Role of beam orientation optimization in intensity-modulated radiation therapy

Deep-neural network approaches for predicting 3D dose distribution in intensity-modulated radiotherapy of the brain tumors

PURPOSE

The aim of this study is to reduce treatment planning time by predicting the intensity-modulated radiotherapy 3D dose distribution using deep learning for brain cancer patients. "For this purpose, two different approaches in dose prediction, i.e., first only planning target volume (PTV) and second PTV with organs at risk (OARs) as input of the U-net model, are employed and their results are compared."

METHODS AND MATERIALS

The data of 99 patients with glioma tumors referred for IMRT treatment were used so that the images of 90 patients were regarded as training datasets and the others were for the test. All patients were manually planned and treated with sixth-field IMRT; the photon energy was 6MV. The treatment plans were done with the Collapsed Cone Convolution algorithm to deliver 60 Gy in 30 fractions.

RESULTS

The obtained accuracy and similarity for the proposed methods in dose prediction when compared to the clinical dose distributions on test patients according to MSE, dice metric and SSIM for the Only-PTV and PTV-OARs methods are on average (0.05, 0.851, 0.83) and (0.056, 0.842, 0.82) respectively. Also, dose prediction is done in an extremely short time.

CONCLUSION

The same results of the two proposed methods prove that the presence of OARs in addition to PTV does not provide new knowledge to the network and only by defining the PTV and its location in the imaging slices, does the dose distribution become predictable. Therefore, the Only-PTV method by eliminating the process of introducing OARs can reduce the overall designing time of treatment by IMRT in patients with glioma tumors.

Implementation and evaluation of an iterative-based algorithm for automatic beam angle optimization in breast cancer treatment planning

INTRODUCTION

A beam angle optimization (BAO) algorithm was developed to evaluate its clinical feasibility and investigate the impact of varying BAO constraints on breast cancer treatment plans.

MATERIALS AND METHODS

A two-part study was designed. In part 1, we retrospectively selected 20 patients treated with radiotherapy after breast-conserving surgery. For each patient, BAO plans were designed using beam angles optimized by the BAO algorithm and the same optimization constraints as manual plans. Dosimetric indices were compared between BAO and manual plans. In part 2, fifteen patients with left breast cancer were included. For each patient, three distinct cardiac constraints (mean heart dose < 5 Gy, 3 Gy or 1 Gy) were established during the BAO process to obtain three optimized beam sets which were marked as BAO_H1, BAO_H3, BAO_H5, respectively. These sets of beams were then utilized under identical IMRT constraints for planning. Comparative analysis was conducted among the three groups of plans.

RESULTS

For part 1, no significant differences were observed between BAO plans and manual plans in all dosimetric indices, except for ipsilateral lung V5, where BAO plans performed slightly better than manual plans (35.5% ± 5.6% vs 36.9% ± 4.3%, p = 0.034). For part 2, Stricter BAO heart constraints resulted in more perpendicular beams. However, there was no significant difference between BAO_H1, BAO_H3 and BAO_H5 with the same IMRT constraint in the heart dose. Meanwhile, the left lung dose was increased while the right breast and lung doses were decreased with stricter heart constraints in BAO. When mean heart dose < 5 Gy in IMRT constraint, the mean dose to the right lung was decreased from 0.46 Gy for BAO_H5 to 0.33 Gy for BAO_H1 (p = 0.027).

CONCLUSIONS

The BAO algorithm can achieve quality plans comparable to manual plans. IMRT constraints dominate the final plan dose, while varying BAO constraints alter the trade-off among structures, providing an additional degree of freedom in planning design.

A unified path seeking algorithm for IMRT and IMPT beam orientation optimization

Objective. Fully automated beam orientation optimization (BOO) for intensity-modulated radiotherapy and intensity modulated proton therapy (IMPT) is gaining interest, since achieving optimal plan quality for an unknown number of fixed beam arrangements is tedious. Fast group sparsity-based optimization methods have been proposed to find the optimal orientation, but manual tuning is required to eliminate the exact number of beams from a large candidate set. Here, we introduce a fast, automated gradient descent-based path-seeking algorithm (PathGD), which performs fluence map optimization for sequentially added beams, to visualize the dosimetric benefit of one added field at a time.Approach. Several configurations of 2-4 proton and 5-15 photon beams were selected for three head-and-neck patients using PathGD, which was compared to group sparsity-regularized BOO solved with the fast iterative shrinkage-thresholding algorithm (GS-FISTA), and manually selected IMPT beams or one coplanar photon VMAT arc (MAN). Once beams were chosen, all plans were compared on computational efficiency, dosimetry, and for proton plans, robustness.Main results. With each added proton beam, Clinical Target Volume (CTV) and organs at risk (OAR) dosimetric cost improved on average across plans by [1.1%, 13.6%], and for photons, [0.6%, 2.0%]. Comparing algorithms, beam selection for PathGD was faster than GS-FISTA on average by 35%, and PathGD matched the CTV coverage of GS-FISTA plans while reducing OAR mean and maximum dose in all structures by an average of 13.6%. PathGD was able to improve CTV [Dmax, D95%] by [2.6%, 5.2%] and reduced worst-case [max, mean] dose in OARs by [11.1%, 13.1%].Significance. The benefit of a path-seeking algorithm is the beam-by-beam analysis of dosimetric cost. PathGD was shown to be most efficient and dosimetrically desirable amongst group sparsity and manual BOO methods, and highlights the sensitivity of beam addition for IMPT in particular.

Patient-specific three-dimensional dose distribution prediction via deep learning for prostate cancer therapy: Improvement with the structure loss

PURPOSE

Deep learning (DL)-based dose distribution prediction can potentially reduce the cost of inverse planning process. We developed and introduced a structure-focused loss (L_struct) for 3D dose prediction to improve prediction accuracy. This study investigated the influence of L_struct on DL-based dose prediction for patients with prostate cancer. The proposed L_struct, which is similar in concept to dose-volume histogram (DVH)-based optimization in clinical practice, has the potential to provide more interpretable and accurate DL-based optimization.

METHODS

This study involved 104 patients who underwent prostate radiotherapy. We used 3D U-Net-based architecture to predict dose distributions from computed tomography and contours of the planning target volume and organs-at-risk. We trained two models using different loss functions: L2 loss and L_struct. Predicted doses were compared in terms of dose-volume parameters and the Dice similarity coefficient of isodose volume.

RESULTS

DVH analysis showed that the L_struct model had smaller errors from the ground truth than the L2 model. The L_struct model achieved more consistent dose distributions than the L2 model, with errors close to zero. The isodose Dice score of the L_struct model was greater than that of the L2 model by >20% of the prescribed dose.

CONCLUSIONS

We developed L_struct using labels of inputted contours for DL-based dose prediction for prostate radiotherapy. L_struct can be generalized to any DL architecture, thereby enhancing the dose prediction accuracy.

Comparing Multi-Objective Local Search Algorithms for the Beam Angle Selection Problem

In intensity-modulated radiation therapy, treatment planners aim to irradiate the tumour according to a medical prescription while sparing surrounding organs at risk as much as possible. Although this problem is inherently a multi-objective optimisation (MO) problem, most of the models in the literature are single-objective ones. For this reason, a large number of single-objective algorithms have been proposed in the literature to solve such single-objective models rather than multi-objective ones. Further, a difficulty that one has to face when solving the MO version of the problem is that the algorithms take too long before converging to a set of (approximately) non-dominated points. In this paper, we propose and compare three different strategies, namely random PLS (rPLS), judgement-function-guided PLS (jPLS) and neighbour-first PLS (nPLS), to accelerate a previously proposed Pareto local search (PLS) algorithm to solve the beam angle selection problem in IMRT. A distinctive feature of these strategies when compared to the PLS algorithms in the literature is that they do not evaluate their entire neighbourhood before performing the dominance analysis. The rPLS algorithm randomly chooses the next non-dominated solution in the archive and it is used as a baseline for the other implemented algorithms. The jPLS algorithm first chooses the non-dominated solution in the archive that has the best objective function value. Finally, the nPLS algorithm first chooses the solutions that are within the neighbourhood of the current solution. All these strategies prevent us from evaluating a large set of BACs, without any major impairment in the obtained solutions’ quality. We apply our algorithms to a prostate case and compare the obtained results to those obtained by the PLS from the literature. The results show that algorithms proposed in this paper reach a similar performance than PLS and require fewer function evaluations.

