Evaluation of dosimetric effect caused by slowing with multi-leaf collimator (MLC) leaves for volumetric modulated arc therapy (VMAT)

We selected 11 VMAT plans (Table 1) on three types of targets: anus, brain and prostate. Leaf travel and modulation complexity score (LTMCS) was used to characterize the modulation complexity of each VMAT plan.15 LTMCS ranges from 0 to 1 and it approaches 0 for increasing degree of modulation and increasing total leaf travel distance. In this study, anal VMAT plans had low LTMCS while brain and prostate VMAT plans had moderate to high LTMCS (Table 1).

LTMCS is derived by the product of leaf travel index (LTi) and modulation complexity score (MCSv).15,16 MCSv was derived by Masi et al to characterize the modulation degree of the MLC leaves of a VMAT plan. MCSv value of 1 indicates no modulation by MLC leaves (i.e. a plan of the least complexity), and the value decreases as modulation complexity increases. Total travel distance of all in-field moving MLC leaves was calculated and normalized to acquire LTi. When LTi approaches 1, it indicates short travel distance of all in-field moving MLC leaves. LTi decreases to zero as total leaf travel distance increases.

All original treatment plan DICOM files were exported from the Eclipse™ (version 10.0, Varian Medical Systems, Inc., Palo Alto, USA) treatment planning system (TPS). The DICOM plans were modified through an in-house developed software. For each arc in the VMAT plan, in-field moving MLC leaves of 178 control points (CPs) on both banks were selected for leaf speed modifications. Speed of each moving MLC leaf per CP was calculated based on MLC leaf position, gantry rotation angle and gantry speed as shown in Equation [1]. [1]Vleaf(m,n)=LP(m,n+1)−LP(m,n)Δt(n)${V_{leaf}}(m,n) = {{LP\left( {m,n + 1} \right) - LP\left( {m,n} \right)} \over {\Delta t\left( n \right)}}$ where Δt(n)=θ(n+1)−θ(n)u(n)$\Delta t\left( n \right) = {{\theta \left( {n + 1} \right) - \theta \left( n \right)} \over {u\left( n \right)}}$ and m: MLC leaf ∊ [1,120]; n: CP ∊ [0,177].

Here ∆t(n) is the gantry rotation time between two adjacent CPs, θ(n) is the gantry angle of CP ‘n’, u(n) is the gantry speed of CP ‘n’, V_leaf (m, n) is the speed of m^th leaf of CP ‘n’ and LP(m, n) is the position of m^th leaf of CP ‘n’. MLC leaves on bank ‘A’ were marked from 1 to 60 while those on bank ‘B’ were marked from 61 to 120.

For each CP of the arc, leaves on both banks (MLC leaf: 1-120) with the highest speed were set to move at 2.3 cm/s, resulting in a leaf position difference at a maximum of 2 mm (Table 1: Range of leaf position chages along 178 CPs). New leaf position of CP ‘n’ is: [2]LPnew(m,n)=LP(m,n−1)+2.3(cm/s)×Δt(n−1).$L{P_{new}}\left( {m,n} \right) = LP\left( {m,n - 1} \right) + 2.3\left( {cm/s} \right) \times \Delta t\left( {n - 1} \right).$

If one leaf was moving with the highest speed at two consecutive CPs, leaf motion direction of each CP was further considered as shown below: 1.

If the motion directions of the next two CPs remained the same, then both leaf positions of corresponding CP were subject to modification (Figure 1A).

Figure 1.

The total modified MLC leaves percentage (Equation 3 and Table 1) was an indicator of the amount of MLC leaves that had been changed to the maximal speed in each arc; [3]TotalmodifiedMLCleaves%=100%×∑i=1178ModifiedfieldleavesonbothbanksofCPi∑i=1178TotalinfieldmovingleavesonbothbanksofCPi$Total\,modified\,MLC\,leaves\% = 100\% \times {{\sum\nolimits_{i = 1}^{178} {Modified\,in\,field\,leaves\,on\,both\,banks\,of\,CPi} } \over {\sum\nolimits_{i = 1}^{178} {Total\,in\,field\,moving\,leaves\,on\,both\,banks\,of\,CPi} }}$ where modified in field leaves on both banks of CPi is the total modified MLC leaves that moving with the highest speed of current CP. Leaf speed modification would not be applied if it caused any leaf pair collision (Gap between leaf pair should be no less than 0.5 mm in actual delivery).

