MSc Physics and Astronomy
Physics of Life and Health
Master Thesis
Knowledge-based radiotherapy treatment planning for
stage III lung cancer patients
by
Evgenia Tourou
11128879
June 2018
60EC
Supervisor/Examiner:
Examiner:
Wilko F.A.R. Verbakel, PhD
Geert J. Streekstra, PhD
Daily Supervisor:
Alexander R. Delaney, MSc
ABSTRACT
Treatment of large volume lung cancer is carried out mostly using two techniques, the full-RapidArc (f-RA) or the hybrid-RapidArc (h-RA). The choice between the two methods depends on the individual characteristics of the patient, while the treatment planners often have to make both plans in order to choose for the optimal treatment technique for the patient. However, manual treatment planning is a labor-intensive and time consuming process which, in many cases, does not yield consistent or optimal plans. RapidPlan (Varian Medical Systems, Palo Alto, USA), a knowledge-based-planning solution, uses the dosimetry and geometry of previous treatment plans to model and predict organ-at-risk (OAR) dose-volume-histograms (DVHs) for future patients based solely on their geometry. The present study investigates the possibility of utilizing RapidPlan, as a tool for selecting f-RA or h-RA technique for individual lung cancer patients, without the requirement of creating actual treatment plans. A f-RA and a f-RA model were created, consisting of 50 clinical plans each, and were used to generate dose predictions and subsequently to optimize model-based plans (MBPs) for a group of 10 patients. MBPs quality was analyzed by benchmarking MBPs against the manual plans (MPs) made by experienced radiotherapy treatment planners. DVH prediction accuracy was analyzed by comparing predicted vs achieved OAR dose metrics. Finally, the number of patients that would have been selected for f-RA or h-RA based solely on OAR predictions was compared to the corresponding number of patients that would have been selected based on the achieved OAR doses in MBPs. MBPs improved contralateral lung (CL) and total lung (TL-PTV) mean dose compared to the manual plans in both techniques. However, CL V5 in the f-RA MBPs increased compared to the MPs. The target coverage was inferior in the MBPs compared to the MPs. RapidPlan was able to accurately predict the mean dose of CL, but it consistently underestimated the amount of sparing that could be achieved for TL-PTV. Based only on comparing single OAR dose volumes, RapidPlan can accurately predict which technique gives the lower dose in 7-9 /10 cases. The results showed that RapidPlan is able to generate MBPs of comparable quality to the MPs for f-RA and h-RA techniques, nevertheless, it requires further validation with a more wise selection of priorities and using generated point-objectives instead of line objectives.
CONTENTS
1. INTRODUCTION ... 1
2. METHODS AND MATERIALS ... 5
2.1 Treatment planning of large volume lung cancer patients ... 5
2.1.1 Full-RapidArc ... 5 2.1.2 Hybrid-RapidArc ... 6 2.2 RapidPlan ... 8 2.2.1 Data extraction ... 9 2.2.2 Model Training ... 11 2.2.3 Generation of DVH Estimations ... 13
2.2.4 Placement of Optimization Objectives ... 13
2.3 Model Libraries ... 14
2.3.1 Patient geometries ... 15
2.3.2 Dosimetry ... 16
2.3.3 Field set-up... 16
2.4 Evaluation of Model Training ... 17
2.4.1 RapidPlan-provided statistical metrics ... 17
2.4.2 Outlier analysis ... 18
2.4.3 Field Geometry ... 19
2.5 Evaluation of model-based plans ... 19
2.5.1 Evaluation group geometries and field-set up ... 20
2.5.2 Assigning Optimization objectives ... 21
2.5.3 Evaluation of prediction accuracy ... 22
2.5.4 Using predictions to select treatment technique ... 23
3. RESULTS ... 24
3.1 Evaluation of Model Training ... 24
3.1.2 Outlier analysis ... 25
3.1.2 Field Geometry ... 26
3.2 Evaluation of Model-Based Plans ... 27
3.3 Evaluation of prediction accuracy ... 32
3.3.1 Contralateral Lung ... 32
3.3.3 Esophagus ... 37
3.4 Individualized analysis ... 38
3.5 Using predictions to select treatment technique ... 43
4. DISCUSSION AND CONCLUSION... 47
References ... 50
APPENTIX A ... 54
1
1. INTRODUCTION
Lung cancer is the most often diagnosed cancer and the first cause of death amongst cancer patients, leading to 1.6 million deaths worldwide every year 1 . The major treatments for lung cancer are surgery, radiotherapy, and chemotherapy. In treatment of large volume lung cancer, radiotherapy, usually in combination with chemotherapy plays an important role2. Radiotherapy treatment of large volume lung cancer is challenging because it requires delivery of high dose levels to large tumor volumes, while sparing the proximal critical organs-at-risk (OARs) such as the esophagus, spinal cord, and the heart. High dose levels to the healthy tissues increases toxicity3 and can lead to side effects such as symptomatic pneumonitis4–6 and esophagitis7.
Radiation therapy makes use of ionizing radiation to kill cancer cells by absorbed energy. Thus, the aim is to deliver maximum dose to the tumor and as low dose as possible to the surrounding normal tissue. The radiation therapy process starts with a computed tomography (CT) scan of the patient to locate the tumor. Then, the physician delineates the relevant targets/tumor volumes and the surrounding OARs that need to be spared. The delivery of the treatment is done by a linear accelerator or a cobalt machine. In order to minimize the dose to normal tissue while ensuring sufficiently high dose to the target, multiple field directions are used. Additionally, a multileaf collimator (MLC) is utilized to shape the radiation beams. The MLC consists of multiple metal leaves that move independently. The leaves are placed such as the aperture of the MLC forms the shape of the tumor, and thus shields the surrounding tissue from radiation.
Three-dimensional conformal radiotherapy (3D-CRT)8 treatment technique involves the use of flattened radiation beams with fixed MLC leave configuration, to deliver uniform radiation dose, while the contribution of each feild to the final dose can vary. Intensity modulated radiotherapy (IMRT)9 delivers non-uniform radiation beam intensities per field by computer-controlled movement of the MLC leaves. The summation of all fields leads to relatively homogenous dose in the target, while the dose in the surrounding healthy structures is minimized. It was proven that IMRT can reduce the dose to the healthy lung, esophagus, and heart in lung cancer patients compared to 3D-CRT 10,11. Volumetric modulated arc therapy (VMAT)12 is an advanced form of IMRT, where the gantry is rotated with simultaneous movement of the MLC leaves and dose rate modulation. VMAT decreases the
2 treatment time and, with the use of full gantry rotation, generates highly conformal treatment plans13.
The planning of 3D-CRT plans is done manually by the planner, who defines the gantry angles, collimator angles, MLC configurations and relative weights of individual fields. In IMRT and VMAT treatment planning, optimization algorithms are needed to determine the MLC leaf movements. During a process called inverse treatment planning, the planner specifies a desirable dose distribution to the target and the normal tissue by a set of dose-volume objectives and priority factors for each delineated structure. These dose-volume objectives include the minimum required dose to the target and the maximum required dose to the OARs. The optimization algorithm tries to find the MLC configurations and dose rates that will approximate the desired dose distribution by minimizing a cost function which weights all dose-volume objectives 14.
Defining the appropriate dose-volume objectives and priorities is an essential part of the process since these will define the final dose distribution and help to achieve the clinical goal. Optimal selection of dose-volume objectives depends on the geometrical characteristics of the patient such as the location and volume of the tumor and its proximity to OARs15, therefore each patent requires special attention. The current practice is that the treatment planner has to evaluate the plan and interactively maneuver the optimization objectives during the optimization process until the best possible set of optimization objectives, and consequently dose distribution- is achieved. This process is time-consuming, and leads to inconsistencies and inter-planner and inter-institutional variability in plan quality16–18.
