Deterministic direct aperture optimization using multiphase piecewise constant segmentation

A hybrid column generation and simulated annealing algorithm for direct aperture optimization

The purpose of this work was to develop a hybrid column generation (CG) and simulated annealing (SA) algorithm for direct aperture optimization (H-DAO) and to show its effectiveness in generating high quality treatment plans for intensity modulated radiation therapy (IMRT) and mixed photon-electron beam radiotherapy (MBRT). The H-DAO overcomes limitations of the CG-DAO with two features improving aperture selection (branch-feature) and enabling aperture shape changes during optimization (SA-feature). The H-DAO algorithm iteratively adds apertures to the plan. At each iteration, a branch is created for each field provided. First, each branch determines the most promising aperture of its assigned field and adds it to a copy of the current apertures. Afterwards, the apertures of each branch undergo an MU-weight optimization followed by an SA-based simultaneous shape and MU-weight optimization and a second MU-weight optimization. The next H-DAO iteration continues the branch with the lowest objective function value. IMRT and MBRT treatment plans for an academic, a brain and a head and neck case generated using the CG-DAO and H-DAO were compared. For every investigated case and both IMRT and MBRT, the H-DAO leads to a faster convergence of the objective function value with number of apertures compared to the CG-DAO. In particular, the H-DAO needs about half the apertures to reach the same objective function value as the CG-DAO. The average aperture areas are 27% smaller for H-DAO than for CG-DAO leading to a slightly larger discrepancy between optimized and final dose. However, a dosimetric benefit remains. The H-DAO was successfully developed and applied to IMRT and MBRT. The faster convergence with number of apertures of the H-DAO compared to the CG-DAO allows to select a better compromise between plan quality and number of apertures.

Reformulated McNamara RBE-weighted beam orientation optimization for intensity modulated proton therapy

PURPOSE

Empirical relative biological effectiveness (RBE) models have been used to estimate the biological dose in proton therapy but do not adequately capture the factors influencing RBE values for treatment planning. We reformulate the McNamara RBE model such that it can be added as a linear biological dose fidelity term within our previously developed sensitivity-regularized and heterogeneity-weighted beam orientation optimization (SHBOO) framework.

METHODS

Based on our SHBOO framework, we formulated the biological optimization problem to minimize total McNamara RBE dose to OARs. We solve this problem using two optimization algorithms: FISTA (McNam-FISTA) and Chambolle-Pock (McNam-CP). We compare their performances with a physical dose optimizer assuming RBE = 1.1 in all structures (PHYS-FISTA) and an LET-weighted dose model (LET-FISTA). Three head and neck patients were planned with the four techniques and compared on dosimetry and robustness.

RESULTS

Compared to Phys-FISTA, McNam-CP was able to match CTV [HI, Dmax, D95%, D98%] by [0.00, 0.05%, 1.4%, 0.8%]. McNam-FISTA and McNam-CP were able to significantly improve overall OAR [Dmean, Dmax] by an average of [36.1%,26.4%] and [29.6%, 20.3%], respectively. Regarding CTV robustness, worst [Dmax, V95%, D95%, D98%] improvement of [-6.6%, 6.2%, 6.0%, 4.8%] was reported for McNam-FISTA and [2.7%, 2.7%, 5.3%, -4.3%] for McNam-CP under combinations of range and setup uncertainties. For OARs, worst [Dmax, Dmean] were improved by McNam-FISTA and McNam-CP by an average of [25.0%, 19.2%] and [29.5%, 36.5%], respectively. McNam-FISTA considerably improved dosimetry and CTV robustness compared to LET-FISTA, which achieved better worst-case OAR doses.

CONCLUSION

The four optimization techniques deliver comparable biological doses for the head and neck cases. Besides modest CTV coverage and robustness improvement, OAR biological dose and robustness were substantially improved with both McNam-FISTA and McNam-CP, showing potential benefit for directly incorporating McNamara RBE in proton treatment planning.