Comparison of non-coplanar optimization of static beams and arc trajectories for intensity-modulated treatments of meningioma cases

Two methods for non-coplanar beam direction optimization, one for static beams and another for arc trajectories, were proposed for intracranial tumours. The results of the beam angle optimizations were compared with the beam directions used in the clinical plans. Ten meningioma cases already treated were selected for this retrospective planning study. Algorithms for non-coplanar beam angle optimization (BAO) and arc trajectory optimization (ATO) were used to generate the corresponding plans. A plan quality score, calculated by a graphical method for plan assessment and comparison, was used to guide the beam angle optimization process. For each patient, the clinical plans (CLIN), created with the static beam orientations used for treatment, and coplanar VMAT approximated plans (VMAT) were also generated. To make fair plan comparisons, all plan optimizations were performed in an automated multicriteria calculation engine and the dosimetric plan quality was assessed. BAO and ATO plans presented, on average, moderate global plan score improvements over VMAT and CLIN plans. Nevertheless, while BAO and CLIN plans assured a more efficient OARs sparing, the ATO and VMAT plans presented a higher coverage and conformity of the PTV. Globally, all plans presented high-quality dose distributions. No statistically significant quality differences were found, on average, between BAO, ATO and CLIN plans. However, automated plan solution optimizations (BAO or ATO) may improve plan generation efficiency and standardization. In some individual patients, plan quality improvements were achieved with ATO plans, demonstrating the possible benefits of this automated optimized delivery technique.

Beam Angle Optimization for Double-Scattering Proton Delivery Technique Using an Eclipse Application Programming Interface and Convolutional Neural Network

To automatically identify optimal beam angles for proton therapy configured with the double-scattering delivery technique, a beam angle optimization method based on a convolutional neural network (BAODS-Net) is proposed. Fifty liver plans were used for training in BAODS-Net. To generate a sequence of input data, 25 rays on the eye view of the beam were determined per angle. Each ray collects nine features, including the normalized Hounsfield unit and the position information of eight structures per 2° of gantry angle. The outputs are a set of beam angle ranking scores (S_beam) ranging from 0° to 359°, with a step size of 1°. Based on these input and output designs, BAODS-Net consists of eight convolution layers and four fully connected layers. To evaluate the plan qualities of deep-learning, equi-spaced, and clinical plans, we compared the performances of three types of loss functions and performed K-fold cross-validation (K = 5). For statistical analysis, the volumes V_27Gy and V_30Gy as well as the mean, minimum, and maximum doses were calculated for organs-at-risk by using a paired-samples t-test. As a result, smooth-L1 loss showed the best optimization performance. At the end of the training procedure, the mean squared errors between the reference and predicted S_beam were 0.031, 0.011, and 0.004 for L1, L2, and smooth-L1 loss, respectively. In terms of the plan quality, statistically, Plan_BAO has no significant difference from Plan_Clinic (P >.05). In our test, a deep-learning based beam angle optimization method for proton double-scattering treatments was developed and verified. Using Eclipse API and BAODS-Net, a plan with clinically acceptable quality was created within 5 min.

Fully automated noncoplanar radiation therapy treatment planning

PURPOSE

To perform fully automated noncoplanar (NC) treatment planning, we propose a method called NC-POPS to produce NC plans using the Pareto optimal projection search (POPS) algorithm.

METHODS

NC radiation therapy treatment planning has the potential to improve dosimetric quality as compared to traditional coplanar techniques. Likewise, automated treatment planning algorithms can reduce a planner's active treatment planning time and remove inter-planner variability. Our NC-POPS algorithm extends the original POPS algorithm to the NC setting with potential applications to both intensity-modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT). The proposed algorithm consists of two main parts: (1) NC beam angle optimization (BAO) and (2) fully automated inverse planning using the POPS algorithm.

RESULTS

We evaluate the performance of NC-POPS by comparing between various NC and coplanar configurations. To evaluate plan quality, we compute the homogeneity index (HI), conformity index (CI), and dose-volume histogram statistics for various organs-at-risk (OARs). As compared to the evaluated coplanar baseline methods, the proposed NC-POPS method achieves significantly better OAR sparing, comparable or better dose conformity, and similar dose homogeneity.

CONCLUSIONS

Our proposed NC-POPS algorithm provides a modular approach for fully automated treatment planning of NC IMRT cases with the potential to substantially improve treatment planning workflow and plan quality.

A reinforcement learning application of a guided Monte Carlo Tree Search algorithm for beam orientation selection in radiation therapy

Current beam orientation optimization algorithms for radiotherapy, such as column generation (CG), are typically heuristic or greedy in nature because of the size of the combinatorial problem, which leads to suboptimal solutions. We propose a reinforcement learning strategy using a Monte Carlo Tree Search (MCTS) that can find a better beam orientation set in less time than CG. We utilize a reinforcement learning structure involving a supervised learning network to guide the MCTS and to explore the decision space of beam orientation selection problems. We previously trained a deep neural network (DNN) that takes in the patient anatomy, organ weights, and current beams, then approximates beam fitness values to indicate the next best beam to add. Here, we use this DNN to probabilistically guide the traversal of the branches of the Monte Carlo decision tree to add a new beam to the plan. To assess the feasibility of the algorithm, we used a test set of 13 prostate cancer patients, distinct from the 57 patients originally used to train and validate the DNN, to solve five-beam plans. To show the strength of the guided MCTS (GTS) compared to other search methods, we also provided the performances of Guided Search, Uniform Tree Search and Random Search algorithms. On average, GTS outperformed all the other methods. It found a better solution than CG in 237 s on average, compared to 360 s for CG, and outperformed all other methods in finding a solution with a lower objective function value in less than 1000 s. Using our GTS method, we could maintain planning target volume (PTV) coverage within 1% error similar to CG, while reducing the organ-at-risk mean dose for body, rectum, left and right femoral heads; the mean dose to bladder was 1% higher with GTS than with CG.

A fast deep learning approach for beam orientation optimization for prostate cancer treated with intensity-modulated radiation therapy

PURPOSE

Beam orientation selection, whether manual or protocol-based, is the current clinical standard in radiation therapy treatment planning, but it is tedious and can yield suboptimal results. Many algorithms have been designed to optimize beam orientation selection because of its impact on treatment plan quality, but these algorithms suffer from slow calculation of the dose influence matrices of all candidate beams. We propose a fast beam orientation selection method, based on deep learning neural networks (DNN), capable of developing a plan comparable to those developed by the state-of-the-art column generation (CG) method. Our model's novelty lies in its supervised learning structure (using CG to teach the network), DNN architecture, and ability to learn from anatomical features to predict dosimetrically suitable beam orientations without using dosimetric information from the candidate beams. This may save hours of computation.

METHODS

A supervised DNN is trained to mimic the CG algorithm, which iteratively chooses beam orientations one-by-one by calculating beam fitness values based on Karush-Kush-Tucker optimality conditions at each iteration. The DNN learns to predict these values. The dataset contains 70 prostate cancer patients - 50 training, 7 validation, and 13 test patients - to develop and test the model. Each patient's data contains 6 contours: PTV, body, bladder, rectum, and left and right femoral heads. Column generation was implemented with a GPU-based Chambolle-Pock algorithm, a first-order primal-dual proximal-class algorithm, to create 6270 plans. The DNN trained over 400 epochs, each with 2500 steps and a batch size of 1, using the Adam optimizer at a learning rate of 1 × 10-5 and a sixfold cross-validation technique.

RESULTS

The average and standard deviation of training, validation, and testing loss functions among the six folds were 0.62 ± 0.09%, 1.04 ± 0.06%, and 1.44 ± 0.11%, respectively. Using CG and supervised DNN, we generated two sets of plans for each scenario in the test set. The proposed method took at most 1.5 s to select a set of five beam orientations and 300 s to calculate the dose influence matrices for 5 beams and finally 20 s to solve the fluence map optimization (FMO). However, CG needed around 15 h to calculate the dose influence matrices of all beams and at least 400 s to solve both the beam orientation selection and FMO problems. The differences in the dose coverage of PTV between plans generated by CG and by DNN were 0.2%. The average dose differences received by organs at risk were between 1 and 6 percent: Bladder had the smallest average difference in dose received (0.956 ± 1.184%), then Rectum (2.44 ± 2.11%), Left Femoral Head (6.03 ± 5.86%), and Right Femoral Head (5.885 ± 5.515%). The dose received by Body had an average difference of 0.10 ± 0.1% between the generated treatment plans.

CONCLUSIONS

We developed a fast beam orientation selection method based on a DNN that selects beam orientations in seconds and is therefore suitable for clinical routines. In the training phase of the proposed method, the model learns the suitable beam orientations based on patients' anatomical features and omits time intensive calculations of dose influence matrices for all possible candidate beams. Solving the FMO to get the final treatment plan requires calculating dose influence matrices only for the selected beams.

