Patient data
A total of 125 patients with stage-I NSCLC underwent SBRT in 2015–2017 according to the protocols of the Zhejiang Cancer Hospital, Zhejiang, China. Clinical treatment plans for all patients were generated using the RayStation TPS (RaySearch Laboratories, Stockholm, Sweden).
The clinical target volume, planning target volume (PTV), and organs at risk (OARs) were delineated by experienced radiation oncologists and reviewed by senior physicians. The data comprised 74 IMRT plans and 51 VMAT plans. The IMRT plans were delivered using 11–13 step-and-shoot coplanar beams with a gantry spacing of 20° between the beams and arranged in a fan shape; the plans had dosimetric features similar to those of the VMAT plans. The latter were delivered using two arcs with a gantry spacing of 4° between the control points, with the distance between the start and stop angles varying from 220° to 260°. The start and stop angles of the arcs were decided by expert planners based on the anatomy of individual patients. The PTV was 3.19–357.20 cm3 (mean, 36.92 cm3). Patients were treated using five fractions and prescribed 50 Gy to the PTV. The prescription dose covered at 95% of the PTV, and the maximum dose did not exceed 150% of the prescription dose. The dosimetric constraints of the OAR partly consulted Radiation Therapy Oncology Group (RTOG) protocols 0813 and 0915, and are listed in Table 3. To conform the ALARA principle, all plans were optimized further using a trial-and-error process to achieve optimal sparing of OARs and were considered expert plans. These plans were used for clinical treatments and for the present study.
Characteristics of plans: geometry features, beam angles, and achievable dose for organs at risk (OARs)
In radiotherapy, the parameters of treatment plans are determined by the planners according to anatomical data based on computed tomography (CT) images. Intuitively, the beam orientation and constraints of OAR dose tend to correlate with the anatomic features of images from patients.
In the present study, 11 anatomical features were extracted from digital imaging and communications in medicine documents: (1) PTV volume (VPTV); (2) lung volume (VLung); (3) heart volume (VHeart); (4) distance between the PTV mass center and the lung-mass center (DPL); (5) distance between the PTV mass center and the heart-mass center (DPH); (6) overlap length of the PTV and the lung in the z-axis (OVZPL, introduced by Wang et al. to predict the Pareto front in esophageal cancer [26]); (7) overlap length of the PTV and the heart in the z-axis (OVZPH,); (8) distance between the PTV mass center and the lung-mass center in the x-axis (XPL); (9) distance between the PTV mass center and the lung-mass center in the y-axis (YPL); (10) distance between the PTV mass center and the heart-mass center in the x-axis (XPH); and (11) distance between the PTV mass center and the heart-mass center in the y-axis (YPH). PTV is major concerned in treatment planning, in that 9 PTV related features were extracted. Meanwhile, delivered tumor cause inevitable dose to lung and heart which may cause radiation toxicity in normal tissue. Five lung-related features and five heart-related features were also extracted to evaluate delivery dose in this study. The OVZPL, XPL, and YPL are shown in Fig. 4. These data could describe the volume, relative position, and shape of the regions of interest (ROIs), because the tissue anatomy of each patient was similar. The start and end angles of the arc or IMRT fan were recorded as features of the beam angle. The couch and collimator angles were 0° for all cases. The V10 (percentage lung volume of 10 Gy) and V20 (percentage lung volume of 20 Gy) of the lung and mean lung dose were recorded to represent the dose features. These dosimetric parameters were exported from the TPS using Python scripts.
Feature selection
Spearman’s rank correlation test was used to evaluate the correlation between the anatomical features and the beam angle and dosimetric features. Spearman’s rank correlation coefficient is a non-parametric rank statistic proposed as a measure of the strength of the association between two variables. It can be used in feature selection without making any assumptions about the frequency distribution of the variables [26]. If the P value was > 0.05, no significant correlation was found between the two variables. Irrelevant anatomical features were excluded from prediction modeling. The reserved features were used to predict beam angle and lung dose before determining the beam angle and objective function parameters for an automated plan using a machine-learning model.