Dose prediction with deep learning for prostate cancer radiation therapy: Model adaptation to different treatment planning practices

PURPOSE

This work aims to study the generalizability of a pre-developed deep learning (DL) dose prediction model for volumetric modulated arc therapy (VMAT) for prostate cancer and to adapt the model, via transfer learning with minimal input data, to three different internal treatment planning styles and one external institution planning style.

METHODS

We built the source model with planning data from 108 patients previously treated with VMAT for prostate cancer. For the transfer learning, we selected patient cases planned with three different styles, 14-29 cases per style, in the same institution and 20 cases treated in a different institution to adapt the source model to four target models in total. We compared the dose distributions predicted by the source model and the target models with the corresponding clinical plan dose used for patient treatments and quantified the improvement in the prediction quality for the target models over the source model using the Dice similarity coefficients (DSC) of 0% to 100% isodose volumes and the dose-volume-histogram (DVH) parameters of the planning target volume and the organs-at-risk.

RESULTS

The source model accurately predicts dose distributions for plans generated in the same source style, but performs sub-optimally for the three different internal and one external target styles, with the mean DSC ranging between 0.81-0.94 and 0.82-0.91 for the internal and the external styles, respectively. With transfer learning, the target model predictions improved the mean DSC to 0.88-0.95 and 0.92-0.96 for the internal and the external styles, respectively. Target model predictions significantly improved the accuracy of the DVH parameter predictions to within 1.6%.

CONCLUSION

We demonstrated the problem of model generalizability for DL-based dose prediction and the feasibility of using transfer learning to solve this problem. With 14-29 cases per style, we successfully adapted the source model into several different practice styles. This indicates a realistic way forward to widespread clinical implementation of DL-based dose prediction.

Using deep learning to predict beam-tunable Pareto optimal dose distribution for intensity-modulated radiation therapy

PURPOSE

Many researchers have developed deep learning models for predicting clinical dose distributions and Pareto optimal dose distributions. Models for predicting Pareto optimal dose distributions have generated optimal plans in real time using anatomical structures and static beam orientations. However, Pareto optimal dose prediction for intensity-modulated radiation therapy (IMRT) prostate planning with variable beam numbers and orientations has not yet been investigated. We propose to develop a deep learning model that can predict Pareto optimal dose distributions by using any given set of beam angles, along with patient anatomy, as input to train the deep neural networks. We implement and compare two deep learning networks that predict with two different beam configuration modalities.

METHODS

We generated Pareto optimal plans for 70 patients with prostate cancer. We used fluence map optimization to generate 500 IMRT plans that sampled the Pareto surface for each patient, for a total of 35 000 plans. We studied and compared two different models, Models I and II. Although they both used the same anatomical structures - including the planning target volume (PTV), organs at risk (OARs), and body - these models were designed with two different methods for representing beam angles. Model I directly uses beam angles as a second input to the network as a binary vector. Model II converts the beam angles into beam doses that are conformal to the PTV. We divided the 70 patients into 54 training, 6 validation, and 10 testing patients, thus yielding 27 000 training, 3000 validation, and 5000 testing plans. Mean square loss (MSE) was taken as the loss function. We used the Adam optimizer with a default learning rate of 0.01 to optimize the network's performance. We evaluated the models' performance by comparing their predicted dose distributions with the ground truth (Pareto optimal) dose distribution, in terms of dose volume histogram (DVH) plots and evaluation metrics such as PTV D98 , D95 , D50 , D2 , Dmax , Dmean , Paddick Conformation Number, R50, and Homogeneity index.