Many-isocenter optimization for robotic radiotherapy

Despite significant dosimetric gains, clinical implementation of the 4π non-coplanar radiotherapy on the widely available C-arm gantry system is hindered by limited clearance, and the need to perform complex coordinated gantry and couch motion. A robotic radiotherapy platform would be conducive to such treatment but a new conflict between field size and MLC modulation resolution needs to be managed for versatile applications. This study investigates the dosimetry and delivery efficiency of purposefully creating many isocenters to achieve simultaneously high MLC modulation resolution and large tumor coverage. An integrated optimization framework was proposed for simultaneous beam orientation optimization (BOO), isocenter selection, and fluence map optimization (FMO). The framework includes a least-square dose fidelity objective, a total variation term for regularizing the fluence smoothness, and a group sparsity term for beam selection. A minimal number of isocenters were identified for efficient target coverage. Colliding beams excluded, high-resolution small-field 4π intensity-modulated radiotherapy (IMRT) treatment plans with 50 cm source-to-isocenter distance (SID-50) on 10 Head and Neck (H&N) cancer patients were compared with low-resolution large-field plans with 100 cm SID (SID-100). With the same or better target coverage, the average reduction of [Dmean, Dmax] of 20-beam SID-50 plans from 20-beam SID-100 plans were [2.09 Gy, 1.19 Gy] for organs at risk (OARs) overall, [3.05 Gy, 0.04 Gy] for parotid gland, [3.62 Gy, 5.19 Gy] for larynx, and [3.27 Gy, 1.10 Gy] for mandible. R50 and integral dose were reduced by 5.3% and 9.6%, respectively. Wilcoxon signed-rank test showed significant difference (p   <  0.05) in planning target volume (PTV) homogeneity, PTV Dmax, R50, Integral dose, and OAR Dmean and Dmax. The estimated delivery time of 20-beam [SID-50, SID-100] plans were [19, 18] min and [14, 9] min, assuming 5 fractions and 30 fractions, respectively. With clinically acceptable delivery efficiency, many-isocenter optimization is dosimetrically desirable for treating large targets with high modulation resolution on the robotic platform.

Dose-volume histogram prediction in volumetric modulated arc therapy for nasopharyngeal carcinomas based on uniform-intensity radiation with equal angle intervals

In this study, we developed a gated recurrent unit (GRU)-based recurrent neural network (RNN) for dose-volume histogram (DVH) prediction in volumetric modulated arc therapy (VMAT) planning for nasopharyngeal carcinomas (NPCs) based on uniform-intensity radiation with equal angle intervals and investigated the feasibility and usefulness of this method for treatment optimization. One hundred twenty-four NPC patients were selected from a database containing clinical VMAT plans from 2015 to 2018; of these, the data from 100 patients were used to train the GRU-RNN, and the data of the other 24 patients were used for testing. For the prescribed doses to D₉₅ (the absorbed dose for 95% of the planning target volume) of all the plans in 30 or 31 fractions, 70 Gy were delivered to PTV70 (the gross tumour volume with circumferential margin), 60 Gy were delivered to PTV60, 54 Gy were delivered to PTV54 and 66 Gy were delivered to PTV66 (lymph node gross tumour volume with circumferential margin). For each NPC patient, an equal-field-weight conformal radiotherapy plan was generated by a treatment planning system (TPS) to offer uniform-intensity radiation. By adjusting the field weights, the dose distribution induced by individual conformal beams was acquired, and the corresponding DVH was calculated. Direction-dependent DVHs were employed to predict the DVH for VMAT with the GRU-RNN, and the regenerated VMAT experimental plans (EPs), guided by the predicted DVHs, were evaluated by comparing them with the clinical plans (CPs). For the 24 test patients, the regenerated EPs guided by the GRU-RNN predictive model achieved good consistency relative to the CPs. The EPs resulted in better dose sparing for many organs at risk (OARs) while still meeting the acceptable criteria for the PTVs. Significant differences were found in the maximum/mean doses to the optic nerves, temporal lobes, lenses, mandibles, temporomandibular joints (TMJs), larynx and inner ears, with P-values of 0.03, 0.01, 0.01, <0.01, 0.02, 0.02 and  <0.01, respectively. On average, compared to the CPs, the maximum/mean doses to these OARs were altered by  -1.38 Gy, -0.92 Gy, 0.53 Gy, -1.19 Gy, -1.16 Gy, 2.39 Gy and  -1.71 Gy, respectively. The results showed the accuracy and effectiveness of the proposed uniform-intensity radiation approach. The regenerated plans guided by the predictive method were not inferior to the manual plans, indicating their great potential for improved planning and quality control in clinical applications.

A convolutional neural network approach for IMRT dose distribution prediction in prostate cancer patients

The purpose of the study was to compare a 3D convolutional neural network (CNN) with the conventional machine learning method for predicting intensity-modulated radiation therapy (IMRT) dose distribution using only contours in prostate cancer. In this study, which included 95 IMRT-treated prostate cancer patients with available dose distributions and contours for planning target volume (PTVs) and organs at risk (OARs), a supervised-learning approach was used for training, where the dose for a voxel set in the dataset was defined as the label. The adaptive moment estimation algorithm was employed for optimizing a 3D U-net similar network. Eighty cases were used for the training and validation set in 5-fold cross-validation, and the remaining 15 cases were used as the test set. The predicted dose distributions were compared with the clinical dose distributions, and the model performance was evaluated by comparison with RapidPlan™. Dose-volume histogram (DVH) parameters were calculated for each contour as evaluation indexes. The mean absolute errors (MAE) with one standard deviation (1SD) between the clinical and CNN-predicted doses were 1.10% ± 0.64%, 2.50% ± 1.17%, 2.04% ± 1.40%, and 2.08% ± 1.99% for D2, D98 in PTV-1 and V65 in rectum and V65 in bladder, respectively, whereas the MAEs with 1SD between the clinical and the RapidPlan™-generated doses were 1.01% ± 0.66%, 2.15% ± 1.25%, 5.34% ± 2.13% and 3.04% ± 1.79%, respectively. Our CNN model could predict dose distributions that were superior or comparable with that generated by RapidPlan™, suggesting the potential of CNN in dose distribution prediction.

Approach and assessment of automated stereotactic radiotherapy planning for early stage non-small-cell lung cancer

BACKGROUND

Intensity-modulated radiotherapy (IMRT) and volumetric-modulated arc therapy (VMAT) are standard physical technologies of stereotactic body radiotherapy (SBRT) that are used for patients with non-small-cell lung cancer (NSCLC). The treatment plan quality depends on the experience of the planner and is limited by planning time. An automated planning process can save time and ensure a high-quality plan. This study aimed to introduce and demonstrate an automated planning procedure for SBRT for patients with NSCLC based on machine-learning algorithms. The automated planning was conducted in two steps: (1) determining patient-specific optimized beam orientations; (2) calculating the organs at risk (OAR) dose achievable for a given patient and setting these dosimetric parameters as optimization objectives. A model was developed using data of historical expertise plans based on support vector regression. The study cohort comprised patients with NSCLC who were treated using SBRT. A training cohort (N = 125) was used to calculate the beam orientations and dosimetric parameters for the lung as functions of the geometrical feature of each case. These plan-geometry relationships were used in a validation cohort (N = 30) to automatically establish the SBRT plan. The automatically generated plans were compared with clinical plans established by an experienced planner.

RESULTS

All 30 automated plans (100%) fulfilled the dose criteria for OARs and planning target volume (PTV) coverage, and were deemed acceptable according to evaluation by experienced radiation oncologists. An automated plan increased the mean maximum dose for ribs (31.6 ± 19.9 Gy vs. 36.6 ± 18.1 Gy, P < 0.05). The minimum, maximum, and mean dose; homogeneity index; conformation index to PTV; doses to other organs; and the total monitor units showed no significant differences between manual plans established by experts and automated plans (P > 0.05). The hands-on planning time was reduced from 40-60 min to 10-15 min.

CONCLUSION

An automated planning method using machine learning was proposed for NSCLC SBRT. Validation results showed that the proposed method decreased planning time without compromising plan quality. Plans generated by this method were acceptable for clinical use.

Robust beam orientation optimization for intensity-modulated proton therapy

PURPOSE

Dose conformality and robustness are equally important in intensity modulated proton therapy (IMPT). Despite the obvious implication of beam orientation on both dosimetry and robustness, an automated, robust beam orientation optimization algorithm has not been incorporated due to the problem complexity and paramount computational challenge. In this study, we developed a novel IMPT framework that integrates robust beam orientation optimization (BOO) and robust fluence map optimization (FMO) in a unified framework.

METHODS

The unified framework is formulated to include a dose fidelity term, a heterogeneity-weighted group sparsity term, and a sensitivity regularization term. The L2, 1/2-norm group sparsity is used to reduce the number of active beams from the initial 1162 evenly distributed noncoplanar candidate beams, to between two and four. A heterogeneity index, which evaluates the lateral tissue heterogeneity of a beam, is used to weigh the group sparsity term. With this index, beams more resilient to setup uncertainties are encouraged. There is a symbiotic relationship between the heterogeneity index and the sensitivity regularization; the integrated optimization framework further improves beam robustness against both range and setup uncertainties. This Sensitivity regularization and Heterogeneity weighting based BOO and FMO framework (SHBOO-FMO) was tested on two skull-base tumor (SBT) patients and two bilateral head-and-neck (H&N) patients. The conventional CTV-based optimized plans (Conv) with SHBOO-FMO beams (SHBOO-Conv) and manual beams (MAN-Conv) were compared to investigate the beam robustness of the proposed method. The dosimetry and robustness of SHBOO-FMO plan were compared against the manual beam plan with CTV-based voxel-wise worst-case scenario approach (MAN-WC).

