Robust optimization of VMAT for lung cancer: Dosimetric implications of motion compensation techniques

Abstract In inverse planning of lung radiotherapy, techniques are required to ensure dose coverage of target disease in the presence of tumor motion as a result of respiration. A range of published techniques for mitigating motion effects were compared for dose stability across 5 breath cycles of ±2 cm. Techniques included planning target volume (PTV) expansions, internal target volumes with (OITV) and without tissue override (ITV), average dataset scans (ADS), and mini‐max robust optimization. Volumetric arc therapy plans were created on a thorax phantom and verified with chamber and film measurements. Dose stability was compared by DVH analysis in calculations across all geometries. The lung override technique resulted in a substantial lack of dose coverage (−10%) to the tumor in the presence of large motion. PTV, ITV and ADS techniques resulted in substantial (up to 25%) maximum dose increases where solid tissue travelled into low density optimized regions. The results highlight the need for care in optimization of highly heterogeneous where density variations may occur with motion. Robust optimization was shown to provide greater stability in both maximum (<3%) and minimum dose variations (<2%) over all other techniques.


| INTRODUCTION
Lung Cancer is the leading cause of cancer death in Australia 1 whilst the American Cancer Society records 5-year survival of lung tumor cases at 17%. 2 Surgery morbidity and a need for multimodality treatments results in over half of all lung cancer patients receiving radiotherapy as some part of their clinical treatment. 2  Recent improvements in the technology of 4-Dimensional Computed Tomography (4DCT) image binning, [15][16][17][18] respiratory motion monitoring, [18][19][20][21][22][23] functional imaging correlation, [24][25][26] and faster imaging techniques have resulted in several delivery methodologies to decrease the impact of lung motion. Another approach to reducing the impact is to minimize the motion itself by incorporating compression belts 27 to restrict diaphragm contraction and expansion, implementing breath hold techniques 23,[28][29][30] or gating the treatment by restricting delivery to particular components of the breathing cycle. 14,20,25,31,32 Recent works from several research groups have also investigated the tracking of tumor by dynamic correction of MLC positions. [33][34][35][36][37] In the majority of these solutions the objective is to minimize the ITV vol- Optimization is the computerization of mathematical problem solving. In the realm of radiotherapy planning the specific problem is the maximization of dose to a target volume whilst minimizing the dose to the surrounding tissue. By this definition a large component of the optimization process is ensuring a minimum dose to the voxels encompassed by a defined target volume.
A fourth potential issue in mobile lung disease is the impact of dose optimization to lung tissue and bronchial airways in the presence of tumor motion, where the objective function is required to ensure target dose coverage to large PTVs that include a volume of lung or air with a density significantly less than the GTV tissue.
Previous literature 44,45 has shown the adverse dosimetric implications of optimizing to and outside of surface contours, where the lack of electron density results in high photon fluence to achieve equivalent doses. In such cases when the patient tissue traverses into the region containing air during treatment, the high intensity fluence results in a sharp increase in primary interactions, liberated secondary electron generation, and resultant dose deposition. 46,47 In the situation of internal lung tissue the effect is less studied.
The electron densities among air, lung, and muscle tissue is similar 48 suggesting the effect is predominantly the result of physical density.
It thus follows that an equivalent but reduced effect may be observed in lung/disease boundaries. In lung patients the result of this effect is complicated by a couple of further considerations; 1. Incident beams on lung tumors will undergo primary attenuation and build-up of secondary electrons by superficial tissue, such as the muscles of the chest wall. These secondary electrons are of an order of magnitude less for surface optimization.
2. The movement is not limited to the target itself but can also include the surrounding tissue with no necessary correlation in direction or magnitude of motion.
Robust optimization is a recent introduction into the world of radiotherapy planning made possible by the increased parallel computational power of Graphic Processer Units (GPUs) along with more efficient threaded allocation of dose computations. Robust optimization allows a plan to be optimized such that it meets planning criteria in not only the planning geometry, but also in given patient and disease position variations. 45 The commercial system used in this paper is Raystation v5.0.1 (Raysearch, Sweden).
Raystation ensures robust planning doses by the incorporation of min-max optimization whereby the geometric uncertainties of the plan are incorporated in the problem function. The formalism includes no dependence on a probability distribution of the potential geometric uncertainty as per Bortfeld et al., 49 Chu et al., 50 Chan et al., 51 and Olafsson and Wright, 52 but rather minimizes the objective function of the worst preforming geometry within the included distribution. This ensures a minimum level of plan quality, but results in a dependence on limitations of uncertainty and the potential for the system to over optimize low probability scenarios at the cost of plan quality of higher probability scenarios. In a paper by Fredriksson,53 in which the formalism was introduced, the method was shown to provide robust plans with increased lung sparing over PTV expansions for intensity modulated proton ther-

