Simultaneous reduction of number of spots and energy layers in intensity modulated proton therapy for rapid spot scanning delivery

BACKGROUND

Reducing proton treatment time improves patient comfort and decreases the risk of error from intrafractional motion, but must be balanced against clinical goals and treatment plan quality.

PURPOSE

To improve the delivery efficiency of spot scanning proton therapy by simultaneously reducing the number of spots and energy layers using the reweightedl 1 $l_1$ regularization method.

METHODS

We formulated the proton treatment planning problem as a convex optimization problem with a cost function consisting of a dosimetric plan quality term plus a weightedl 1 $l_1$ regularization term. We iteratively solved this problem and adaptively updated the regularization weights to promote the sparsity of both the spots and energy layers. The proposed algorithm was tested on four head-and-neck cancer patients, and its performance, in terms of reducing the number of spots and energy layers, was compared with existing standardl 1 $l_1$ and groupl 2 $l_2$ regularization methods. We also compared the effectiveness of the three methods (l 1 $l_1$ , groupl 2 $l_2$ , and reweightedl 1 $l_1$ ) at improving plan delivery efficiency without compromising dosimetric plan quality by constructing each of their Pareto surfaces charting the trade-off between plan delivery and plan quality.

RESULTS

The reweightedl 1 $l_1$ regularization method reduced the number of spots and energy layers by an average over all patients of40 % $40\%$ and35 % $35\%$ , respectively, with an insignificant cost to dosimetric plan quality. From the Pareto surfaces, it is clear that reweightedl 1 $l_1$ provided a better trade-off between plan delivery efficiency and dosimetric plan quality than standardl 1 $l_1$ or groupl 2 $l_2$ regularization, requiring the lowest cost to quality to achieve any given level of delivery efficiency.

CONCLUSIONS

Reweightedl 1 $l_1$ regularization is a powerful method for simultaneously promoting the sparsity of spots and energy layers at a small cost to dosimetric plan quality. This sparsity reduces the time required for spot scanning and energy layer switching, thereby improving the delivery efficiency of proton plans.

Simultaneous Reduction of Number of Spots and Energy Layers in Intensity Modulated Proton Therapy for Rapid Spot Scanning Delivery

Reducing proton treatment time improves patient comfort and decreases the risk of error from intra-fractional motion, but must be balanced against clinical goals and treatment plan quality. We formulated the proton treatment planning problem as a convex optimization problem with a cost function consisting of a dosimetric plan quality term plus a weighted $l_1$ regularization term. We iteratively solved this problem and adaptively updated the regularization weights to promote the sparsity of both the spots and energy layers. The proposed algorithm was tested on four head-and-neck cancer patients, and its performance was compared with existing standard $l_1$ and group $l_2$ regularization methods. We also compared the effectiveness of the three methods ($l_1$, group $l_2$, and reweighted $l_1$) at improving plan delivery efficiency without compromising dosimetric plan quality by constructing each of their Pareto surfaces charting the trade-off between plan delivery and plan quality. The reweighted $l_1$ regularization method reduced the number of spots and energy layers by an average over all patients of 40% and 35%, respectively, with an insignificant cost to dosimetric plan quality. From the Pareto surfaces, it is clear that reweighted $l_1$ provided a better trade-off between plan delivery efficiency and dosimetric plan quality than standard $l_1$ or group $l_2$ regularization, requiring the lowest cost to quality to achieve any given level of delivery efficiency. In summary, reweighted $l_1$ regularization is a powerful method for simultaneously promoting the sparsity of spots and energy layers at a small cost to dosimetric plan quality. This sparsity reduces the time required for spot scanning and energy layer switching, thereby improving the delivery efficiency of proton plans.

Automated planning of stereotactic spine re-irradiation using cumulative dose limits

Background and Purpose

The lack of dedicated tools in commercial planning systems currently restricts efficient review and planning for re-irradiation. The aim of this study was to develop an automated re-irradiation planning framework based on cumulative doses.

Materials and Methods

We performed a retrospective study of 14 patients who received spine SBRT re-irradiation near a previously irradiated treatment site. A fully-automated workflow, DART (Dose Accumulation-based Re-irradiation Tool), was implemented within Eclipse by leveraging a combination of a dose accumulation script and a proprietary automated optimization algorithm. First, we converted the prior treatment dose into equivalent dose in 2 Gy fractions (EQD2) and mapped it to the current anatomy, utilizing deformable image registration. Subsequently, the intersection of EQD2 isodose lines with relevant organs at risk defines a series of optimization structures. During plan optimization, the residual allowable dose at a specified tissue tolerance was treated as a hard constraint.

Results

All DART plans met institutional physical and cumulative constraints and passed plan checks by qualified medical physicists. DART demonstrated significant improvements in target coverage over clinical plans, with an average increase in PTV D99% and V100% of 2.3 Gy [range -0.3-7.7 Gy] and 3.4 % [range -0.4 %-7.6 %] (p < 0.01, paired t-test), respectively. Moreover, high-dose spillage (>105 %) outside the PTV was reduced by up to 7 cm3. The homogeneity index for DART plans was improved by 19 % (p < 0.001).