RESULTS

With SHBOO-FMO method, the beams with superior range robustness over manual beams were selected while the setup robustness was maintained or improved. On average, the lowest [D95%, V95%, V100%] of CTV were increased from [93.85%, 91.06%, 70.64%] in MAN-Conv plans, to [98.62%, 98.61%, 96.17%] in SHBOO-Conv plans with range uncertainties. With setup uncertainties, the average lowest [D98%, D95%, V95%, V100%] of CTV were increased from [92.06%, 94.83%, 94.31%, 78.93%] in MAN-Conv plans, to [93.54%, 96.61%, 97.01%, 91.98%] in SHBOO-Conv plans. Compared with the MAN-WC plans, the final SHBOO-FMO plans achieved comparable plan robustness and better OAR sparing, with an average reduction of [Dmean, Dmax] of [6.31, 6.55] GyRBE for the SBT cases and [1.89, 5.08] GyRBE for the H&N cases from the MAN-WC plans.

CONCLUSION

We developed a novel method to integrate robust BOO and robust FMO into IMPT optimization for a unified solution of both BOO and FMO, generating plans with superior dosimetry and good robustness.

Automated prediction of dosimetric eligibility of patients with prostate cancer undergoing intensity-modulated radiation therapy using a convolutional neural network

The quality of radiotherapy has greatly improved due to the high precision achieved by intensity-modulated radiation therapy (IMRT). Studies have been conducted to increase the quality of planning and reduce the costs associated with planning through automated planning method; however, few studies have used the deep learning method for optimization of planning. The purpose of this study was to propose an automated method based on a convolutional neural network (CNN) for predicting the dosimetric eligibility of patients with prostate cancer undergoing IMRT. Sixty patients with prostate cancer who underwent IMRT were included in the study. Treatment strategy involved division of the patients into two groups, namely, meeting all dose constraints and not meeting all dose constraints, by experienced medical physicists. We used AlexNet (i.e., one of common CNN architectures) for CNN-based methods to predict the two groups. An AlexNet CNN pre-trained on ImageNet was fine-tuned. Two dataset formats were used as input data: planning computed tomography (CT) images and structure labels. Five-fold cross-validation was used, and performance metrics included sensitivity, specificity, and prediction accuracy. Class activation mapping was used to visualize the internal representation learned by the CNN. Prediction accuracies of the model with the planning CT image dataset and that with the structure label dataset were 56.7 ± 9.7% and 70.0 ± 11.3%, respectively. Moreover, the model with structure labels focused on areas associated with dose constraints. These results revealed the potential applicability of deep learning to the treatment planning of patients with prostate cancer undergoing IMRT.

Lung IMRT planning with automatic determination of beam angle configurations

Beam angle configuration is a major planning decision in intensity modulated radiation treatment (IMRT) that has a significant impact on dose distributions and thus quality of treatment, especially in complex planning cases such as those for lung cancer treatment. We propose a novel method to automatically determine beam configurations that incorporates noncoplanar beams. We then present a completely automated IMRT planning algorithm that combines the proposed method with a previously reported OAR DVH prediction model. Finally, we validate this completely automatic planning algorithm using a set of challenging lung IMRT cases. A beam efficiency index map is constructed to guide the selection of beam angles. This index takes into account both the dose contributions from individual beams and the combined effect of multiple beams by introducing a beam-spread term. The effect of the beam-spread term on plan quality was studied systematically and the weight of the term to balance PTV dose conformity against OAR avoidance was determined. For validation, complex lung cases with clinical IMRT plans that required the use of one or more noncoplanar beams were re-planned with the proposed automatic planning algorithm. Important dose metrics for the PTV and OARs in the automatic plans were compared with those of the clinical plans. The results are very encouraging. The PTV dose conformity and homogeneity in the automatic plans improved significantly. And all the dose metrics of the automatic plans, except the lung V_{5 Gy}, were statistically better than or comparable with those of the clinical plans. In conclusion, the automatic planning algorithm can incorporate non-coplanar beam configurations in challenging lung cases and can generate plans efficiently with quality closely approximating that of clinical plans.

The Scatter Search Based Algorithm for Beam Angle Optimization in Intensity-Modulated Radiation Therapy

This article introduces a new framework for beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) using the Scatter Search Based Algorithm. The potential benefits of plans employing the coplanar optimized beam sets are also examined. In the proposed beam angle selection algorithm, the problem is solved in two steps. Initially, the gantry angles are selected using the Scatter Search Based Algorithm, which is a global optimization method. Then, for each beam configuration, the intensity profile is calculated by the conjugate gradient method to score each beam angle set chosen. A simulated phantom case with obvious optimal beam angles was used to benchmark the validity of the presented algorithm. Two clinical cases (TG-119 phantom and prostate cases) were examined to prepare a dose volume histogram (DVH) and determine the dose distribution to evaluate efficiency of the algorithm. A clinical plan with the optimized beam configuration was compared with an equiangular plan to determine the efficiency of the proposed algorithm. The BAO plans yielded significant improvements in the DVHs and dose distributions compared to the equispaced coplanar beams for each case. The proposed algorithm showed its potential to effectively select the beam direction for IMRT inverse planning at different tumor sites.

Integrated beam orientation and scanning-spot optimization in intensity-modulated proton therapy for brain and unilateral head and neck tumors

PURPOSE

Intensity-Modulated Proton Therapy (IMPT) is the state-of-the-art method of delivering proton radiotherapy. Previous research has been mainly focused on optimization of scanning spots with manually selected beam angles. Due to the computational complexity, the potential benefit of simultaneously optimizing beam orientations and spot pattern could not be realized. In this study, we developed a novel integrated beam orientation optimization (BOO) and scanning-spot optimization algorithm for intensity-modulated proton therapy (IMPT).

METHODS

A brain chordoma and three unilateral head-and-neck patients with a maximal target size of 112.49 cm³ were included in this study. A total number of 1162 noncoplanar candidate beams evenly distributed across 4π steradians were included in the optimization. For each candidate beam, the pencil-beam doses of all scanning spots covering the PTV and a margin were calculated. The beam angle selection and spot intensity optimization problem was formulated to include three terms: a dose fidelity term to penalize the deviation of PTV and OAR doses from ideal dose distribution; an L1-norm sparsity term to reduce the number of active spots and improve delivery efficiency; a group sparsity term to control the number of active beams between 2 and 4. For the group sparsity term, convex L2,1-norm and nonconvex L2,1/2-norm were tested. For the dose fidelity term, both quadratic function and linearized equivalent uniform dose (LEUD) cost function were implemented. The optimization problem was solved using the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The IMPT BOO method was tested on three head-and-neck patients and one skull base chordoma patient. The results were compared with IMPT plans created using column generation selected beams or manually selected beams.

RESULTS

The L2,1-norm plan selected spatially aggregated beams, indicating potential degeneracy using this norm. L2,1/2-norm was able to select spatially separated beams and achieve smaller deviation from the ideal dose. In the L2,1/2-norm plans, the [mean dose, maximum dose] of OAR were reduced by an average of [2.38%, 4.24%] and[2.32%, 3.76%] of the prescription dose for the quadratic and LEUD cost function, respectively, compared with the IMPT plan using manual beam selection while maintaining the same PTV coverage. The L2,1/2 group sparsity plans were dosimetrically superior to the column generation plans as well. Besides beam orientation selection, spot sparsification was observed. Generally, with the quadratic cost function, 30%~60% spots in the selected beams remained active. With the LEUD cost function, the percentages of active spots were in the range of 35%~85%.The BOO-IMPT run time was approximately 20 min.

CONCLUSION

This work shows the first IMPT approach integrating noncoplanar BOO and scanning-spot optimization in a single mathematical framework. This method is computationally efficient, dosimetrically superior and produces delivery-friendly IMPT plans.

A knowledge-based approach to automated planning for hepatocellular carcinoma

PURPOSE

To build a knowledge-based model of liver cancer for Auto-Planning, a function in Pinnacle, which is used as an automated inverse intensity modulated radiation therapy (IMRT) planning system.

METHODS AND MATERIALS

Fifty Tomotherapy patients were enrolled to extract the dose-volume histograms (DVHs) information and construct the protocol for Auto-Planning model. Twenty more patients were chosen additionally to test the model. Manual planning and automatic planning were performed blindly for all twenty test patients with the same machine and treatment planning system. The dose distributions of target and organs at risks (OARs), along with the working time for planning, were evaluated.

RESULTS

Statistically significant results showed that automated plans performed better in target conformity index (CI) while mean target dose was 0.5 Gy higher than manual plans. The differences between target homogeneity indexes (HI) of the two methods were not statistically significant. Additionally, the doses of normal liver, left kidney, and small bowel were significantly reduced with automated plan. Particularly, mean dose and V15 of normal liver were 1.4 Gy and 40.5 cc lower with automated plans respectively. Mean doses of left kidney and small bowel were reduced with automated plans by 1.2 Gy and 2.1 Gy respectively. In contrast, working time was also significantly reduced with automated planning.

