On the implementation of dose‐volume objectives in gradient algorithms for inverse treatment planning

Hristov, Dimitre; Stavrev, Pavel; Sham, E; Fallone, B

doi:10.1118/1.1469629

Cited by 20 publications

(16 citation statements)

References 24 publications

(43 reference statements)

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“…However, in clinical practice, dose-volume constraints are commonly used in addition to mean-dose constraints. Previous studies have incorporated dose-volume constraints in gradient-based algorithms for inverse treatment planning [26]. One disadvantage of dose-volume constraints is that they introduce nonconvex feasibility spaces into the optimization problem, potentially creating multiple local minima and associated issues in solver accuracy and run-time efficiency [27].…”

Section: Discussionmentioning

confidence: 99%

A Novel Reduced-Order Prioritized Optimization Method for Radiation Therapy Treatment Planning

Kalantzis

Apte

2014

IEEE Trans. Biomed. Eng.

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In this study, a novel reduced order prioritized algorithm is presented for optimization in radiation therapy treatment planning. The proposed method consists of three stages. In the first stage, the intensity space was sampled by solving a series of unconstrained optimization problems. The objective function of the first stage is expressed as a scalarized weighted sum of partial objectives for the target and organ at risk. Latin hypercube sampling was utilized to define the weights for each run of the unconstrained optimizations. In the second stage, principal component analysis is applied to the solutions determined in the first stage to identify the major eigen modes in the intensities space, significantly reducing the number of independent variables. In the third stage, treatment planning goals/objectives are prioritized, and the problem is solved in the reduced order space. After each objective is optimized, that objective function is converted into a constraint for the lower-priority objectives. In the current formulation, a slip factor is used to relax the hard constraints for planning target volume (PTV) coverage. The applicability of the proposed method is demonstrated for one prostate and one lung intensity-modulated radiation therapy treatment plan. Upon completion of the sequential prioritized optimization, the mean dose at the rectum and bladder was reduced by 21.3% and 22.4%, respectively. Additionally, we investigated the effect of the slip factor ‘s’ on PTV coverage and we found minimal degradation of the tumor dose (~4%). Finally, the speed up factors upon the dimensionality reduction were as high as 49.9 without compromising the quality of the results.

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Section: Discussionmentioning

confidence: 99%

A Novel Reduced-Order Prioritized Optimization Method for Radiation Therapy Treatment Planning

Kalantzis

Apte

2014

IEEE Trans. Biomed. Eng.

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“…This definition of the dose-volume histogram was initially used implicitly by Hristov et al 44 From the definition of an integral DVH it is clear that any monotonically decreasing function in the region ͓0,1͔ ϫ ͓0,1͔ could represent a normalized integral DVH.…”

Section: A Some Definitionsmentioning

confidence: 99%

A theoretical approach to the problem of dose-volume constraint estimation and their impact on the dose-volume histogram selection

Schinkel

Stavrev²,

Stavreva³

et al. 2006

Med. Phys.

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This paper outlines a theoretical approach to the problem of estimating and choosing dose-volume constraints. Following this approach, a method of choosing dose-volume constraints based on biological criteria is proposed. This method is called "reverse normal tissue complication probability (NTCP) mapping into dose-volume space" and may be used as a general guidance to the problem of dose-volume constraint estimation. Dose-volume histograms (DVHs) are randomly simulated, and those resulting in clinically acceptable levels of complication, such as NTCP of 5 +/- 0.5%, are selected and averaged producing a mean DVH that is proven to result in the same level of NTCP. The points from the averaged DVH are proposed to serve as physical dose-volume constraints. The population-based critical volume and Lyman NTCP models with parameter sets taken from literature sources were used for the NTCP estimation. The impact of the prescribed value of the maximum dose to the organ, D(max), on the averaged DVH and the dose-volume constraint points is investigated. Constraint points for 16 organs are calculated. The impact of the number of constraints to be fulfilled based on the likelihood that a DVH satisfying them will result in an acceptable NTCP is also investigated. It is theoretically proven that the radiation treatment optimization based on physical objective functions can sufficiently well restrict the dose to the organs at risk, resulting in sufficiently low NTCP values through the employment of several appropriate dose-volume constraints. At the same time, the pure physical approach to optimization is self-restrictive due to the preassignment of acceptable NTCP levels thus excluding possible better solutions to the problem.