RESULTS

Our deep learning models predicted voxel-level dose distributions that precisely matched the ground truth dose distributions. The DVHs generated also precisely matched the ground truth. Evaluation metrics such as PTV statistics, dose conformity, dose spillage (R50), and homogeneity index also confirmed the accuracy of PTV curves on the DVH. Quantitatively, Model I's prediction error of 0.043 (confirmation), 0.043 (homogeneity), 0.327 (R50), 2.80% (D95), 3.90% (D98), 0.6% (D50), and 1.10% (D2) was lower than that of Model II, which obtained 0.076 (confirmation), 0.058 (homogeneity), 0.626 (R50), 7.10% (D95), 6.50% (D98), 8.40% (D50), and 6.30% (D2). Model I also outperformed Model II in terms of the mean dose error and the max dose error on the PTV, bladder, rectum, left femoral head, and right femoral head.

CONCLUSIONS

Treatment planners who use our models will be able to use deep learning to control the trade-offs between the PTV and OAR weights, as well as the beam number and configurations in real time. Our dose prediction methods provide a stepping stone to building automatic IMRT treatment planning.

Incorporating human and learned domain knowledge into training deep neural networks: A differentiable dose-volume histogram and adversarial inspired framework for generating Pareto optimal dose distributions in radiation therapy

PURPOSE

We propose a novel domain-specific loss, which is a differentiable loss function based on the dose-volume histogram (DVH), and combine it with an adversarial loss for the training of deep neural networks. In this study, we trained a neural network for generating Pareto optimal dose distributions, and evaluate the effects of the domain-specific loss on the model performance.

METHODS

In this study, three loss functions - mean squared error (MSE) loss, DVH loss, and adversarial (ADV) loss - were used to train and compare four instances of the neural network model: (a) MSE, (b) MSE + ADV, (c) MSE + DVH, and (d) MSE + DVH+ADV. The data for 70 prostate patients, including the planning target volume (PTV), and the organs at risk (OAR) were acquired as 96 × 96 × 24 dimension arrays at 5 mm3 voxel size. The dose influence arrays were calculated for 70 prostate patients, using a 7 equidistant coplanar beam setup. Using a scalarized multicriteria optimization for intensity-modulated radiation therapy, 1200 Pareto surface plans per patient were generated by pseudo-randomizing the PTV and OAR tradeoff weights. With 70 patients, the total number of plans generated was 84 000 plans. We divided the data into 54 training, 6 validation, and 10 testing patients. Each model was trained for a total of 100,000 iterations, with a batch size of 2. All models used the Adam optimizer, with a learning rate of 1 × 10-3 .

RESULTS

Training for 100 000 iterations took 1.5 days (MSE), 3.5 days (MSE+ADV), 2.3 days (MSE+DVH), and 3.8 days (MSE+DVH+ADV). After training, the prediction time of each model is 0.052 s. Quantitatively, the MSE+DVH+ADV model had the lowest prediction error of 0.038 (conformation), 0.026 (homogeneity), 0.298 (R50), 1.65% (D95), 2.14% (D98), and 2.43% (D99). The MSE model had the worst prediction error of 0.134 (conformation), 0.041 (homogeneity), 0.520 (R50), 3.91% (D95), 4.33% (D98), and 4.60% (D99). For both the mean dose PTV error and the max dose PTV, Body, Bladder and rectum error, the MSE+DVH+ADV outperformed all other models. Regardless of model, all predictions have an average mean and max dose error <2.8% and 4.2%, respectively.

CONCLUSION

The MSE+DVH+ADV model performed the best in these categories, illustrating the importance of both human and learned domain knowledge. Expert human domain-specific knowledge can be the largest driver in the performance improvement, and adversarial learning can be used to further capture nuanced attributes in the data. The real-time prediction capabilities allow for a physician to quickly navigate the tradeoff space for a patient, and produce a dose distribution as a tangible endpoint for the dosimetrist to use for planning. This is expected to considerably reduce the treatment planning time, allowing for clinicians to focus their efforts on the difficult and demanding cases.

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.