In this study, modified plans were considered as ‘standard’ plans where MLC leaves were allowed to move at the maximal speed (2.3 cm/s). The original plans were considered as ‘slowing MLC’ plans where the highest MLC speed was lower than 2.3 cm/s. There were no changes in monitor unit (MU) and gantry speed per CP in all modified VMAT plans.

Having increased the leaf speed of one CP to the maximal limit without triggering the MLC error interlock (i.e. MLC leaf position difference was less than 2 mm), leaf speed of the next CP would be affected by this modification. With ∆t(n) of each CP remained unchanged, increasing leaf speed by modifying leaf position of current CP while keeping the leaf position of the next CP unchanged resulted in consequential change of leaf speed of the next CP. As a result, total number of leaf speed changes in one arc is twice as many as the total number of MLC leaves that were set to the maximal leaf speed (see Equation [4] below). This accompanied effect caused by the MLC leaf modification either increases or decreases the MLC leaf speed of the next CP according to the leaf motion direction (Table 2). We have taken this accompanied leaf speed modification into account when evaluating dosimetric changes.

Because of the high complexity (i.e. low LTMCS) of the anal VMAT plans, we further analyzed MLC leaf changes in these VMAT plans. The average percentage of modified MLC leaves (Table 3) was the summation of total percentage of modified MLC leaves for all arcs (Table 1: Total Modified MLC leaves %) divided by number of total arcs in the plan. The average percentage of faster moving leaves depends on MLC leaves that were set to the maximal speed and total faster moving leaves after modifications including those modified leaves of current CP and affected leaves of the next CP (Equation [4]); [4]FasterMovingLeaves%=∑arc=1nleavesofhigherspeedaftermodifications∑arc=1n2×MLCleavessettothemaximedspeed×100$Faster\,Moving\,Leaves\% = {{\sum\nolimits_{arc = 1}^n {leaves\,of\,higher\,speed\,after\,modifications} } \over {\sum\nolimits_{arc = 1}^n {2 \times MLC\,leaves\,set\,to\,the\,maximed\,speed} }} \times 100$ where n is the number of total arcs.

In this study, we used MapCHECK®2 2D diode array system (Model 1177, Sun Nuclear Co., Melbourne, FL) for evaluating the effect of slowing MLC leaves on planar dose delivery accuracy. MapCHECK®2 along with its software have been widely used as the clinical implementation for patient-specific verification of VMAT plans due to its compact diode size (0.8 mm×0.8 mm), dose linearity, real-time measurement, reproducibility and sensitivity.17–21

Figure 2 demonstrated pass rate of each arc and variation of measurements based on repeated measurements on two consecutive days. Among all the arcs in both ‘standard’ and ‘slowing MLC’ plans, the maximal variation found was 0.3% with respect to the 91.5% pass rate.

Figure 2.

For all three prostate cases, PS_standard and PS_{slowing MLC} using 3%/ 3 mm and 2%/2 mm criteria were all higher than 90% (Figure 3 and 4: Prostate). Dosimetric differences of Dmean, D95, NTCP (bladder, rectum, leaf and right femoral heads) between ‘slowing MLC’ plans and ‘standard’ plans were: 0.47 ± 0.17 Gy (p > 0.05), 0.33 ± 0.13 Gy (p > 0.05), 1% ± 1%_bladder (p > 0.05), 3% ± 2%_rectum (p > 0.05), 2% ± 1%_{left fem} (p > 0.05), 2% ± 1%_{right fem} (p > 0.05), respectively.

Figure 3.

For all three brain cases, PS_standard and PS_{slowing MLC} using 3%/ 3 mm and 2%/2 mm criteria were all higher than 90% (Figure 3 and 4: Brain) except for arc 2 of brain case B2. Dosimetric differences of Dmean, D95, NTCP (brain stem, cerebellum, spinal cord, left and right cochlea) between ‘slowing MLC’ plans and ‘standard’ plans were: 0.13 ± 0.05 Gy (p > 0.05), 0.17 ± 0.09 Gy (p > 0.05), 1% ± 1%_{brain stem} (p > 0.05), 1% ± 1%_cerebellum (p > 0.05), 0% ± 1%_{spinal cord} (p > 0.05), 1% ± 2%_{left cochlea} (p > 0.05), 1% ± 1%_{right cochlea} (p > 0.05), respectively.

Figure 4.