In recent years, there has been wide interest in the development and application of automated treatment planning solutions, aiming to improve the consistency and quality of radiotherapy treatment plans. Knowledge-based planning utilizes a large number of prior treatment plans to create a model based on the dose distribution and the geometrical characteristics of the patients19–22. This model is used to predict achievable OAR dose-volume histograms (DVH) for prospective patients, based on its individual anatomical characteristics. Then, for the optimization process, a line objective is generated for each OAR below the range of the predicted OAR DVHs. Knowledge-based planning offers patient-specific optimization objectives and thereby semi-automates the optimization process. It is not a fully automated process because the user needs to manually define the OAR structures and target, the prescription dose and the field set-up.
RapidPlan (Varian Medical Systems, Palo Alto, USA) is a knowledge-based treatment solution which was developed based on the work of the groups of the Duke University15,23,24
3 and Washington University19,25. Pre-clinical evaluation of RapidPlan suggested that it is capable of generating clinically acceptable plans for lung, head and neck, esophageal, breast, hepatocellular and prostate cancer 20,21,26–31. Particularly for large volume lung cancer, only Fogliata et al.26 have evaluated the use of RapidPlan on VMAT technique with promising results.
At the VUmc radiotherapy department, treatment of large volume lung cancer is carried out mostly using two techniques, the full-RapidArc (f-RA) or the hybrid-RapidArc (h-RA). RapidArc is the trademark used by Varian for VMAT optimization. In f-RA plans, the radiation fields are composed of two VMAT arcs, while h-RA is a combination of multiple conventional 3D-CRT fields and a VMAT field32. H-RA technique usually provides better planning target volume (PTV) coverage and reduced dose to the healthy contralateral lung32,33, but it delivers high dose levels outside the PTV within the 3D-CRT fields. On the other hand, f-RA can spare better the spinal cord and the heart but increases the volume of contralateral lung receiving low dose32–34.The choice between the two methods is critical and depends on the individual characteristics of the patient. It often happens that the treatment planners have to make both plans in order to choose for the optimal treatment technique for the patient. This is apparently a time-consuming process.
RapidPlan has been proven not only to generate good quality plans but also to provide accurate achievable OAR dose predictions. Tol et al.35 showed that RapidPlan predictions only could be used as for quality assurance of head and neck plan. Furthermore, Delaney et al.36 suggested that RapidPlan can provide accurate predictions to be used for selecting patients for proton therapy for head and neck cancer patients. The present study investigated the possibility of utilizing RapidPlan as a tool for selecting f-RA or h-RA technique for individual lung cancer patients, without the requirement of creating actual treatment plans. It must be noted the RapidPlan is designed only for IMRT and VMAT plans, therefore, there have been no studies which investigated the application of RapidPlan on a h-RA method.
To conduct the research, two RapidPlan models were created, one for h-RA and one for f-RA, consisting of clinical plans of patients treated at VUmc. Both models were validated on an initial set of patients, and then dosimetry and geometric outliers were removed. Next, the two models were used to generate dose predictions and subsequently optimize model-based plans (MBPs) for a group of 10 patients. To evaluate the quality of the MBPs, they were benchmarked against the manual plans (MPs) made by experienced radiotherapy treatment planners. Then, to evaluate the accuracy of the predictions, the generated MBPs where compared to the predicted DVHs. Finally, the number of patients that
4 would have been selected for f-RA or h-RA based solely on OAR predictions was compared to the corresponding number of patients that would have been selected based on the achieved OAR doses in MBPs.
5
2. METHODS AND MATERIALS
2.1 Treatment planning of large volume lung cancer patients
Treatment planning of large volume lung cancer at our department has been detailed previously in the studies of Verbakel 32 and Blom 37. Treatment plans are optimized using the Progressive Resolution Optimizer (PRO) algorithm version 10.0.28 in the Eclipse treatment planning system and dose calculation is carried out using either ACUROS 11.0.31 or the Anisotropic Analytical Algorithm (AAA) 10.0.28 using a 2.5mm grid resolution.
The targets are the internal target volume (ITV) and the planning target volume (PTV). ITV consists of the primary tumor and regional lymph nodes with metastatic disease and PTV includes the ITV and a margin of 10mm to compensate for any geometric inaccuracies. Prescription dose (PD) to the ITV and PTV is typically 50-66 Gy and is delivered in 23-33 fractions. Treatment plans aim to deliver 97% of the PD to at least 95% of the PTV, while V107%(the volume receiving at least 107% of the PD) should be lower than 5%.
The spared OARs typically include the contralateral lung (CL), the total lung minus PTV (TL-PTV) (the summation of the two lungs from which the PTV volume is subtracted), the esophagus (ESO), the spinal cord (SC), and the SC plus a 3mm margin (SC+3mm). Generally, the CL is constrained such that the total volume receiving 5Gy (V5) is lower than 40%6. Meanwhile, objectives for the TL-PTV are V20<35%, and V5<60%. For SC and SC+3mm, a maximum point dose objective is applied: <50Gy and <54Gy respectively. The maximum dose for ESO should, in general, be less than 100% of the PD, but in cases where the ESO overlaps with the PTV, a higher dose is acceptable. In order to avoid hotspots outside the PTV, a control region (OAR-control) is created which surrounds the PTV and contains most of the body in the planes of the PTV. Additionally, a maximum dose objective is applied for the OAR-control at 100% of the PD.
2.1.1 Full-RapidArc
For f-RA plans, typically two full-arcs (gantry rotates from 179º to 181º) VMAT fields with 6 MV beams are optimized simultaneously, using avoidance sectors (control
6 points where the beam is off) to avoid direct irradiation to the contralateral lung. Typically the avoidance sectors are 90-100° long. However, there is a limitation in their use: each beam-on and beam-off sector must be at least 15 degrees. Thus, if the beam needs to be off from the starting angle of the rotation, partial-arcs have to be used instead. Collimator angles are typically 10° and 15°.
The optimizer uses a simple dose calculation algorithm that does not model well lateral electron transport, and overestimates the dose in low-density PTV regions. In the final dose calculation, which takes into account this lateral electron transport, the dose in that region is lower. To overcome this problem, the PTV is divided into the part that overlaps with the lungs (PTVinLung) and the part that is out of the lung (PTVoutLung). Then, we typically apply a PTVinLung lower objective which is placed a few Gy higher than the PTVoutLung lower objective. Subsequently, a ‘continue previous optimization’ (CPO) is performed with increased PTV priorities to improve PTV homogeneity38.
Typically two optimization objectives are used for each of the following treatment planning aims : CL V5 , TL-PTV V5 and TL-PTV V20. These objectives are interactively placed below the DVH line displayed during optimization and adapted until the lowest possible dose is achieved, whilst maintaining good PTV dose coverage/homogeneity. For the ESO three optimization objectives are placed around V40, V50,V60 and one maximum dose objective of 66Gy.
2.1.2 Hybrid-RapidArc
H-RA plans consist of a conventional and a VMAT component. The conventional component consist of typically three 3D-CRT fields of 15MV, and delivers 90% of the PD. Field orientation generally consists of one anterior-posterior (AP) field, one posterior-anterior (PA) field and one oblique-posterior field, with field-weights roughly set to 0.5, 0.25 and 0.25, respectively. Thus, the AP and PA fields spare the contralateral lung, while the oblique field decreases direct irradiation through the spinal cord. The dose distribution achieved using the conventional fields is calculated and used as a “base dose plan” for the optimizer, which is subsequently configured to optimize the RapidArc component.
The RapidArc component delivers the remaining 10% of the dose, using 6MV beams. Since the base dose plan delivers an inhomogeneous dose to the PTV, the RapidArc component is meant to homogenize the dose to the PTV. A single partial-arc is typically used
7 from 181° to 30° for left-sided tumors or from 330° to 179° for right-sided tumors. The partial-arc length can vary depending on the size and location of the tumor and, alternatively, in some cases a full-arc with avoidance sector is used. The RapidArc component contributes most to the outer part of the PTV, improving the dose homogeneity32.
