Automated proton treatment planning with robust optimization using constrained hierarchical optimization

Compressed radiotherapy treatment planning: A new paradigm for rapid and high-quality treatment planning optimization

BACKGROUND

Radiotherapy treatment planning involves solving large-scale optimization problems that are often approximated and solved sub-optimally due to time constraints. Central to these problems is the dose influence matrix-also known as the dij matrix or dose deposition matrix-which quantifies the radiation dose delivered from each beamlet to each voxel. Our findings demonstrate that this matrix is highly compressible, enabling a compact representation of the optimization problems and allowing them to be solved more efficiently and accurately.

PURPOSE

To develop a compressed radiotherapy treatment planning framework based on a sparse-plus-low-rank matrix compression technique. This approach circumvents conventional sparsification methods that discard small matrix elements-often representing scattering components-and may compromise the quality of the treatment plan.

METHODS

We precompute the primary ( S $S$ ) and scattering ( L $L$ ) dose contributions of the dose influence matrix A $A$ separately for photon therapy, expressed as:A = S + L $A = S + L$ . Our analysis reveals that the singular values of the scattering matrix L $L$ exhibit exponential decay, indicating that L $L$ is a low-rank matrix. This allows us to compress L $L$ into two smaller matrices:L m × n ≈ H m × r W r × n ${{L}^{m \times n}} \approx {{H}^{m \times r}}{{W}^{r \times n}}$ , where r $r$ is relatively small (approximately 5-10). Since the primary dose matrix S $S$ is sparse, this supports the use of the well-established "sparse-plus-low-rank" decomposition technique for the influence matrix A $A$ , approximated as:A ≈ S + H × W $A\ \approx \ S + H\ \times \ W$ . We introduce an efficient algorithm for sparse-plus-low-rank matrix decomposition, even without direct access to the scattering matrix. This algorithm is applied to optimize treatment plans for ten lung and ten prostate patients, using both compressed and sparsified versions of matrix A $A$ . We then evaluate the dose discrepancy between the optimized and final plans. We also integrate this compression technique with our in-house automated planning system, ECHO, and evaluate the dosimetric quality of the generated plans with and without compression.

RESULTS

Compressed planning offers superior trade-offs between accuracy and computational efficiency, adjustable through algorithm parameters. For example, we achieved average reductions in dose discrepancy and optimization time of 73% and 20%, respectively, for 10 prostate patients, and 83% and 13% for lung patients. By using the compressed matrix within our automated ECHO planning system, we maintained comparable PTV coverage while significantly enhancing the sparing of organs at risk. Specifically, mean doses to the bladder and rectum for prostate patients were reduced by 8.8% and 12.5%, respectively. For lung patients, mean doses to the lungs (left and right, excluding GTV) and heart were reduced by 10.8% and 11.2%, respectively, compared to plans generated with the sparsified matrix.

CONCLUSION

The proposed framework enables rapid, high-quality treatment planning without compromising data integrity and plan quality. By integrating that with recent advancements in AI-driven influence matrix calculations, this platform has the potential to facilitate fast and efficient online adaptive radiotherapy treatment planning, enhancing both speed and accuracy in clinical workflows.

Scenario-free robust optimization algorithm for IMRT and IMPT treatment planning

BACKGROUND

Robust treatment planning algorithms for intensity modulated proton therapy (IMPT) and intensity modulated radiation therapy (IMRT) allow for uncertainty reduction in the delivered dose distributions through explicit inclusion of error scenarios. Due to the curse of dimensionality, application of such algorithms can easily become computationally prohibitive.

PURPOSE

This work proposes a scenario-free probabilistic robust optimization algorithm that overcomes both the runtime and memory limitations typical of traditional robustness algorithms.

METHODS

The scenario-free approach minimizes cost-functions evaluated on expected-dose distributions and total variance. Calculation of these quantities relies on precomputed expected-dose-influence and total-variance-influence matrices, such that no scenarios need to be stored for optimization. The algorithm is developed within matRad and tested in several optimization configurations for photon and proton irradiation plans. A traditional robust optimization algorithm and a margin-based approach are used as a reference to benchmark the performance of the scenario-free algorithm in terms of plan quality, robustness, and computational workload.

RESULTS

The implemented scenario-free approach achieves plan quality similar to traditional robust optimization algorithms, and it reduces the distribution of standard deviation within selected structures when variance reduction objectives are defined. Avoiding the storage of individual scenario information allows for the solution of treatment plan optimization problems, including an arbitrary number of error scenarios. The observed computational time required for optimization is close to a nominal, non-robust algorithm and substantially lower compared to the traditional robust approach. Estimated gains in relative runtime range from approximately5 $\hskip.001pt 5$ -600 $\hskip.001pt 600$ times with respect to the traditional approach.