CONCLUSIONS

Auto-Planning shows availability and effectiveness in our knowledge-based model for liver cancer.

A new sparse optimization scheme for simultaneous beam angle and fluence map optimization in radiotherapy planning

[Formula: see text]-minimization-based sparse optimization was employed to solve the beam angle optimization (BAO) in intensity-modulated radiation therapy (IMRT) planning. The technique approximates the exact BAO formulation with efficiently computable convex surrogates, leading to plans that are inferior to those attainable with recently proposed gradient-based greedy schemes. In this paper, we alleviate/reduce the nontrivial inconsistencies between the [Formula: see text]-based formulations and the exact BAO model by proposing a new sparse optimization framework based on the most recent developments in group variable selection. We propose the incorporation of the group-folded concave penalty (gFCP) as a substitution to the [Formula: see text]-minimization framework. The new formulation is then solved by a variation of an existing gradient method. The performance of the proposed scheme is evaluated by both plan quality and the computational efficiency using three IMRT cases: a coplanar prostate case, a coplanar head-and-neck case, and a noncoplanar liver case. Involved in the evaluation are two alternative schemes: the [Formula: see text]-minimization approach and the gradient norm method (GNM). The gFCP-based scheme outperforms both counterpart approaches. In particular, gFCP generates better plans than those obtained using the [Formula: see text]-minimization for all three cases with a comparable computation time. As compared to the GNM, the gFCP improves both the plan quality and computational efficiency. The proposed gFCP-based scheme provides a promising framework for BAO and promises to improve both planning time and plan quality.

Investigating multi-objective fluence and beam orientation IMRT optimization

Radiation Oncology treatment planning requires compromises to be made between clinical objectives that are invariably in conflict. It would be beneficial to have a 'bird's-eye-view' perspective of the full spectrum of treatment plans that represent the possible trade-offs between delivering the intended dose to the planning target volume (PTV) while optimally sparing the organs-at-risk (OARs). In this work, the authors demonstrate Pareto-aware radiotherapy evolutionary treatment optimization (PARETO), a multi-objective tool featuring such bird's-eye-view functionality, which optimizes fluence patterns and beam angles for intensity-modulated radiation therapy (IMRT) treatment planning. The problem of IMRT treatment plan optimization is managed as a combined monolithic problem, where all beam fluence and angle parameters are treated equally during the optimization. To achieve this, PARETO is built around a powerful multi-objective evolutionary algorithm, called Ferret, which simultaneously optimizes multiple fitness functions that encode the attributes of the desired dose distribution for the PTV and OARs. The graphical interfaces within PARETO provide useful information such as: the convergence behavior during optimization, trade-off plots between the competing objectives, and a graphical representation of the optimal solution database allowing for the rapid exploration of treatment plan quality through the evaluation of dose-volume histograms and isodose distributions. PARETO was evaluated for two relatively complex clinical cases, a paranasal sinus and a pancreas case. The end result of each PARETO run was a database of optimal (non-dominated) treatment plans that demonstrated trade-offs between the OAR and PTV fitness functions, which were all equally good in the Pareto-optimal sense (where no one objective can be improved without worsening at least one other). Ferret was able to produce high quality solutions even though a large number of parameters, such as beam fluence and beam angles, were included in the optimization.

An effective calculation method for an overlap volume histogram descriptor and its application in IMRT plan retrieval

To effectively calculate an overlap volume histogram (OVH) descriptor and improve intensity modulated radiation treatment (IMRT) planning by basing it on previous plans with similar features, a method based on morphology for OVH calculation was proposed and a novel similarity measurement was employed for retrieval of a suitable IMRT plan. First, the minimum and maximum distances between the tumor and organs at risk (OARs) were calculated as the start and end points for contraction or expansion, and a suitable step size for contraction or expansion was determined according to these distances. Then, a dilation or erosion morphology operator was employed to compute the OVH descriptor. Finally, the performance of IMRT plan retrieval was evaluated, where the area between OVH descriptors was taken as the similarity measurement, and a 3D reconstruction for each case was also performed for visual comparison. Twenty-eight nasopharyngeal carcinoma (NPC) cases were evaluated. The results show that OVH descriptors can be calculated effectively with the proposed method, and match well to the 3D geometrical features of the tumor and OARs. Further, the IMRT plan retrieval results match well based on a visual inspection of their 3D geometrical features, and an increase of the area between OVH descriptors leads to a decrease of visual similarity. Therefore, the proposed method can be used effectively for the calculation of an OVH descriptor as well as the retrieval of similar IMRT cases.

New Developments in Intensity Modulated Radiation Therapy

As intensity modulated radiation therapy (IMRT) becomes routine clinical practice, its advantages and limitations are better understood. With these new understandings, some new developments have emerged in an effort to alleviate the limitations of the current IMRT practice. This article describes a few of these efforts made at the University of Maryland, including: i) improving IMRT efficiency with direct aperture optimization; ii) broadening the scope of optimization to include the mode of delivery and beam angles; and iii) new planning methods for intensity modulated arc therapy (IMAT).

Intelligence-guided beam angle optimization in treatment planning of intensity-modulated radiation therapy

An intelligence guided approach based on fuzzy inference system (FIS) was proposed to automate beam angle optimization in treatment planning of intensity-modulated radiation therapy (IMRT). The model of FIS is built on inference rules in describing the relationship between dose quality of IMRT plan and irradiated region of anatomical structure. Dose quality of IMRT plan is quantified by the difference between calculated and constraint doses of the anatomical structures in an IMRT plan. Irradiated region of anatomical structure is characterized by the metric, covered region of interest, which is the region of an anatomical structure under radiation field while beam's eye-view is conform to target volume. Initially, an IMRT plan is created with a single beam. The dose difference is calculated for the input of FIS and the output of FIS is obtained with processing of fuzzy inference. Later, a set of candidate beams is generated for replacing the current beam. This process continues until no candidate beams is found. Then the next beam is added to the IMRT plan and optimized in the same way as the previous beam. The new beam keeps adding to the IMRT plan until the allowed beam number is reached. Two spinal cases were investigated in this study. The preliminary results show that dose quality of IMRT plans achieved by this approach is better than those achieved by the default approach with equally spaced beam setting. It is effective to find the optimal beam combination of IMRT plan with the intelligence-guided approach.

Automatic learning-based beam angle selection for thoracic IMRT

PURPOSE

The treatment of thoracic cancer using external beam radiation requires an optimal selection of the radiation beam directions to ensure effective coverage of the target volume and to avoid unnecessary treatment of normal healthy tissues. Intensity modulated radiation therapy (IMRT) planning is a lengthy process, which requires the planner to iterate between choosing beam angles, specifying dose-volume objectives and executing IMRT optimization. In thorax treatment planning, where there are no class solutions for beam placement, beam angle selection is performed manually, based on the planner's clinical experience. The purpose of this work is to propose and study a computationally efficient framework that utilizes machine learning to automatically select treatment beam angles. Such a framework may be helpful for reducing the overall planning workload.

METHODS

The authors introduce an automated beam selection method, based on learning the relationships between beam angles and anatomical features. Using a large set of clinically approved IMRT plans, a random forest regression algorithm is trained to map a multitude of anatomical features into an individual beam score. An optimization scheme is then built to select and adjust the beam angles, considering the learned interbeam dependencies. The validity and quality of the automatically selected beams evaluated using the manually selected beams from the corresponding clinical plans as the ground truth.

RESULTS

The analysis included 149 clinically approved thoracic IMRT plans. For a randomly selected test subset of 27 plans, IMRT plans were generated using automatically selected beams and compared to the clinical plans. The comparison of the predicted and the clinical beam angles demonstrated a good average correspondence between the two (angular distance 16.8° ± 10°, correlation 0.75 ± 0.2). The dose distributions of the semiautomatic and clinical plans were equivalent in terms of primary target volume coverage and organ at risk sparing and were superior over plans produced with fixed sets of common beam angles. The great majority of the automatic plans (93%) were approved as clinically acceptable by three radiation therapy specialists.

CONCLUSIONS

The results demonstrated the feasibility of utilizing a learning-based approach for automatic selection of beam angles in thoracic IMRT planning. The proposed method may assist in reducing the manual planning workload, while sustaining plan quality.

