4D VMAT planning and verification technique for dynamic tracking using a direct aperture deformation (DAD) method

Abstract We developed a four‐dimensional volumetric modulated arc therapy (4D VMAT) planning technique for moving targets using a direct aperture deformation (DAD) method and investigated its feasibility for clinical use. A 3D VMAT plan was generated on a reference phase of a 4D CT dataset. The plan was composed of a set of control points including the beam angle, MLC apertures and weights. To generate the 4D VMAT plan, these control points were assigned to the closest respiratory phases using the temporal information of the gantry angle and respiratory curve. Then, a DAD algorithm was used to deform the beam apertures at each control point to the corresponding phase to compensate for the tumor motion and shape changes. Plans for a phantom and five lung cases were included in this study to evaluate the proposed technique. Dosimetric comparisons were performed between 4D and 3D VMAT plans. Plan verification was implemented by delivering the 4D VMAT plans on a moving QUASAR™ phantom driven with patient‐specific respiratory curves. The phantom study showed that the 4D VMAT plan generated with the DAD method was comparable to the ideal 3D VMAT plan. DVH comparisons indicated that the planning target volume (PTV) coverages and minimum doses were nearly invariant, and no significant difference in lung dosimetry was observed. Patient studies revealed that the GTV coverage was nearly the same; although the PTV coverage dropped from 98.8% to 94.7%, and the mean dose decreased from 64.3 to 63.8 Gy on average. For the verification measurements, the average gamma index pass rate was 98.6% and 96.5% for phantom 3D and 4D VMAT plans with 3%/3 mm criteria. For patient plans, the average gamma pass rate was 96.5% (range 94.5–98.5%) and 95.2% (range 94.1–96.1%) for 3D and 4D VMAT plans. The proposed 4D VMAT planning technique using the DAD method is feasible to incorporate the intra‐fraction organ motion and shape change into a 4D VMAT planning. It has great potential to provide high plan quality and delivery efficiency for moving targets.

were not taken into account properly. 7,8,9 Several methods have been proposed to manage the intra-fraction tumor motion, including margin expansion, 10 gating techniques [11][12][13][14] and tracking techniques. [15][16][17] Important considerations for SABR treatment include minimizing the volume of the normal tissues outside the tumor receiving high doses per-fraction and achieving acceptable dose inhomogeneity inside the tumor. Therefore, the common use of large treatment margins in lung cancer is in conflict with SABR's requirement of minimal treatment field sizes. 10 Gating techniques reduce the volume of healthy tissue exposed to high doses of radiation. [11][12][13][14] However, gating techniques have limited beam output, therefore, gating techniques increase the treatment delivery time especially for SABR treatments. Rigid tracking techniques can be used to compensate for tumor motion but cannot deal with deformable motion effects. [15][16][17] Four-dimensional volumetric modulated arc therapy (4D VMAT) is a treatment strategy for lung cancers that aims to exploit relative target and tissue motion to improve target coverage and organ at risk (OAR) sparing. [18][19][20] With the development of sophisticated imaging techniques that provide information on tumor motion and deformation, such as 4D-CT [21][22][23] and 4D-CBCT, [24][25][26] the 4D plan optimization strategy presents a logical solution to account for the intra-fractional organ motion. An inverse planning framework for 4D VMAT was proposed by Ma 18 to provide tempo-spatially optimized VMAT plans. The cumulative dose distribution was optimized by iteratively adjusting the aperture shape and weight of each beam through the minimization of the planning objective function. The proposed 4D VMAT planning formulism provided useful insight on how the "time" dimension could be exploited in rotational arc therapy to maximally compensate for the intra-fraction organ motion. Chin 19,20 investigated a novel algorithm for true 4D-VMAT planning by incorporating the 4D volumetric target and OAR motions directly into the optimization process. During optimization, phase correlated beam samples were progressively added throughout the full range of gantry rotation. The resulting treatment plans had respiratory phaseoptimized apertures whose deliveries were synchronized to the patient's respiratory cycle. The 4D VMAT system has the potential to improve radiation therapy of periodically moving tumors over 3D VMAT, gating or tracking methods. However, the complex dose calculation and optimization may prolong the treatment planning time and cannot be implemented on commercial treatment planning systems.
In this work, we propose a 4D VMAT planning technique by applying a direct aperture deformation algorithm to a 3D VMAT plan. This method accounts for both the rigid and non-rigid respiration-induced target motion and is simple and feasible for clinical setup.