CONCLUSION

This work introduces a novel scenario-free optimization approach relying on the precomputation of probabilistic quantities while preserving compatibility with state-of-the-art uncertainty modeling. The measured runtime and memory footprint are independent of the number of included error scenarios and similar to those of non-robust margin-based optimization algorithms, while achieving the required dose and robustness specifications under multiple different optimization conditions. These properties make the scenario-free approach suitable and beneficial for 3D and 4D robust optimization involving a high number of error scenarios and/or CT phases.

Evaluating photon-counting computed tomography for quantitative material characteristics and material differentiation in radiotherapy

Objective.Photon-counting computed tomography (PCCT) counts the individual photons and measures their energy, which allows for energy binning and thereby multi-energy CT imaging. It is expected that quantitative data can be accurately extracted from the images and enable accurate material separation, yet its potential in radiotherapy is mostly unexplored. In this study, PCCT was assessed by evaluating estimation accuracies for relative electron density (RED), effective atomic number (Zeff), and proton stopping-power ratio (SPR), as well as the potential for material differentiation.Approach.PCCT images of a Gammex Advanced Electron Density phantom (Sun Nuclear) with tissue-equivalent materials were acquired in a small and large phantom setup on a NAEOTOM Alpha PCCT scanner (Siemens Healthineers). The scans were performed at 120 and 140 kVp, and virtual monoenergetic images (VMIs) were generated. These VMIs were used to estimate RED,Zeff, and SPR based on two calibration methods for each of the two phantom sizes. These results were compared to findings obtained based on dual-energy CT (DECT) scans acquired on a SOMATOM Confidence scanner (Siemens Healthineers) at 80 and 140 kVp, by using the low and high energy pair and VMIs. Calibration accuracy was quantified by the root-mean-squared error. Additional, material differentiation was assessed for both tissue-equivalent and calcium/iodine inserts by creating [RED/Zeff]-space plots.Main results.There was minimal differences between the two PCCT x-ray spectra, with SPR errors below 0.8% for the large phantom and 0.7% for the small phantom, which was comparable to DECT using VMIs. Material differentiation showed similar results for DECT and PCCT using VMIs, and resulted in lessZeffspread, than the regular DECT kVp pair, possibly due to denoising.Significance.This study showed the ability of PCCT to retrieve material characteristics and possibility for material differentiation between tissue-equivalent material and calcium/iodine, with results comparable to DECT.

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.

SISS-MCO: large scale sparsity-induced spot selection for fast and fully-automated robust multi-criteria optimisation of proton plans

Objective.Intensity modulated proton therapy (IMPT) is an emerging treatment modality for cancer. However, treatment planning for IMPT is labour-intensive and time-consuming. We have developed a novel approach for multi-criteria optimisation (MCO) of robust IMPT plans (SISS-MCO) that is fully automated and fast, and we compare it for head and neck, cervix, and prostate tumours to a previously published method for automated robust MCO (IPBR-MCO, van de Water 2013).Approach.In both auto-planning approaches, the applied automated MCO of spot weights was performed with wish-list driven prioritised optimisation (Breedveld 2012). In SISS-MCO, spot weight MCO was applied once for every patient after sparsity-induced spot selection (SISS) for pre-selection of the most relevant spots from a large input set of candidate spots. IPBR-MCO had several iterations of spot re-sampling, each followed by MCO of the weights of the current spots.Main results.Compared to the published IPBR-MCO, the novel SISS-MCO resulted in similar or slightly superior plan quality. Optimisation times were reduced by a factor of 6 i.e. from 287 to 47 min. Numbers of spots and energy layers in the final plans were similar.Significance.The novel SISS-MCO automatically generated high-quality robust IMPT plans. Compared to a published algorithm for automated robust IMPT planning, optimisation times were reduced on average by a factor of 6. Moreover, SISS-MCO is a large scale approach; this enables optimisation of more complex wish-lists, and novel research opportunities in proton therapy.

Clinical benefit of range uncertainty reduction in proton treatment planning based on dual-energy CT for neuro-oncological patients

OBJECTIVE

Several studies have shown that dual-energy CT (DECT) can lead to improved accuracy for proton range estimation. This study investigated the clinical benefit of reduced range uncertainty, enabled by DECT, in robust optimisation for neuro-oncological patients.

METHODS

DECT scans for 27 neuro-oncological patients were included. Commercial software was applied to create stopping-power ratio (SPR) maps based on the DECT scan. Two plans were robustly optimised on the SPR map, keeping the beam and plan settings identical to the clinical plan. One plan was robustly optimised and evaluated with a range uncertainty of 3% (as used clinically; denoted 3%-plan); the second plan applied a range uncertainty of 2% (2%-plan). Both plans were clinical acceptable and optimal. The dose-volume histogram parameters were compared between the two plans. Two experienced neuro-radiation oncologists determined the relevant dose difference for each organ-at-risk (OAR). Moreover, the OAR toxicity levels were assessed.