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“…1 Dose-volume histogram (DVH)-based optimization is widely used for the optimization process. [2][3][4][5][6][7][8] DVH-based optimization systematically addresses the three-dimensional (3D) dose distribution using the parameters of dose and volume with a priority weight ratio for optimization (hereinafter called the optimization weight), whereas treatment regions in the planning target volume (PTV) often occur near organs at risk (OARs), and this complicated balance often causes difficulties for the treatment plan. 3 Therefore, the optimization process is usually dependent on the experience of the planner and treatment clinical goals that reflect the facility characteristics of radiotherapy.…”

Section: Introductionmentioning

confidence: 99%

“…3 Therefore, the optimization process is usually dependent on the experience of the planner and treatment clinical goals that reflect the facility characteristics of radiotherapy. 9 Maximal and minimal dose-volume (DV) constraints are typically used to perform clinical inverse treatment planning, 4,5 which is a standard criterion to evaluate whether the treatment plans are clinically acceptable. 6,8 Moreover, DV optimization efficiently and effectively addresses the complicated relationship of between the tumor target and OARs.…”

Section: Introductionmentioning

confidence: 99%

Relativistic Optimization Force Concept for gEUD Biological Optimization and Novel a-value Selection Viewpoint

Anetai

Takegawa

Koike

et al. 2021

Preprint

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Generalized equivalent uniform dose (gEUD) optimization is a biological optimization method used for intensity modulated radiation therapy (IMRT). Although parametric analyses have been widely reported, the use of parameter a-value in the optimization method remains elusive. This study aims to clarify the mathematical characteristics of the gEUD and to provide effective a-value selection. The gEUD is typically obtained using a differential dose volume histogram (DVH). This can be rewritten using a cumulative DVH (cDVH) and applied to variational analysis. The equivalence between the gEUD and the dose is then obtained; a low or high a-value corresponds to a wide or narrow dose range of optimization, respectively. Next, we focused on the gEUD curve behavior against a-value shifts and it retained its curve characteristics despite optimization. Using differential geometry, this curve shift can be considered as a geodesic deviation between pre- and post-optimization by a relativistic optimization force. The total action enacted by the force includes the curvature of the gEUD curve. This idea provides a novel viewpoint that the curvature of the gEUD curve is influenced by the optimization effect. The curvature stationary point of the gEUD curve (the vertex point, a = a_k) is expected to be a special point that leads to effective a-value selection. Eleven head and neck patient cases were used to verify the curvature effect. We used the Photon Optimizer (PO) of Eclipse for optimization and focused the upper gEUD to simplify the dose constraint for the organ at risk (OAR) that requires balancing of the overlapped planning target volume(PTV). Static seven-field IMRT was used for optimization, changing the a-value of the affected side of the parotid and retaining PTV D95% = 70Gy at the different a-value optimization. Finally, cDVH shift (ΔDVH), gEUD shift (ΔgEUD), their average values, and a_k were evaluated. The a = a_k optimization showed an intermediate effect of lower and higher a-values on ΔDVH, ΔgEUD, and their averages. “Lower” (a=0.5/1.0/2.0/3.0), “middle” (a=4.0/5.0/6.0/8.0/10/a_k), and “higher” (a=12/15/20/40) were defined using a=a_k as a base point. Lower a-value optimization was effective for the low-dose region and weakly affected the whole range of cDVH weight. In contrast, higher a-value optimization addressed the high-dose region and strongly affected the high-dose range of the cDVH weight as theoretically predicted. In addition, the middle range of the a-value optimization induced a decrease in the clinically important middle-to-high dose range, which retained the high dose of the PTV. Interestingly, the average ΔDVH and ΔgEUD corresponded exponentially to the curvature and the gradient of the gEUD curve. Using our relativistic optimization force concept, gEUD optimization is represented as a gEUD curve shift, highlighting that the curvature of the gEUD curve is the essence of gEUD optimization. The curvature stationary point (a = a_k), namely the vertex point of the gEUD curve, played an intermediate role in the low-to-high a-value condition. We can effectively select a lower/middle/higher a-value from a base point of a = a_k under clinically complex optimization situation.

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On the implementation of dose‐volume objectives in gradient algorithms for inverse treatment planning

Cited by 20 publications

References 24 publications

A Novel Reduced-Order Prioritized Optimization Method for Radiation Therapy Treatment Planning

A Novel Reduced-Order Prioritized Optimization Method for Radiation Therapy Treatment Planning

A theoretical approach to the problem of dose-volume constraint estimation and their impact on the dose-volume histogram selection

Relativistic Optimization Force Concept for gEUD Biological Optimization and Novel a-value Selection Viewpoint

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