Similar optimization objectives to the f-RA plans are used for CL and TL-PTV, while the maximum dose objectives for the ESO, SC and SC+3mm are usually 1-2Gy lower. The ESO is not always actively spared. The division of the PTV between in- and out-of-lung and a CPO is not needed in h-RA plans as the majority of the dose is delivered using the conformal-fields.
Figure 2.1 shows the field set-up and the resulting dose distribution of a left-sided cancer patient, treated with f-RA (a,c) and h-RA (b,d). In the h-RA plan, the dose is distributed to the anterior-posterior direction, while f-RA results in a more conformal dose distribution. However, f-RA produces a larger low-dose volume in the surrounding normal tissue39, which also covers a larger part of the CL.
8
Figure 2.1: Field geometry of f-RA and h-RA plans of the same patient and the
corresponding dose distributions. The PTV is depicted with red color. a) Field set-up f-RA plan, b) Field set-up of h-RA plan, c) Dose distribution of f-RA plan, d)Dose distribution of h-RA plan.
2.2 RapidPlan
RapidPlan is a commercial knowledge-based treatment planning system that utilizes previous treatment plans to create DVH-estimation models which can predict a range of DVHs for the organs-at-risk of prospective patients. It is integrated into the Eclipse treatment planning system (Varian Medical Systems, Palo Alto, CA) and can be used to generate dose-volume objectives which subsquently guide the optimization process of a new treatment plan.
RapidPlan is comprised of a model configuration component and a DVH estimation component. In the model configuration component, the information of the planned patients is
9 extracted and used to train the DVH estimation model. The DVH estimation component uses the trained model to make predictions for the OARs of a prospective patient and automatically place dose-volume objectives on the lower boundary of these predictions. This semi-automates the treatment planning process and these steps are further explained below.
2.2.1 Data extraction
First, a number of treatment plans (minimum 20) are selected to populate the model library. Then, a model structure set is created by the user containing the targets and the relevant OARs. Each structure of the treatment plans is then matched to the corresponding structure of the model structure set. During the data extraction phase, the geometry and dose of each structure, along with the field geometry and the prescription dose of the plan, are extracted and converted into some characteristic metrics. Each OAR structure is divided into the following regions (Figure 2.2):
In-field region: The part of the structure that overlaps with target projection at least from one field view. This is the most heavily modulated region, since it receives direct irradiation and its dose is minimized by the movement of the MLC leaves. Overlap region: The part that is anatomically overlapping the target. This part has
dose level comparable to the target dose.
Leaf-transmission region: The part that is visible from the jaw aperture of at least one field but is not overlapping with the target projection from any field. It receives some dose through the closed leaves of the MLC but it does not strongly affect the optimization.
Out-of-field region: The volume of the structure that is not visible from jaw aperture of any field direction. This part does not receive direct irradiation.
10 Figure 2.2: Schematic represention of volume partition in transversal view40.
The relative volume of each OAR region is calculated, as well as the cumulative DVH based on the extracted dose, sampled into 2.5mm resolution. Additionally, RapidPlan calculates the cumulative DVH of the Geometry Expected Dose (GED) for each OAR region.
The GED is a metric that calculates the dose that would be expected in a voxel at a certain distance from the target given the patient anatomy, prescribed dose to the target, and position and orientation of the concerned fields. The GED does not take into account the different levels of sparing of the OARs; it only considers general sparing of the tissue outside the target while delivering the desired dose to the target. The dose expected in an OAR voxel depends on the distance from the target and the fields, the orientation of the fields, the nominal field energy, and the physical characteristics of photons15. The GED calculation also includes heuristics about the optimal inter-field and intra-field modulation that lead to sparing of the normal tissue. Meaning that each field can be weighted differently and each beamlet within a field can deliver different dose by the MLC modulation, based on the shape and orientation of the target. Therefore, if two or more fields have the same geometry, the duplicates are not taken into account. Furthermore, the jaw position is not considered in the calculation41.
For the whole OAR structures, the following geometric features are calculated: OAR volume in cm3, overlap volume percentage with the joint targets, out-of-field volume percentage and joint target volume in cm3.
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2.2.2 Model Training
For each of the above-mentioned OAR regions, a separate DVH estimation model is constructed during the model training phase. The in-field-region uses a combination of Principal Component Analysis (PCA) and regression analysis, while the other three regions use a simpler method that calculates the mean DVH and the standard deviation. A schematic representation of training phase for the in-field region model is shown in Figure 2.3.
The PCA is applied to the DVHs of all OARs in the training set, to describe the variance of DVH shapes in the population and to select the most significant parameters [Sohn 2007]. The methodology is based on the assumption that each DVH can be reconstructed from the sum of the mean DVH and a few weighted Principal Components (PC). First, the mean DVH over all the DVHs in the training set is calculated, and then subtracted from each DVH in the training set. Then, the first PC (PC1) curve is calculated such that it explains the most amount of variation in the training set. The projection of this PC is subtracted from each DVH of the set and then the next PC is calculated by maximizing the variance of the remaining curves. This process continues until at least 95% of the variance is explained by the PCs 41. Each particular DVH of the training set is parametrized by subtracting the mean DVH and then projecting the residual curve to each of the PCs to find the corresponding PC coefficients or PC scores (PCS). The same principal component analysis is applied to the GEDs of the training set and the respective GED-PCs are calculated.
The correlation between the PC scores of the DVHs (DVH-PCS) and the geometrical features (absolute OAR volume, absolute target volume, overlap volume percentage, out-of-field volume percentage, and GED-PCSs) in the training set is determined by stepwise regression analysis. For each PC a separate model is used, which also includes the second order terms of the parameters to account for the non-linear effect between two features15. The stepwise regression procedure follows an iterative forward and backward method. First, the most significant geometrical parameter is added in the model, and more parameters are added in each step only if they have a significance level higher than 5%. Then, the parameters that have a level of significance less than 5% are removed41. This results in a regression model including the most significant geometrical parameters, whose coefficients are stored in a matrix that can be used to estimate the DVH PCS from the geometric features. Additionally, the standard error of each DVH PCS is calculated in order to determine the upper and lower boundary of the estimation DVH range.
12
Figure 2.3: Schematic representation of the training phase and PCSs estimation. First, the
PCs are extracted from the DVHs. Then, each individual DVH is parameterized based on the PCs. The regression model finds the relation between the PCSs and the geometrical parameters. Finally, the PCSs of a new plan are estimated from the regression model and the geomtrical parameters of patient.
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2.2.3 Generation of DVH Estimations
The trained DVH estimation model is used to generate predictions for a new patient. The patient's anatomy (targets and OARs), the field geometry and the prescription dose are used as the input for the DVH estimation model. The algorithm calculates the same features as in the data extraction phase (volume partition, geometric features, GED histograms), except for the DVHs. For the in-field region, the GED histograms are parameterized using the GED principal components calculated in the training phase. Then, the regression model is applied to estimate the DVH PCSs from the geometric features. The estimated PCSs and the stored principal components are then combined to calculate the most probable DVH curve. The DVH estimation range is calculated from the standard error related to the regression model. For other regions, the stored mean DVH is obtained and the estimation range is calculated by adding and subtracting on standard deviation. Finally, the estimated DVHs from the different OAR regions are weighted based on the relative volume of each region and are summed together to construct the final DVH estimate for the OAR (Figure 2.4).
2.2.4 Placement of Optimization Objectives
When the DVH estimation range is generated, RapidPlan converts it into optimization objectives to semi-automate the optimization process. A line of optimization objectives is placed just below the lower boundary of the prediction range as seen in Figure 2.4. The objectives pull all parts of the DVH curve with the same strength, aiming to produce a resultant DVH which is representative of the DVH-prediction. However, if an OAR structure overlaps with the target, the objective line corresponding to the volume that overlaps with the target is placed horizontally so that it does not conflict with the targets lower objectives (Figure 2.4). RapidPlan users may also specify dose-volume objectives with a certain volume value for which the corresponding dose will be generated by the DVH-prediction range. This can be utilized, for example, to lower specific parameters such as the V5 of an OAR, rather than the dose to the entire OAR, which the line objective caters to.
