Different aspects of plan complexity in prostate VMAT plans

In this work we evaluated VMAT plan complexity by using different methods and approaches: complexity related to the aperture shape, the nature of the dynamic delivery, the impact of delivery variations as well as complexity analyses based on measurements. Prostate cancer treatment plans with different levels of complexity were created for three different patient cases. The plans intended to be most complex were also scored to be the most complex according to the evaluation methods used. The results for the other plans were more diverse. The methods that included 3D spatial information on complexity gave additional information important for the analysis of clinical relevance. In order to use specific complexity estimation methods for taking clinical decisions it is essential to understand how different aspects of complexity are incorporated in each method.


Introduction
The absorbed dose distribution delivered to a patient using VMAT is determined by the treatment machine, the treatment plan characteristics, and the patient geometry.The delivered dose distribution is calculated using an algorithm in the treatment planning system (TPS).The calculation algorithm includes limitations and approximations and, furthermore, assumes a perfect treatment delivery and most often one single static patient geometry.This means that the calculated dose distribution is not a perfect description of the delivered dose distribution.Difference between doses calculated and the delivered doses to the patient can be referred to as the dosimetric uncertainty of the treatment.
The dosimetric uncertainty of a treatment plan, i.e., without taking the patient geometry into account, is related to the plan complexity [1].Plan complexity includes three sources of dosimetric uncertainty:

Dose calculation errors
Limitations and approximations in the dose calculation, for example the definition of the beam model in the TPS.

Delivery variations
Differences between planned and actual position of treatment machine parameters, such as for example collimator jaw and multi leaf collimator (MLC) positions.
Earlier studies have shown that VMAT plan uncertainties can be quantified by complexity metrics [2].Suggested metrics focus on specific aspects of plan complexity and are therefore not generally interconvertible but could be complementary.In this work different aspects of complexity were investigated by using four different approaches: the edge area metric (EAM) which is related to the aperture shape and designed to include both dose calculation errors and delivery variations [3], the modulation index MIT designed to include dynamic delivery uncertainties [4], theoretical simulations of delivery variations, and finally quasi-3D measurements that include all aspects of plan complexity.

Treatment plans
For the purpose of this study, three VMAT plans for prostate cancer have been selected to represent different patient geometries.The treatment plan used for the actual treatment of the patient ("clinical plan") was reoptimized using the Eclipse TPS (Varian Medical Systems) to create one plan with reduced complexity ("simple plan") and one of higher complexity ("complex plan").These two additional plans were generated by altering the monitor unit (MU) objective and the aperture shape controller (ASC) level [5].These are the only available tools designed to regulate plan complexity, within Eclipse.The use of the ASC tool has been shown to be able to reduce plan complexity without altering the plan quality metric, including a set of DVH-metrics [6].The weight of the aperture shape penalty can be adjusted by the user and in five steps, ranging from "Very Low" to "Very High".The highest level of ASC was used when creating the "simple plans", while for the creation of the complex plans ASC was turned off.Besides altering MU objective and ASC, the number of arcs was also varied to regulate plan complexity.Based on the clinical plan, that was created with two arcs in all cases, the number of arcs were reduced by one when creating the simple plan and increased by one for the creation of the complex plan.All plans were created for 6 MV photons and a TrueBeam with a Millennium MLC (Varian Medical Systems).Effort was put into creating dose distributions similar to the clinical treatment plan for the case of each patient.Photon Optimizer (PO version 16.1.0)was used for the optimisation of all treatment plans and the dose was calculated with the Anisotropic Analytical Algorithm (AAA version 16.1.0)with a 2.5 x 2.5 mm calculation grid.In total 9 treatment plans were incorporated in this study, including the 3 clinical plans.

Evaluations based on complexity metrics
Complexity scores were calculated according to the complexity metrics EAM and MIT.The EAM describes the aperture shape by defining a complex region close to the MLC edges in relation to the open part of the aperture [7].Small and/or irregular aperture shapes results in an EAM score closer to 1, while larger less complex apertures are described by a lower score.The calculation of the EAM was performed with a complexity region of 2.5 mm inside and outside of the MLC edge.The modulation index MIT takes into account the MLC speed and the acceleration/deceleration for each MLC leaf and gantry rotation as well as dose rate variations.Should the variation in the MLC speed or acceleration for a single leaf between two consecutive control points exceed a certain threshold value the modulation increases.This threshold value was defined by the observed values standard deviation in the actual plan (i.e.speed or acceleration) multiplied with a spectrum function z(f) as defined by Webb [8].In this work a maximum value of f = 0.5 with an interval of 0.01 was used.