| METHODS
Plans for a QUASAR TM phantom with a tumor insert and for five patients who received lung SABR treatments were included in this study. Figure 1 shows the scheme of this study from 4D CT to 4D VMAT plan verification. First, a 3D VMAT plan was optimized based on patient's anatomy on the reference (50%) phase of a 4D CT dataset using Eclipse treatment planning system. The 3D VMAT plans consisted of a sequence of control points each defining the gantry angle, dose weight, and MLC aperture, the gantry speed for each control point was also calculated as can be seen from the beam properties for each control point in Eclipse. Second, the gantry angle for each control point generated from the 3D VMAT plans could be used to link the plan time points and the tumor motion, which is illustrated in the next paragraph. Once the 4D VMAT plan and the tumor motion was synchronized, the DAD method was used to modify the MLC leaf positions at each control point of the plan to synchronize the VMAT delivery with the respiratory motion. Third, the quality of the resultant 4D VMAT plan was investigated by comparing its isodose distribution and DVHs with the 3D VMAT plan.
Fourth, plan verification was implemented by delivering the 4D VMAT plans on a moving QUASAR TM phantom driven with patientspecific respiratory curves.
The gantry angle and gantry speed information could be used to synchronize the plan time points with the phase of breathing motion.
Since the only difference between the 3D and the 4D VMAT plans was the MLC apertures, and the dose rate for each control point was less than the maximum value, therefore, the 4D VMAT plans could be delivered with the same gantry angle and gantry speed for each control point once the MLC leaf travel speed be constrained to a value less than the physical maximum speed. (a) During the 3D VMAT optimization, preserving the maximum speed of leaf motion to below the speed of v max had to be compromised such that the leaf velocity in the target-reference frame could be constrained to v max . The MLC leaf travel speed was set to 1.5 cm/s for 3D VMAT planning optimization in this study; other planning parameters were gantry speed 0.5 to 4.8 degrees/s, and dose rate 0 to 1400 MU/ min, and the physical maximum leaf travel speed 2.5 cm/s (b) once the 4D VMAT plan was generated based on the DAD method, the speed of a MLC leaf at position X as a function of gantry angle g, V (g) = dX/dg, could be related with gantry speed dg/dt and MLC physical leaf speed as follows Where dX dt denotes the leaf travel speed and dt dg denotes the reciprocal of gantry speed. The MLC leaf speed should be less than 2.5 dt dg at each control point. (c) We compared the gantry angles recorded at each control point within the trajectory log files with the 3D and the 4D VMAT plans. Once the 4D VMAT plan could not be delivered with the planned gantry speed due to limited leaf travel speed, the MLC leaf position at that control point had to be modified such that the 4D VMAT plan deliveries could be synchronized with the breathing motion. were imported into the Varian Eclipse treatment planning system (TPS) for contouring and treatment planning. The gross tumor volumes (GTVs) were delineated on each of the ten respiratory phases of the 4D CT. The planning target volumes were defined as the GTVs plus a 5 mm isotropic margin. The amplitude of tumor motion was determined by measuring the peak-to-peak tumor position from different phases of the breathing cycle for each patient. The target volumes and motion amplitudes are listed in Table 1. For the 5 patients in this study, the tumor motion was greater than 5 mm. The prescription dose to the PTV was 60 Gy to be delivered in three fractions with a 6 MV Flattening Filter Free (6X-FFF) X-ray beam from a TrueBeam TM STx linear accelerator. The prescribed isodose line was individually selected for each plan such that at least 95% of the PTV was covered by the prescription dose. In our study, the 50% respiratory phase of the 4D CT image sets (corresponding to end exhalation) was selected as the reference image for 3D VMAT planning and dose verification.

2.B | 4D VMAT plan generation algorithm
Where A i and B i are the position of the leading and trailing leaves of the ith leaf pair. The superscript "O" stands for the target and leaf sequence in the original plan. The superscript "N" stands for the target and new leaf sequence for the Nth Phase. Y i is the geometric center of the projected outline in the Y-direction under the ith leaf pair and can be obtained by leaf pair for the Nth phase. Scale i is calculated by Where TV PI is the target volume within the prescribed isodose volume PI, TV is the target volume.