Conclusions

DART provides a powerful framework to achieve more tailored re-irradiation plans by accounting for dose distributions from the previous treatments. The superior plan quality could improve the therapeutic ratio for re-irradiation patients.

Automated VMAT treatment planning using sequential convex programming: algorithm development and clinical implementation

OBJECTIVE

To develop and clinically implement a fully automated treatment planning system for volumetric modulated arc therapy (VMAT).&#xD;Approach: We solve two constrained optimization problems sequentially. The tumor coverage is maximized at the first step while respecting all maximum/mean dose clinical criteria. The second step further reduces the dose at the surrounding organs-at-risk (OARs) as much as possible. Our algorithm optimizes the machine parameters (leaf positions and monitor units) directly and the resulting mathematical non-convexity is handled using thesequential convex programmingby solving a series of convex approximation problems. We directly integrate two novel convex surrogate metrics to improve plan delivery efficiency and reduce plan complexity by promoting aperture shape regularity and neighboring aperture similarity. The entire workflow is automated using the Eclipse treatment planning system (TPS) application program interface (API) scripting and provided to users as a plug-in, requiring the users to solely provide the contours and their preferred arcs. Our program provides the optimal machine parameters and does not utilize the Eclipse optimization engine, however, it utilizes the Eclipse final dose calculation engine. We have tested our program on 60 patients of different disease sites and prescriptions for stereotactic body radiotherapy (SBRT) (paraspinal (24Gy x 1, 9Gy x 3), oligometastis (9Gy x 3), lung (18Gy x 3, 12Gy x 4)) and retrospectively compared the automated plans with the manual plans used for treatment. The program is currently deployed in our clinic and being used in our daily clinical routine to treat patients. &#xD;Main results: The automated plans found dosimetrically comparable or superior to the manual plans. For paraspinal (24Gy x 1), the automated plans especially improved tumor coverage (the average PTV95% from 96% to 98% and CTV100% from 95% to 97%) and homogeneity (the average PTV maximum dose from 120% to 116%). For other sites/prescriptions, the automated plans especially improved the duty cycle (23%-39.4%).&#xD;Significance: This work proposes a fully automated approach to the mathematically challenging VMAT problem. It also shows how the capabilities of the existing FDA-approved commercial TPS can be enhanced using an in-house developed optimization algorithm that completely replaces the TPS optimization engine. The code and pertained models along with a sample dataset will be released on our ECHO-VMAT GitHub (https://github.com/PortPy-Project/ECHO-VMAT).

Built-in wavelet-induced smoothness to reduce plan complexity in intensity modulated radiation therapy (IMRT)

Objective.Reducing plan complexity in intensity modulated radiation therapy (IMRT) to ensure dosimetric accuracy and delivery efficiency of the radiation treatment plans. We propose a novel approach by representing the beamlet intensities using an incomplete wavelet basis that explicitly excludes fluctuating intensity maps from the decision space (explicit hard constraint). This technique provides a built-in wavelet-induced smoothness that improves both dosimetric plan quality and delivery efficiency.Approach.The beamlet intensity maps need to be especially smooth in the leaf travel direction (referred to as theX-direction). We treat the intensity map of each beam as a 2D image and represent it using the wavelets corresponding to low-frequency changes in theX-direction (i.e. approximation and horizontal). The absence of wavelets corresponding to high-frequency changes (i.e. vertical and diagonal) induces built-in smoothness. We still utilize a regularization term in the objective function to promote smoothness in theY-direction (perpendicular to theX-direction) and further possible smoothness in theX-direction. This technique has been tested on three patient cases of different disease sites (paraspinal, lung, prostate) and all final evaluations and comparisons have been performed on an FDA-approved commercial treatment planning system (Varian Eclipse^TM).Main results.Wavelet-induced smoothness reduced monitor units by about 10%, 45%, and 14% for paraspinal, lung, and prostate cases, respectively. It also improved organ at risk sparing, especially on the complex paraspinal case where it resulted in about 7%, 13%, and 14% less mean dose to esophagus, lung, and cord, respectively. Moreover, built-in wavelet-induced smoothness desensitizes the results to changing the weight associated to the regularization term, and thereby mitigates the weight fine-tuning difficulty.Significance.Fluence smoothness is often achieved by smoothing the beamlet intensity maps using a proper regularization term in the objective function aiming at disincentivizing fluctuation in the beamlet intensities (implicit soft constraint). This work reports a novel application of wavelets in imposing an explicit smoothness hard constraint in the search space using an incomplete wavelet basis. This idea has been successfully applied to exclude complex and clinically irrelevant radiation plans from the search space. The code and pertained models along with a sample dataset are released on our LowDimRT GitHub (https://github.com/PortPy-Project/LowDimRT).