A modular approach to intensity-modulated arc therapy optimization with noncoplanar trajectories

Utilizing noncoplanar beam angles in volumetric modulated arc therapy (VMAT) has the potential to combine the benefits of arc therapy, such as short treatment times, with the benefits of noncoplanar intensity modulated radiotherapy (IMRT) plans, such as improved organ sparing. Recently, vendors introduced treatment machines that allow for simultaneous couch and gantry motion during beam delivery to make noncoplanar VMAT treatments possible. Our aim is to provide a reliable optimization method for noncoplanar isocentric arc therapy plan optimization. The proposed solution is modular in the sense that it can incorporate different existing beam angle selection and coplanar arc therapy optimization methods. Treatment planning is performed in three steps. First, a number of promising noncoplanar beam directions are selected using an iterative beam selection heuristic; these beams serve as anchor points of the arc therapy trajectory. In the second step, continuous gantry/couch angle trajectories are optimized using a simple combinatorial optimization model to define a beam trajectory that efficiently visits each of the anchor points. Treatment time is controlled by limiting the time the beam needs to trace the prescribed trajectory. In the third and final step, an optimal arc therapy plan is found along the prescribed beam trajectory. In principle any existing arc therapy optimization method could be incorporated into this step; for this work we use a sliding window VMAT algorithm. The approach is demonstrated using two particularly challenging cases. The first one is a lung SBRT patient whose planning goals could not be satisfied with fewer than nine noncoplanar IMRT fields when the patient was treated in the clinic. The second one is a brain tumor patient, where the target volume overlaps with the optic nerves and the chiasm and it is directly adjacent to the brainstem. Both cases illustrate that the large number of angles utilized by isocentric noncoplanar VMAT plans can help improve dose conformity, homogeneity, and organ sparing simultaneously using the same beam trajectory length and delivery time as a coplanar VMAT plan.

Standardized beam bouquets for lung IMRT planning

The selection of the incident angles of the treatment beams is a critical component of intensity modulated radiation therapy (IMRT) planning for lung cancer due to significant variations in tumor location, tumor size and patient anatomy. We investigate the feasibility of establishing a small set of standardized beam bouquets for planning. The set of beam bouquets were determined by learning the beam configuration features from 60 clinical lung IMRT plans designed by experienced planners. A k-medoids cluster analysis method was used to classify the beam configurations in the dataset. The appropriate number of clusters was determined by maximizing the value of average silhouette width of the classification. Once the number of clusters had been determined, the beam arrangements in each medoid of the clusters were designated as the standardized beam bouquet for the cluster. This standardized bouquet set was used to re-plan 20 cases randomly selected from the clinical database. The dosimetric quality of the plans using the beam bouquets was evaluated against the corresponding clinical plans by a paired t-test. The classification with six clusters has the largest average silhouette width value and hence would best represent the beam bouquet patterns in the dataset. The results shows that plans generated with a small number of standardized bouquets (e.g. 6) have comparable quality to that of clinical plans. These standardized beam configuration bouquets will potentially help improve plan efficiency and facilitate automated planning.

Trajectory optimization for dynamic couch rotation during volumetric modulated arc radiotherapy

Non-coplanar radiation beams are often used in three-dimensional conformal and intensity modulated radiotherapy to reduce dose to organs at risk (OAR) by geometric avoidance. In volumetric modulated arc radiotherapy (VMAT) non-coplanar geometries are generally achieved by applying patient couch rotations to single or multiple full or partial arcs. This paper presents a trajectory optimization method for a non-coplanar technique, dynamic couch rotation during VMAT (DCR–VMAT), which combines ray tracing with a graph search algorithm. Four clinical test cases (partial breast, brain, prostate only, and prostate and pelvic nodes) were used to evaluate the potential OAR sparing for trajectory-optimized DCR–VMAT plans, compared with standard coplanar VMAT. In each case, ray tracing was performed and a cost map reflecting the number of OAR voxels intersected for each potential source position was generated. The least-cost path through the cost map, corresponding to an optimal DCR–VMAT trajectory, was determined using Dijkstra's algorithm. Results show that trajectory optimization can reduce dose to specified OARs for plans otherwise comparable to conventional coplanar VMAT techniques. For the partial breast case, the mean heart dose was reduced by 53%. In the brain case, the maximum lens doses were reduced by 61% (left) and 77% (right) and the globes by 37% (left) and 40% (right). Bowel mean dose was reduced by 15% in the prostate only case. For the prostate and pelvic nodes case, the bowel V50 Gy and V60 Gy were reduced by 9% and 45% respectively. Future work will involve further development of the algorithm and assessment of its performance over a larger number of cases in site-specific cohorts.

Comparison of beam angle selection strategies for intracranial IMRT

PURPOSE

Various strategies to select beneficial beam ensembles for intensity-modulated radiation therapy (IMRT) have been suggested over the years. These beam angle selection (BAS) strategies are usually evaluated against reference configurations applying equispaced coplanar beams but they are not compared to one another. Here, the authors present a meta analysis of four BAS strategies that incorporates fluence optimization (FO) into BAS by combinatorial optimization (CO) and one BAS strategy that decouples FO from BAS, i.e., spherical cluster analysis (SCA). The underlying parameters of the BAS process are investigated and the dosimetric benefits of the BAS strategies are quantified.

METHODS

For three intracranial lesions in proximity to organs at risk (OARs) the authors compare treatment plans applying equispaced coplanar beam ensembles with treatment plans using five different BAS strategies, i.e., four CO techniques and SCA, to establish coplanar and noncoplanar beam ensembles. Treatment plans applying 5, 7, 9, and 11 beams are investigated. For the CO strategies the authors perform BAS runs with a 5°, 10°, 15°, and 20° angular resolution, which corresponds to a minimum of 18 coplanar and a maximum of 1400 noncoplanar candidate beams. In total 272 treatment plans with different BAS settings are generated for every patient. The quality of the treatment plans is compared based on the protection of OARs yet integral dose, target homogeneity, and target conformity are also considered.

RESULTS

It is possible to reduce the average mean and maximum doses in OARs by more than 4 Gy (1 Gy) with optimized noncoplanar (coplanar) beam ensembles found with BAS by CO or SCA. For BAS including FO by CO, the individual algorithm used and the angular resolution in the space of candidate beams does not have a crucial impact on the quality of the resulting treatment plans. All CO algorithms yield similar target conformity and slightly improved target homogeneity in comparison to equispaced coplanar setups. Furthermore, optimized coplanar (noncoplanar) beam ensembles enabled more than a 6% (5%) reduction of the integral dose. For SCA, however, integral dose was increased and target conformity was decreased in comparison to equispaced coplanar setups-especially for a small number of beams.

CONCLUSION

Both BAS strategies incorporating FO by CO and independent BAS strategies excluding FO provide dose savings in OARs for optimized coplanar and especially noncoplanar beam ensembles; they should not be neglected in the clinic.

Uncertainty incorporated beam angle optimization for IMPT treatment planning

PURPOSE

Beam angle optimization (BAO) by far remains an important and challenging problem in external beam radiation therapy treatment planning. Conventional BAO algorithms discussed in previous studies all focused on photon-based therapies. Impact of BAO on proton therapy is important while proton therapy increasingly receives great interests. This study focuses on potential benefits of BAO on intensity-modulated proton therapy (IMPT) that recently began available to clinical cancer treatment.

METHODS

The authors have developed a novel uncertainty incorporated BAO algorithm for IMPT treatment planning in that IMPT plan quality is highly sensitive to uncertainties such as proton range and setup errors. A linear programming was used to optimize robust intensity maps to scenario-based uncertainties for an incident beam angle configuration. Unlike conventional intensity-modulated radiation therapy with photons (IMXT), the search space for IMPT treatment beam angles may be relatively small but optimizing an IMPT plan may require higher computational costs due to larger data size. Therefore, a deterministic local neighborhood search algorithm that only needs a very limited number of plan objective evaluations was used to optimize beam angles in IMPT treatment planning.

RESULTS

Three prostate cancer cases and two skull base chordoma cases were studied to demonstrate the dosimetric advantages and robustness of optimized beam angles from the proposed BAO algorithm. Two- to four-beam plans were optimized for prostate cases, and two- and three-beam plans were optimized for skull base cases. By comparing plans with conventional two parallel-opposed angles, all plans with optimized angles consistently improved sparing at organs at risks, i.e., rectum and femoral heads for prostate, brainstem for skull base, in either nominal dose distribution or uncertainty-based dose distributions. The efficiency of the BAO algorithm was demonstrated by comparing it with alternative methods including simulated annealing and genetic algorithm. The numbers of IMPT plan objective evaluations required were reduced by up to a factor of 5 while the same optimal angle plans were converged in selected comparisons.

CONCLUSIONS

Uncertainty incorporated BAO may introduce pronounced improvement of IMPT plan quality including dosimetric benefits and robustness over uncertainties, based on the five clinical studies in this paper. In addition, local search algorithms may be more efficient in finding optimal beam angles than global optimization approaches for IMPT BAO.