14
Figure 2.4: Predicted DVH ranges of various organs-at-risk with the
generated optimization objective lines.
2.3 Model Libraries
Fifty-five patients previously treated with f-RA and 55 patients previously treated with h-RA (planned according to the protocol described in section 2.1) were selected to populate two models, the f-RA model and the h-RA model. The clinical plans were added to the models without any modification.
In the f-RA model-library the PD for the ITV and PTV varies from 50Gy to 66Gy: 19 plans with 66Gy, 17 plans with 65Gy, 15 plans with 60Gy, 1 with 57Gy, 1 with 56Gy, 1 with 52Gy and 1 with 50Gy. Dose was delivered with fractions of 2.0-2.6Gy. The variation in PD was not expected to affect the performance of the model as this has been previously reported without any apparent degradation in resulting plan quality26.
In the h-RA model, the PD was 66Gy for 27 plans, 65Gy for 13 plans, and 60Gy for 15 plans. One difference between the two model-libraries was that only 16 of the 55 plans in the h-RA model used optimization objectives for V40,V50,V60, while all plans in the f-RA model included esophageal sparing for dose lower than 60Gy.
The following structure set was created for each model: ITV, PTV (PTVinLung and PTVoutLung for the f-RA model), CL, TL-PTV, ESO, SC, SC+3mm, OAR-control, and ipsilateral lung (IL). The corresponding structures were matched for each patient.
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2.3.1 Patient geometries
A heterogeneous patient population in terms of tumor size and location was selected in order to make the model applicable to a large variety of patient geometries. Furthermore, it was intended that both models have patients with a similar range of volumes. Of the 55 plans of the f-RA model, 35 had right-sided tumors while the remainder were left-sided cases, and the PTV volume ranged from 205-1361 cm3 with an average of 589 cm3. In the h-RA model, 36/55 patients had right-sided tumors and the rest were left-sided cases, while the PTV volume ranged from 201-1236 cm3, with a mean of 596 cm3. The geometric characteristics of the PTV and OARs in the f-RA and h-RA models are listed in Table 2.1 and 2.2 respectively.
Table 2.1: Geometric features of structures in the f-RA model Structure Mean volume (𝐜𝐦𝟑) Minimum volume (𝐜𝐦𝟑) Maximum volume (𝐜𝐦𝟑) Overlap with the target % In-field volume % PTV 589 ± 314 205 1361 - - CL 2023 ± 604 769 3503 0.51 ± 1.23 73.1 ± 17.2 TL-PTV 36701 ± 1114 1564 7254 0.03 ± 0.05 70.9 ± 17.6 ESO 29.1 ± 15.7 6.8 91.1 21.0 ± 17.4 64.8 ± 21.0 SC 37.0 ± 17.6 11.4 82.7 0.22 ± 1.66 77.3 ± 23.1 OAR-control 5653 ± 2686 527.9 13967.4 0.08 ± 0.11 98.1 ± 5.7 IL 1869 ± 627 679.1 3868.6 11.52 ± 6.53 60.1 ± 15.4
Table 2.2: Geometric features of structures in h-RA model library Structure Mean volume (𝐜𝐦𝟑) Minimum volume (𝐜𝐦𝟑) Maximum volume (𝐜𝐦𝟑) Overlap with the target % In-field volume % PTV 596 ± 262 201 1236 - - CL 2044 ± 656 1016 3413 0.14 ± 0.27 75.0 ± 14.2 TL-PTV 3672 ± 1230 1473 6461 0.03 ± 0.06 71.9 ± 15.1 ESO 27.9 ± 12.5 5.9 78.9 27.3 ± 22.3 62.8 ± 22.3 SC 34.6 ± 15.4 14.1 74.9 0.01 ± 0.10 79.6 ± 22.9 OAR-control 4942 ± 2158 1365 11673 0.07 ± 0.11 97.3 ± 4.9 IL 1860 ± 672 657 3434 13.10 ±6.62 59.3 ± 14.5
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2.3.2 Dosimetry
Table 2.3 contains the average dosimetry of plans in both the f-RA model and h-RA model.
Table 2.3: Dosimetric features in the model libraries
Structure
f-RA model h-RA model
Mean dose (%) Minimum dose (%) Maximum dose (% ) Mean dose (%) Minimum dose (%) Maximum dose (% ) PTV 101.2 ± 1.3 99.0 103.9 100.7±1.2 98.6 104.0 CL 9.0 ± 6.2 1.1 27.5 6.06 ± 4.17 0.96 15.6 TL-PTV 19.4 ± 6.5 2.9 31.9 20.9 ±5.4 6.5 33.09 ESO 48.6 ± 19.8 8.6 84.7 55.0 ± 23.6 5.02 96.9 SC 34.1 ± 13.8 5.0 63.1 34.2 ± 16.2 5.2 71.5 OAR-control 39.6 ± 9.7 27.8 64.9 46.9 ± 15.2 27.5 74.5 IL 40.8 ± 13.0 7.5 68.9 48.0 ± 12.6 15.2 75.0 2.3.3 Field set-up
Field set-ups varied largely between plans of both the f-RA model and h-RA model, as seen in Table 2.4 and Table 2.5, respectively. In the f-RA model, 48/55 plans used 2 full-arcs, whilst using an avoidance sector to prevent irradiation through the healthy contralateral lung (full-arc plans). 7/55 plans used 2 partial arcs for the same purpose (partial-arc plans). The irradiation-arc length for the full-arc plans ranged from 240° to a maximum of 310° for a centrally located tumor, with a mean of 270 ± 14°. Partial arcs were used in cases where the tumors were relatively small (< 400 cm3) and the irradiation-arcs covered relatively shorter angles, with their length ranging from 200° to 260° with mean 223 ± 23°.
Evaluation of plans in the h-RA model showed that the AP field was placed between 355°and 10° (at 0° in 51/55, at 10° in 1/55, at 8° in 1/55 and at 355 in 1/55 of plans), while the PA field was placed between 170° and 195° (at 180° in 52/55, at 170° in 1/55 and at 195° in 1/55). For right-sided tumors an oblique field was typically placed between 195 - 215° with 210° and 200° being the most common field angles. In the left-sided cases, the oblique field was placed at 150° in 9/19 cases, at 160° in 5/19 and at 155 in the remainder of cases. Two plans used an additional oblique field: one at 210° for a left-sided tumor and one at 270° for a right-sided tumor, while 2 other plans did not use any oblique field. In one particular patient, with a centrally located tumor, 3 oblique fields were used at 340º, 160º, and 210º but
17 no AP or PA field was included. Regarding the RapidArc component, a full-arc was used in 12/55 plans with the irradiation-arc length ranging from 206° to 290°, with a mean of 251° ± 27°. The remainder 43 plans consisted of partial-arcs with the irradiation-arc length ranging between 210-240°.
Table 2.4: Field geometry of plans in the f-RA model
Field set up # Plans Irradiation-arc length
Range Mean
Full-arc 48 240-310° 270 ± 14°
Partial-arc 7 200-260° 223 ± 23°
Table 2.5: Field geometry of plans in the h-RA model Conventional component Tumor
position # Plans
AP field PA field Oblique field
Angle range Angle range Angle range
Right 36
355-10° 170-195° 195-215°
Left 19 150-160°
RapidArc component
Field set up # plans Irradiation-arc length
Range Mean
Full-arc 12 206-290° 251 ± 27°
Partial-arc 43 210-240° 215 ± 8°
2.4 Evaluation of Model Training
2.4.1 RapidPlan-provided statistical metrics
Subsequent to model training, RapidPlan provides the user with certain quality metrics regarding the goodness of fit and the goodness of estimation of the model. Amongst others, RapidPlan provides the user with residual, regression, geometric and DVH-plots so that the quality of the model can be visually assessed, as described by Delaney et al. 42. According to the manufacturer, these metrics, as well as plots, should be evaluated before model validation.