RMSim: controlled respiratory motion simulation on static patient scans

Objective.This work aims to generate realistic anatomical deformations from static patient scans. Specifically, we present a method to generate these deformations/augmentations via deep learning driven respiratory motion simulation that provides the ground truth for validating deformable image registration (DIR) algorithms and driving more accurate deep learning based DIR.Approach.We present a novel 3D Seq2Seq deep learning respiratory motion simulator (RMSim) that learns from 4D-CT images and predicts future breathing phases given a static CT image. The predicted respiratory patterns, represented by time-varying displacement vector fields (DVFs) at different breathing phases, are modulated through auxiliary inputs of 1D breathing traces so that a larger amplitude in the trace results in more significant predicted deformation. Stacked 3D-ConvLSTMs are used to capture the spatial-temporal respiration patterns. Training loss includes a smoothness loss in the DVF and mean-squared error between the predicted and ground truth phase images. A spatial transformer deforms the static CT with the predicted DVF to generate the predicted phase image. 10-phase 4D-CTs of 140 internal patients were used to train and test RMSim. The trained RMSim was then used to augment a public DIR challenge dataset for training VoxelMorph to show the effectiveness of RMSim-generated deformation augmentation.Main results.We validated our RMSim output with both private and public benchmark datasets (healthy and cancer patients). The structure similarity index measure (SSIM) for predicted breathing phases and ground truth 4D CT images was 0.92 ± 0.04, demonstrating RMSim's potential to generate realistic respiratory motion. Moreover, the landmark registration error in a public DIR dataset was improved from 8.12 ± 5.78 mm to 6.58mm ± 6.38 mm using RMSim-augmented training data.Significance.The proposed approach can be used for validating DIR algorithms as well as for patient-specific augmentations to improve deep learning DIR algorithms. The code, pretrained models, and augmented DIR validation datasets will be released athttps://github.com/nadeemlab/SeqX2Y.

Distributed and scalable optimization for robust proton treatment planning

BACKGROUND

The importance of robust proton treatment planning to mitigate the impact of uncertainty is well understood. However, its computational cost grows with the number of uncertainty scenarios, prolonging the treatment planning process.

PURPOSE

We developed a fast and scalable distributed optimization platform that parallelizes the robust proton treatment plan computation over the uncertainty scenarios.

METHODS

We modeled the robust proton treatment planning problem as a weighted least-squares problem. To solve it, we employed an optimization technique called the alternating direction method of multipliers with Barzilai-Borwein step size (ADMM-BB). We reformulated the problem in such a way as to split the main problem into smaller subproblems, one for each proton therapy uncertainty scenario. The subproblems can be solved in parallel, allowing the computational load to be distributed across multiple processors (e.g., CPU threads/cores). We evaluated ADMM-BB on four head-and-neck proton therapy patients, each with 13 scenarios accounting for 3 mm setup and 3.5% range uncertainties. We then compared the performance of ADMM-BB with projected gradient descent (PGD) applied to the same problem.

RESULTS

For each patient, ADMM-BB generated a robust proton treatment plan that satisfied all clinical criteria with comparable or better dosimetric quality than the plan generated by PGD. However, ADMM-BB's total runtime averaged about 6 to 7 times faster. This speedup increased with the number of scenarios.

CONCLUSIONS

ADMM-BB is a powerful distributed optimization method that leverages parallel processing platforms, such as multicore CPUs, GPUs, and cloud servers, to accelerate the computationally intensive work of robust proton treatment planning. This results in (1) a shorter treatment planning process and (2) the ability to consider more uncertainty scenarios, which improves plan quality.

Domain knowledge driven 3D dose prediction using moment-based loss function

Objective. To propose a novel moment-based loss function for predicting 3D dose distribution for the challenging conventional lung intensity modulated radiation therapy plans. The moment-based loss function is convex and differentiable and can easily incorporate clinical dose volume histogram (DVH) domain knowledge in any deep learning (DL) framework without computational overhead. Approach. We used a large dataset of 360 (240 for training, 50 for validation and 70 for testing) conventional lung patients with 2 Gy × 30 fractions to train the DL model using clinically treated plans at our institution. We trained a UNet like convolutional neural network architecture using computed tomography, planning target volume and organ-at-risk contours as input to infer corresponding voxel-wise 3D dose distribution. We evaluated three different loss functions: (1) the popular mean absolute error (MAE) loss, (2) the recently developed MAE + DVH loss, and (3) the proposed MAE + moments loss. The quality of the predictions was compared using different DVH metrics as well as dose-score and DVH-score, recently introduced by the AAPM knowledge-based planning grand challenge. Main results. Model with (MAE + moment) loss function outperformed the model with MAE loss by significantly improving the DVH-score (11%, p < 0.01) while having similar computational cost. It also outperformed the model trained with (MAE + DVH) by significantly improving the computational cost (48%) and the DVH-score (8%, p < 0.01). Significance. DVH metrics are widely accepted evaluation criteria in the clinic. However, incorporating them into the 3D dose prediction model is challenging due to their non-convexity and non-differentiability. Moments provide a mathematically rigorous and computationally efficient way to incorporate DVH information in any DL architecture. The code, pretrained models, docker container, and Google Colab project along with a sample dataset are available on our DoseRTX GitHub (https://github.com/nadeemlab/DoseRTX)

