respectively, showing minimal differences between plan and delivery.²⁵ We guess that the reason for the lack of correlations between MU errors with MLC speeds and MLC accelerations was owing to the relatively accurate control system of MU delivery compared with the control systems of MLC movement or gantry rotation, as Nicolini et al²⁶ demonstrated.

Nelms et al¹⁵ previously showed that gamma passing rates had little clinical relevance by introducing intentional errors in intensity-modulated radiation therapy plans. In this study, the statistically significant r_s values (p < 0.05) between global gamma passing rates with 2%/2 mm gamma criterion, which has been recommended for VMAT pre-treatment QA in previous studies,^7,8 and the dose–volumetric parameter changes were observed in 16 cases from a total of 35 tested cases (data are not shown). As shown in previous studies, gamma passing rates as well as analysis on the MLC speed and acceleration variations are indicators evaluating overall accuracy of VMAT delivery comprehensively.^15,25 On the other hand, dose–volumetric parameter changes are indicators evaluating VMAT delivery accuracy partially for specific structures, since only part of the mechanical operation of the linac is involved in irradiation of a specific dose–volumetric parameter. For example, some, but not all, MLC movements were involved in the dose delivered to lens in the case of H&N VMAT plans. The mechanical or dosimetric errors involved in those 16 dose–volumetric parameters might lower the values of global gamma passing rates with the 2%/2 mm criterion. Therefore, global gamma passing rates with 2%/2 mm showed clinical relevance in 16 cases in this study. Since a detailed analysis on the relationship between gamma passing rates and changes in dose–volumetric parameters is out of the scope of this study, further analysis was not performed.

To comprehensively review the r_s values of MLC speeds and accelerations to the results of the three verification methods for VMAT delivery accuracy, S_1.2–1.6 and the mean values of MLC accelerations generally showed stronger correlations with statistical significances than did the others. The global gamma passing rates with 1%/2 mm vs S_1.2–1.6 and mean MLC acceleration as well as MLC positional errors vs S_1.2–1.6 and mean MLC acceleration are plotted in Figure 3. The highest performance was achieved with S_1.2–1.6 and mean MLC accelerations in the changes in dose–volumetric parameters, showing statistically significant r_s values in 14 and 12 cases, respectively. The S_1.2–1.6 and mean MLC acceleration also showed generally stronger correlations to plan delivery accuracy than did previously suggested indices, including MCS_v, LTMCS and MI_SPORT.²⁵ Since all VMAT plans in this study were clinically acceptable and the sample size was only 40, the potential and threshold values of S_1.2–1.6 and mean acceleration as modulation indices for VMAT remain unclear in lieu of further evidence. Therefore, further investigation should be carried out utilizing more VMAT plans, including clinically unacceptable plans owing to excessive modulation. Further investigation on S_1.2–1.6 and mean MLC acceleration will be performed as a future work.

Each of the mechanical parameters used for modulation of photon beam intensities of VMAT, which are MLC positions, gantry angles and dose rates, are synchronized with one another. In addition, the values of those mechanical parameters are determined at each CP considering mechanical limits and mutual operational synchronization when VMAT plans are optimized during the plan generation process. Therefore, by analysing the variations of MLC speeds and accelerations of VMAT plans, we could predict not only errors in MLC positions but also gantry angle errors resulting in both poor gamma passing rates and differences in dose–volumetric parameters between plan and delivery. Although MLC speeds and accelerations varied within mechanical limits of the linac when generating VMAT plans, as the proportions of CPs with MLC speeds >0.4 cm s⁻¹ and MLC accelerations >4 cm s⁻² increased, differences between original treatment plans and actual delivery increased. If we control MLC movements at the planning stage to avoid creation of VMAT plans expected to be delivered inaccurately, and also limit the MLC speeds and accelerations in such a way as to not critically degrade plan quality, then we can increase our confidence that the plan will be delivered as intended. The results of this study seem to be used practically by limiting MLC speeds and accelerations to be <0.4 and 4 cm s⁻², respectively. Additionally, S_1.2–1.6 and mean MLC acceleration showed potential as modulation indices for VMAT, showing generally stronger correlations to VMAT delivery accuracy than to MCS_v, LTMCS and MI_SPORT.

The limitation of this study is that the investigated sections of MLC speeds as well as accelerations were divided randomly (intervals of 0.4 cm s⁻¹ for speeds and 4 cm s⁻² for accelerations). Therefore, although the results showed worse VMAT delivery accuracy as the portions of MLC speeds >0.4 cm s⁻¹ and MLC accelerations >4 cm s⁻² increased, those numbers, i.e. 0.4 and 4 cm s⁻², are not necessarily the optimal tolerance levels. To find optimal tolerance levels of both MLC speeds and accelerations for an accurate VMAT delivery, further investigation with fine resolution should be performed and this will be carried out as a future work. The other limitation of this study is that the data analysed in this study were acquired from a single TPS in a single institution. Moreover, we analysed only two kinds of VMAT plans, which were for H&N cancer and prostate cancer. To generalize the results, multicentre study with various TPS as well as various kinds of VMAT plans should be performed. This also will be carried out as a future work.

CONCLUSION

In this study, the variations in MLC speeds and accelerations at each CP were comprehensively analysed in relation to the plan delivery accuracy. Plan delivery accuracy was assessed using passing rates with the 2D gamma-index method, mechanical parameter differences between the original treatment plan and log files, and the changes in dose–volumetric parameters of plans reconstructed with log files. When MLC speed or MLC accelerations were >0.4 and 4 cm s⁻², respectively, the plan delivery accuracy decreased. Generally S_1.2–1.6 and mean acceleration of MLC showed stronger correlations to VMAT delivery accuracy than did other modulation indices, such as MCS_v, LTMCS and MI_SPORT.