18 The goodness of fit statistics describe how well the DVH estimation model represents the data in the training set. The coefficient of determination of the regression model parameters, R2, describes how much of the variance is explained by the regression model. It is scaled from 0 to 1, with a large value indicating a better fit. High values may also indicate that the model is over-fitting the data, meaning that model overreacts to minor fluctuations in the data. The regression model parameters such as the average chi square, 𝜒2, describes the quality of the regression model. It is measured from the residual difference between the original data and the estimated data. The closer the value is to 1, the better the quality of the regression model. However, if it is very close to 1 it is possible that the model is being over-fitted.
RapidPlan performs an internal cross-validation for the trained models. The plans are divided into 10 groups. The plans of the 9 groups are used for model training, while the remaining group is used for validating the model. This process is repeated 10 times until all groups are used for validation. The average results of the validation processes represent the ability of the model to estimate the DVH of a plan that is part of the training set. The mean squared error between the original and the estimated data measures the distance between the original DVH and the mean of the upper and lower bounds of the estimated DVH-range.
2.4.2 Outlier analysis
An outlier in the model can be a structure whose dosimetry or geometry differs from the rest of the population, or it has a substantial effect on the model fit. RapidPlan provides some statistical metrics and the reporting thresholds for the structures in the training set, namely: cook’s distance (CD) which indicates influential data points, modified Z-score (mZ) which indicates geometrical outliers and studentized residual (SR) which indicates dosimetric outliers.
In order to examine if the model would be improved by removing the outliers, the indicated outliers were removed from the model and the model was re-trained. The resulting “cleaned model” and the initial “uncleaned model” were used to generate plans for 4 patients not included in the models. The MBPs were then compared to decide which model provides better plans.
19
2.4.3 Field Geometry
Since field set-ups in both models varied quite substantially, it was investigated whether this variation was visible amongst the provided RapidPlan plots and statistical metrics for these models. Furthermore, since both partial arcs and avoidance sectors were used to limit irradiation of the contralateral lung, it was examined whether RapidPlan could appropriately model both of these techniques. This was done by observation of the RapidPlan provided CL regression plot: the principal component score 1 of the DVH (DVH-PCS1) versus the principal component score 1 of the GED (GED-PCS1) (Figure 2.5); and the
residual plot: the DVH-PCS1 versus the estimated PCS1 for the DVH. In these plots, each
plan of the training set is represented by one data point. The lines represent one standard deviation away from the regression line. Points falling outside of the lines are possible outliers.
Figure 2.5 Regression plot: DVH-PCS1 versus the GED-PCS1 of a particular
OAR
2.5 Evaluation of model-based plans
A 10 patient evaluation group was selected arbitrarily, and already had respective f-RA and h-RA MPs created according to the protocol mentioned in section 2.1. The PD for all the plans was 66Gy delivered in 33 fractions. These MPs were optimized using PRO v10.0.28 and dose calculation was carried out with AAA v10.0.28. To investigate the performance of both models, MBPs were created for this evaluation group and compared with respective
20 MPs. MBPs were optimized using the PO 13.6.23 optimization algorithm and the AAA v10.0.28 for dose calculation, using a 2.5mm grid resolution. Field set-ups for MBPs were the same as those for the respective MPs. For comparison reasons, the MBPs were normalized such that the mean dose of the PTV is equal to the PTV mean dose of the MPs. To assess the quality of f-RA and h-RA MBPs, MBPs were compared with respective MPs on the basis of the following dosimetric parameters:
For the PTV: V95%(%) , V107%(%) , the maximum dose at the PTV in Gy Dmax(Gy), homogeneity index (HI) defined as the minimum dose in 2% of the PTV (D2) minus D98 divided by D50 , conformity index (CL) calculated as the absolute PTV volume receiving 95% of the PD divided by absolute total body volume receiving 95% of the PD.
For the OARs: V5(%) , Dmean(Gy) for the CL; V5(%) , V20(%), and Dmean(Gy) for the TL-PTV; Dmax(Gy) for SC and SC+3mm; Dmax(Gy) and Dmean(Gy) for ESO; and Dmax(Gy) for the OAR-control.
Paired, 2-sided student t-tests were performed to identify significant differences between the MPs and MBPs with p<0.05.
2.5.1 Evaluation group geometries and field-set up
Table 2.6 shows the geometries of the 10 patient evaluation group.
Table 2.6 Geometric features of test patients Patient
#
Tumor side
PTV Contralateral lung Total lung-PTV Esophagus
Volume (𝐜𝐦𝟑) Volume (𝐜𝐦𝟑) Overlap % Volume (𝐜𝐦𝟑) Overlap % Volume (𝐜𝐦𝟑) Overlap % 1 L 1065 3186 0.04 4964 0.0 49.8 22.4 2 R 1017 3665 0.01 5893 0.0 63.9 11.3 3 L 936 1396 0.39 1913 0.0 75.1 27.9 4 L 987 1934 0.00 2971 0.0 60.5 48.1 5 R 861 2056 0.00 3830 0.17 33.9 10.6 6 R 1210 1920 0.54 3876 0.1 11.2 90.9 7 R 888 2510 0.27 4969 0.0 27.6 10.7 8 L 1250 1947 0.66 3090 0.0 43.2 37.6 9 R 789 1975 0.00 3858 0.18 46.8 0.4 10 L 1119 2581 0.01 3983 0.0 63.2 26.2 Average: 1012±150 2317±680 0.19±0.26 3935±1140 0.05±0.08 47.5±19.3 28.6±26.1
21 f-RA plans for all 10 evaluation patients utilized a full-arc with avoidance sector such that the irradiation-arc length varied from 240º to 280 º. This length was within the range of the f-RA model.
h-RA plans for 8/10 evaluation patients used partial-arcs with length between 210 º and 220º. The remaining 2 plans (patient 6 and 8) utilized full-arc set-up with avoidance sector, with a beam-on arc length of 250º. Regarding the conventional component, the majority of the evaluation patients had a field set-up which was within the range of field-geometries/characteristics of the h-RA model. However, 2 patients had a largely differing field set-up: (1) patient 3 had a plan with an oblique field set to 140º, while in the model it is between 150º and 160º ; (2) patient 6, although the PTV was mainly located in the right lung, had 2 oblique fields, set on 200 º and 160 º with equal weight.
2.5.2 Assigning Optimization objectives
Both the f-RA and h-RA models were used to generate objectives for the following OARs of the evaluation group: CL objective), TL-PTV objective) and ESO (line-objective and a generated maximum point dose (line-objective at 0% volume). The priorities for the h-RA MBPs were reflective of those in the h-RA model. The f-RA model priorities were adjusted after validation testing on 3 patients. It was found that the f-RA model did not appropriately spare the contralateral lung, thus incrementally increasing the priority of this structure, and re-testing, led to the resultant priorities in Table 2.7. Line-objectives for CL and TL-PTV were chosen over point-objectives after validation testing on 3 patients: the line-objectives found to reduce the mean dose of the lungs, while not affecting V5 and V20.
For certain OARs manual dose-volume objectives, stipulated during model creation, were used for all plans: SC (maximum point dose-objective), SC+3mm (maximum point objective) and OAR-control (maximum point objective). These manual dose-volume objectives, and their respective priorities, were derived from averaging the same values of the plans in the model libraries.