Automated and Clinically Optimal Treatment Planning for Cancer Radiotherapy

Each year, approximately 18 million new cancer cases are diagnosed worldwide, and about half must be treated with radiotherapy. A successful treatment requires treatment planning with the customization of penetrating radiation beams to sterilize cancerous cells without harming nearby normal organs and tissues. This process currently involves extensive manual tuning of parameters by an expert planner, making it a time-consuming and labor-intensive process, with quality and immediacy of critical care dependent on the planner's expertise. To improve the speed, quality, and availability of this highly specialized care, Memorial Sloan Kettering Cancer Center developed and applied advanced optimization tools to this problem (e.g., using hierarchical constrained optimization, convex approximations, and Lagrangian methods). This resulted in both a greatly improved radiotherapy treatment planning process and the generation of reliable and consistent high-quality plans that reflect clinical priorities. These improved techniques have been the foundation of high-quality treatments and have positively impacted over 4,000 patients to date, including numerous patients in severe pain and in urgent need of treatment who might have otherwise required longer hospital stays or undergone unnecessary surgery to control the progression of their disease. We expect that the wide distribution of the system we developed will ultimately impact patient care more broadly, including in resource-constrained countries.

Deep learning auto-segmentation and automated treatment planning for trismus risk reduction in head and neck cancer radiotherapy

Background and Purpose

Reducing trismus in radiotherapy for head and neck cancer (HNC) is important. Automated deep learning (DL) segmentation and automated planning was used to introduce new and rarely segmented masticatory structures to study if trismus risk could be decreased.

Materials and Methods

Auto-segmentation was based on purpose-built DL, and automated planning used our in-house system, ECHO. Treatment plans for ten HNC patients, treated with 2 Gy × 35 fractions, were optimized (ECHO₀). Six manually segmented OARs were replaced with DL auto-segmentations and the plans re-optimized (ECHO₁). In a third set of plans, mean doses for auto-segmented ipsilateral masseter and medial pterygoid (MI_Mean, MPI_Mean), derived from a trismus risk model, were implemented as dose-volume objectives (ECHO₂). Clinical dose-volume criteria were compared between the two scenarios (ECHO₀vs. ECHO₁; ECHO₁vs. ECHO₂; Wilcoxon signed-rank test; significance: p < 0.01).

Results

Small systematic differences were observed between the doses to the six auto-segmented OARs and their manual counterparts (median: ECHO₁ = 6.2 (range: 0.4, 21) Gy vs. ECHO₀ = 6.6 (range: 0.3, 22) Gy; p = 0.007), and the ECHO₁ plans provided improved normal tissue sparing across a larger dose-volume range. Only in the ECHO₂ plans, all patients fulfilled both MI_Mean and MPI_Mean criteria. The population median MI_Mean and MPI_Mean were considerably lower than those suggested by the trismus model (ECHO₀: MI_Mean = 13 Gy vs. ≤42 Gy; MPI_Mean = 29 Gy vs. ≤68 Gy).

Conclusions

Automated treatment planning can efficiently incorporate new structures from DL auto-segmentation, which results in trismus risk sparing without deteriorating treatment plan quality. Auto-planning and deep learning auto-segmentation together provide a powerful platform to further improve treatment planning.

Solving the volumetric modulated arc therapy (VMAT) problem using a sequential convex programming method

The volumetric modulated arc therapy (VMAT) problem is highly non-convex and much more difficult than the fixed-field intensity modulated radiotherapy optimization problem. To solve it efficiently, we propose a sequential convex programming algorithm that solves a sequence of convex optimization problems. Beginning by optimizing the aperture weights of many (72) evenly distributed beams using the beam's eye view of the target from each direction as the initial aperture shape, the search space is constrained to allowing the leaves to move within a pre-defined step-size. A convex approximation problem is introduced and solved to optimize the leaf positions and the aperture weights within the search space. The algorithm is equipped with both local and global search strategies, whereby a global search is followed by a local search: a large step-size results in a global search with a less accurate convex approximation, followed by a small step-size local search with an accurate convex approximation. The performance of the proposed algorithm is tested on three patients with three different disease sites (paraspinal, prostate and oligometastasis). The algorithm generates VMAT plans comparable to the ideal 72-beam fluence map optimized plans (i.e. IMRT plans before leaf sequencing) in 14 iterations and 36 mins on average. The algorithm is also tested on a small down-sampled prostate case for which we could computationally afford to obtain the ground-truth by solving the non-convex mixed-integer optimization problem exactly. This general algorithm is able to produce results essentially equivalent to the ground-truth but 12 times faster. The algorithm is also scalable and can handle real clinical cases, whereas the ground-truth solution using mixed-integer optimization can only be obtained for highly down-sampled cases.

Automating proton treatment planning with beam angle selection using Bayesian optimization

PURPOSE

To present a fully automated treatment planning process for proton therapy including beam angle selection using a novel Bayesian optimization approach and previously developed constrained hierarchical fluence optimization method.