A method to reconstruct intra-fractional liver motion in rotational radiotherapy using linear fiducial markers

Complex intra-fractional motion and deformation of the liver significantly impacts the accuracy of delivered dose in radiotherapy. It limits margin reduction, dose escalation and normal tissue sparing. A critical component of motion management is to accurately reconstruct tumor motion. In this study, we developed a six degrees of freedom projection marker matching method (6-DoF PM3) to reconstruct translational and rotational liver tumor motion in a rotational treatment delivery, such as volumetric modulated arc therapy (VMAT). Specifically, we modeled the use of two gold markers implanted in a linear form. The four endpoints of the two gold linear markers were used as tracking surrogates. During delivery, kV x-ray projection images were acquired. A method was developed to automatically identify the 2D marker-endpoints on the projection images. 3D marker positions were determined by solving an optimization problem with the objective function penalizing the distance from the reconstructed 3D position of each fiducial marker endpoint to the corresponding straight line defined by the kV x-ray projection of the endpoints. We performed a series of tests to evaluate different components of the method. For 2D marker endpoints identification, 99.9% of the marker endpoints were identified with an error [Formula: see text] (1 pixel) along both u and v directions. For 3D reconstruction of motion in simulation studies, error of rotational angle was [Formula: see text]° without considering the 2D marker identification error. The rotational angle error was relatively sensitive to the accuracy of 2D marker identification. When the 2D error raised from 0.22 mm to 0.776 mm, the error of 3D rotational angle increased from 0.5° to 2.5°. In the experimental end-to-end tests, the mean root-mean square error of the 3D reconstructed marker positions was 0.75 mm and the mean error of rotational angle was within 1.7°. Our method can accurately determine intra-fractional liver tumor motion in rotational radiotherapy using kV projections of only two linear fiducial markers.

Image reconstruction by Mumford-Shah regularization for low-dose CT with multi-GPU acceleration

Mumford-Shah (MS) functional has emerged as a regularization technique in x-ray computed tomography (CT) recently. However, for high-resolution CT applications, the huge size of both projection data and image leads to an implementation difficulty. In this work, we propose an approach to implement and accelerate MS regularization on a multi-GPU platform to resolve the issue of data size and rich onboard memory and computing units. We have established a novel partition scheme of the 3D volume under reconstruction and corresponding multithread parallel acceleration strategy to fully utilize the computing resource of multi-GPUs. Our implementation is highly modularized and can be easily scaled with the configuration of GPUs. Experiment results with simulation data as well as real data demonstrate a superior reconstruction quality in contrast to the total variation regularization approach, especially for the ultra-low-dose case. Moreover, this is the first time that MS regularization is used for 3D reconstruction of huge images up to 3072³ voxels within 12 min.

A feasibility study for predicting optimal radiation therapy dose distributions of prostate cancer patients from patient anatomy using deep learning

With the advancement of treatment modalities in radiation therapy for cancer patients, outcomes have improved, but at the cost of increased treatment plan complexity and planning time. The accurate prediction of dose distributions would alleviate this issue by guiding clinical plan optimization to save time and maintain high quality plans. We have modified a convolutional deep network model, U-net (originally designed for segmentation purposes), for predicting dose from patient image contours of the planning target volume (PTV) and organs at risk (OAR). We show that, as an example, we are able to accurately predict the dose of intensity-modulated radiation therapy (IMRT) for prostate cancer patients, where the average Dice similarity coefficient is 0.91 when comparing the predicted vs. true isodose volumes between 0% and 100% of the prescription dose. The average value of the absolute differences in [max, mean] dose is found to be under 5% of the prescription dose, specifically for each structure is [1.80%, 1.03%](PTV), [1.94%, 4.22%](Bladder), [1.80%, 0.48%](Body), [3.87%, 1.79%](L Femoral Head), [5.07%, 2.55%](R Femoral Head), and [1.26%, 1.62%](Rectum) of the prescription dose. We thus managed to map a desired radiation dose distribution from a patient's PTV and OAR contours. As an additional advantage, relatively little data was used in the techniques and models described in this paper.