Additionally, for the f-RA and h-RA MBPs, the automatic normal tissue objective (NTO) provided by RapidPlan which guides the dose fall-off outside the target was used with a priority of 80 and 50 respectively. For CPOs of f-RA MBPs and MPs, the priorities of the PTVinLung and PTVoutLung were increased to 200 and 180, respectively.
22
Table 2.7 Optimization objectives and priorities for the evaluation group MPs and MBPs
Structure f-RA h-RA MP MBP MP MBP Objective (Gy) Priority Objective (Gy) Priority Objective (Gy) Priority Objective (Gy) Priority ITV lower 66 110 66 110 66 100 66 110 PTV lower in lung: 70 out of lung: 65 120 120 in lung: 66 out of lung: 65 120 120 65 130 65 130 PTV upper in lung: 74 out of lung: 69 130 130 in lung: 69 out of lung: 68 130 130 67 120 67 120 CL a 130 Line 200 a 100 Line 110 TL-PTV b 130 Line 120 b 100 Line 110 SC 45-46 130-140 43.5 140 44 110-130 43.5 120 SC+3mm 47-48 130-150 45.7 150 46 120-140 45.7 120
OES c 90 Line 90 - - Line 90
OES max 66 120 Generated 150 65 130 Generated 130
OARcontrol 67 130 66 150 66 130 66 130
NTO - - Auto 80 - - Auto 50
a: Two objectives on V5, below the DVH line that was displayed during the optimization.
b: Two objectives on V5 and two on V20 , below the DVH line that was displayed during the optimization. c: Objectives were placed on V40, V50, V60.
2.5.3 Evaluation of prediction accuracy
RapidPlan provides a prediction range of DVHs for each OAR. In order to evaluate the accuracy of the predictions the mid-prediction DVH line was created running through the middle of the prediction range as described by Tol et al.35 and can be seen in Figure 2.5. Consequently the following parameters were calculated:
- Predicted Dmean: mean dose of the mid-prediction DVH line.
- Upper boundary Dmean: mean dose of the upper boundary of the prediction range. - Lower boundary Dmean: mean dose of the lower boundary of the prediction range. - Predicted Dmean range = Upper boundary Dmean - Lower prediction Dmean
Besides the mean dose of the OARs, the following point-volume predictions were extracted from the mid-prediction DVH and upper and lower boundaries: Predicted V5, Upper boundary V5, Lower prediction V5 for CL and Predicted V20, Upper boundary V20, Lower prediction V20 for TL-PTV as well as the corresponding predicted ranges.
23 The prediction accuracy was investigated by comparing the achieved MBP dosimetry metrics to the predicted aforementioned parameters. The difference between predicted and achieved dose metrics ΔV5, ΔV20 and ΔDmean was calculated for example as Predicted V5 minus achieved MBP V5. Linear regression analysis using the least square method was performed between the predicted and achieved dose parameters.
Figure 2.5: The DVH prediction range (shaded region) and the
mid-prediction DVH line running through the middle of it (dashed line).
2.5.4 Using predictions to select treatment technique
DVH-predictions were used to assess the possibility that RapidPlan can be used to select which modality should be used for a prospective patient. It was examined if RapidPlan can accurately predict which technique results in lower dose for the following parameters; CL Dmean , TL-PTV V20 , TL-PTV Dmean and ESO Dmean. These parameters were found to be mostly associated with high risk of pneumonitis and esophagitis after radiation treatment5,6. CL V5 has been proven to be significantly lower in the h-RA plans compared to MPs33,34, and was therefore excluded from this analysis. The number of patients for whom the predicted f-RA parameter was lower than the predicted h-f-RA parameter (for ex. f-f-RA Predicted CL Dmean < h-RA Predicted CL Dmean ), was compared to the numbers of patients for whom f-RA MBP parameter was lower than h-f-RA MBP parameter (f-f-RA MBP CL Dmean < h-RA MBP CL Dmean).
24
3. RESULTS
3.1 Evaluation of Model Training
3.1.1 RapidPlan-provided statistical metrics
Table 3.1 shows all the structures trained in the model, and the respective R2 and χ2, the mean squared error between the original and the estimated data (MSE) and the number of DVH-PCs and GED-PCs extracted during model training. Regression models for both f-RA and h-RA showed good correlation between the geometric and dosimetric features of the CL, TL-PTV, and ESO with R2>0.8. However, the TL-PTV of the h-RA model had a slightly inferior R2 of 0.65. 𝜒2 values were close to 1 for all OAR structures, showing that residuals from the regression model are independent43.MSE values for the CL, TL-PTV and ESO were 0.0013, 0.0011 and 0.0063 respectively for the f-RA model, and 0.0010, 0.0016 and 0.0045 for the h-RA model, respectively, showing good estimation capability of both models.
SC, SC+3mm, OARcontrol models were not used for generating optimization-objectives because training results showed poor quality. However, the results are reported for analytical purposes. SC and SC+3mm models resulted in very low R2 values. There is also large variance in the DVH shapes, as indicated by the large number of DVH-PCs needed to describe the dosimetric variability. The IL model training results are comparable to the CL although it was not spared in the MPs. Nevertheless, the TL-PTV, which includes the IL, was spared, and thus the IL DVHs shapes did not vary a lot.
Table 3.1: Summary of training results
Model structure
f-RA model h-RA model
𝐑𝟐 𝐱𝟐 DVH-PCs GED-PCs MSE 𝐑𝟐 𝐱𝟐 DVH-PCs GED-PCs MSE
CL 0.834 1.082 2 2 0.0013 0.807 1.099 2 2 0.0010 TL-PTV 0.848 1.116 3 2 0.0011 0.647 1.068 3 3 0.0016 IL 0.800 1.102 2 3 0.0015 0.706 1.099 2 3 0.0022 ESO 0.841 1.094 3 3 0.0063 0.886 1.102 2 3 0.0045 SC 0.586 1.024 4 4 0.0135 0.710 1.078 3 3 0.0187 SC+3mm 0.636 1.066 3 3 0.0120 0.712 1.059 3 3 0.0146 OARcontrol 0.932 1.056 2 2 0.0015 0.667 1.084 1 1 0.0071
R2: Coefficient of determination for the regression model parameters. x2: Average chi square for the regression model parameters.
25
3.1.2 Outlier analysis
In the f-RA model, 5 plans where indicated as outliers for the CL structure by the model statistics: 3 plans had high CD value, indicating possible influential data points, while 2 plans had large mZ value, indicating possible geometrical outliers. Three TL-PTV structures were indicated as outliers, one of them had high CD value and the rest high mZ value. The same holds for the ESO model. After visual observation of the residual and regression plots, only one plan from the suggested outliers could be noticed laying more than 2 sd away from the regression line for CL and TL-PTV, while it was close to identity line in the residual plot. However, the geometry of this patient did not largely differ from the rest of the patients. In the h-RA model, there was only one geometric outlier for the esophagus structure. Since RapidPlan statistics did not suggest any outliers for CL and TL-PTV for the h-RA model, the uncleaned h-RA model was used for the rest of the study.
After removing the suggested outliers from the f-RA model and retraining the model, the resulting “cleaned model” had 3 new CL outliers and the R2 value was considerably reduced from 0.834 to 0.580. There were also 3 new outliers for the TL-PTV model structure and the R2 value was slightly decreased from 0.848 to 0.826.
The “cleaned” and “uncleaned” models were tested on 4 patients not included in the model libraries. The dosimetric results, normalized to the mean PTV dose, are shown in Table 3.2. Predicted Dmean range for CL were comparable for both models, while TL-PTV predictions of the cleaned model were considerably narrower than those of the uncleaned model. However, the uncleaned model provided lower CL and TL-PTV plan doses than that of the cleaned model plans, while the PTV coverage was comparable between the two models. Therefore, the uncleaned model including all the 55 plans was selected to guide the optimization of the 10 test patients plans.