METHODS

We adapted our in-house automated intensity modulated radiation therapy (IMRT) treatment planning system, which is based on constrained hierarchical optimization and referred to as ECHO (expedited constrained hierarchical optimization), for proton therapy. To couple this to beam angle selection, we propose using a novel Bayesian approach. By integrating ECHO with this Bayesian beam selection approach, we obtain a fully automated treatment planning framework including beam angle selection. Bayesian optimization is a global optimization technique which only needs to search a small fraction of the search space for slowly varying objective functions (i.e., smooth functions). Expedited constrained hierarchical optimization is run for some initial beam angle candidates and the resultant treatment plan for each beam configuration is rated using a clinically relevant treatment score function. Bayesian optimization iteratively predicts the treatment score for not-yet-evaluated candidates to find the best candidate to be optimized next with ECHO. We tested this technique on five head-and-neck (HN) patients with two coplanar beams. In addition, tests were performed with two noncoplanar and three coplanar beams for two patients.

RESULTS

For the two coplanar configurations, the Bayesian optimization found the optimal beam configuration after running ECHO for, at most, 4% of all potential configurations (23 iterations) for all patients (range: 2%-4%). Compared with the beam configurations chosen by the planner, the optimal configurations reduced the mandible maximum dose by 6.6 Gy and high dose to the unspecified normal tissues by 3.8 Gy, on average. For the two noncoplanar and three coplanar beam configurations, the algorithm converged after 45 iterations (examining <1% of all potential configurations).

CONCLUSIONS

A fully automated and efficient treatment planning process for proton therapy, including beam angle optimization was developed. The algorithm automatically generates high-quality plans with optimal beam angle configuration by combining Bayesian optimization and ECHO. As the Bayesian optimization is capable of handling complex nonconvex functions, the treatment score function which is used in the algorithm to evaluate the dose distribution corresponding to each beam configuration can contain any clinically relevant metric.

Automated proton treatment planning with robust optimization using constrained hierarchical optimization

PURPOSE

We present a method for fully automated generation of high quality robust proton treatment plans using hierarchical optimization. To fill the gap between the two common extreme robust optimization approaches, that is, stochastic and worst-case, a robust optimization approach based on the p-norm function is used whereby a single parameter, p , can be used to control the level of robustness in an intuitive way.

METHODS

A fully automated approach to treatment planning using Expedited Constrained Hierarchical Optimization (ECHO) is implemented in our clinic for photon treatments. ECHO strictly enforces critical (inviolable) clinical criteria as hard constraints and improves the desirable clinical criteria sequentially, as much as is feasible. We extend our in-house developed ECHO codes for proton therapy and integrate it with a new approach for robust optimization. Multiple scenarios accounting for both setup and range uncertainties are included (13scenarios), and the maximum/mean/dose-volume constraints on organs-at-risk (OARs) and target are fulfilled in all scenarios. We combine the objective functions of the individual scenarios using the p-norm function. The p-norm with a parameter p = 1 or p = ∞ result in the stochastic or the worst-case approach, respectively; an intermediate robustness level is obtained by employing p -values in-between. While the worst-case approach only focuses on the worst-case scenario(s), the p-norm approach with a large p value ( p ≈ 20 ) resembles the worst-case approach without completely neglecting other scenarios. The proposed approach is evaluated on three head-and-neck (HN) patients and one water phantom with different parameters, p ∈ 1 , 2 , 5 , 10 , 20 . The results are compared against the stochastic approach (p-norm approach with p = 1 ) and the worst-case approach, as well as the nonrobust approach (optimized solely on the nominal scenario).

RESULTS

The proposed algorithm successfully generates automated robust proton plans on all cases. As opposed to the nonrobust plans, the robust plans have narrower dose volume histogram (DVH) bands across all 13 scenarios, and meet all hard constraints (i.e., maximum/mean/dose-volume constraints) on OARs and the target for all scenarios. The spread in the objective function values is largest for the stochastic approach ( p = 1 ) and decreases with increasing p toward the worst-case approach. Compared to the worst-case approach, the p-norm approach results in DVH bands for clinical target volume (CTV) which are closer to the prescription dose at a negligible cost in the DVH for the worst scenario, thereby improving the overall plan quality. On average, going from the worst-case approach to the p-norm approach with p = 20 , the median objective function value across all the scenarios is improved by 15% while the objective function value for the worst scenario is only degraded by 3%.

CONCLUSION

An automated treatment planning approach for proton therapy is developed, including robustness, dose-volume constraints, and the ability to control the robustness level using the p-norm parameter p , to fit the priorities deemed most important.

Integrating soft and hard dose-volume constraints into hierarchical constrained IMRT optimization

PURPOSE

Dose-volume constraints (DVCs) continue to be common features in intensity-modulated radiation therapy (IMRT) prescriptions, but they are non-convex and difficult to incorporate. We propose computationally efficient methods to incorporate dose-volume constraints (DVCs) into automated IMRT planning.

METHODS

We propose a two-phase approach: in phase-1, we solve a convex approximation with DVCs. Although this convex approximation does not guarantee DVC satisfaction, it provides crucial initial information about voxels likely to receive doses below DVC thresholds. Subsequently, phase-2 solves an optimization problem with maximum dose constraints imposed on those subthreshold voxels. We further categorize DVCs into hard- and soft-DVCs, where hard-DVCs are strictly enforced by the optimization and soft-DVCs are encouraged in the objective function. We tested this approach in our automated treatment planning system which is based on hierarchical constrained optimization. Performance is demonstrated on a series of paraspinal, lung, oligometastasis, and prostate cases as well as a small paraspinal case for which we can computationally afford to obtain a ground-truth by solving a non-convex optimization problem.

