The dose–volume constraint satisfaction problem for inverse treatment planning with field segments

Michalski, Darek; Xiao, Ying; Censor, Yair; Galvin, James M.

doi:10.1088/0031-9155/49/4/010

Cited by 32 publications

(24 citation statements)

References 27 publications

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“…15,16 Segment-based optimization algorithms achieve small numbers of segments by imposing the physical constraints of beam apertures in the optimization. [7][8][9][10][11][12][13][14]28 In a sense, this is similar to what many investigators have done in the context of 3D conformal therapy plan optimization, where the machine related parameters such as the beam weights and wedge angles are optimized. These algorithms eventually search in a space of all possible segments for a sparse optimal solution.…”

supporting

confidence: 53%

“…Segment-based methods tackle the problem from the delivery aspect typically by enforcing a prechosen ͑often unjustified͒ number of segments for each incident beam and then optimizing the shapes and weights of the apertures. [7][8][9][10][11][12][13][14] However, searching for an optimal solution by using segmentbased optimization is inherently complicated because of the highly nonconvex dependence of the objective function on the multi-leaf collimator ͑MLC͒ coordinates and the optimality of the final solution is not always guaranteed when an iterative algorithm is used.…”

Section: Introductionmentioning

confidence: 99%

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Search for IMRT inverse plans with piecewise constant fluence maps using compressed sensing techniques

Zhu

2009

Medical Physics

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An intensity-modulated radiation therapy ͑IMRT͒ field is composed of a series of segmented beams. It is practically important to reduce the number of segments while maintaining the conformality of the final dose distribution. In this article, the authors quantify the complexity of an IMRT fluence map by introducing the concept of sparsity of fluence maps and formulate the inverse planning problem into a framework of compressing sensing. In this approach, the treatment planning is modeled as a multiobjective optimization problem, with one objective on the dose performance and the other on the sparsity of the resultant fluence maps. A Pareto frontier is calculated, and the achieved dose distributions associated with the Pareto efficient points are evaluated using clinical acceptance criteria. The clinically acceptable dose distribution with the smallest number of segments is chosen as the final solution. The method is demonstrated in the application of fixed-gantry IMRT on a prostate patient. The result shows that the total number of segments is greatly reduced while a satisfactory dose distribution is still achieved. With the focus on the sparsity of the optimal solution, the proposed method is distinct from the existing beamlet-or segment-based optimization algorithms.

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supporting

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Search for IMRT inverse plans with piecewise constant fluence maps using compressed sensing techniques

Zhu

2009

Medical Physics

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“…Starkschall et al (2001) modify the cyclic subgradient projection algorithm to incorporate dose-volume constraints. Michalski et al (2004) solve dose-volume constraint satisfaction problems using the simultaneous subgradient projection algorithm. They state that the algorithm is easy to implement and has minimal memory requirements.…”

Section: The Feasibility Problem and Algorithmsmentioning

confidence: 99%

Mathematical optimization in intensity modulated radiation therapy

et al. 2009

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The design of an intensity modulated radiotherapy treatment includes the selection of beam angles (geometry problem), the computation of an intensity map for each selected beam angle (intensity problem), and finding a sequence of configurations of a multileaf collimator to deliver the treatment (realization problem). Until the end of the last century research on radiotherapy treatment design has been published almost exclusively in the medical physics literature. However, since then, the attention of researchers in mathematical optimization has been drawn to the area and important progress has been made. In this paper we survey the use of optimization models, methods, and theories in intensity modulated radiotherapy treatment design. This is an updated version of the paper that appeared in 4OR, 6(3), 199-262 (2008).

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“…IMRT inverse planning can be broadly divided into two types of optimization algorithms: direct aperture optimization (DAO) (Refs. [8][9][10][11][12]) and beamlet based optimization (BBO). [13][14][15][16][17][18] Although DAO takes the physical constraints of the delivery system into consideration, it suffers from the problem of multiple local minima due to the nonconvex cost function.…”

Section: Introductionmentioning

confidence: 99%

Dose optimization with first‐order total‐variation minimization for dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM‐RT)

Kim

Lee³

et al. 2012

Med. Phys.

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Purpose:A new treatment scheme coined as dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM-RT) has recently been proposed to bridge the gap between IMRT and VMAT. By increasing the angular sampling of radiation beams while eliminating dispensable segments of the incident fields, DASSIM-RT is capable of providing improved conformity in dose distributions while maintaining high delivery efficiency. The fact that DASSIM-RT utilizes a large number of incident beams represents a major computational challenge for the clinical applications of this powerful treatment scheme. The purpose of this work is to provide a practical solution to the DASSIM-RT inverse planning problem. Methods: The inverse planning problem is formulated as a fluence-map optimization problem with total-variation (TV) minimization. A newly released L1-solver, template for first-order conic solver (TFOCS), was adopted in this work. TFOCS achieves faster convergence with less memory usage as compared with conventional quadratic programming (QP) for the TV form through the effective use of conic forms, dual-variable updates, and optimal first-order approaches. As such, it is tailored to specifically address the computational challenges of large-scale optimization in DASSIM-RT inverse planning. Two clinical cases (a prostate and a head and neck case) are used to evaluate the effectiveness and efficiency of the proposed planning technique. DASSIM-RT plans with 15 and 30 beams are compared with conventional IMRT plans with 7 beams in terms of plan quality and delivery efficiency, which are quantified by conformation number (CN), the total number of segments and modulation index, respectively. For optimization efficiency, the QP-based approach was compared with the proposed algorithm for the DASSIM-RT plans with 15 beams for both cases. Results: Plan quality improves with an increasing number of incident beams, while the total number of segments is maintained to be about the same in both cases. For the prostate patient, the conformation number to the target was 0.7509, 0.7565, and 0.7611 with 80 segments for IMRT with 7 beams, and DASSIM-RT with 15 and 30 beams, respectively. For the head and neck (HN) patient with a complicated target shape, conformation numbers of the three treatment plans were 0.7554, 0.7758, and 0.7819 with 75 segments for all beam configurations. With respect to the dose sparing to the critical structures, the organs such as the femoral heads in the prostate case and the brainstem and spinal cord in the HN case were better protected with DASSIM-RT. For both cases, the delivery efficiency has been greatly improved as the beam angular sampling increases with the similar or better conformal dose distribution. Compared with conventional quadratic programming approaches, firstorder TFOCS-based optimization achieves far faster convergence and smaller memory requirements in DASSIM-RT. Conclusions:The new optimization algorithm TFOCS provides a practical and timely solution to the DASSIM-RT or other inverse pla...

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The dose–volume constraint satisfaction problem for inverse treatment planning with field segments

Cited by 32 publications

References 27 publications

Search for IMRT inverse plans with piecewise constant fluence maps using compressed sensing techniques

Search for IMRT inverse plans with piecewise constant fluence maps using compressed sensing techniques

Mathematical optimization in intensity modulated radiation therapy

Dose optimization with first‐order total‐variation minimization for dense angularly sampled and sparse intensity modulated radiation therapy (DASSIM‐RT)

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