Table 3.2: Results of f-RA MBPs made using uncleaned model and cleaned model. Patient
#
CL V5 (Gy) TL–PTV 𝐕𝟓 (Gy) TL–PTV 𝐕𝟐𝟎(Gy) PTV 𝐕𝟗𝟓%(%)
Uncleaned model Cleaned model Uncleaned model Cleaned model Uncleaned model Cleaned model Uncleaned model Cleaned model 1 31.9 32.9 38.9 39.5 16.2 17.5 97.3 98.7 2 33.2 44.4 50.0 56.9 26.1 27.9 97.3 97.7 3 60.6 60.5 71.3 71.2 29.4 29.3 92.8 93.0 4 39.0 43.5 60.3 63.2 27.2 27.3 99.2 98.9 Average 41.2 45.3 55.1 57.7 24.7 25.5 96.7 97.1
26
3.1.2 Field Geometry
Figure 3.1 shows the regression and residual plots for the CL and TL-PTV for the f-RA model. The same plots of the h-f-RA model are shown in Figure 3.2. In Figure 3.1, the partial-arc plans in the f-RA model are marked with red circles, while the rest of the plans used full-arc incorporating an avoidance sector (full-arc plans). In Figure 3.2, for the h-RA model, the full-arc plans are marked with red squares, while the rest is partial-arc plans.
The library of the f-RA model contains 7 partial-arc plans having typically low GED-PCS1. However, in regression and residual plots, the partial-arc plans fall within 1 standard deviation. In the h-RA model, the full-arc plans form a group on the right side of the regression plot, having high GED-PCS1 value. Further analysis of the relationship between the GED-PCS1 and the geometrical features showed that during the calculation of the GED the field geometry is not modeled correctly when the avoidance sector is used (see details in Appendix A). This problem caused the predictions of CL and TL-PTV to be higher. However, the problem was partially solved by optimizing the plan twice (see Appendix A).
The h-RA model library contains two plans with 2 oblique fields instead of one like the rest of the population. The first plan is also an avoidance sector plan and does not deviate from the avoidance sector group. In the second plan, the direction of the extra oblique field is at 270º, causing an unusually high exiting dose to the CL, for the relatively small PTV volume of the patient (209 cm3). Thus, the plan lies above the regression and the residual lines, meaning that the estimated CL dose is much lower than the actual dose, as expected. Even though it can be considered as a negative outlier for the model, the CD value is 4.5, while the threshold for outliers is 10, thus it does not have a significant effect on the regression line. For the plan that had 3 oblique fields, the fields do not deviate more than 20º from the AP and PA directions and thus the plan does not deviate from the rest of the training set.
27
Figure 3.1: Regression and residual plots of the f-RA model. In red circles are the plans with partial-arc
field set-up. (a) Regression plot for CL. (b) Residual plot for CL.
Figure 3.2: Regression and residual plots of the h-RA model. In red squares are the plans with
avoidance sector field set-up. (a) Regression plot for CL. (b) Residual plot for CL.
3.2 Evaluation of Model-Based Plans
Dosimetry of the MPs and MBPs for both f-RA and h-RA method is summarized in Table 3.3. The results are averaged over the 10-patient evaluation group. The dosimetric results for individual patients are shown in Figure 3.3 and Figure 3.4.
In f-RA, 5/10 MBPs (#1, 2, 4, 9 and 10) and 6/10 MPs (# 1, 2, 5, 7, 9, 10) satisfied all the clinical objectives for the OARs and the PTV. For h-RA, also 5/10 MBPs (#2, 4, 7, 9, 10) were clinically acceptable and 6/10 MPs (# 1, 2, 4, 7, 9, 10). For the rest of them, the PTV V95% was lower than 97%, while in some, one or more OAR requirements was also not achieved. These plans were examined individually, and after adjusting some parameters and repeating the optimization, it was possible to improve the plan quality (see Section 3.4).
The PTV coverage was sufficient in 5/10 MBPs and 9/10 MPs using the f-RA method, and in 5/10 MBPs and 8/10 MPs using the h-RA method. Quantitatively, both f-RA and h-RA MBPs resulted in lower PTV V95% on average when compared to the MPs: from 97.50±0.67 to 96.39±1.90 for the f-RA plans, and from 97.25±1.95 to 96.56±1.48 for the
h-28 RA plans. However, the difference was not statistically significant. The conformity index and PTV V107% were slightly improved, while the PTV HI slightly increased in the MBPs.
F-RA plans were able to achieve the aim of CL V5<40% in 6/10 MBPs and 6/10 MPs. TL-PTV V20 was clinically acceptable in 9/10 MBPs and 9/10 MPs, while TL-PTV V5 was lower than 60% in 5/10 MBPs, and 6/10 MPs. In f-RA MBPs, CL V5 and TL–PTV V5 and V20 increased by 4.1%, 2.5% and 1.1% on average respectively over MPs, with the increase in TL–PTV V20 being statistically significant. However, 4/10 f-RA MBPs resulted in lower CL V5 and TL-PTV V5 , while two of them also improved TL-PTV V20 over the respective MPs.
Regarding the clinical aims in h-RA method, MPs and MBPs performed similarly achieving CL V5 <40% in 7/10 patients, TL-PTV V20<35% in 9/10 patients and TL-PTV V5<60% in 8/10 cases. In actual numbers, CL V5 and TL–PTV V5 were slightly increased -by 0.9% and 0.6% respectively- in MBPs compared to MPs, while TL–PTV V20 remained almost the same.
MBPs improved the CL Dmean in the f-RA technique, as well as the CL Dmean (p<0.05) and TL-PTV Dmean (p<0.05) of the h-RA technique, possibly due to the use of a line-objective throughout the whole dose range instead of separate point objectives. Furthermore, MBPs have a considerably lower ESO Dmax and Dmean, and SC, SC+3mm, and OAR-control Dmax for both techniques. The MBP objectives for spinal cord and spinal cord + 3mm were stricter compared to the objectives used for the MPs and resulted in lower Dmax for these structures. The lower ESO Dmean is attributed to the use of line objectives over the entire dose range instead of only a few point objectives in large doses. The improved conformity index is due to the use of the automatic NTO during the optimization of MPBs.
29 Table 3.3: Average values of dosimetric data for 10 evaluation patients
f-RA h-RA MP MBP MP MBP PTV V95%(%) 97.5 ± 0.7 96.4 ± 1.9 97.3 ± 2.0 96.6 ± 1.5 V107%(%) 3.1 ± 1.5 2.8 ± 1.9 1.6 ± 2.4 0.8 ± 1.1 Dmax(Gy) 74.5 ± 0.6 74.7 ± 1.5 72.6 ± 1.6 72.0 ± 1.1 HI 0.13 ± 0.01 0.13 ± 0.02 0.11 ± 0.03 0.12 ± 0.02 CI 0.74 ± 0.06 0.78 ± 0.07ᵃ 0.50 ± 0.08 0.54 ± 0.11 CL V5(%) 40.2 ± 13.2 44.3 ± 12.6 25.6 ± 15.0 26.5 ± 16.5 Dmean(Gy) 7.1 ± 2.4 6.8 ± 1.9 5.9 ± 2.6 5.7 ± 2.7ᵃ TL – PTV V5(%) 55.6 ± 11.9 58.1 ± 12.1 47.5 ± 11.6 48.1 ± 12.4 V20(%) 26.2 ± 6.3 27.3 ± 6.2ᵃ 26.3 ± 6.3 26.2 ± 6.3 Dmean(Gy) 15.6 ± 3.3 15.8 ± 3.0 16.6 ± 3.7 16.6 ± 3.8ᵃ SC Dmax(Gy) 49.2 ± 1.4 49.0 ± 1.7 48.4 ± 2.5 47.8 ± 2.4 SC + 3mm Dmax(Gy) 55.6 ± 2.8 53.9 ± 3.3ᵃ 53.6 ± 3.9 53.1 ± 3.7 ESO Dmax(Gy) 69.9 ± 0.8 68.6 ± 2.8 68.7 ± 1.3 67.8 ± 1.8 Dmean(Gy) 33.2 ± 10.4 31.8 ± 10.0 34.3 ± 11.8 33.1 ± 11.5ᵃ OAR -control Dmax(Gy) 74.2 ± 1.3 72.8 ± 1.1ᵃ 72.4 ± 2.6 71.6 ± 1.6
30
Figure 3.3: Dosimetric results of f-RA and h-RA MPs and MBPs per patient for PTV and
31
Figure 3.4: Dosimetric results of f-RA and h-RA MPs and MBPs per patient for TL-PTV,
32
3.3 Evaluation of prediction accuracy
The dose metrics predicted by the f-RA and h-RA models plotted against the achieved MBP dose metrics for multiple organs-at-risk is shown in Figure 3.5, along with the linear fit through all data points and the corresponding coefficient of determination R2 and the standard error of the estimate σ. The difference between predicted and achieved dose metrics ΔV5, ΔV20 and ΔDmean for each patient is shown in Table 3.4 and Table 3.5 for the f-RA and the h-f-RA plans respectively. Furthermore, the achieved MBP metrics were visualized in relation to the prediction ranges in Figure 3.6: the predicted Dmean, the upper boundary Dmean and the lower boundary Dmean along with the achieved MBP Dmean for CL, TL-PTV, and esophagus. The volume predictions for CL V5 and TL-PTV V20 with the corresponding V5 and V20 of the upper and lower boundaries of the prediction range, and the achieved V5 and V20 are shown in Figure 3.7. The DVH plots along with the prediction ranges can be found in the Appendix B.