2.B | Breathing cycles and plan parameters
All breathing cycle scans were imported into the Raystation system as 4DCT groups. Geometric contours representing the heart, left and right lungs, spinal cord and ribs were propagated across all datasets. The target volume was defined as GTV in each dataset individually, and an ITV was created as a summation of all GTVs registered back to the primary central dataset. A uniform expansion of 0.5 cm was applied to the GTV/ITV to create a PTV in each case. The margin was selected as per clinical protocol to account for imaging set-up tolerances. All tumor motion margin was assumed to be included in the robust method incorporated.
To promote conformal dose distributions and to correlate with typical planning convention a ring geometry was created around the target ITV volume. An example of the target geometries is shown in Fig. 3, inclusive of a demonstration of the average 4DCT scan.  For this work a density override was set to 0.6 g/cm À3 to correlate with a midpoint density between solid tissue and the sur- A further set of square 10 9 10 Ant-Post beams was added as a standard reference-conditioned field to verify the accuracy of reference dose.

2.C | Optimization
Prior to planning a set of clinical goals were set for the acceptance of plans. The goals were set arbitrarily to push the optimization system and create difficult but achievable modulated plans. The evaluation of clinical goals was performed solely on the planning (offset = 0 cm) geometry. These were loosely guided by common goals for typical dose and fractionation levels at the centre.
A list of the applied clinical goals is provided in Fig. 4.
For robust planning the motion of the ITV becomes redundant as the travel of the GTV is encompassed within the optimization system rather than a geometry expansion. For this reason, the ITV coverage was not optimized for robust plans.
Plans were accepted when they met the criteria set out in Fig. 4.
In some scenarios these goals were exceeded. As plan quality was not a metric in this study, once clinical goals were satisfied the optimization ceased. As a result, the variation between final plan quality among all plans was negligible.
A concerted attempt was made to meet all clinical goals in each plan. In situations where goals could not be met, the plan was optimized such that the max dose control was the least critical. All but one plan of 14 (2 9 7 optimization techniques) met all clinical goals which exceeded the max constraint by <0.05% of TD.
For each case the final calculated dose, DVH curves, and dose statistics were recorded.

2.D | Calculation on breath cycle
Each of the completed plans was recalculated on each phase of the 4DCT datasets. In Raystation, for CT datasets with identical UID and frame of reference, the plan isocenter is intrinsically correlated between datasets by the common DICOM co-ordinates, providing consistency in set-up with the exception of the moving lung insert.
Comparisons were then made between DVH curves, organ statistics, and 2D dose distributions in each geometry. As the images were not taken as 4D binned sets calculation accuracy was reviewed on a per set basis independent of phase weightings.

2.E.1 | Chamber measurements
For each plan two sets of chamber measurements were taken; one at the central tumor and one at the inferior lung. Chamber measurements at lung position were taken simultaneously with film measurements at a distance 1.5 cm inferior to the film insert as shown in showed perturbation correction factors as much as À3% for 3 9 3 fields and À1% for 5 9 5 fields in 6MV beams. The predominant size of beams used in this work was approximately 5 9 3 cm and thus À3% represents a worst case scenario in the subsequent measurements. These perturbation factors were not applied to the final measurements, but were included within the total chamber uncertainty of AE4.5%. Chamber measurements in more standard conditions, in the tumor measurements, were accurate within a more typical uncertainty of AE1.5%, accounting for standards calibration, temperature, and pressure uncertainties.
Total uncertainty, inclusive of calculation and measurement, when summated in quadrature was 2.1 and 4.7% for tissue and lung measurements respectively.