RESULTS

The proposed algorithm successfully meets all the hard-DVCs while increasing the overall computational time of the baseline planning process (without DVCs) by 20%, 10%, and 11% for paraspinal, oligometastasis, and prostate cases, respectively. For a soft-DVC applied to the lung case, the dose-volume histogram curve moves toward the desired direction and the computational time is increased by 11%. For a low-resolution paraspinal case, the ground-truth solution process using mixed-integer programming methods required 15 h while the proposed algorithm converges in only 2 min with a proximal solution.

CONCLUSIONS

A computationally tractable algorithm to handle hard- and soft-DVCs is developed which is capable of satisfying DVCs without any parameter tweaking. Although the algorithm is demonstrated in our in-house developed automated treatment planning system, it can potentially be used in any constrained optimization framework.

Clinical Experience of Automated SBRT Paraspinal and Other Metastatic Tumor Planning With Constrained Hierarchical Optimization

Purpose

We report on the clinical performance of a fully automated approach to treatment planning based on a Pareto optimal, constrained hierarchical optimization algorithm, named Expedited Constrained Hierarchical Optimization (ECHO).

Methods and materials

From April 2017 to October 2018, ECHO produced 640 treated plans for 523 patients who underwent stereotactic body radiation therapy (RT) for paraspinal and other metastatic tumors. A total of 182 plans were for 24 Gy in a single fraction, 387 plans were for 27 Gy in 3 fractions, and the remainder were for other prescriptions or fractionations. Of the plans, 84.5% were for paraspinal tumors, with 69, 302, and 170 in the cervical, thoracic, and lumbosacral spine, respectively. For each case, after contouring, a template plan using 9 intensity modulated RT fields based on disease site and tumor location was sent to ECHO through an application program interface plug-in from the treatment planning system. ECHO returned a plan that satisfied all critical structure hard constraints with optimal target volume coverage and the lowest achievable normal tissue doses. Upon ECHO completion, the planner received an e-mail indicating the plan was ready for review. The plan was accepted if all clinical criteria were met. Otherwise, a limited number of parameters could be adjusted for another ECHO run.

Results

The median planning target volume size was 84.3 cm³ (range, 6.9-633.2). The median time to produce 1 ECHO plan was 63.5 minutes (range, 11-340 minutes) and was largely dependent on the field sizes. Of the cases, 79.7% required 1 run to produce a clinically accepted plan, 13.3% required 1 additional run with minimal parameter adjustments, and 7.0% required ≥2 additional runs with significant parameter modifications. All plans met or bettered the institutional clinical criteria.

Conclusions

We successfully implemented automated stereotactic body RT paraspinal and other metastatic tumors planning. ECHO produced high-quality plans, improved planning efficiency and robustness, and enabled expedited treatment planning at our clinic.

Automated intensity modulated treatment planning: The expedited constrained hierarchical optimization (ECHO) system

PURPOSE

To develop and implement a fully automated approach to intensity modulated radiation therapy (IMRT) treatment planning.

METHOD

The optimization algorithm is developed based on a hierarchical constrained optimization technique and is referred internally at our institution as expedited constrained hierarchical optimization (ECHO). Beamlet contributions to regions-of-interest are precomputed and captured in the influence matrix. Planning goals are of two classes: hard constraints that are strictly enforced from the first step (e.g., maximum dose to spinal cord), and desirable goals that are sequentially introduced in three constrained optimization problems (better planning target volume (PTV) coverage, lower organ at risk (OAR) doses, and smoother fluence map). After solving the optimization problems using external commercial optimization engines, the optimal fluence map is imported into an FDA-approved treatment planning system (TPS) for leaf sequencing and accurate full dose calculation. The dose-discrepancy between the optimization and TPS dose calculation is then calculated and incorporated into optimization by a novel dose correction loop technique using Lagrange multipliers. The correction loop incorporates the leaf sequencing and scattering effects into optimization to improve the plan quality and reduce the calculation time. The resultant optimal fluence map is again imported into TPS for leaf sequencing and final dose calculation for plan evaluation and delivery. The workflow is automated using application program interface (API) scripting, requiring user interaction solely to prepare the contours and beam arrangement prior to launching the ECHO plug-in from the TPS. For each site, parameters and objective functions are chosen to represent clinical priorities. The first site chosen for clinical implementation was metastatic paraspinal lesions treated with stereotactic body radiotherapy (SBRT). As a first step, 75 ECHO paraspinal plans were generated retrospectively and compared with clinically treated plans generated by planners using VMAT (volumetric modulated arc therapy) with 4 to 6 partial arcs. Subsequently, clinical deployment began in April, 2017.

RESULTS

In retrospective study, ECHO plans were found to be dosimetrically superior with respect to tumor coverage, plan conformity, and OAR sparing. For example, the average PTV D95%, cord and esophagus max doses, and Paddick Conformity Index were improved, respectively, by 1%, 6%, 14%, and 15%, at a negligible 3% cost of the average skin D10cc dose.