2.D | 4D VMAT plan verification
3D and 4D plan verifications were performed using EDR 2 film in a QUASAR TM phantom (see Fig. 4). First, the phantom was positioned on the couch using a laser based patient positioning system. Then, the target was accurately localized using kilo-Voltage (kV) orthogonal setup images to ensure the accuracy of target positioning. 3D VMAT plan was delivered to the static phantom and validated using gamma analysis between the film measurement and the planar dose distribution from the TPS. The gamma index criterion was set to 3%/3 mm.
For 4D VMAT plan validation, the QUASAR TM phantom was animated using the real patient-respiration curve, the amplitude of the respiratory curve of a patient was normalized to match the tumor motion amplitude. The variation in the amplitude and frequency was not translated to change for the internal target. The Varian RPM system was used to synchronize the treatment delivery with the phantom motion. The measured dose distribution was compared with the calculated 4D dose distribution. In our work, the 50% phase of respiratory was used as the beam starting time for the treatment delivery.
We assumed that the characteristics of the motion are known (from 4D-CT data) at the treatment planning stage, the adaptive planning strategies from fraction to fraction would not be discussed.
However, in this study, the effects of the changes of breathing amplitude and the phase shift between the tumor motion and the treatment delivery to the total dose distribution were simulated using the Eclipse treatment planning system. The motion amplitude was manually changed and the breathing cycle was shifted for the treatment delivery, the resultant dose distributions were calculated and compared with the original 4D VMAT plan dose distributions (see fig. 5).

3.A | Dosimetric comparison of 4D VMAT plan
with 3D VMAT plan F I G . 5. The effects of the breathing amplitude change and phase shift during 4D VMAT deliveries were simulated in Eclipse. The motion amplitude was manually changed by 1 mm, 2 mm, and 3 mm (a) and a 10% breathing cycle shift (b) was introduced during the 4D VMAT deliveries, the resultant dose distributions were calculated and compared with that of the original 4D VMAT plans.

3.B | Plan verification
The results of the phantom plan verification for 3D and 4D VMAT plans are shown in Fig. 11. The gamma pass ratio is 98.6% for the 3D VMAT plan and 95.7% for the 4D VMAT plan with the criteria of 3%/ 3 mm.   F I G . 8. DVH comparison of the 4D VMAT plans calculated with the rigid registration (lines with rectangle symbols) and the deformable registration (lines with triangle symbols). The GTV coverage and the dose to the lungs are similar for both registration methods, though the PTV coverage for the rigid registration is lower (96.5%) than that for the deformable registration (99.5%).
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The results of the patient plan verification for 3D and 4D VMAT plans are shown in Fig. 14. The measured dose distribution has a good agreement to that of the calculation. The gamma passing ratio is 94.5% and 94.1% for 3D and 4D VMAT plans separately. The statistics of the gamma pass ratio for 3D and 4D VMAT plans is shown in Fig. 15. The average gamma pass ratio is 96.5% for 3D and 95.2% for 4D VMAT plans, respectively.

| DISCUSSION
The 4D VMAT has the potential to improve radiation therapy of periodically moving tumors over 3D VMAT, gating, or tracking methods. Generally, the 4D VMAT plans can be implemented either by independently optimizing each of the phases or by considering all the phases simultaneously. [22][23][24][25] The inverse planning frameworks proposed by Ma 23   The motion effects should be carefully evaluated and will be the focus of our future work.

| CONCLUSION S
The work presented a 4D VMAT planning technique for dynamic targets using a DAD method. The proposed method is a practical and simple approach to account for both rigid and non-rigid target motion. The plan quality of the 4D VMAT plans is comparable to the 3D optimal plans in terms of the tumor coverage and the normal tissue sparing. Because the target motion is continuous, this DAD method generates continuous MLC sequences between apertures of successive phases. The 4D VMAT plans were verified with the QUA-SAR TM phantom, and the effects of the motion amplitude and the phase shift were simulated in Eclipse. The 4D treatment delivery time is the same as the optimal 3D VMAT plan.

ACKNOWLEDG MENT
The authors would like to thank Edward Brandner for his assistance and comments that greatly improved the manuscript. Dr. Xiang Li and Dr. Tianfang Li were supported in part through the NIH/NCI Cancer Center Support Grant P30 CA008748.

CONFLI CT OF INTEREST
The authors declare there are no conflicts of interest in connection with this work.