Characterizing the combinatorial beam angle selection problem

The beam angle selection (BAS) problem in intensity-modulated radiation therapy is often interpreted as a combinatorial optimization problem, i.e. finding the best combination of η beams in a discrete set of candidate beams. It is well established that the combinatorial BAS problem may be solved efficiently with metaheuristics such as simulated annealing or genetic algorithms. However, the underlying parameters of the optimization process, such as the inclusion of non-coplanar candidate beams, the angular resolution in the space of candidate beams, and the number of evaluated beam ensembles as well as the relative performance of different metaheuristics have not yet been systematically investigated. We study these open questions in a meta-analysis of four strategies for combinatorial optimization in order to provide a reference for future research related to the BAS problem in intensity-modulated radiation therapy treatment planning. We introduce a high-performance inverse planning engine for BAS. It performs a full fluence optimization for ≈3600 treatment plans per hour while handling up to 50 GB of dose influence data (≈1400 candidate beams). For three head and neck patients, we compare the relative performance of a genetic, a cross-entropy, a simulated annealing and a naive iterative algorithm. The selection of ensembles with 5, 7, 9 and 11 beams considering either only coplanar or all feasible candidate beams is studied for an angular resolution of 5°, 10°, 15° and 20° in the space of candidate beams. The impact of different convergence criteria is investigated in comparison to a fixed termination after the evaluation of 10 000 beam ensembles. In total, our simulations comprise a full fluence optimization for about 3000 000 treatment plans. All four combinatorial BAS strategies yield significant improvements of the objective function value and of the corresponding dose distributions compared to standard beam configurations with equi-spaced coplanar beams. The genetic and the cross-entropy algorithms showed faster convergence in the very beginning of the optimization but the simulated annealing algorithm eventually arrived at almost the same objective function values. These three strategies typically yield clinically equivalent treatment plans. The iterative algorithm showed the worst convergence properties. The choice of the termination criterion had a stronger influence on the performance of the simulated annealing algorithm than on the performance of the genetic and the cross-entropy algorithms. We advocate to terminate the optimization process after the evaluation of 1000 beam combinations without objective function decrease. For our simulations, this resulted in an average deviation of the objective function from the reference value after 10 000 evaluated beam ensembles of 0.5% for all metaheuristics. On average, there was only a minor improvement when increasing the angular resolution in the space of candidate beam angles from 20° to 5°. However, we observed significant improvements when considering non-coplanar candidate beams for challenging head and neck cases.

Dose optimization with first-order total-variation minimization for dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT)

PURPOSE

A new treatment scheme coined as dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT) has recently been proposed to bridge the gap between IMRT and VMAT. By increasing the angular sampling of radiation beams while eliminating dispensable segments of the incident fields, DASSIM-RT is capable of providing improved conformity in dose distributions while maintaining high delivery efficiency. The fact that DASSIM-RT utilizes a large number of incident beams represents a major computational challenge for the clinical applications of this powerful treatment scheme. The purpose of this work is to provide a practical solution to the DASSIM-RT inverse planning problem.

METHODS

The inverse planning problem is formulated as a fluence-map optimization problem with total-variation (TV) minimization. A newly released L1-solver, template for first-order conic solver (TFOCS), was adopted in this work. TFOCS achieves faster convergence with less memory usage as compared with conventional quadratic programming (QP) for the TV form through the effective use of conic forms, dual-variable updates, and optimal first-order approaches. As such, it is tailored to specifically address the computational challenges of large-scale optimization in DASSIM-RT inverse planning. Two clinical cases (a prostate and a head and neck case) are used to evaluate the effectiveness and efficiency of the proposed planning technique. DASSIM-RT plans with 15 and 30 beams are compared with conventional IMRT plans with 7 beams in terms of plan quality and delivery efficiency, which are quantified by conformation number (CN), the total number of segments and modulation index, respectively. For optimization efficiency, the QP-based approach was compared with the proposed algorithm for the DASSIM-RT plans with 15 beams for both cases.

RESULTS

Plan quality improves with an increasing number of incident beams, while the total number of segments is maintained to be about the same in both cases. For the prostate patient, the conformation number to the target was 0.7509, 0.7565, and 0.7611 with 80 segments for IMRT with 7 beams, and DASSIM-RT with 15 and 30 beams, respectively. For the head and neck (HN) patient with a complicated target shape, conformation numbers of the three treatment plans were 0.7554, 0.7758, and 0.7819 with 75 segments for all beam configurations. With respect to the dose sparing to the critical structures, the organs such as the femoral heads in the prostate case and the brainstem and spinal cord in the HN case were better protected with DASSIM-RT. For both cases, the delivery efficiency has been greatly improved as the beam angular sampling increases with the similar or better conformal dose distribution. Compared with conventional quadratic programming approaches, first-order TFOCS-based optimization achieves far faster convergence and smaller memory requirements in DASSIM-RT.

CONCLUSIONS

The new optimization algorithm TFOCS provides a practical and timely solution to the DASSIM-RT or other inverse planning problem requiring large memory space. The new treatment scheme is shown to outperform conventional IMRT in terms of dose conformity to both the targetand the critical structures, while maintaining high delivery efficiency.

Unsupervised clustering of multivariate circular data

In this paper, we study an unsupervised clustering problem. The originality of this problem lies in the data, which consist of the positions of five separate X-ray beams on a circle. Radiation therapists positioned the five X-ray beam 'projectors' around each patient on a predefined circle. However, similarities exist in positioning for certain groups of patients, and we aim to describe these similarities with the goal of creating pre-adjustment settings that could help save time during X-ray positioning. We therefore performed unsupervised clustering of observed X-ray positions. Because the data for each patient consist of five angle measurements, Euclidean distances are not appropriated. Furthermore, we cannot perform k-means algorithm, usually used for minimizing corresponding distortion because we cannot calculate centers of clusters. We present here solutions to these problems. First, we define a suitable distance on the circle. Then, we adapt an algorithm based on simulated annealing to minimize distortion. This algorithm is shown to be theoretically convergent. Finally, we present simulations on simulated and real data.

How important is dosimetrist experience for intensity modulated radiation therapy? A comparative analysis of a head and neck case

PURPOSE

Treatment planning for IMRT is a complex process that requires additional training and expertise. The aim of this study was to compare and analyze IMRT plans generated by dosimetrists with varying levels of IMRT planning experience.

METHODS AND MATERIALS

The computed tomography (CT) data of a patient previously treated with IMRT for left tonsillar carcinoma were used. The patient's preexisting planning target volumes (PTVs) and all organs at risk were provided with the CT data set. Six dosimetrists with variable IMRT planning experience generated IMRT plans according to the department's protocol. Plan analysis included visual inspection and comparison of dose-volume histogram, conformity indices, treatment delivery efficiency, and dose delivery accuracy.

RESULTS

Visual review of the dose distribution showed that the 6 plans were comparable. However, only the 2 most experienced dosimetrists were able to meet the strict PTV aims and critical structure constraints. The least experienced dosimetrist had the worst planning outcome. Comparison of delivery efficiency showed that the number of segments, total monitor units, and treatment time increased as the IMRT planning experience decreased.

CONCLUSIONS

Dosimetrists with higher levels of IMRT planning experience produced a better quality head and neck IMRT plan. Different planning experience may need to be considered when organizing appropriate departmental resources.

Feasibility of non-coplanar tomotherapy for lung cancer stereotactic body radiation therapy

To quantify the dosimetric gains from non-coplanar helical tomotherapy (HT) arcs for stereotactic body radiation therapy (SBRT) of lung cancer, we created oblique helical arcs by rotating patient's CT images. Ten, 20 and 30 degrees of yaws were introduced in the treatment planning for a patient with a hypothetical lung tumor at the upper, middle and lower portion of the right lung, and the upper and middle left lung. The planning target volume (PTV) was 43 cm(3). 60 Gy was prescribed to the PTV. Dose to organs at risk (OARs), which included the lungs, heart, spinal cord and chest wall, was optimized using a 2.5 cm jaw, 0.287 pitch and modulation factor of 2.5. Composite plans were generated by dose summation of the resultant plans. These plans were evaluated for its conformity index (R(x)) and percentile volume of lung receiving radiation dose of x Gy (V(x)). Conformity index was defined by the ratio of x percent isodose volume and PTV. The results show that combination of non-coplanar arcs reduced R(50) by 4.5%, R(20) by 26% and R(10) by 30% on average. Non-coplanar arcs did not affect V(20) but reduced V(10) and V(5) by 10% and 24% respectively. Composite of the non-coplanar arcs also reduced maximum dose to the spinal cord by 20-39%. Volume of chest wall receiving higher than 30 Gy was reduced by 48% on average. Heart dose reduction was dependent on the location of the PTV and the choice of non-coplanar orientations. Therefore we conclude that non-coplanar HT arcs significantly improve critical organ sparing in lung SBRT without changing the PTV dose coverage.

Knowledge-based IMRT treatment planning for prostate cancer

PURPOSE

To demonstrate the feasibility of using a knowledge base of prior treatment plans to generate new prostate intensity modulated radiation therapy (IMRT) plans. Each new case would be matched against others in the knowledge base. Once the best match is identified, that clinically approved plan is used to generate the new plan.