CONCLUSION

Hierarchical constrained optimization is a powerful and flexible tool for automated IMRT treatment planning. The dosimetric correction step accurately accounts for detailed dosimetric multileaf collimator and scattering effects. The system produces high-quality, Pareto optimal plans and avoids the time-consuming trial-and-error planning process.

Inverse optimization for multi-objective linear programming

This paper generalizes inverse optimization for multi-objective linear programming where we are looking for the least problem modifications to make a given feasible solution a weak efficient solution. This is a natural extension of inverse optimization for single-objective linear programming with regular "optimality" replaced by the "Pareto optimality". This extension, however, leads to a non-convex optimization problem. We prove some special characteristics of the problem, allowing us to solve the non-convex problem by solving a series of convex problems.

An Automated Treatment Plan Quality Control Tool for Intensity-Modulated Radiation Therapy Using a Voxel-Weighting Factor-Based Re-Optimization Algorithm

Intensity-modulated radiation therapy (IMRT) currently plays an important role in radiotherapy, but its treatment plan quality can vary significantly among institutions and planners. Treatment plan quality control (QC) is a necessary component for individual clinics to ensure that patients receive treatments with high therapeutic gain ratios. The voxel-weighting factor-based plan re-optimization mechanism has been proved able to explore a larger Pareto surface (solution domain) and therefore increase the possibility of finding an optimal treatment plan. In this study, we incorporated additional modules into an in-house developed voxel weighting factor-based re-optimization algorithm, which was enhanced as a highly automated and accurate IMRT plan QC tool (TPS-QC tool). After importing an under-assessment plan, the TPS-QC tool was able to generate a QC report within 2 minutes. This QC report contains the plan quality determination as well as information supporting the determination. Finally, the IMRT plan quality can be controlled by approving quality-passed plans and replacing quality-failed plans using the TPS-QC tool. The feasibility and accuracy of the proposed TPS-QC tool were evaluated using 25 clinically approved cervical cancer patient IMRT plans and 5 manually created poor-quality IMRT plans. The results showed high consistency between the QC report quality determinations and the actual plan quality. In the 25 clinically approved cases that the TPS-QC tool identified as passed, a greater difference could be observed for dosimetric endpoints for organs at risk (OAR) than for planning target volume (PTV), implying that better dose sparing could be achieved in OAR than in PTV. In addition, the dose-volume histogram (DVH) curves of the TPS-QC tool re-optimized plans satisfied the dosimetric criteria more frequently than did the under-assessment plans. In addition, the criteria for unsatisfied dosimetric endpoints in the 5 poor-quality plans could typically be satisfied when the TPS-QC tool generated re-optimized plans without sacrificing other dosimetric endpoints. In addition to its feasibility and accuracy, the proposed TPS-QC tool is also user-friendly and easy to operate, both of which are necessary characteristics for clinical use.

Simultaneous beam sampling and aperture shape optimization for SPORT

PURPOSE

Station parameter optimized radiation therapy (SPORT) was recently proposed to fully utilize the technical capability of emerging digital linear accelerators, in which the station parameters of a delivery system, such as aperture shape and weight, couch position/angle, gantry/collimator angle, can be optimized simultaneously. SPORT promises to deliver remarkable radiation dose distributions in an efficient manner, yet there exists no optimization algorithm for its implementation. The purpose of this work is to develop an algorithm to simultaneously optimize the beam sampling and aperture shapes.

METHODS

The authors build a mathematical model with the fundamental station point parameters as the decision variables. To solve the resulting large-scale optimization problem, the authors devise an effective algorithm by integrating three advanced optimization techniques: column generation, subgradient method, and pattern search. Column generation adds the most beneficial stations sequentially until the plan quality improvement saturates and provides a good starting point for the subsequent optimization. It also adds the new stations during the algorithm if beneficial. For each update resulted from column generation, the subgradient method improves the selected stations locally by reshaping the apertures and updating the beam angles toward a descent subgradient direction. The algorithm continues to improve the selected stations locally and globally by a pattern search algorithm to explore the part of search space not reachable by the subgradient method. By combining these three techniques together, all plausible combinations of station parameters are searched efficiently to yield the optimal solution.

RESULTS

A SPORT optimization framework with seamlessly integration of three complementary algorithms, column generation, subgradient method, and pattern search, was established. The proposed technique was applied to two previously treated clinical cases: a head and neck and a prostate case. It significantly improved the target conformality and at the same time critical structure sparing compared with conventional intensity modulated radiation therapy (IMRT). In the head and neck case, for example, the average PTV coverage D99% for two PTVs, cord and brainstem max doses, and right parotid gland mean dose were improved, respectively, by about 7%, 37%, 12%, and 16%.

CONCLUSIONS

The proposed method automatically determines the number of the stations required to generate a satisfactory plan and optimizes simultaneously the involved station parameters, leading to improved quality of the resultant treatment plans as compared with the conventional IMRT plans.

A DVH-guided IMRT optimization algorithm for automatic treatment planning and adaptive radiotherapy replanning

PURPOSE

To develop a novel algorithm that incorporates prior treatment knowledge into intensity modulated radiation therapy optimization to facilitate automatic treatment planning and adaptive radiotherapy (ART) replanning.