The LTMCS scores of Anal VMAT plans were smaller than both brain and prostate VMAT plans (Table 1: LTMCS) indicating higher modulation by MLC leaves. For anal VMAT cases, PS_standard and PS_{slowing MLC} using 3%/3 mm criteria were all higher than 90% while ‘slowing MLC’ plans of cases A3, A4 and A5 demonstrated less than 90% pass rates using 2%/2 mm criteria (Figure 4: Anus). Dosimetric differences of NTCP (bladder, rectum, large bowel and femoral heads) between ‘slowing MLC’ plans and ‘standard’ plans were: 2% ± 2%_bladder (p > 0.05), 3% ± 1%_rectum (p > 0.05), 2% ± 1%_{large bowel} (p > 0.05), 1% ± 1%_femheads (p > 0.05), respectively. Compared with anal case A3 and A5, case A4 demonstrated substantial dosimetric differences between the ‘standard’ and ‘slowing MLC’ plans where ∆D_mean and ∆D₉₅ were 2.2 Gy and 1.0 Gy respectively (Figure 5 and Table 3).

Figure 5 (A)

The correlation between decreases in pass rates of VMAT arcs using 2%/2 mm criteria and LTMCS is moderate to strong (r_s = 0.597, Figure 6A). When using 3%/3 mm criteria, the correlation is weak to moderate (r_s = 0.453, Figure 6B).

Figure 6

By using lasers and front pointer for device positioning, the measurement setup was of high consistency. Absolute dose calibration for MapCHECK®2 was performed every day before dose measurement.25,26 Therefore, the source of the uncertainty is mainly due to variability of MLC leaf motion. The small error bars in Figure 2 indicate that the measurement variability is very small.

For anal case A4, since the MU of each control point remained unchanged, and ‘slowing MLC’ plan had more slowly moving MLC leaves, more area were being irradiated that resulted in higher dose. The average percentage of faster moving leaves indicates the amount of MLC leaves moving back-and-forth. The average percentages of modified MLC leaves (2.3%) and average percentage of faster moving leaves (69%) of anal case A4 are higher compared with other analp>cases (Table 3), indicating that more high speed MLC leaves were moving back and forth to create a highly modulated VMAT plan. Accordingly, the anal case A4 has the minimal LTMCS among all anal cases studied.

Moreover, all four arcs of anal case A4 have large fields (e.g. 14 cm ×30 cm, 14 cm ×29 cm, 30 cm ×14 cm, 30 cm ×14 cm for arc 1, 2, 3, 4 respectively). Wijesooriya et al reported the accuracy of RapidArc delivery holds for leaf velocities with small dosimetric uncertainties for 5 mm width MLC leaves which are in the central 20 cm of field.7 They found that three VMAT plans with large MLC leaves with 1cm width at high speed (2.1–2.4 cm/s) demonstrated higher leaf position inaccuracy. Therefore, large MLC leaves in the VMAT plan of anal case A4 have more effect on dose delivery inaccuracy.

When using 3%/3 mm criteria, all 11 cases including ‘standard’ and ‘slowing MLC’ plans passed the institutional 90% acceptance threshold of absolute dose DTA comparison. Dosimetric differences (e.g. ∆D_mean, ∆D₉₅ and NTCP) between ‘standard’ and ‘slowing MLC’ plans in targets and normal tissues were minimal indicating that VMAT plans with non-beam-hold MLC leaf errors (leaf position difference ≤ 2 mm) remain the planned dose coverage except for anal case A4. Using 2%/2 mm criteria, decrease in pass rates of VMAT arcs demonstrated stronger correlation with VMAT modulation complexity which is characterized by LTMCS (Figure 6A).

Some arcs in ‘slowing MLC’ plans of anal cases A3 and A5 showed less than 90% pass rates using 2%/2mm criteria although differences in dosimetric parameters are small (e.g. ∆D_mean and ∆D₉₅). However, anal case A4 showed a consistent decrease in pass rates and dose conformity. Compared with the ‘standard’ plan, ‘slowing MLC’ plan of anal case A4 delivered higher planar dose (Figure 7) which is consistent with the changes in DVH curves in Figure 5B. To further ensure the dosimetric quality of VMAT plans like anal case A4 that have the following features: 1. Highly modulated multiple arc VMAT plan (e.g. LTMCS < 0.1); and 2. Arc has large field size that involves more thick MLC leaves, we recommend 2%/2mm criteria for absolute dose Van Dyk DTA comparison which is more sensitive to non-beam-hold leaf position errors.

Figure 7