Delivery simulations
The effect of delivery variations was estimated with the aid of an inhouse developed MATLAB (MathWorks, Natick, MA, USA) script which introduced systematic (i.e., same for the whole plan) and random (i.e., specific for each control point) offsets in certain treatment machine parameters.The variation of a machine parameter value was randomly generated consistent with the probability described by a normal distribution centred at the value specified in the treatment plan and truncated at 3σ corresponding to the maximum value of variation for this parameter.More specifically, a maximum systematic offset (3σ) of ±2 mm and ±1 mm were applied for the Y and X jaw position respectively.For the MLC position, a systematic offset with a maximum of ±1 mm was applied for all leaves in both banks, and an additional systematic shift of maximum ±0.3 mm was applied for one of the banks.A random offset of a maximum of ±0.35 mm was applied for each individual leaf.The collimator and gantry angle for each field were allowed to vary to a maximum of ±0.6 and ±0.3 degrees respectively.This MATLAB simulation script yielded a treatment plan, where the dose was recalculated with small variations in machine parameters.To evaluate the impact of these delivery variations, we performed twenty simulations for each plan.The output dose distribution of these simulations were inputted in an Eclipse Scripting Application Programming Interface (ESAPI script) to create a combined 3D distribution, where instead of voxel dose we displayed the standard deviation (SD) of dose over all simulations in that voxel.The mean SD (Gy) for all voxels receiving greater than 20% of the prescribed dose in the original plan was reported.

Delta 4 measurements
Positioning errors of the Delta 4 phantom (ScandiDos, Uppsala Sweden) were minimized by adjusting the treatment couch (six degrees of freedom) using cone beam computed tomography (CBCT) imaging and registration to a reference CBCT image of the phantom in optimal position.
All treatment plans were measured on the same day with the exact same phantom positioning to assure consistency within our results.The plans were recalculated in the Delta 4 phantom using AAA and prior to the delivery of the treatment plans, a half arc calibration field was delivered to correct for the output of the machine determined daily.The calculated and measured dose distributions were normalized to the maximum three-dimensional planned dose.The 3% global dose difference fail rate in the measurement points was evaluated in the Delta 4 software.Diodes receiving a dose less than 20% were excluded from the analysis.

Results and Discussion
The average EAM scores were 0.42, 0.62 and 0.78 for the simple, clinical and complex treatment plans respectively.The choice of ASC and MU objective affected the EAM score.For the MIT, no obvious relation between the different plans was observed.(Figure 1A).The tools available in Eclipse to regulate complexity had higher impact on the aperture-shape than on the dynamical nature of the plan.
The mean SD due to delivery variations, EAM and measured dose difference fail rate were the highest for the plans designed to be most complex.The results for the simple and clinical plans were more diverse where EAM always resulted in lower scores for the simple plan while no obvious relations between simple and clinical plans were found for SD due to delivery variations or measured dose difference fail rate.The delivery simulations do not take into account uncertainties due to calculation errors which is included in both EAM and the measurement evaluations.One reason why the SD was lower for the clinical compared to the simple plan in two of the three cases is probably because of the increased number of arcs used in the clinical plan that will contribute to a blurring of the uncertainties related to the different arcs.Uncertainty estimations based on measurements with the Delta 4 includes several sources of uncertainties.Besides the fact that the measurement procedure includes uncertainties in itself and that the results are limited to a few measurement points located in the two detector planes of the Delta 4 , the measurement result was based on only one delivery and does therefore show only one case of possible delivery variations.The mentioned uncertainties might lead to that the measurement evaluations cannot dissolve smaller dosimetric uncertainties.Whether the differences between EAM and dose difference fail rate are due to a non-optimal design of EAM or mentioned limitations in the measurement procedure needs further investigation.
In Figure 1(C-E) the 3D SD distribution of the dose is displayed for one of the prostate plans.For the simple plan the SD of the dose was higher on the edge of the PTV, especially in the caudal-cranial direction.For the complex plan the SD was higher for voxels at PTV borders but also inside the structure, in comparison to the clinical plan where the SD was lower.Hence clinical plans appear to be less susceptible to machine parameters variations.
Measurement points with a dose deviation higher than 3% were located mostly in the dose falloff region for the simple and clinical plans.However, for the complex plans, deviations were spotted in several regions within the dose distribution.The SD analysis and measurement evaluations were the only methods in this work that could describe uncertainty in a 3D volume.The spatial information of uncertainties is important to be able to conclude on the clinical relevance.Furthermore, analyses that does not include 3D evaluation inevitably include some kind of averaging where important uncertainties can be evened out.

Conclusion
Different types of complexities are not necessarily related to each other.One plan can have a low complexity regarding aperture-shape but at the same time high complexity regarding the dynamic delivery or the delivery variations.In order to use specific complexity evaluation methods for taking clinical decisions it is essential to understand how different aspects of complexity are incorporated in each method.

Figure 1 .
Figure 1.(A) EAM and MIT values and (B) 3% dose difference fail rate (%) and mean SD in dose due to delivery variations (Gy) is shown for all nine prostate plans.Triangle points refer to the value of the MIT and STD values while circle points to EAM and fail rate.Treatment plans originating from the same patient are colour coded.InC, D and E, the distribution of the SD of dose due to delivery variations is displayed in a central frontal slice for prostate case #2 for the clinical, simple and complex plans respectively.The red contour depicts the planning target volume and the colour wash scale in these distributions ranges from 0.1 up to 3 SD (Gy).