METHODS

The algorithm automatically creates a treatment plan guided by the DVH curves of a reference plan that contains information on the clinician-approved dose-volume trade-offs among different targets/organs and among different portions of a DVH curve for an organ. In ART, the reference plan is the initial plan for the same patient, while for automatic treatment planning the reference plan is selected from a library of clinically approved and delivered plans of previously treated patients with similar medical conditions and geometry. The proposed algorithm employs a voxel-based optimization model and navigates the large voxel-based Pareto surface. The voxel weights are iteratively adjusted to approach a plan that is similar to the reference plan in terms of the DVHs. If the reference plan is feasible but not Pareto optimal, the algorithm generates a Pareto optimal plan with the DVHs better than the reference ones. If the reference plan is too restricting for the new geometry, the algorithm generates a Pareto plan with DVHs close to the reference ones. In both cases, the new plans have similar DVH trade-offs as the reference plans.

RESULTS

The algorithm was tested using three patient cases and found to be able to automatically adjust the voxel-weighting factors in order to generate a Pareto plan with similar DVH trade-offs as the reference plan. The algorithm has also been implemented on a GPU for high efficiency.

CONCLUSIONS

A novel prior-knowledge-based optimization algorithm has been developed that automatically adjust the voxel weights and generate a clinical optimal plan at high efficiency. It is found that the new algorithm can significantly improve the plan quality and planning efficiency in ART replanning and automatic treatment planning.

A multicriteria framework with voxel-dependent parameters for radiotherapy treatment plan optimization

PURPOSE

To establish a new mathematical framework for radiotherapy treatment optimization with voxel-dependent optimization parameters.

METHODS

In the treatment plan optimization problem for radiotherapy, a clinically acceptable plan is usually generated by an optimization process with weighting factors or reference doses adjusted for a set of the objective functions associated to the organs. Recent discoveries indicate that adjusting parameters associated with each voxel may lead to better plan quality. However, it is still unclear regarding the mathematical reasons behind it. Furthermore, questions about the objective function selection and parameter adjustment to assure Pareto optimality as well as the relationship between the optimal solutions obtained from the organ-based and voxel-based models remain unanswered. To answer these questions, the authors establish in this work a new mathematical framework equipped with two theorems.

RESULTS

The new framework clarifies the different consequences of adjusting organ-dependent and voxel-dependent parameters for the treatment plan optimization of radiation therapy, as well as the impact of using different objective functions on plan qualities and Pareto surfaces. The main discoveries are threefold: (1) While in the organ-based model the selection of the objective function has an impact on the quality of the optimized plans, this is no longer an issue for the voxel-based model since the Pareto surface is independent of the objective function selection and the entire Pareto surface could be generated as long as the objective function satisfies certain mathematical conditions; (2) All Pareto solutions generated by the organ-based model with different objective functions are parts of a unique Pareto surface generated by the voxel-based model with any appropriate objective function; (3) A much larger Pareto surface is explored by adjusting voxel-dependent parameters than by adjusting organ-dependent parameters, possibly allowing for the generation of plans with better trade-offs among different clinical objectives.

CONCLUSIONS

The authors have developed a mathematical framework for radiotherapy treatment optimization using voxel-based parameters. The authors can improve the plan quality by adjusting voxel-based weighting factors and exploring the unique and large Pareto surface which include all the Pareto surfaces that can be generated by organ-based model using different objective functions.

Automatic treatment plan re-optimization for adaptive radiotherapy guided with the initial plan DVHs

Adaptive radiation therapy (ART) can reduce normal tissue toxicity and/or improve tumor control through treatment adaptations based on the current patient anatomy. Developing an efficient and effective re-planning algorithm is an important step toward the clinical realization of ART. For the re-planning process, manual trial-and-error approach to fine-tune planning parameters is time-consuming and is usually considered unpractical, especially for online ART. It is desirable to automate this step to yield a plan of acceptable quality with minimal interventions. In ART, prior information in the original plan is available, such as dose-volume histogram (DVH), which can be employed to facilitate the automatic re-planning process. The goal of this work is to develop an automatic re-planning algorithm to generate a plan with similar, or possibly better, DVH curves compared with the clinically delivered original plan. Specifically, our algorithm iterates the following two loops. An inner loop is the traditional fluence map optimization, in which we optimize a quadratic objective function penalizing the deviation of the dose received by each voxel from its prescribed or threshold dose with a set of fixed voxel weighting factors. In outer loop, the voxel weighting factors in the objective function are adjusted according to the deviation of the current DVH curves from those in the original plan. The process is repeated until the DVH curves are acceptable or maximum iteration step is reached. The whole algorithm is implemented on GPU for high efficiency. The feasibility of our algorithm has been demonstrated with three head-and-neck cancer IMRT cases, each having an initial planning CT scan and another treatment CT scan acquired in the middle of treatment course. Compared with the DVH curves in the original plan, the DVH curves in the resulting plan using our algorithm with 30 iterations are better for almost all structures. The re-optimization process takes about 30 s using our in-house optimization engine.