Hierarchical Constrained Optimization Research Articles

Automated and Clinical-Criteria-Driven Planning for Lung Cancer Using the Expedited Constrained Hierarchical Optimization (ECHO) System

<h3>Purpose/Objective(s)</h3> Treatment planning for locally advanced non-small cell lung cancer (NSCLC) has always been challenging due to the variabilities of the planning target volume (PTV) and competing constraints of organs at risk such as lung, cord, esophagus, and heart. We share our experience in developing a fully automatic treatment planning solution for NSCLC. <h3>Materials/Methods</h3> Automated plans for NSCLC radiotherapy patients with static IMRT fields were designed using an in-house-developed automated planning system named Expedited Constrained Hierarchical Optimization (ECHO) which is integrated into the treatment planning system (TPS) using API scripting. ECHO does not use TPS optimization algorithms, but utilizes TPS leaf sequencing and final dose calculation. ECHO applies advanced optimization tools (such as hierarchical constrained optimization, convex approximations and Lagrangian methods) to produce Pareto optimal plans that meet clinical constraints and improve desired clinical objectives as much as possible. ECHO optimization parameters were tuned with 29 NSCLC patients and validated retrospectively using 113 NSCLC patients treated with prescription doses including conventional (1.8Gy-2Gy x 25-35 fractions) and hypofractionation (2.75Gy-4Gy x 10-20 fractions). Clinically treated plans were created manually using either static IMRT or VMAT. Automated plans were created using static IMRT fields with beam templates based on the location of PTV within the lung. Dosimetric metrics were evaluated with respect to tumor coverage and normal tissue sparing. <h3>Results</h3> PTV sizes ranged from 64cc to 2297cc (median 292cc). Median planning time for ECHO was 23 minutes (range: 8min-78min). Both manual and ECHO plans met all established clinical criteria. Compared with manual plans, ECHO plans produced significantly improved and more consistent PTV coverage and better sparing of esophagus, heart and cord while maintaining similar lung doses (Table 1). <h3>Conclusion</h3> An automated and clinical-criteria-driven treatment planning system has been validated and clinically implemented in our institution for NSCLC radiotherapy. Use of automation improves efficiency, plan consistency and quality for NSCLC treatment planning.

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.

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

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. 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. 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 15h while the proposed algorithm converges in only 2min with a proximal solution. 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.

Decentralized hierarchical constrained convex optimization

This paper proposes a decentralized optimization algorithm for the triple-hierarchical constrained convex optimization problem of minimizing a sum of strongly convex functions subject to a paramonotone variational inequality constraint over an intersection of fixed point sets of nonexpansive mappings. The existing algorithms for solving this problem are centralized optimization algorithms using all the information in the problem, and these algorithms are effective, but only under certain additional restrictions. The main contribution of this paper is to present a convergence analysis of the proposed algorithm in order to show that the proposed algorithm using incremental gradients with diminishing step-size sequences converges to the solution to the problem without any additional restrictions. Another contribution of this paper is the elucidation of the practical applications of hierarchical constrained optimization in the form of network resource allocation and optimal control problems. In particular, it is shown that the proposed algorithm can be applied to decentralized network resource allocation with a triple-hierarchical structure.

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

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

A Hierarchical Optimization Approach to Robot Teleoperation and Virtual Fixtures Rendering

Abstract This paper presents a novel controller for bilateral teleoperation based on hierarchical constrained optimization techniques, that exploits motion constraints for the definition of virtual fixtures and haptic rendering. Our method allows the description of both rigid and compliant virtual fixtures, without the need of relative weight tuning as in previous approaches. Moreover, kinesthetic feedback due to each active constraint can be directly evaluated from the dual solution of the optimization algorithm, removing constraint penetration typical of penalty-based approaches and critical for telemanipulation where high accuracy is required. A transparency and stability analysis in case of communication delays is provided by relying on the classical two-port network formalism and linear control theory. An experimental evaluation of the approach for an object tracking task is carried out on a teleoperation system consisting of a 7-axis position-controlled slave robot with an eye-in-hand camera, and a 3 d.o.f. force-controlled master device.

PO-0823: Hierarchical constrained optimization for automated SBRT paraspinal IMRT planning

PO-0823: Hierarchical constrained optimization for automated SBRT paraspinal IMRT planning

Steepest-Descent Approach to Triple Hierarchical Constrained Optimization Problems

We introduce and analyze a hybrid steepest-descent algorithm by combining Korpelevich’s extragradient method, the steepest-descent method, and the averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to the unique solution of a triple hierarchical constrained optimization problem (THCOP) over the common fixed point set of finitely many nonexpansive mappings, with constraints of finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and a convex minimization problem (CMP) in a real Hilbert space.

Strong convergence of relaxed hybrid steepest-descent methods for triple hierarchical constrained optimization

Abstract Up to now, a large number of practical problems such as signal processing and network resource allocation have been formulated as the monotone variational inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms for solving these problems have been proposed. The purpose of this article is to investigate a monotone variational inequality with variational inequality constraint over the fixed point set of one or finitely many nonexpansive mappings, which is called the triple-hierarchical constrained optimization. Two relaxed hybrid steepest-descent algorithms for solving the triple-hierarchical constrained optimization are proposed. Strong convergence for them is proven. Applications of these results to constrained generalized pseudoinverse are included. AMS Subject Classifications: 49J40; 65K05; 47H09.