Prediction and validation
Figure 5 is a flowchart of the major steps in the automated planning. The goal of training is to establish two mathematic correlations. One maps the anatomic information extracted from patient images and the selection of the beam angle. The other maps the anatomic information and V10, V20, and the mean dose of the lung. For convenience in the modeling, all plans were normalized at 95% of PTV in 50 Gy. All training data were standardized by removing the mean values and scaling to unit variance as a common requirement for machine-learning estimators.
Support vector regression (SVR) was implemented as the modeling method. SVR is a supervised learning method used for data regression. For complicated problems that are not regressed to a linear function, SVR introduces a kernel function that projects the data into a higher dimensional space where it can be regressed to a linear function. By introducing the kernel, SVR gains flexibility in the choice of the form of regression function, which needs not be linear and even needs not have the same functional form for all data, since its function is non-parametric and operates locally. As a consequence, they can work with geometry features which show a non- linearly relation to the beam angles and OAR doses. SVR also introduces a tube of width ε; and finding a function that is at most ε deviations from the targets actually obtained for all the training data becomes problematic [44, 45]. By choosing an appropriate ε, SVR can be robust even when the training data have some bias; for example, the results of training plans are slightly variation according to the discretion of planers. In machine learning, a hyperparameter is a parameter whose value is set before the learning process begins. Hyperparameters include ε and the kernel function, which are not learned directly within the estimators in SVR. An exhaustive grid-search method was introduced to find the appropriate values for the two hyperparameters, by searching the parameter space for the best cross-validation (CV) score. The CV method is used to determine how the results of statistical analysis generalize to an independent data set. The leave-one-out (LOO) method was used in each model for CV. In LOO, an entire data set with n patients was separated into a training data set with n − 1 patients and a validation data set with 1 patient [46]. The SVR model was developed using the training data set and applied to the validation data set. The SVR and Gridsearch algorithms were implemented using Scikit-learn [47].
A total of 125 cases were used in the training data set. With an LOO method, in each iteration, one case was randomly chosen as validation set and other 124 cases were training sets for cross validation. After models training, 30 cases outside the training pool were used as a test set for external validation. The actual values of the gantry start angle and stop angles, V10, V20, and mean dose of the lung were collected from the treatment plans generated by expert planners. The corresponding predicted value was calculated using a prediction model and the standard deviation of the resulting error was calculated.
Automated planning approach and assessment
Two factors of planning were determined automatically: gantry angles and objective functions. The start and stop gantry angles were predicted and used as an arc parameter for VMAT. Objective function parameters were calculated from the machine-learning model and individualized. For each patient, an automated plan was generated based on the predicted arc start and stop angles and the optimization objectives.
As a test for the automated planning procedure, two strategies were used to develop SBRT plans for the 30 cases in the testing set: (1) manual plan (designed by an experienced planner through trial-and-error) and (2) automated plan (designed by the automated planning procedure). All 60 plans were normalized at a 50-Gy dose (for 5 fractions) covering 95% of the PTV.
Two experienced radiation oncologists at Zhejiang Cancer Hospital reviewed the dose–volume histograms (DVHs) and dose distributions of the 30 automated plans and judged the acceptability of the plans for clinical treatments. The radiation oncologists was asked to decide each plan was clinical acceptable or not. For the PTV, the mean dose (Dmean), maximum dose (Dmax), minimum dose (Dmin), and homogeneity index (HI) as defined by the International Commission on Radiation Units and Measurements 83 [48], and the conformity index (CI) as defined by Paddick et al. [49] were evaluated. For OARs, Dmax for the bronchus, esophagus, spine, ribs, and heart, as well as Dmean, V10, and V20 for the lung, were evaluated for comparison.
Statistical analyses
Statistical analyses of dosimetric differences were performed using the Wilcoxon rank test based on the correlation between the manual plan and the automated plan using SPSS v21 (IBM, NY, USA). A P value < 0.05 was considered significant.