METHODS

A database of 100 prostate IMRT treatment plans was assembled into an information-theoretic system. An algorithm based on mutual information was implemented to identify similar patient cases by matching 2D beam's eye view projections of contours. Ten randomly selected query cases were each matched with the most similar case from the database of prior clinically approved plans. Treatment parameters from the matched case were used to develop new treatment plans. A comparison of the differences in the dose-volume histograms between the new and the original treatment plans were analyzed.

RESULTS

On average, the new knowledge-based plan is capable of achieving very comparable planning target volume coverage as the original plan, to within 2% as evaluated for D98, D95, and D1. Similarly, the dose to the rectum and dose to the bladder are also comparable to the original plan. For the rectum, the mean and standard deviation of the dose percentage differences for D20, D30, and D50 are 1.8% +/- 8.5%, -2.5% +/- 13.9%, and -13.9% +/- 23.6%, respectively. For the bladder, the mean and standard deviation of the dose percentage differences for D20, D30, and D50 are -5.9% +/- 10.8%, -12.2% +/- 14.6%, and -24.9% +/- 21.2%, respectively. A negative percentage difference indicates that the new plan has greater dose sparing as compared to the original plan.

CONCLUSIONS

The authors demonstrate a knowledge-based approach of using prior clinically approved treatment plans to generate clinically acceptable treatment plans of high quality. This semiautomated approach has the potential to improve the efficiency of the treatment planning process while ensuring that high quality plans are developed.

Optimization of beam angles for intensity modulated radiation therapy treatment planning using genetic algorithm on a distributed computing platform

Planning intensity modulated radiation therapy (IMRT) treatment involves selection of several angle parameters as well as specification of structures and constraints employed in the optimization process. Including these parameters in the combinatorial search space vastly increases the computational burden, and therefore the parameter selection is normally performed manually by a clinician, based on clinical experience. We have investigated the use of a genetic algorithm (GA) and distributed-computing platform to optimize the gantry angle parameters and provide insight into additional structures, which may be necessary, in the dose optimization process to produce optimal IMRT treatment plans. For an IMRT prostate patient, we produced the first generation of 40 samples, each of five gantry angles, by selecting from a uniform random distribution, subject to certain adjacency and opposition constraints. Dose optimization was performed by distributing the 40-plan workload over several machines running a commercial treatment planning system. A score was assigned to each resulting plan, based on how well it satisfied clinically-relevant constraints. The second generation of 40 samples was produced by combining the highest-scoring samples using techniques of crossover and mutation. The process was repeated until the sixth generation, and the results compared with a clinical (equally-spaced) gantry angle configuration. In the sixth generation, 34 of the 40 GA samples achieved better scores than the clinical plan, with the best plan showing an improvement of 84%. Moreover, the resulting configuration of beam angles tended to cluster toward the patient's sides, indicating where the inclusion of additional structures in the dose optimization process may avoid dose hot spots. Additional parameter selection in IMRT leads to a large-scale computational problem. We have demonstrated that the GA combined with a distributed-computing platform can be applied to optimize gantry angle selection within a reasonable amount of time.

Intensity-modulated arc therapy for pediatric posterior fossa tumors

PURPOSE

To compare intensity-modulated arc therapy (IMAT) to noncoplanar intensity-modulated radiation therapy (IMRT) in the treatment of pediatric posterior fossa tumors.

METHODS AND MATERIALS

Nine pediatric patients with posterior fossa tumors, mean age 9 years (range, 6-15 years), treated using IMRT were chosen for this comparative planning study because of their tumor location. Each patient's treatment was replanned to receive 54 Gy to the planning target volume (PTV) using five different methods: eight-field noncoplanar IMRT, single coplanar IMAT, double coplanar IMAT, single noncoplanar IMAT, and double noncoplanar IMAT. For each method, the dose to 95% of the PTV was held constant, and the doses to surrounding critical structures were minimized. The different plans were compared based on conformity, total linear accelerator dose monitor units, and dose to surrounding normal tissues, including the entire body, whole brain, temporal lobes, brainstem, and cochleae.

RESULTS

The doses to the target and critical structures for the various IMAT methods were not statistically different in comparison with the noncoplanar IMRT plan, with the following exceptions: the cochlear doses were higher and whole brain dose was lower for coplanar IMAT plans; the cochleae and temporal lobe doses were lower and conformity increased for noncoplanar IMAT plans. The advantage of the noncoplanar IMAT plan was enhanced by doubling the treatment arc.

CONCLUSION

Noncoplanar IMAT results in superior treatment plans when compared to noncoplanar IMRT for the treatment of posterior fossa tumors. IMAT should be considered alongside IMRT when treatment of this site is indicated.

An algorithm for fast beam angle selection in intensity modulated radiotherapy

PURPOSE

This article aims to introduce a novel algorithm for fast beam angle selection in intensity modulated radiotherapy (IMRT).

METHODS

The algorithm models the optimization problem as a beam angle ranking problem and chooses suitable beam angles according to their rank. A new parameter called "beam intensity profile perturbation score (BIPPS)" is used for ranking the beam angles. The BIPPS-based beam angle ranking implicitly accounts for the dose-volume effects of the involved structures. A simulated phantom case with obvious optimal beam angles is used to verify the validity of the presented technique. In addition, the efficiency of the algorithm was examined in three clinical cases (prostate, pancreas, and head and neck) in terms of DVH and dose distribution. In all cases, the judgment of the algorithm's efficiency was based on the comparison between plans with equidistant beams (equal-angle-plan) and plans with beams obtained using the algorithm (suitable-angle-plan).

RESULTS

It is observed from the study that the beam angle ranking function over BIPPS instantly picks up a suitable set of beam angles for a specific case. It takes only about 15 min for choosing the suitable beam angles even for the most complicated cases. The DVHs and dose distributions confirm that the proposed algorithm can efficiently reduce the mean or maximum dose to OARs, while guaranteeing the target coverage and dose uniformity. On the average, about 17% reduction in the mean dose to critical organs, such as rectum, bladder, kidneys and parotids, is observed. Also, about 12% (averaged) reduction in the maximum dose to critical organs (spinal cord) is observed in the clinical cases presented in this study.

CONCLUSIONS

This study demonstrates that the algorithm can be effectively applied to IMRT scenarios to get fast and case specific beam angle configurations.

Spherical cluster analysis for beam angle optimization in intensity-modulated radiation therapy treatment planning

An intuitive heuristic to establish beam configurations for intensity-modulated radiation therapy is introduced as an extension of beam ensemble selection strategies applying scalar scoring functions. It is validated by treatment plan comparisons for three intra-cranial, pancreas, and prostate cases each. Based on a patient specific matrix listing the radiological quality of candidate beam directions individually for every target voxel, a set of locally ideal beam angles is generated. The spherical distribution of locally ideal beam angles is characteristic for every treatment site and patient: ideal beam angles typically cluster around distinct orientations. We interpret the cluster centroids, which are identified with a spherical K-means algorithm, as irradiation angles of an intensity-modulated radiation therapy treatment plan. The fluence profiles are subsequently optimized during a conventional inverse planning process. The average computation time for the pre-optimization of a beam ensemble is six minutes on a state-of-the-art work station. The treatment planning study demonstrates the potential benefit of the proposed beam angle optimization strategy. For the three prostate cases under investigation, the standard treatment plans applying nine coplanar equi-spaced beams and treatment plans applying an optimized non-coplanar nine-beam ensemble yield clinically comparable dose distributions. For symmetric patient geometries, the dose distribution formed by nine equi-spaced coplanar beams cannot be improved significantly. For the three pancreas and intra-cranial cases under investigation, the optimized non-coplanar beam ensembles enable better sparing of organs at risk while guaranteeing equivalent target coverage. Beam angle optimization by spherical cluster analysis shows the biggest impact for target volumes located asymmetrically within the patient and close to organs at risk.

Dosimetric comparison between 3D conformal and intensity-modulated radiation therapy for prostate cancer

Background and Purpose: Intensity-modulated radiation therapy (IMRT) is considered by many to be the standard of care in the delivery of external-beam radiotherapy treatments to the prostate. The purpose of this study is to assess the validity of the purported benefits of IMRT.

Materials and Methods: Treatment plans were produced for 10 patients using both 3D conformal radiation therapy (3D-CRT) and IMRT, utilising the dose constraints recommended by the Radiation Therapy Oncology Group (RTOG) 0415 protocol. Three IMRT modalities used in this study were linear accelerator based IMRT, helical tomotherapy, and serial tomotherapy. The prescription to the target, 76 Gy, was the same for all plans.

Results: In general the 3D-CRT plans satisfied the RTOG criteria for planning target volume (PTV) coverage, and met or bettered the dose criteria for the organs at risk. PTV coverage was more homogeneous for the IMRT plans than the 3D-CRT plans but not significantly improved.

Conclusions: Technically, because the IMRT plans required greater effort for the optimisation, longer treatment times and higher monitor units, the use of IMRT for the fulfilment of the protocol’s dosimetric goals was not justified using these constraints.