RESULTS

For 24 patients, a dose reduction >0.5/1 Gy (relevant dose difference depending on the OAR) was seen in one or more OARs for the 2%-plan; e.g. for brainstem D0.03cc in 10 patients, and hippocampus D40% in 6 patients. Furthermore, 12 patients had a reduction in toxicity level for one or two OARs, showing a clear benefit for the patient.

CONCLUSION

Robust optimisation with reduced range uncertainty allows for reduction of OAR toxicity, providing a rationale for clinical implementation. Based on these results, we have clinically introduced DECT-based proton treatment planning for neuro-oncological patients, accompanied with a reduced range uncertainty of 2%.

ADVANCES IN KNOWLEDGE

This study shows the clinical benefit of range uncertainty reduction from 3% to 2% in robustly optimised proton plans. A dose reduction to one or more OARs was seen for 89% of the patients, and 44% of the patients had an expected toxicity level decrease.

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.

Automation of pencil beam scanning proton treatment planning for intracranial tumours

PURPOSE

To evaluate the feasibility of comprehensive automation of an intra-cranial proton treatment planning.

MATERIALS AND METHODS

Class solution (CS) beam configuration selection allows the user to identify predefined beam configuration based on target localization; automatic CS (aCS) will then explore all the possible CS beam geometries. Ten patients, already used for the evaluation of the automatic selection of the beam configuration, have been also employed to training an algorithm based on the computation of a benchmark dose exploit automatic general planning solution (GPS) optimization with a wish list approach for the planning optimization. An independent cohort of ten patients has been then used for the evaluation step between the clinical and the GPS plan in terms of dosimetric quality of plans and the time needed to generate a plan.

RESULTS

The definition of a beam configuration requires on average 22 min (range 9-29 min). The average time for GPS plan generation is 18 min (range 7-26 min). Median dose differences (GPS-Manual) for each OAR constraints are: brainstem -1.60 Gy, left cochlea -1.22 Gy, right cochlea -1.42 Gy, left eye 0.55 Gy, right eye -2.33 Gy, optic chiasm -1.87 Gy, left optic nerve -4.45 Gy, right optic nerve -2.48 Gy and optic tract -0.31 Gy. Dosimetric CS and aCS plan evaluation shows a slightly worsening of the OARs values except for the optic tract and optic chiasm for both CS and aCS, where better results have been observed.

CONCLUSION

This study has shown the feasibility and implementation of the automatic planning system for intracranial tumors. The method developed in this work is ready to be implemented in a clinical workflow.

Clinical implementation and validation of an automated adaptive workflow for proton therapy

Background and purpose

Treatment quality of proton therapy can be monitored by repeat-computed tomography scans (reCTs). However, manual re-delineation of target contours can be time-consuming. To improve the workflow, we implemented an automated reCT evaluation, and assessed if automatic target contour propagation would lead to the same clinical decision for plan adaptation as the manual workflow.

Materials and methods

This study included 79 consecutive patients with a total of 250 reCTs which had been manually evaluated. To assess the feasibility of automated reCT evaluation, we propagated the clinical target volumes (CTVs) deformably from the planning-CT to the reCTs in a commercial treatment planning system. The dose-volume-histogram parameters were extracted for manually re-delineated (CTV_manual) and deformably mapped target contours (CTV_auto). It was compared if CTV_manual and CTV_auto both satisfied/failed the clinical constraints. Duration of the reCT workflows was also recorded.

Results

In 92% (N = 229) of the reCTs correct flagging was obtained. Only 4% (N = 9) of the reCTs presented with false negatives (i.e., at least one clinical constraint failed for CTV_manual, but all constraints were satisfied for CTV_auto), while 5% (N = 12) of the reCTs led to a false positive. Only for one false negative reCT a plan adaption was made in clinical practice, i.e., only one adaptation would have been missed, suggesting that automated reCT evaluation was possible. Clinical introduction hereof led to a time reduction of 49 h (from 65 to 16 h).

Conclusion

Deformable target contour propagation was clinically acceptable. A script-based automatic reCT evaluation workflow has been introduced in routine clinical practice.

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.

Adaptive proton therapy

Radiation therapy treatments are typically planned based on a single image set, assuming that the patient's anatomy and its position relative to the delivery system remains constant during the course of treatment. Similarly, the prescription dose assumes constant biological dose-response over the treatment course. However, variations can and do occur on multiple time scales. For treatment sites with significant intra-fractional motion, geometric changes happen over seconds or minutes, while biological considerations change over days or weeks. At an intermediate timescale, geometric changes occur between daily treatment fractions. Adaptive radiation therapy is applied to consider changes in patient anatomy during the course of fractionated treatment delivery. While traditionally adaptation has been done off-line with replanning based on new CT images, online treatment adaptation based on on-board imaging has gained momentum in recent years due to advanced imaging techniques combined with treatment delivery systems. Adaptation is particularly important in proton therapy where small changes in patient anatomy can lead to significant dose perturbations due to the dose conformality and finite range of proton beams. This review summarizes the current state-of-the-art of on-line adaptive proton therapy and identifies areas requiring further research.

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.