3.A | Chamber measurements
The results of comparison between calculated (in the associated tumor geometry) and delivered doses to the chamber volumes are shown in Tables 1 and 2. For clarity individual reading variation is not provided, however, across all chamber readings variation per measurement were <0.3%.

3.B.1 | Film Measurements
Analysis of distributions along the length of travel of the primary tumor site are presented in Table 3. Results are presented as the percentage of points passing the gamma analysis at a 3%/3 mm tolerance.

3.B.2 | Tumor dose distributions
There is strong agreement between both film and chamber dosimetry and calculations performed in each breathing phase. Given this strong agreement the planning system was utilized to quantify the dose distribution effects to the tumor and lung due to breathing motion.    Tumor dose variation was larger in the travel toward air in comparison to lung, resulting in variations in maximum dose from plan of 9, 5, 8% into lung and 26, 22, and 21% into air for GTV, ITV, and average plans respectively.

3.B.3 | Lung dose distributions
Measurements of lung maximum and mean dose variations are displayed in Figs. 8 and 9.
The GTV plan resulted in the lowest mean dose to the lung, a natural result of the reduced length of treatment. Of the remaining methodologies the ITV, lung override, and robust optimization across all datasets resulted in a decrease in mean lung dose of over 1.5 Gy from the average dataset methodology.
The average plan methodology produced the highest lung max dose in all breathing cycles. In all but one case the ITV plan methodology produced higher lung maximum doses than the robust optimization methodologies.

4.A | Dose accuracy
Of the 40 central GTV measurements the mean variation from calculated dose was 0.0% AE 2.3%. The GTV plan showed the poorest agreement with an average 2.5% dose escalation from planned and a significant 5.1% dose discrepancy in the 2 cm inferior geometry.
Measurement of lung doses shows excellent agreement with calculation. Over all measurements the average discrepancy between measured and calculated dose was 1.1% AE 1.9%. All chamber measurements taken showed agreement within the uncertainty range AE6%, with a maximum discrepancy of 5.7%.
1D gamma analysis results for all 40 delivered breathing cycles are shown in Table 3. Excellent agreement is seen across all dose profiles with an average of 96.4% of all points passing the 3%/3 mm criteria, and only 2 of 40 plans resulting in a pass rate under 90%.
The worst performing result was recorded with the lung override technique in the central geometry.
F I G . 6. Planned 98% coverage of GTV with tumor displacement.

| 111
The results demonstrate that the TPS accurately models the delivered dose in the offset geometries for all plans. This provides the foundation for analysis of plans primarily through the Raystation planning system calculated doses.

4.B | Plan dosimetry
The gamma analysis curves in Fig. 10 show the agreement between planned and delivered dose for the 2 cm offset toward the optimized air cavity for three different plans, verifying the effect is a real delivery consequence rather than solely computational error. It can be seen that the 130% dose escalation greater than that planned seen in the GTV and ITV plans are avoided in the robust optimization plan. This is an extreme scenario in which a 2.5 cm diameter cylinder of air resides adjacent to the tumor volume, and therefore may be clinically unrealistic.
However, results in Fig. 11  It should be noted that the effect does not appear to be linear in nature. Dose escalations when optimizing to air, 0.2 g/cm3 lung, and 0.6 g/cm3 lung were 25, 9,  Whether such an improvement is clinically significant is difficult to ascertain. The dose escalation of in-air optimization for GTV, ITV and average datasets in the superior offset geometries would be considered clinically significant in almost all cases at over 20% F I G . 1 0 . 1D dose profiles and gamma analysis for 2 cm sup plans of (a) Robust All, (b) GTV and (c) ITV optimization methodologies.

4.C | Further considerations
This study has intentionally focused on an extremely simple repre-

| CONCLUSION
A range of optimization techniques, including implementation of robust optimization, were used to create VMAT deliveries for moving targets in a lung phantom. All plans have been recalculated in the RayStation treatment planning system across five breathing cycles.
Chamber and film measurements were used to verify the accu-

ACKNOWLEDG MENTS
Thank you to ICON Cancer Care for the commitment to research in the aim of improved patient outcomes and to Louise Christophersen for tolerating the long nights at work to finalize the research.

CONFLI CTS OF INTEREST
The authors declare no conflict of interest.