3.3.1 Contralateral Lung
For f-RA plans, predicted and achieved CL Dmean shows good correlation with R2 value of 0.89 and σ of 0.70 Gy, while for the h-RA the correlation is slightly poorer with R2 of 0.84 and σ of 1.2 Gy. f-RA model was able to predict the mean dose with ΔDmean of less than 1 Gy for all the cases (Table 3.4) and also achieved Dmean was between the predicted range (Figure 3.6). The h-RA model was accurate in predicting the mean CL dose with ΔDmean less than 1 Gy only for 6 of the patients (Table 3.5), while two of them were also out of the predicted range (Figure 3.6). Although the predicted Dmean range of h-RA model (2.4±1.2 Gy) is on average relatively narrow compared to that for the f-RA model (3.6±0.5 Gy), the predictions are less accurate.
When observing the V5 predictions, the f-RA model predicts generally lower V5 than what is achieved by the MBPs and the standard error is 5.5 %. The predicted CL V5 is on average 6.1% lower than the achieved (Table 3.4). On the other hand, h-RA model predicts either higher or lower CL V5, yet with a higher standard error of 8%. The predicted V5 range depicted in Figure 3.7 is on average 14.7±3.3% for the f-RA model and 11.9±2.1% for the h-RA model. Nevertheless, 7/10 f-h-RA plans and 6/10 h-h-RA plans fall within the predicted range.
33
Figure 3.5: The correlation between predicted and achieved DVH metrics of h-RA and f-RA
MBPs for multiple organs-at-risk. The solid lines represent linear regression fits (with R2 the coefficient of determination), while the dashed lines represent one standard error of the regression σ. The dashed black line represents the identity line (y=x).
34 Table 3.4: Difference between predicted and achieved MBP dose metrics for the f-RA model
Patient # Contralateral lung Total lung-PTV Esophagus
𝚫𝐕𝟓(%) 𝚫𝐃𝐦𝐞𝐚𝐧(𝐆𝐲) 𝚫𝐕𝟐𝟎(%) 𝚫𝐃𝐦𝐞𝐚𝐧(𝐆𝐲) 𝚫𝐃𝐦𝐞𝐚𝐧(𝐆𝐲) 1 -5.6 -0.1 8.2 2.8 0.3 2 -3.6 0.3 5.3 1.7 1.1 3 -8.2 0.5 1.8 0.4 0.9 4 1.2 0.7 1.5 1.4 -1.4 5 -11.2 -0.7 -2.7 -1.9 0.6 6 -15.4 -0.9 -0.2 -0.6 -1.1 7 -1.1 0.9 1.0 1.1 3.2 8 -14.5 -0.7 -0.6 -1.3 -1.4 9 -0.2 0.7 0.4 -0.4 4.1 10 -2.5 0.7 3.5 1.0 -1.0 Average -6.1±6.0 0.1±0.7 1.8±3.1 0.4±1.5 0.5±1.9
Negative values mean that the predicted value is lower than the achieved MBP value.
Table 3.5: Difference between predicted and achieved MBP dose metrics for the h-RA model
Patient # Contralateral lung Total lung-PTV Esophagus
𝚫𝐕𝟓(%) 𝚫𝐃𝐦𝐞𝐚𝐧(𝐆𝐲) 𝚫𝐕𝟐𝟎(%) 𝚫𝐃𝐦𝐞𝐚𝐧(𝐆𝐲) 𝚫𝐃𝐦𝐞𝐚𝐧(𝐆𝐲) 1 1.2 -0.46 2.9 0.9 -0.6 2 8.5 0.75 -0.8 -1.5 -2.5 3 -16.89 -2.07 0.6 0.1 -4 4 1.2 -0.8 5.6 2.4 -3.1 5 -3.7 -1.5 -1.2 -1.6 -0.5 6 -1.8 -0.26 -0.5 -0.8 2 7 8.4 1.16 -0.1 1.1 -7.1 8 -0.1 1.9 -3.6 -3.5 0 9 8 0.75 1.3 0.3 4.9 10 5.9 0.5 0.7 -0.6 -2.6 Average 1.1±7.7 0.0±1.2 0.5±2.5 -0.3±1.7 -1.4±3.3
35
Figure 3.6: Predicted and achieved Dmean for CL, TL-PTV, and ESO for f-RA and h-RA
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Figure 3.7: Predicted and achieved MBP CL V5, and TL-PTV V20 for both f-RA and h-RA
techniques. The error bars represent V5 and V20 of the upper boundary the lower boundary of the prediction range.
3.3.2 Total Lung – PTV
The two models showed comparable quality of linear correlation between predicted and achieved TL-PTV mean dose (Figure 3.5). The slope is higher than 1 for both methods, while R2 and σ values are 0.80 and 1.4 Gy for the f-RA model respectively, and 0.85 and 1.5
37 Gy for the h-RA model. For the f-RA model, the prediction range was on average 3.1±0.4 Gy and the achieved Dmean was within the predicted range in 7/10 cases. For the h-RA model, the predicted range was slightly wider; 3.6±1.8 Gy on average, and it was representative for 8/10 patients.
Predicted and achieved V20 showed poor correlation for f-RA plans with R2 value of 0.77 and σ of 3.1 %. Although achieved MBP V20 was within the prediction range for 7/10 patients, achieved V20 was lower than the mid prediction most of the cases. The h-RA plans showed stronger correlation and smaller standard error with R2 and σ values of 0.90 and 2.2% respectively, and achieved MBP V20 was within the prediction range for 7/10 patients. The predicted V20 range was the same on average for both techniques; 5.0±1.2% for f-RA and 5.0±0.9% for h-RA.
3.3.3 Esophagus
The linear regression analysis revealed a strong correlation between predicted and achieved ESO Dmean , for both techniques, with R2 values of 0.97 and 0.93 for f-RA and h-RA respectively, while the slope was close to 1. However, σ was 1.8Gy for the f-h-RA plans and 3.2Gy for the h-RA. The average predicted Dmean range was 6.3±3.1 Gy for the f-RA model and 5.0±1.7 for the h-RA model. Achieved esophagus Dmean was within the predicted range in 9/10 f-RA plans, while only in 5/10 h-RA plans. Moreover, the h-RA model predicted lower Dmean than the achieved for 7/10 patients.
